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Frederic Schuller: The Physicist Who Derived Gravity From Electromagnetism
August 21, 2025
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The Economist covers math, physics, philosophy, and AI in a manner that shows how different countries perceive developments and how they impact markets. They recently published a piece on China's new neutrino detector. They cover extending life via mitochondrial transplants, creating an entirely new field of medicine. But it's also not just science they analyze.
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I was stunned as a theoretical physicist. We now believe to have cracked at least two of the three most prominent problems. Professor Frederick Schuler has done something that should be impossible. He's derived Einstein's general relativity from Maxwell's electromagnetism alone. Not postulated, not assumed, but derived.
So you start with electromagnetic fields on an arbitrary background, you demand predictivity, and out pops not only that must the geometry be Lorentzian, but the dynamics must be Einsteinian. However, Stuhler's maverick conclusions don't end there.
He's found a formalism from engineering which may help shed light on the measurement problem from an extremely unlikely place. This podcast was tremendously impactful to me, which is not something I often say about the math and physics podcasts on this channel.
The heartfelt impacts tend to come from explorations of meaning and even consciousness, but today, Frederick reveals for the first time his teaching philosophy and why starting from propositional logic and building all the way through set theory to differential geometry has resonated with millions of people. Professor Schuler shows physics as it actually is, a conceptual masterpiece where every piece interlocks like a da Vinci painting.
This podcast will not only give you a new perspective on physics, but will fundamentally change how you think about physics. Welcome, Professor. Thank you very much, Kurt. This was a long time in the making, right? Yes, many, many months. Yes, yes. So tell me, what are you working on these days? What's in your mind research-wise? Research-wise, I'm thinking about foundations of quantum mechanics these days.
and i never wanted to do that because that's a very very thorny subject and of course there are obvious problems the measurement problem above all that bother me but they bother me from a new angle and this new angle is that in engineering i work a lot with engineers these days at the university of 20 right and with a very strong robotics lab many groups
and i learned something in two thousand twenty actually i was invited to participate in a small conference actually not that small after all in paris and i saw their engineers and they talked about something that's called the port hamiltonian approach to dynamics and this is
In essence, an extension of Hamiltonian theory is just that you do not only provide the formalism to talk about a closed system where no energy can flow out or in, you talk about open systems where energy can flow out, but
You don't say how it flows out. There is an open port that gives you the possibility for it to flow out. And if you take two such systems, you can connect them via something called the Dirac structure that has been studied before. And that is a different decomposition of a physical system governed by Hamiltonian say classical mechanics, classical field theory. Then we would usually have, we would usually describe it as one big system.
And we would talk a lot about energy flowing from that part of the system to that part of the system. Especially if you think about kinetic and potential energy, even in the introductory lectures, we talk about energy flowing from the kinetic energy to the potential energy back and forth, such that all of energy is conserved. We do a good talk on this, right? But ultimately, it's just talk. It's not reflected in the formalism and how we describe the theory.
Why is that? What is that good for? It's just a rewriting, right? But engineers have the need to control energy flows. For instance, if you have robots interacting with humans.
and the robots have you know joints and so on if the robot interacts there's of course energy being transmitted from from the human being and so on and how do you actually capture this how does the robot react to this if you want to study this and you need to study this because that robot might otherwise decapitate you
There is an unwanted energy flow, so to speak. It's moderately important. It's moderately important if you wanted to survive, but who knows whether we do anyway. Joking apart, engineers understand the need of this. Also huge networks like, say, the French electricity network. What happens if certain power plants all of a sudden shut down or there are other problems? They need to get the energy routing through the system right.
Okay and this is done these days by port hamiltonian approach to all of this and i was stunned as a theoretical physicist because i thought oh yes this is something is a good form is you know every time you reflect something in the formalism.
You can then calculate with it if you have just a good idea about you say yeah yeah we know all about that and of course of us but if it's not reflected in the formalism you can't really apply the mathematics to it.
And so it's important or it could be important depending on what you want to do to reformulate theories like this well long story short in the classical domain this has been developed over decades by i think it originated with arian fundershaft and bernard maschke and many other people work on this now in germany there's a big
Research center on this so this port hamiltonian viewpoint is very interesting one it won't solve everything maybe it shows nothing but it gives you a new perspective okay that that's what it is. And i started thinking together with collaborators on how this could turn out to play out in quantum mechanics.
Any quantum mechanics we superficially we also talk about energy we have a hamiltonian we could make energy measurements the hamilton is still the generator of the time evolution as long as you don't measure right for the unitary evolution right so could we talk about these energy flows in quantum systems and the answer is if you look closely at it know that doesn't seem to make much sense.
But it's something else that flows there. It's probability that flows in quantum systems between subsystems. And that's the next thorny issue. How do you do with subsystems in quantum mechanics and so on? And we now believe to have cracked at least two of the three most prominent problems. How does this work? What is actually flowing there? How do you actually get this onto the street formally?
And also how do you deal with composed systems because quantum systems famously composed by tensor products. So the Hilbert space of composite system is the tensor product of the Hilbert spaces of what we think are the constituent systems, but of course the tensor product contains many states.
That could never be understood in terms of the state of one subsystem and the other subsystem, the entangled states, of course, right? And so any idea of decomposition into systems and probability flows, all of this must work together. And we now think we made good progress. And one thing we haven't done yet, and that's, of course, the most difficult thing we would like to
Formulate the measurement axioms as they are in quantum mechanics as you postulate them they're a little mysterious to say the least but most of all they contain a lot of talk you say you conduct a measurement
For that you have a Hermitian operator, let's talk finite dimensions, otherwise self-adjoint operator, okay let's think finite dimensions. Quantum information technology justifies us in doing that, right? You have a Hermitian operator and then you find the eigenvalues and of course you can then calculate from the spectral decomposition, you can calculate the probability with which a certain measurement will occur if you measure now. But what do you mean will occur and if you measure now and what does this all mean
It's just talk it's talk that works spectacularly well as we know right quantum mechanics in a sense it's work spectacular but much of this talk especially around measurement is not all reflected in the formalism.
And of course, many people have worked on that. Many very smart people have worked on that, trying to explain measurement, the idea that decoherence may play a role. I guess it does. But is that the whole answer to the measurement problem? No, it is not. You know, all of these things. But this what we're trying to do is very modest.
But maybe therefore it can be successful we try to give an extended formalism not deviating from quantum mechanics but capturing much of the talk as much as we can in a formalism in this idea of parts but now not energy parts but probability parts play a big role. So it's a natural idea everybody can have it we work for a long time to really get this onto the street because there are many little
Things you can trip over and now I think we made some good progress and well once you're convinced we went to a point that it's worth putting it out so that other people can start thinking about too if they like you will hear from it that's it so but that's what I'm thinking about from about quantum mechanics and it's a very thorny issue because you know I mean it's also very easy to talk about the measurement problem because yeah yeah it has been talked a lot about it is a little bit
quite dramatically a problem, right? I mean, Roger Penrose talks about it, of course, is true. That's not a secret, so to speak. And we try to have a modest new approach to it. But the claim to fame, well, not fame, but you know what I mean, right? The reason why I think it might be useful, it uses a new technique and a new formalism with a purpose.
So that's what I'm thinking about on that side. OK, so earlier you said that undergrads, well, you didn't use the word undergrad, but undergrads are taught about kinetic and potential and how you can flow between them as long as energy is conserved. But then you said it was all talk. What do you mean that it's all talk and not reflected in the formalism? And also port, because people keep hearing this word port, port is spelled P-O-R-T and refers to the boundary ports. Yes, the boundary ports, the other ports,
It's very easily explained if we write it down. We can't do that right now. They're simple examples. Well, the point is what is not reflected is you have a total energy that's conserved and of course you can define a potential and a kinetic energy and you say it flows between them because the sum of them is preserved, right? So yeah, I mean, I'm not saying it's wrong talk.
What I mean by it's only talk is, is it built into the formalism that you make use of that insight? Now you're just saying you're looking at two observables, kinetic and potential energy. Yeah, okay. And they change their values as your system evolves classically. You can monitor that classically. But as I said, we're not making use of that in any way.
We're not now. And then the question is, is really the kinetic energy? Does that constitute a constitute a
Conceptual subsystem from which something flows elsewhere, you know, this all sounds good I think this also in some videos that that you talk about where the mathematics One confuses what physically happens with the mathematics and so on it's of this type I think it's really I could now try to explain in words what a port is and it would sound very fancy with dual variables and
Note, I'll be placing these notes from this podcast in my sub stack, which you can get by searching my name and the word sub stack or by visiting curtjimongle.com. I know it's a mouthful.
There are a couple of questions here that I have. You said
The phrase, it's a modest proposal, therefore it could be successful. Now that's interesting. Not it's a modest proposal and it could be successful. It's a modest proposal, therefore it could be successful. So I have a stickler for words and I noticed that. Yes, yes, yes. Please tell me what did you mean by that?
Why is the modesty connected to the success? Okay, at least for my means, I always think if I have one idea about something, a measurement problem or something else, one idea, you know, ideas are cheap in our field. We can have many, many ideas, right? And we can then find the fifth and the sixth idea. And if we take these 10 ideas together, I believe trying to bring one idea to success,
works because you have this one idea and then this idea, if it's any good, will lead you, if you try to implement it, will lead you to more insights. And then the problem dictates you what your next idea would have to be something like that. Okay. Um, uh, I think, look, this is a very, it's a philosophical subject, right? So, um, uh, and I claim no, no truth to this, of course, but
If you asked, I don't know, you could view say the whole development up to general relativity starting from Maxwell theory that Einstein stared at the Maxwell equations and the longer he stared and the more he thought about it, he realized there is something at odds with the idea of, you know,
the speed of light being in there. I mean, the constant, the C constant by what is an epsilon times times mu is in there. How can that be in that equation? Because if you go to a moving system, shouldn't it be C plus V where we use the moving system? So Einstein looked at Maxwell. In a sense, you can say Einstein took Maxwell theory very seriously. Okay. And taking Maxwell theory very seriously, he was prompted to change
the idea of space and time, or even the separate existence of something like space and something of time, there's only space-time. So it's a very simple idea, it's very modest to say there is a theory that tells you how electromagnetic signals, Heinrich Hertz, I think 1888, he proved that you can actually transmit by electromagnetic waves, you can send signals in the lab and stuff like this.
I think it makes it was something like eighteen fifty eighteen sixty something like this with his equations in eighty eight this was demonstrated so the predicted electromagnetic waves they really exist and it works and so on, send saying what that works and then we have a radio in the radio so it's a modest idea to say let's take mexico theory very very seriously.
And then it leads to special relativity. And then for the inclusion of gravity, by whatever way you want to take there, say the Einstein way, it leads to the curvature of space and time. And if you want to a prediction in that theory and that view to the prediction of the Big Bang. Right. So in a sense, it's very, it's a very modest idea seen through, you see through this idea that you say Maxwell theory is correct. Right.
And so I think seeing through one idea can open doors. Yeah, so that's what I mean by it's a modest idea. One can make many constructions and ideas and intuitions and so on. I always think we need to rely on nature giving us a hint because theory spaces
Infinite dimensional. And if you tip with your finger somewhere and you say, oh, the metric may be non-symmetric. Einstein did that, right? I mean, Einstein in his later years, he fanatically looked for for the inclusion of of Maxwell theory into the geometric framework of general relativity. And of course, we had to lose the client, all these nice things, all very nice. But ultimately, it doesn't work. So far, we think Einstein didn't find it.
And so once Einstein let's take Einstein also as a counter example in the sense once he started thinking in this formal way and have an idea we could include this here that didn't work so much anymore I think because he didn't have nature on his side like he had before with Maxwell theory. Yes.
I have the advantage that I've gone through your work, so I know that you're presaging constructive gravity.
Yeah and I'll place a link on screen as a preview. We're going to talk about that about how you derive gravity from matter dynamics rather than seeing gravity and matter as separate postulates. We'll talk about that.
Well, right. Yes, yes. So I can tell you where this came from, this whole thing. So absolutely counter to what I just said in the past. I also looked at modified gravity theories for this reason and for that reason. And of course, these are all reasons that are dreamt up. There's a lot of modified gravities ideas out there. And how do we know which one is right?
And at some point i came to the conclusion for myself of course that doesn't disparate anybody else's attempts in any other direction. It's a little bit hopeless to just try to think that you think up something half formal half motivated and then write down a new lagrangian. That's easy you can do that everybody can write down a lagrangian a modified grid lagrangian for theory.
I thought, what could actually give us a hint at modified gravity if we don't just look at gravity itself? And well, we do a lot of observations about matter, right? We do very precise observations about matter. And the question was, is it actually true that you have to postulate both the dynamics for gravity and the dynamics for the matter?
At some point we stumbled across this that we thought, no, it's a crazy idea, but maybe if you're given a metal Lagrangian on an assumed background, and I mean just the geometric structure, so to speak, of the background, but not the concrete
Say you could say on a Lorentzian background on a background that allows for by refringence or something like this, you actually determine from the meta action, how this background has to get its dynamics in order to be compatible with this meta action. And the only connection we saw is that the meta action and the gravity action, they must both have
They must evolve together. Say if you speak mathematically from the same cushy surfaces, they must take the initial data. Those must be evolved to again a shared cushy surface or a whole family of shared cushy surfaces. This seems to be a minimal requirement if you want a predictive classical theory. Predictive being the key and quantizable, not for the gravity, but for the matter. Yeah.
What are quantized? This is that came in as a technical, but let's let's quantize about for the moment. It became in order to justify an apparently classical condition, technical condition to do that. That's why we let's leave it out for for the clarity of the.
So, and now you might think that's a very weak connection that they have to have the same Cauchy surfaces, so to speak, the meta dynamics on the background you give me and what dynamics the background could get to evolve together with the meta dynamics. And it turns out it's a very strong connection, actually. In fact, you can write down equations that you need to solve in order to get as a result, as a solution to these equations, you get the gravity action.
that you would have to give to that geometric structure. Yes. That is in the background of the meta theory. All right. Sorry, just a moment. I just want to make sure I'm understanding. So let's just make this concrete. How do you go from Maxwell's equations to the action of Einstein and Hilbert? Spell that out. So you know how in physics we like to reduce something that's complex into something that's more elegant, more efficient, more simple. Turns out you can do that
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How do you go from Maxwell's equations?
To the action of Einstein-Hilbert. Spell that out. Okay, so to ask how does this bigger scheme work in the special case if you would say start with matter that is Maxwell electrodynamics, right? Yes. On some metric background. Let's not even say Lorentzian, any metric, any signature. Well, the first thing you would do, you would find out
And for what background signature, if you start with a metric like this, would you have a well-defined Cauchy problem for Maxwell theory? And then it turns out immediately only for Lorentzian signature, right? So, but then the question is, aha, so a Lorentzian metric is in the background of this theory, and that's also clear from the phenomenology that we see. Aha, but what is now the dynamics for that background metric? That's the question.
Of course, the textbook answer is Einstein's equation. Why? Because Einstein told us so and there are good reasons and it works out. But in fact, you can derive if you solve these equations, we call them construction equations. You set them up only with information extracted from the matter action. You set up these construction equations, you solve them and their solution give you the action
That is Einstein-Hilbert with the cosmological constant and of course a gravitational constant undetermined. So you can say, aha, well, we didn't learn anything new and no, we didn't. But we learned new that if you just say Maxwell and you want the background to evolve together with it, it must be Einstein. It must be Einstein-Hilbert.
Now, is that true with other fields, other standard model fields, not just Maxwell? Yes, we also investigated with other standard model fields. Of course, if that hadn't also yielded Einstein theory, there would be something terribly wrong either with our construction or with the physics as we do it. No, indeed,
Everything works out even if you take nonabilia engaged theories actually had a very good master's student alexander witz but he worked on that and and we figured out and no nothing new comes up we also try to use the same method to break because you see what it is if you say you have the meta action say you keep the background constant like an eta mu nu and minkowski metric right flat space
Then you could count this as a constant, but the idea of gravity is to make it dynamic. And what we then did is say, okay, but there are other parameters in matter actions. Maybe for them, we can also predict dynamics and that would of course be interesting, right? If some neutrino masses or something like this, but no, these are things we had a lot of hopes for once the actual thing worked, what we'd wanted to do to predict the gravity or to derive the gravity theory from a new matter theory.
okay so look the thing would be as well let me tell you a fantasy story okay okay fantasy story is that tomorrow we look into the universe and we see somewhere either directly or indirectly a light ray split right so like in the birefringent medium well
again directly indirectly we could see it in the hydrogen spectrum and stuff like this but let's say for simplicity the light ray splits in space as it is bent in space time you know yes before einstein if somebody would have said you the light ray bends around something without there being a lens you would say no in materials this is possible it's called glasses right but without any material how would it happen
Well, so again, it's a fantasy story assume the light ray would split in vacuum. So one photon is coming. One photon is moving. Let's let's take classical a light ray, a light ray, a laser ray, something like this. You know, I mean, it's fantasy anyway. But if that would be seen directly or indirectly general relativity, and you can ensure it's vacuum and stuff like this, right? General relativity would be dead.
Because a Lorentzian metric does not support the splitting of light rays into different polarizations. So with one observation, you can state the depth of general relativity.
Sure, I mean, with the usual caveats, is there another effect we don't take into account? You're talking to a theorist, right? So I can dream. So let's say something like this, but if something that dramatic happened, or another case, so many years ago when I developed this theory at the Max Planck Institute for Gravitational Physics,
There was this group in the Gran Sasso laboratory. They ran experiments. So the renowned group is a renowned group, obviously, and they measured faster than speed of light neutrinos.
that was announced and that was exciting and it was a serious group. I think something in the end somebody forgot to unplug something or plug something that that was the reason so there are the end it was clarified but but I mean if that had been true and actually that day Herman Nicolai the director of the Max Planck Institute there at the time and he came into my office said can you do this with the theory you're working on
And i will of course he was my director says of course you can do it we could do this week we could do this but what we would need is a particle phenomenologist right and like i mean all physics is phenomenology a particle phenomenologist to write down a really good model for it and that good model couldn't be built. On if it was really in documents or couldn't be built on a lorenzo metric.
It needs a more refined structure. For instance, you could take a fourth rank tensor as a geometric background with symmetries like the Riemann tensor, anti-symmetric pairs and stuff like this.
It's just a model. The point is we are prepared for something that hasn't happened yet, right? If somebody sees matter that cannot have due to their behavior, a Lorentzian background, but you would then phenomenologists would pretty quickly figure out what we may be the simplest background that could do that. Then the question comes up, but what's the action for that background? It can't be Einstein, right? Einstein is a for a Lorentzian metric.
Or metric in general, but then you would try to solve our equations and they're hard to solve in the Einstein for the Maxwell case. We can solve them. We get Einstein. They're hard to solve, but the result would be the action for that geometry in the background that could support that new exotic, but the new required matter.
So in a sense we converted the physical question, what's the gravity theory that can support such matter into a mathematical question, solve these equations whose coefficients are constructed in various ways from the properties of the matter action.
That's the idea. That's the idea. And there are many technical issues. Anyway, that was our idea. How can we actually say something about modified gravity that takes seriously some other physical observation we make about matter?
And it's quite remarkable that this is possible in the first case. Yes. I mean, all of this builds on earlier work by Kukash and Title Boym and ADM. I mean, there's lots of predecessors, but we kind of, in a sense, pushed it, pushed it there because in a sense, I guess before people didn't have the motivation to look at this. But, yeah. I have a quick technical question. So I can see how you can get the signature. You just talked about it with Maxwell. What makes a Lorentzian metric isn't just its
It's a 02 tensor. It also has a certain signature and then it's non degenerate and so on. But how do you get the condition that it is compatible with the connection?
Is that a condition from the principle polynomial? Yeah. So this is also something, it is very elegant. Actually, Schrödinger did that, right? Schrödinger had a modified idea. Again, Schrödinger had an idea of modified gravity and he said, no, no, no, Einstein does this non-symmetric matrix, but actually a deeper structural concept than the metric is the connection. And there are connections that come from a metric and they're more general connections, right? So that was,
Schrodinger's idea, actually a wonderful book by Schrodinger, Space Time Structure, a very beautiful, thin book on general relativity for a beginner. But then he follows this route and it's technically and conceptually wonderful. And then he assigns to this connection a deeper meaning than to the metric, you could argue. And he tries to make a theory for connections rather than for metrics as the fundamental structure.
I think he even announced this in the New York Times or something like this and Einstein was angry. I don't know whether this is historically correct. This is the rumor. Anyway, it didn't work, right? I mean, we would know about it. And you can say, okay, the all the idea with Palatini action, all of these things come from there and relate to this. But it wasn't new physics. So you
The idea that generalization of relativity goes via a connection, if you go away from a metric, is an old idea by Schrodinger, but it's not the idea here. Here the idea is, why do we talk about a space-time metric in the first place? Well, because of Maxwell. Remember, the pluses and the minuses, say, in the Minkowski metric are the pluses and minuses undergraduate students have to learn in the badly written three plus one decomposed Maxwell equations, right?
But if we have matter that has a different causality, then the regular cones, it would be cones that are a little bit more folded like this and so on. I'll place an image on screen at this point. Okay. Okay. Okay. Okay. Okay. No. Yeah. Yeah. No. And again, this is all this is all theoretical considerations, right?
I'm sorry, what did you ask before? Oh, I was saying, okay, so in the principal polynomial, I can imagine how you can get symmetry or anti symmetry conditions, I can imagine how you can get signature, I can imagine how you get that is non degenerate, or that is degenerate. But I don't see how you get compatibility with connection as a condition of the principal polynomial. But but there's no connection at all. So
So, okay, what we call signature in the metric, if I look at it from the point of Cauchy surfaces, is to say that the theory, the matter theory that has an underlying background of a Lorentzian signature metric, that the theory is hyperbolic, globally hyperbolic. You have a Cauchy surface and so on. For a metric, it translates into this algebraic condition of having a certain signature, 1.3 or Lorentzian signature.
For a non-metric structure, say a fourth rank tensor that could produce as a background to Maxwell theory, it could produce by refringence. There still the global hyperbolicity of the matter theory
Is the condition we need, but it translates not directly into a signature condition. There are many other algebraic classes. So the point is, well, this is a whole thing when one has to work out, but it's the global hyperbolicity of the matter action. Tells you how to construct. Cauchy surfaces also for the matter action and remarkably also how this matter action must look like.
So at the end of the day, it's a very simple idea, execute, it has some technical hurdles in between, but it's a cute idea. And that's what it is. I mean, we have no claim that it's realized in nature, but in a sense, if really tomorrow somebody discovered something like I said, something that would be faster than like neutrinos.
Yeah, faster light neutrinos could have been a possibility or by refringence in vacuum. Because some people say the whole theory of physics or Einsteinian physics is dead. We don't know what to do tomorrow if we saw faster than light particles. Exactly, exactly. I mean, general relativity couldn't be right, right? I mean, it builds with the Lorentzian metric. This is just not possible.
But if dense again, I'm not saying I couldn't immediately say how the gravity theory looks like. But if some phenomenologist makes a really good model for this matter now, so say standard model grade model, right? So to be incorporated in the standard model, let's fantasize. And then we have a standard model with faster than speed of light neutrinos, say, okay, say, then I would say now is the time to invest the time and money.
to set up our construction equations well that can be done over the weekend so to speak but then to solve them and there you might really i mean you know it's very complicated equations but if you solve them you get the gravity action that would support the new full matter model so so we think we think we showed that
Okay, I'd like to talk about your mind. When we spoke a couple months ago, off air, we were speaking about how there are toy models in physics, and you were thinking, okay, well, what is it that compels a theorist to go in this direction? That's the question you would ask them. If you're getting too abstract, you just want to say, well, what compels you? Can you please talk about that and how that guides your own research, maybe your teaching, maybe your philosophy? Yes, yes.
Well, you see, in research, we're always tiptoeing the line between the known and the unknown. Right. If we stay firmly in the known, we're not conducting research. We say that's the theory. That's how we look at it. Nothing to change about it. Yes, there are problems, but who knows what that is. Okay. I'm simplifying here, but especially as a theorist, we're tiptoeing on this line. We're always with one foot in the certainty and one foot in the unknown.
And so if you want to do research we need to introduce a new idea into something otherwise at least as a theorist what are you doing there needs to be one new element in it. As i mentioned before i believe if you say oh i have five new ideas how things could be different at once i think it's not manageable.
You have a new idea and you have the old. First of all, are they compatible or not? Well, if they're not really compatible, you have a problem to solve because you have to incorporate this new idea without
and thereby you typically have to also change the old theory right yes if they're not the new ideas not fully compatible okay and typically this leads to a contradiction in the old theory to a prediction of the modified theory in three lines i exaggerate where you say yeah but late nature isn't like that well what happens then well you throw away your new idea right
think Verizon the best 5G network is expensive think again bring in your AT&T or T-Mobile bill to a Verizon store
But if you have a new idea and it
If you start incorporating or modifying the old theory or aspects of the old theory in that according to this idea or incorporating this idea or incorporating this technique, you get something slightly new, which is not immediately obviously false. And then the question is, what do you do next? And the answer is, well, I hope at least usually it is.
What you're doing there, if you keep looking at it and keep working with it, you will be forced, you will be compelled to maybe to do a next step. For instance, you could have a new idea, let's do this and that. And then it tells you, oh, but unless you choose this object to be of this and that class, rather than the other class it could have, then there's an immediate contradiction. Well, you already have learned you need this other class of object and so on, another algebraic class or whatnot. Yeah.
Can you be more concrete? Can you give a specific example? Maybe you're trying to tiptoe and be diplomatic and non offensive. No, no, no. No, not really. You see that that's the problem of this. All I say are vague ideas of how to not run away in a theoretical direction that doesn't lead nowhere. Right. It's very easy. You see, and I think a lot of physics maybe always has been maybe is
including some of my own work in the past is having an idea and going here and going there and trying to implement it here and here it's a little bit we need what guides us what is the guiding principles we use right and yeah more concrete
Let's say what i said in the beginning with this port hamiltonian series where you reformulate classical theories such that you have the energy flow the fundamental variables. Immediately relate to the energy flow between subsystems is a reformulation of hamiltonian mechanics.
and i said let's apply to quantum mechanics okay okay but then we played around for a few months with energy flows in quantum mechanics in the end we discarded the idea well essentially because in quantum mechanics you don't have a continuous energy variable that describes the system you have a hamiltonian
But you see, if you have Hamiltonian, let's say you take two states that are two different eigenstates of that Hamiltonian, right, two different energy eigenstates, and you take their superposition. Well, then you have a new state, right? The superposition of two states is a new state.
But for this Hamiltonian upon measurement, you would get either one or the other value, right? You would get one eigenvalue or the other one. You wouldn't get the average of the eigenvalues, right? So this state itself, the superposition state of two different energy eigenstates, I don't know how we would say it has this and that energy. It doesn't.
So that means most states, almost all states in a Hilbert space, let's say a finite dimensional one, almost all states in a finite dimensional Hilbert space do not have an energy with respect to a given Hamiltonian operator, right?
Yes, that that that that that's a fact. So and then this whole idea of construction of ports for reasons that are not clear now, but fails because you would need a continuous continuously in time evolving or even differentially in time evolving. Of quantity, whatever it's supposed to be, you would would need in order to create these ports. But energy is not the right thing.
While energy plays in quantum theory also the role of the generator of the time evolution like in classical theory energies generator of time evolution it is not the right quantity to introduce these parts in in quantum theory.
Right. So you what I say you need to you can't just push an idea. I want energy flows. I want to study energy flows. You need to react what the theory reports back to you if you try to modify it like that. That's that's the rough idea. Look, I think we're talking a little bit too much about
How i think one could could constrain oneself to make good progress without running away uncontrollably but this is very personal you see if i thought this had deep philosophical value what i say i would have written it up and published it. Okay but it's something i discuss a lot with my with my research students i tell them what ideas are cheap.
very easy to
I want to qualify what I say. It's not offending anybody, but I think it's the truth. These are basic ideas of how to orient one's own research, but that's very personal. These are yours. You're not advocating that if people aren't following it, then they're doing something incorrectly? No. How do you say?
I mean look at the history of physics in the 20th century, right? I mean the revolutions that were there and what people predicted about it before it would be totally absurd to say because it's not on my radar right now or I can't imagine this to be a good way to say nobody should do this, of course not. I tell it to my students though.
I put this on my students and my justification is well they don't have to listen to me right and they can take it as one element of what one could think about and hopefully they add something else to it or they rejected or they take it over.
I learned from other colleagues to from other sources to say i think we should speak out about these things these are subtle things you know probably somebody not doing research doesn't know the hell what i'm talking about here and but these ideas and we should put them on our research students but not to force them to take them but just as.
Because otherwise we can't teach them. You can teach people by telling them your own ideas about something and they are less attached to them. They might change them a little and have more success, for instance. Speaking of teaching, you're a world-class teacher. You've won several awards, some of the most prestigious awards.
Yeah, no, I was very lucky because I was in sort of history, I tell you the history of one of these awards. I was very lucky to have been invited by the German Physical Society. They have a youth organization. Actually, the German Physical Society is, I think, the biggest physical society in the world. It's a little bit funny, but they have many, many members and they have a youth organization. And they invited me in 2015 to give a big lecture series on general relativity.
And so I did and we did this in Austria and they gave us a fantastic place to do that and out of that came these gravity and light lectures on YouTube and we put them on YouTube and we didn't think anything of it and they took off quite a bit.
and then there were other lectures taken in Erlangen University on the geometric anatomy of fundamental physics or whatever I call it, geometric anatomy of theoretical physics. Yes, it's about differential geometry.
Yeah yeah it was one of these things that that they do in germany which is fantastic every now and then you can give a lecture that you want to give a lecture course right you give of course lecture courses that need to be given they're part of the curriculum but then there are optional courses where if you have an idea and you want to do it you do it and i just wanted to teach people
differential geometry from the ground up as it's then used in theoretical physics and so it's more of a applied mathematics course than it's a theoretical physics course and that kind of took off once the university put this on youtube or first on itunes or something like this and yeah that gave me some international followership and also national followership and then at some point i was proposed for the ars legendi prize
which is the top German teaching prize for university teachers. They were so kind to find that in that year to meet the best candidate. They like the best at least. So you have this Geometric Anatomy course? Yes. And that didn't have a curriculum before you came up with that? That's right. Do you have other ideas for courses?
Yeah, all the time, all the time, but the question is whether you can give them, right? Whether the university gives the opportunity to give these courses or give these courses or when they say, no, we are already busy with the curriculum, right? But what's in your mind? I'm curious. So for instance, for people who understand differential geometry, what's extremely interesting about your course is you started in the first lecture with propositional logic.
Right, right. And then you built up to the empty set. I think in the second or third lecture. Yeah, yeah. No course on differential geometry starts with the empty set, let alone propositional logic. You started from the ground up. That was extremely interesting. You're exceptionally clear, exceptionally clear. I absolutely love that. Yeah, I think I've rewatched those. I may have rewatched that
As many times as I've rewatched Seinfeld, which is many times. Yes, yes. Well, I mean, look, it was a course because it was an extracurricular course. I had some mathematicians in it, some physicists and so on.
I can tell you the reason was very simple. If you want to tell people what a manifold is, you need to tell them what the topological manifold is. They need to know what a topological space is. A topological space is a very simple thing. If you know that you have a set and then the set has a power set, how do you know the set has a power set? How do you know the power set is a power set? You need to have some set theory.
Now, if you do naive set theory, you have all kinds of contradictions in two lines. If you say a set is a collection of elements, that sounds good, but that doesn't make any sense. First of all, I didn't tell you what a collection is. Second, I didn't tell you what an element is. So to define a set as a collection of elements is not particularly insightful. And in fact, as we as well known, I mean, this is naive set theories is contradictory in line two.
And so ultimately, if I want to tell people from a broader range of backgrounds, also in physics and mathematics, what are we actually talking about here? I have to tell them also about the axioms of set theory. Now that's a thorny issue. It's a very kind of complicated issue if you really go deeply into this. But if you want to do it, you can do it.
Actually, if you wanted to explain what set theory is, you need to write down the axioms. If you want to write down the axioms, you need a formalism in which you formulate these axioms, because if I then formulate them with other flowery words, I'm as bad as I was before. And so there was the idea, okay, we have to do some quantours and so on.
some propositional logic before. Well that can actually be pushed even deeper and I didn't do that in this course to some first order logic and so on. So there are many steps. Ultimately, I mean it's now known it was Hilbert's dream but it's now known ultimately it's very difficult to find a really foundational beginning from nothing even if you say you have an alphabet and symbols and so on.
but what i wanted to do at least i wanted to go beyond the usual undergrad or even master level idea about what a set is for these students they're all very excellent students in in erlang back then they had also this elite graduate program and so on i mean super students top top top students so i could could deliver that to them it was an attempt at at
some type of completeness of the presentation starting virtually from nothing. And then you see rigor in mathematics, of course, extremely important. But for me, the best rigor is the conceptual rigor. I mean, of course, you can write down things with epsilons and deltas and can make it very, very, very, very rigorous. Before that, actually, you need to be conceptually rigorous. If I say set,
We just have a vague idea about it and i build a big edifice on it and then at every other junk shaft to say well now you can show that whatever that a vector space always has a basis in an infinite dimensional one well how do we know that will ultimately this comes from the action of choice right.
Well why do you have the action of choice because at some point i required it you see so i wanted to give it the full picture without claiming that this is at the same time the foundation logic cause of foundation set theory cause because you could probably spend your life if you want to fill in all the details at least i want to be a bit more clear about what all the assumptions are.
And this is a general because you're asked about teaching. This is something that's very important in teaching. And I always joke with people when they ask me, I say my assumptions in teaching, the foundational assumptions are two. A, students, no matter who comes to you, beginners, master students, they know nothing, nothing at all. And second, they're infinitely intelligent.
Okay. Okay. So both assumptions are slightly wrong, right? Students know things and they're not infinitely intelligent. But I present my courses a little bit like that. And I like to develop things from the beginning because I don't know what they know and I don't know in which way they know it.
So I like to start from scratch. Yes. You even told me that instead of starting with a textbook, you'll go into a room, a blank room with blank paper and think, how can I teach the subject? Right. Right. Well, I mean, I think that that's so that's another thing I think was all not my original ideas, a very old idea, you know, unity of research and teaching. I think at university, only people who bring to the table some research grade
Thinking should actually teach the important lectures, at least for the students who take the subject very seriously. Let's say it like this. Also, if some biology student has a physics course that can be excellently taught without
Much do but if you say educate the next generation of theoretical physics and maybe you hope that some of them might make groundbreaking discoveries or something well we better we better give them our best and don't just repeat what what in the how we learned it right.
And so how do you do this? And how do you not just follow what is written in the textbook? I think you say this in one of your videos where you say, oh, yeah, we just often just repeat what we have heard. Was it you who said that? Yes. Somebody else you interviewed. And you can recognize this if you would never use this phrase somewhere else. Exactly. On an equal footing, I think it was. There are many such phrases. I keep a catalog of them.
All possible paths seems to be echoed due to doctrinal inheritance without thinking, just like the word equal footing. Time and space are relative and treated on equal footing. Time and space are supposed to enter on equal footing. We should think of space and time on the same footing. What is equal footing? Have you seen a mathematical definition of equal footing? We're supposed to be rigorous. Yeah, yeah, yeah, space and time on an equal footing. Oh, yeah, indeed. What the heck is that supposed to mean? Okay.
Nevertheless we all do that but indeed i would say one way to make a research much better is to try to detect where you using such phrases in order to justify something well there of course placeholders for. A better explanation.
Interesting. Sometimes you have a much better explanation. Everybody knows the better explanation and then you refer to it on an equal footing and then everybody, however, if pushed would give you a brilliant explanation to it, then you're allowed to use this short term. Yes. But if it's just used to gloss over your own ignorance consciously or unconsciously, one should eliminate it. But we all do this. So first of all, if people ask me, how do I teach better?
very well i say something like that right and then say i
I mean, general relativity is one of my expertise. So if I teach a course in general relativity, I can teach this in any number, in two or three different ways. Okay, not any number, in two or three different ways. And then I first of all think, what is the best way for this group? And for instance, I once had the task to teach physics to material scientists.
They're not hardcore physicists, but they need some good quantum mechanics and it was quantum mechanics course. And I decided that because they need the energy bands, you know, in solids and so on. I teach them a tempered distribution theory.
right? Schwartz spaces, tempered distributions and so on a distribution theory, which you would say is a very advanced subject. I mean, most physicists don't hear this in the undergraduate studies, right? Right. But I decided before for the applications we want to do, we just need this. I taught this to them. It's not that difficult after all. They all did pretty well. Right. So sometimes we must not shy away from using very advanced methods, of course, explained very well from the bottom up.
Also to people where you say oh normally they wouldn't use this theory but I think they should right so and then I usually textbooks many textbooks don't offer them precisely the line you want to take and I think it's also good for for the lecturing style if I don't take a particular textbook certainly in a subject I know very well yeah I take a stack of paper in the summer break
And I start sketching what is a good storyline, but I mean, scientifically conceptually rigorous storyline as today one would have to present it in order to get it accepted in a very good journal. If this was a discovery, so to speak. Right. So, um, yeah.
So I try to apply research-grade thinking to the design or redesign, that's the better word, the redesign of also very established courses. And very often you change the order in which you teach subjects. What you think is an advanced subject is typically something you learned later. And a less advanced subject or topic is one you yourself learned earlier. But that's not a particularly meaningful
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Classification of advanced not advanced, right? For instance, in Erlangen, I taught the classical mechanics course, I decided to teach it using half of the semester to develop differential geometry. Then I did the mechanics. And in the last lecture, I could tell them what general relativity is.
Okay. Um, uh, that worked pretty well. Colleagues said you're crazy, right? I mean, you have bad passing rates. Not true. We have excellent passing rates or very good passes, at least the usual ones. Uh, and, and, and some of these students to just absolutely spectacularly, because once you do it properly, you see, you should never do something because it looks fancy. Oh, we did it with differential geometry. No, I need to tell you what the cove vector is. If I want to talk about momenta.
right because momenta canonical momenta are covectors they're not vectors how do i tell you do i tell you about this in in vector space i could but then people think about the position vector but position is not a vector and and you can't get away from this
Structurally, conceptually wrong idea unless you immediately put it in the setting of a manifold. And then, of course, if you do then Lagrangian mechanics or something, you anyway generalize coordinates are nothing than what the differential geometry calls coordinates. They are generalized. They are coordinates. It's actually Cartesian coordinates, which are very, very special. Coordinates is existing under very special circumstances. And then you don't have to choose them necessarily. Right.
So you put the whole conceptual basis properly rather than giving people the wrong idea. Because once you taught something in a way that is ultimately not correct, ultimately doesn't carry you far and you have to replace it later on anyway, you shouldn't teach people in the wrong way. And that's why it's important to be a researcher because you know where it's going to be carried. Whereas if you're just a general teacher, you don't know the forefront of the field.
i think many both somehow yes it's because you need to know where you where you want to go and no but the other thing is you see in research you learn this oh could i explain this this other way oh this is a new take on let's let's explain it that way and but what if it's almost only slightly wrong
If you do something in a new way you need to apply the criticism of research to it to say is this really a valid derivation and is it really as general as the one that you get otherwise you know.
So I'm a big skeptic of teaching methods as a one-size-fits-all method of how you teach better, whether you teach the piano or you teach general relativity. I do not believe that is true. I would never dare to recommend to a piano teacher my teaching methods because I think, oh boy, I mean, you're a concert pianist. I mean, the really good piano teachers that people study with, they're concert pianists.
They don't have just a fancy teaching method. They can play it at a really great level. And then they have methods to teach them, which you can't come up from general considerations. So in physics is also like this teaching. I think good teaching always springs from a deep understanding of the subject coupled with an awareness of what you already explained and what you didn't.
Sometimes people say, oh, that person is a really brilliant scientist, but he doesn't teach well. That's often the case in the University of Toronto. It's infamous for having great researchers, but they don't care about the teaching. Maybe they would be great if they okay. Okay. That's of course one possibility. You don't care about it or you hate your students.
I think a more benevolent view could be they want to explain it well. Let's take those hypothetical ones who are really great, who really know their subject and who really want to explain well but don't. I think the most likely cause in those cases, and I know such cases, but not many actually.
I think they're not fully aware of what they already explained. They explain some things. Oh, I forgot this. And then, okay, you forgot. Okay, I put this as an aside. That happens to all of us. But it's the next thing. Oh, and I did this. And as we know, and as you could show, but you know, then it's a mess. Then it's all over the place. Left as a homework exercise. There's a homework exercise. Yeah, yeah, yeah, yeah, yeah. Well, that's that's an easy opt out. Nice. Say you show this young man or young lady. Yeah.
No, seriously, it's I believe it's certainly the implication error goes in one direction. I think you need to know your subject really well, really deep, really far in order to design a really nice lecture course on it. It's a necessary condition.
the necessary condition. And yeah, and we all are fallible, right? I mean, I think I eradicated these and those problems from this subject and teaching it and how it's strangely taught and things like this. But then do I know, right? I mean, then somebody else must come and do it better. But at least we do better and better. I think if I can improve 5% of how I learned a subject,
Um, uh, and it's really solid, a solid 5% improvement. I think we, yeah, we can tap our own shoulders, right. And say, you know, but that's what we owe our students. So it's what we owe our students to, to, to really improve it because otherwise they must have a better starting point than we did. Although our, my starting point was excellent. I had brilliant teachers everywhere. Some of the privileges in life. Well, for me, I think for anyone is running water.
Air conditioning and if you're a physics student, it's taking one of your courses. Oh, wow. Immediately after what an air conditioner. I'm not even kidding. It's an absolute joy. I don't know. So why do you care so much? Why do you care so much about teaching? That's a very good question. You see, I think and then I think it's a good lesson to to maybe young people out there.
When I went to study to university, I was just so wanting to understand physics and to also make new discoveries in mathematics as well. I studied both in parallel. That was my aim. And if I now look back,
Even before that, when I was a younger man, I did lots of sports and I actually started working as a trainer already at a very early time, myself being active, but also teaching youth groups and so on. And if I look back in my life, I think from the age of 15 onwards, I have always in one or the other capacity in sports or elsewhere, I have been teaching, I have been teaching and
More or less what I told you is my philosophy about teaching today was my teaching back then I wanted to make them really good I wanted to make them really good competition sportsmen and women and things like that and I had this idea and I had myself good teachers in all of these fields and I passed this on but not out of a reflected moral imperative or something it just in retrospect I saw this.
When I went to university in the first semester I had little meetings in the library where I told my fellow students things that we were currently discussing and that I understood before and I taught them on the blackboard in the library in the university.
I always did this was not sure when i was at university and research institutes i was also invited well i am driving has a very sophisticated talent promotion program we have something called the scholarship foundation is the state
Organization the select point one percent of the best high school university students in any subject and they are they get special summer schools by top professors and so on and we have a similar thing for last year high school students where every high school in germany can send their one best student.
What did I do?
Well, told them differential geometry, told them general relativity, right? Wow. So I have always done that and my aim is always to make the people as good as can be. So I'm a little bit of an elitist this way. I think, look, you come here to study, I give you the real thing, but the real thing is hard. And I do my very best that I deliver to you so that you can live up to the demands I put on you.
Right. So I put high demands, but at the same time, I know I'm responsible for teaching them. And in the end, if it fails, if not a significant proportion of them takes a big benefit, which from your kind words, I take it many people do. Right. It's now more obvious through YouTube than I'm at university to, of course, I got always good evaluations or very good evaluations. Not a doubt. But then I think I succeeded. I succeeded.
I once had a student who I met in Erlangen on the street years after he took my classical mechanics course I told you about that started with differential geometry and he stopped me and he was very kind and he said because of you I stopped physics and I thought oh really he said no no it was the best thing ever your course was great but I just realized I'm not good enough and I said maybe you should have tried more no no no absolutely not I'm so grateful to you because I realized
i should have understood it so many in my course said it was great i thought it was great but i just couldn't do it so it's it's a weird uh how do you say compliment but but it was genuine i think it was genuine he meant it and i said again apologized and i say i hope i didn't do anything wrong and so on and said no no no no he's very happy now with what he's doing and so on
Today we have a lot of talk in teaching circles about people being demotivated by high demand. I think high demand, if it's justified from what you yourself as a teacher deliver,
is the biggest motivator of all because the good students are pushed beyond what would be their comfort zone and the not so good students see that a good number of students succeed very well so it is possible yes maybe they need to up their game maybe they need to spend more time on it or be more courageous or be less disheartened or you know
Anyway, that's my view. Maybe that's the nicest outcome or conclusion for me from all these awards. I got others and the many, many, many thousands of emails I got. Of course, not of course, but I got kindly and many I couldn't even read.
Because it was just too much at some time. One year I got 6,000 emails on these YouTube lectures. It was impossible for me to read. They all go to some folder, but I feel very guilty about it because some people write very nice things. I just can't cope with these masses of emails. So maybe hear my thank you to everybody who wrote and addressed very kind words to me.
But the nicest conclusion of that for me is I think my method is at least justified. So to high demands and trying to deliver what it takes to satisfy them. One of the reasons I resonate with you and your lectures is that I care about mathematical rigor. Although you don't just care about rigor for rigor's sake or formality for formality's sake. You care about it because what is required to understand subject X, you have to drill down to
point y. So you don't care about point z and a, b, c, you care about point y as it relates to x, not just what's around y. Yes. Yes. Although also you see the coherence is actually what we're saying. Well, true is, is it really conclusive what we're saying? Is it compelling?
Right so we set up a theory we start with assumptions that could be wrong or false as far as physics is concerned wrong or false true or false physics is concerned but then once we set down our assumptions is everything else we say.
Is it actually conclusive is that actually at least compatible with what we said and then you need to be very careful because many things are plausible but just not correct and if we start hand waving it's always very cool right it's a little bit sometimes I blame it on Feynman who was cause quite a charismatic character right and and and and and fill system.
Yes, why don't you be concrete? Why don't you give an example of what ordinarily is hand wavy, but then when you examine it, at least to something wrong?
Oh God, a million things, a million things. It's very easy to, for instance, talk about the center of mass of two particles, right? Two particles are flying around center of mass. Now think of it relativistically and blah, blah, blah. For instance, relativistically, there is no center of mass.
of mass of course requires you to take the positions of it says they spent flat space are not even curved space flat space you need to take the positions of the two particles same in koski space they could be position vectors in quotation marks okay and and then
you find the middle point right but for parties at the same time you find the middle point right the position positions at the same time but we know there is no simultaneity in objective simultaneity in special relativity even so in special relativity there is no center of mass that's a concept that cant i think is interesting because cant
Says this is a what is it a synthetic a priori or something like this something like this or even analytic and analytic truth. No it's just not true in nature isn't like this nature doesn't have simultaneously as a foundational thing that you can talk about that makes sense right.
So it's very easy to give arguments, hand waving arguments, if you don't define it very precisely and then check whether it's well defined under whatever. Yeah, you got to be very careful now. So the hand wavy stuff is very, very dangerous.
I mean, even the written down, the rigorous stuff is very dangerous. We all know this, right? We call it a side error or some other conceptual error. So it's not like because it's written in mathematics is necessarily conceptually coherent or consistent. Of course, then there is ultimately a mistake somewhere, but it becomes mere talk if we start hand waving. Of course, if you do formalism and you don't occasionally bring it to life, say to the students,
I understand we don't have a blackboard and we don't have the ability for you to draw right now, but if you were to explain to the audience and they're educated in physics and math, what is the problem with quantum gravity? How would you say it? Oh, well, that's why is this so difficult to make gravity into a quantum theory? Should gravity be a quantum theory? Exactly, exactly.
Exactly. I want to hear your viewpoint. Well, I mean, okay, I don't think I have anything new to add, but I think if you ask me as a little examination, I'm happy to oblige. Yes, it's a PhD defense.
Okay, we have a nice theory of gravity. General relativity is the best one we have. We use it. It's subject to the interpretation of the data we get and so on. It has the following form. G mu nu is T mu nu and G mu nu is the space-time curvature and T mu nu is the annoyingly metric containing energy momentum tensor of the matter. So the metric is also in the T mu nu. But very roughly speaking, the T mu nu
Of course, it's mainly determined by the matter content and distribution in the universe, say. Now, there are many issues to be discussed. Well, this is already a godlike view on all of space time. You would actually have to go to three plus one to talk about evolution and so on. But let's leave this all out. The problem is on the matter side, as long as you have classical fields like Maxwell feels classical. This team you knew is a classical field, a tensor on a smooth manifold.
It can be beautifully equated to the G mu nu Einstein curvature tensor on the manifold. This is mathematically meaningful. And then you solve that there's a big elephant there, but you solve these equations and you get the prediction of how the gravity and the matter in the end work together. You also need the matter field equations. But
Unfortunately Planck got us the idea and then people said oh yeah that's true there seems to be no classical matter all the matter light and particles and so on they're all quantum. I don't think this is to be doubted that that seems to be the case at least the way we look at it fine but then how do you build this T mu nu tensor on the right hand side of this equation g mu nu is T mu nu
Because now all of a sudden there are quantum fields there. Okay, big question. And then the easiest, so then you can say also in a sense, this team you knew is also more like an operator operating on some vector space here, but so Hilbert space Fox space was not no matter how you there are many, many issues with perturbative theory. And so anyway, you have this on the team you knew side.
And then you say that doesn't fit. You can't equate a classical tensor to some operator. The equal sign makes no sense anymore. Right. The matter you want to put on the right hand side is quantum, but the right hand side is formulated only for classical fields and many things you can try. Oh, we take the expectation value. All of this doesn't work. Right. All of this doesn't work. Obviously. So then the, in a sense, laziest idea, and I'm
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unnecessarily provocative but the laziest ideas to say why don't we make the left hand side also an operator or bit more seriously formulated maybe gravity should also be quantized then we have both theories matter and gravity in the same formalism and then we can
Write down a new equation roughly speaking in this new formalism where now the matter and the space-time speak the same language or we speak the same language in looking at them and that's the origin of the idea we should quantize gravity at least from a formal point of view there are other good reasons what happens with black holes what's with singularities
Big Bang. Was there a Big Bang? Is the theory actually to be extrapolated up down to the Big Bang? Many questions. There's Heisenberg's idea. What does it actually mean to talk about space-time as a smooth manifold and the metric measuring so precisely? How would you measure? He would use higher and higher frequency to be more precise.
Say photons to check something, but then that would disturb the space time, the very space time you'd like to measure. There are many, many reasons that you can concoct a whole bouquet of reasons why you think quantum gravity, quantum formulation of gravity might address, solve, enlighten us concerning all these problems. Okay.
But this comes ultimately from the way we look at things in the first place. And I think there is no really compelling reason why gravity has to be quantized in the first place. Maybe something very different is going on. So that's the first thing. Do I know? No, I don't know. I don't know better than anybody else.
But it's not so clear that we want to quantize gravity. Look, I mean, there are many things, many questions one could ask and probably none of them is original. If you do quantum theory, say ordinary quantum three and three dimensional, say in Euclidean space and you do, I don't know, quantum information or deal with qubits. What your quantum systems are, at least the constituents of it, the opposite, they must come from
representations if it's elementary irreducible representations of the universal covering group of the symmetry group of the classical space in which you think about this quantum system.
This is how you get the spin one halves in three dimension. They come from the three dimension Euclidean group and you look at all the projective unitary representations of the group of this Euclidean group or technically you can also look at the universal covering group that would be then something like
So if you just take SO3, universal covering group is SU2, you find the unitary representations of those and then you know how you can build your quantum systems that live in such a space. And the same then works in with the Poincare group and Wigner figured that out. What are actually the possible representations of the SL2C?
of this universal covering group of the symmetry group of physical space. Why do I say this? Well, the whole standard model is built on this. It has very clear conceptual reasons why it must be done like this. It's not an abstract thing. But that means physical classical space, be it space time or space, you need to have a concept of classical space in order to talk about quantum matter in the way we do it.
yes aha if you now say i want to quantize this classical geometry or you know whatever ideas you might get the dynamics of it the drum well in a sense undermining the very foundation of what brought you to the quantum matter right you see so
That's not immediately plausible to me. Of course, you can always say, yeah, that was just the ladder we used to get up to the theory. And in the end, it all works out. And then we throw away the original idea of this. But you know, the point is, I don't know, probably nobody knows. But these are also, I think probably to most of the ideas, why gravity should be quantized, one could at least make intelligent counter arguments, why that is a funny idea.
Okay, so maybe something else is at work. There were these proposals by Oppenheim and collaborators on this idea that that gravity is not to be quantized, but rather it's to be treated as a stochastic theory, classical stochastic theory, interacting with the matter. That's an interesting idea, I find, because the quantum axioms and
Never. Yeah, the quantum axioms say something like this. You say you can't measure, you can't predict what the measurement outcome is, but you can give a probability distribution, a classical probability distribution. So the axioms tell you classically, you're not connecting to a classical theory in a pure state. You connect into a classical probability distribution.
And i think that's a little bit the idea they have i hope i don't misrepresent that you should ask them but you see this is a priori also a very plausible way whether this works out and whether what they work that's not the question the question is there many other.
i don't know many that that for instance is a plausible thing we see from the quantum axis the quantum axioms at no point instruct us to quantize the space time behind it yes right and maybe this uh representation theory construction accepted construction uh speaks against it say no no you need this classical space idea otherwise we don't know what we're talking about the quantum theory either and so
But the quantum axioms talk about the contact to the classical world as a kind of a stochastic system contact. Maybe there's something in the idea. You know, so the and I mean, it has failed for so long to bring this idea to quantize gravity to success. But I mean, who knows? I mean, there's a lot of criticism of string theory these days and hey, I share it. But you know what? Maybe they pull it off.
You know we don't know we should be not very not so judgmental about I mean very clever people spend a lot of time and very clever people in the past were wrong about what they wanted to do although they were very clever and sometimes people are lucky I also wouldn't discard the string theorists who keep pursuing it.
I wouldn't but who am i to say who's anybody to say i think that's the good thing about science that everybody can and should do what what they think is right and it is enough if one of us at some point is right about something and that's progress.
The project of science is fantastic. Everybody does what they think they should do. I mean, in a sense, that has changed a little bit. There are also some commentators of that, also in the German speaking area, I think Sabine Hosenfelder and so on.
She brings some very strong criticism of how the scientific system works these days and so on. And some of these points are just valid. Yes, absolutely valid. Well, the old idea is freedom of teaching and research. There's a Humboldtian idea. Humboldt had this idea when he was asked to, I think, to create a educational system for Prussia.
or got my history, but I think something like that. Okay. And, and he said, education at university is not vocational training. It's not for you to find a job. It's for you to learn to think. And if you learn to think, and if you dig deep, well, I don't know whether he said it like this, let me say what he wanted to say if he was alive today. Okay. If, if, if, if you dig deep in physics,
And you become a really good physicist and then you talk to a lawyer and legal scholar who really dig deep on legal thinking you recognize a good thinker.
because you learned thinking well in your subject and the other way around and if you can do that and you go out in the world you're infinitely more useful for a company who has a good thinker with a lot of skill and has learned to think deeply to think critically in the long run that produces growth for the company right at least on average the idea that we educate people to conform with the expectations of current employers well
The current employers do not know how the world looks like in ten or twenty years when thirty years i don't know. Nobody knows right but for eight hundred years universities have actually provided us with thinkers who then took on the problems of that time.
you have to be educated to do that and what is not going well it's what there is the idea of freedom of teaching and research and the diversity to use that trigger word but there it's actually appropriate the diversity of different thinkers because we're all naturally diverse we're all different um
We should be allowed to do what we want to do and then society has to decide to whose people to people this privilege to which people this privilege is given. What is however happening at the moment? Say if you're in the in the European Union universities, of course they want you to gain grants and the biggest grants are the European grants from the European Union and they decide on topics
They are open grants to be fair. They are open grants. You can bring your topic, but some very big grants, they decide on topics what it would be important to have scientific research on and they are decided politically. How does that work? Well, would you think that in the current situation, energy situations on energy would be such a topic? Of course, such a energy is such a topic. Energy is such a topic. Okay.
That means if you do energy research, you're good. You can apply for these big grants. I mean, I'm caricaturing the whole thing a little bit, but that's what is ultimately what we do research on is decided by bureaucrats and politicians who thinks that is plausible. And of course it's plausible to do energy research. But even if we look in the past, did nuclear power be invented by government programs looking for energy research? It came out of blue sky research.
Right. So, so it, if you look at the financial situation is no longer true, uh, that researchers really decide entirely freely on what they do research. That's a fact. It's a fact. And the problem with that is a monoculture explained. Well, well, if, if, if people go for the big grants,
Either they're already famous they've already done fantastic things and i would also say give them another grant very high probability they keep doing very good work. But new ideas that a little bit out of the box and again they're also funded i'm just giving the general idea it's much harder because.
One look research doesn't work by you telling me I need you to research this in this it works if I have to research a travel journey for you I can do that for you I can deliver that but if you say I need you to find the solution to the problem of quantum gravity it's nice that you think it's important or anybody thinks it's important I think it's important it's a good research field but but that doesn't mean that that is where the next breakthrough will be
So you think that the academics should be more free? Oh, yeah. Oh, yeah. Oh, yeah. Of course. Freedom. Look, look, it's yeah. Look, it's the same. Let's go back to teaching because the similar argument. I think every professor who has the right background, educated in it and specialist in it and so on, who should be given total freedom on how he teaches a, say, quantum theory course.
for audience x total freedom this principle gets you some of the worst lecture courses you have ever attended well that's unfortunate but i also believe it gives you the most brilliant lecture courses you have ever attended and i think it's better to have in your student life two or three or four or five would be luxury brilliant lecture courses i think i had as many brilliant ones thank you to my teachers right
But then there's some that are not that good that also comes from the freedom but the freedom is necessary to develop new things to do it better to do it differently. Not that that's what is no general commission that can decide i mean should we very simple curriculum should we teach momentum vectors of course we should we need it.
There's no momentum vector. It's a covector. So, you know, even if a committee agrees this is important stuff, what if you say, yeah, but that doesn't really fit together at a deeper level of analysis. Should I teach it because the committee decided it, you know, the accreditation committee for the courses or whatever? I don't think so. I don't think so. Huh? Look,
If we had a wild west of teaching and everybody would give terrible lectures and everybody did what they wanted and nothing would ever fit together, I would advocate for some structure. At the moment we have, at least in Europe, the tendency of more and more structure of more and more ideas of centrally accredited courses and core systems and so on. And what you get is an average good thing.
But if you want to get something really good, you need to give freedom. It's a belief, I admit, but it's an old Humboldt idea. And certainly it served Germany very, very well for very long in educating an extremely broad part of the society, educating them very, very excellently in engineering and also in mathematics and physics and so on.
Early 20th century, Germany was quite the powerhouse of all these fields. Can I state this with sociological, how do you say, scientific certainty? No, but I think it's an outflow of the humble principles of how you teach at high level, at university level. Don't look at the vocational use first.
the vocational use and that companies and the economy profits from these people. This is doubtless afterwards. Don't be too short-sighted. And so, yeah, the diversity of the approach is important and you have only diversity with freedom. I restrict this statement really to what I'm talking about here. Different researchers should follow their way. And then it's a question, who do you make a researcher? Right. So fair question.
Well, a teacher at university. Yeah. So let me ask you, I've already asked you about what you're pursuing, but I'm curious also, there are some fashionable subjects, the subjects that are in vogue, like ADS, CFT, or quantum information or black hole information, string theory, and so on. Why are you not pursuing the more fashionable ones? If it merely is just you're not interested in it?
What is it? That's not true. And some of them are interest with some of them, I have some contact, some of them I understand others I didn't look into, I mean, it's a lot of stuff out there. I like to follow the ideas I my collaborators have, and I try to make my contribution that way. So I mainstream subjects on which already 1000s of people work, will I make the difference? Well, maybe I would. But
I think it neither takes justification to work on a mainstream subject or on a more on a sideline. I was educated at Cambridge University by excellent people, Michael Green and Peter Goddard, John Stewart, Gary Gibbons, all prominent people, obviously string theory people and general relativity people.
I know certainly the foundations of many of these things quite well, and some attracted me more than others. So, string theory didn't attract me so much. At the time, there was the saying, all the best students go to string theory, and it was true. The best students went to string theory. I think I was a reasonably good student there, but I kind of didn't really feel it. I didn't really feel it.
I'm not saying I was prescient and I knew it was not going to work. Of course not, of course not. You know, you make a pick. It's also emotional to make it, not when you say, I thought that I find interesting this direction I would go on. And you weren't feeling it? I wasn't feeling it. No, no, no.
Well, I didn't understand one thing. Actually, I once discussed with I think with Peter Goddard for a short while and I asked him, so why do we take the Minkowski metric in our what was the 26 dimensional space? I mean, basic strength.
And he told us, he told me, well, because Einstein told us so. And I say, yeah, but he told us for four dimensional space and didn't, isn't the reason for using it that you have point particles that move there. And he want to get the clock postulate by the length of the curve and stuff like this. But this is a point particle based idea. But now if you think about strings being the fundamental objects,
Rather than point particles wouldn't you rather have something that measures area fundamentally rather than length much later wrote a paper about these things and setting up a plausible idea okay finds plausible idea i also did something i don't think it solves anything but you see the point is i did the set up i found it to at hock in a way.
In a sense, the only idea, at least as it was communicated to us back then, later on, of course, people change perspective. I'm not a specialist. It's like, let's rather start from little strings close to open and quantize them difficult enough, quantize them rather than point particles as a first quantization. And let's see what happens. And there were some remarkable results. And
At least at the time I thought it was remarkable that the Einstein action kind of drops out if you look at it in a certain way and so on. Later on I thought well it's not so remarkable because if you didn't do anything wrong from a differential geometry point of view or from a calculation point of view what else would you get but in lowest order general relativity maybe the factor could be zero in front of the Ricci scalar or something right.
So look, I mean, were these mature reasons to reject it? Of course not. I was a student, right? But I wasn't pulled in that direction. And I'm happy that many other people did, right?
so far it wasn't successful, which is maybe just very unfortunate. I would much rather have that the people who did it were successful and would have an exciting new discovery in theory and that I would say look fool me. We don't know, right? It's like investing in the stock market. Will the stock go up and down? Nobody knows. Nobody knows, right?
And then it's the same here we can just try to do our best and i think it's good in academic life you do research you really try to push something and to do something and but then on the side you educate the next generation if you don't educate them to a higher level to improve it by five percent what you present them with we also did a great thing.
So that's the nice thing about the academic job, right? I mean, you're not only relying on winning or doing Nobel or similar worthy work, of course, would be nice. But we have another very, very important task in society, because if we don't at least pass on what we have and make it a little bit better so that more can be passed on,
was more efficient, then we lose that knowledge. That would be also catastrophic. So I sleep very well. I sleep very well. Passing on stuff is very important. And trying to do new things. Yeah, trying to new things is an audible thing. And this is exciting. And it's also training for students to for them to do research. I mean, you can do research, which goes that far, but maybe a student learned many things
contents wise and and method wise and they bring something else to success right so so so i mean that that's that's the life of an academic no we're often talking about the the the the holiest grail right there is the big open questions and um uh uh yeah that's important i'm also thinking about some of these things um uh um but i think the the the path there is is is more modest steps uh more modest steps
So you just did something psychologically interesting with the string theory case when they were extending to 26 or 10 dimensions with the Minkowski metric. They said, it's because Einstein told us. And then you said, well, what was the motivation for Einstein? It was point particles in four dimensions and light clocks. Okay. Even in your constructive gravity approach, where you were saying Einstein tried to anti-symmetrize the metric or at least not make it symmetric, metric symmetric.
that if you're doing so then raising and lowering isn't going to be the same but you can only see that from your approach because there's a gauss map and there's a legendre map if i recall correctly oh yeah that's right well okay that's one of the okay okay we can get into the technicalities of that i would like to at some point but yeah but the point is that what you just did there was extremely interesting you said look we don't willy-nilly modify up here without understanding the reason from which here came from
because if you modify here maybe you don't have to modify just this you think you do but it's all of this oh yeah i mean or it's only this why don't you talk on that then well i mean that's that's that's so so what you're describing there is one could summarize it abstractly as follows formal generalizations typically fail that's what i understand it i have a symmetric metric
Now I do a non-symmetric one there's a motivation because F mu nu is not symmetric right today of course we we smile a little bit at that because the F mu nu is the field strength and not the potential stuff like that but we had some reason for making it non-symmetric right but then if you formally say we generalized this formally
Then you don't know what you're doing. You need to generalize conceptually. So you have to ask why was it symmetric there? Why was it the metric? And then you might have a starting point to say under what circumstances with the same why question have a different answer. Yes. All right. So, so, so yeah, you have to think conceptually, not formally. Formal is good. Once, once look, I mean, every equation in physics,
is only a secondary product. Let's take the first thing. So what is energy? What does Einstein do? Einstein said energy is what is it MC squared plus and then all the higher order terms in the P nice the square root of them. You have all these and you can say Einstein Newton wrote the P squared over two M term for say kinetic energy.
But if you do relativity, you have also a P cubed, a P, well, at least a P square, a P quarter, the fourth power to the sixth power, you have this whole expansion coming from the square roots, right? In relativity. So you say, ah, look here, Newton didn't see or didn't consider the higher order terms in P. That's correct, right? They're there in relativity, if you write it in this form. But Newton also didn't see the zero order term.
The MC squared. You see what I mean? So the point is, if you say energy, it's a different concept in relativity than it is in classical physics. And if you think you come from one theory to the next by adding higher order terms, because that is the only thing that could happen measurement wise or something, you make, I don't know whether it's a category error, but something like this, you want a new
Idea of energy then you have to first have a concept for that and don't do it purely formally. You see what i mean that's why you need to think conceptually and once you have the conception right. I'm simply fine a little bit then the equation flows out of the idea. It's not the equation first.
It's the concept for us. Yes. Yes. Okay. Cause otherwise the ambitious undergraduate would say, well, maybe there's a fifth order term in energy. Let me try that. But then you're wondering, well, where did that fifth order, where was the impetus for the second order coming from? Something like that. Something like that. You always in order to generalize a theory, you must understand the to be generalized theory first at a deeper conceptual level.
And that's already ambiguous because you can look at things at different conceptual levels, right? You can describe, take gravity. Okay. High school question. High school teacher asks the student here, final fail or pass will be decided on your correct answer to the following question. Student says, okay, is gravity a force? And we mean Newtonian gravity because high school only Newtonian gravity. Is Newtonian gravity a force?
a student will say yes it's a force and he says excellent you passed but if the student had said no it's not a force he should also pass because you can rewrite newtonian gravity as a curvature of space and of newtonian space time not relative is newtonian space time is also curved in the time direction which there is now a unique time direction and
fully equivalently fully different conceptualization of what gravity is not a force but a curvature of the space and you know freefall is geodesics auto-parallel in that context because you have to do it with a with a connection in Newtonian space-time. So that means the answer to the question is is gravity Newtonian gravity a force yes or no both answers are correct if you conceptualize differently predictions are the same.
What does that tell us? Well, gravity is gravity, what it does. And our formalism for it could come in many different guises, and it could give the same result. So we shouldn't confuse the formalism for the physics or the objects in the form is I mean, force is a concept in Newtonian mechanics.
And gravitational force is then also there, but you could argue, well, gravity also Newtonian theory should be made a curvature of Newtonian space time. And then the first axiom starts making sense. The first axiom sense says a particle under the influence of no force moves along a straight line. Okay. So you can say, do you know an example for that? No force. And you would say, well, at least where we live on earth,
The first axiom is out of work, right? It's unemployed because there's always the gravitational force. It's just there. So what do you mean a particle under the influence of no force? If you ever say no, gravity, also Newtonian theory, is the curvature of Newtonian space-time, then it would mean any particle
on which no force other than gravity which we no longer consider a force acts moves along a straight line that defines straight line in an operational way and then the second axiom says and should you ever see a particle not move along the lines that particles on which no force acts then those are those other particles are force acted yes otherwise the first axioms a special case of the second
Exactly that makes no sense. Newton wasn't stupid. He doesn't say I first do it for the beginners. I say no force, then do it with the force for people who can't set the right hand side of MA double dot or MA equals F to zero, right? I mean, no, no, no, right? He wasn't silly. No, the first one defines what a straight line is.
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How is it that you get to learn a subject? How is it that you, Frederick Schuler, learn a subject? Now, you said you had great teachers and so on, but let's remove that self-studying. How is it that you learn a subject so well? What is it that you do to learn a subject conceptually well? Well, if you're an absolute beginner, you do need a teacher because in the flood of textbooks and lectures, you need a guide. You need a good guide.
But if you now say forget about the teachers, how do you learn it? Well, it's different at different times. As a student, I learned the lecture notes, I learned the textbook in the sense I've tried to understand every equal sign. I still tell this my student, every implication arrow, I must be able to say why precisely this is a valid step. It's a passive approach, right?
Great people set this up. If it's properly presented, I can check. I can check that what is said makes sense, fits together. This is very far away from finding it, right? And then the quality of material reveals itself. If you can start on page one and you're properly equipped, you know, if you can start on page one and you really try hard to understand it,
But again and again, there are jumps and gaps and things you don't understand. It might be you, but I always, yeah, but actually good material goes step by step. And I always tell my students, my quality guarantee or my hope is that if you don't understand something in lecture 23, then the answer should be in lectures one to 22. Otherwise I need to up my game. Look,
Do I satisfy this in the strictest sense? Of course not. I'm human like everybody is human, right? We all make mistakes. As we said before, we all use ways to think about it, which one could would better think about twice when this is really a good argument and so on. But at least we should try to eliminate that as much as possible. But as you ask the question from a student side, I judge I judged material. Is it can I understand every step in detail?
Okay. And then you have a lot to do this as a student. Now, of course, with so many years of experience, I look at things, I read over them, I read the gist of them and I say, okay, what do they actually do? And then I apply all my my knowledge as far as it's existent. And I try to redevelop it. As I think what they actually wanted to say, but might not have said.
and half of
No, no, no, no, no, that's more like and then I tried to set it up new. And so in some cases I really succeed in this and then I bring this into my lectures and I redevelop a course entirely from there. There's of course a difference of how I did it as a student and how I did it later. However, what I did as a graduate student, as a PhD student, I often sat in the cafeteria on Fridays and I also took only white paper. So that's
I think that started there. And I thought, okay, now I'm here doing my PhD in theoretical physics. Let me write down for myself, what is actually the basic subjects, quantum mechanics, classical mechanics, quantum mechanics, Maxwell electromagnetism. What is it really? How would I write it down now if I had to write some summary of it? And then I realized all my gaps and all my lack of understanding. And sometimes this lack of understanding was simply because it wasn't properly said.
and taught. I confronted myself with what happens if I have no textbook with me and I'm supposed to write up a subject, a defined subject, a lecture course type subject, as we know classical mechanics, Lagrangian mechanics, from scratch, including its justification, the whole setting, what is the scope of it and so on.
That's very humbling. It's very humbling, but it's a very good training. And I think meanwhile I can make more out of it. I can then make it better.
Okay, so let me see if I can formalize that. You are in a room, you're alone, you have blank paper, and you're thinking you pick a subject arbitrarily, or is it just whatever is next up? Back then, no. Back then, I thought, let me go through the four elementary things, something like classical mechanics, electronics, quantum mechanics, statistical physics. You know, these are standard big lecture courses, say in Germany, but anywhere, right? In theory, theoretical thinking.
What is the formalism? How does it start? What are the concepts? And how do I bring this into an order that makes sense? A, B, C, D, E, not in another order, right?
So, and if one really tries this, and even as a very good student and very good graduate student, I realized, oh my gosh, I mean, there's more holes than anything, right? And then you will recognize the holes, then you can start to fill them. And in a sense, I'm still filling them on some points, right? I also noticed that when you're lecturing, sometimes you'll pause at the blackboard,
And you'll derive, you'll make sure that you can derive it right then and there, even in front of the students. Oh, yeah. I wasn't sure if that was for you, for your own pride that you need to be able to derive it or for your own intellectual satisfaction or if it's to role model for the students, because it seemed clear to me you have lecture notes behind you. You could actually look, well, what's the final formula? Where am I trying to get to and use that as a hint? But then you don't. Yeah. Well, the reason is all of the above plus a sanity check
that what I with all my experience of doing this for what 30 years can't do freely after I of course had the think about thought about it for four hours in the morning I always prepare my lectures four hours earlier in the morning and then I go and I write them up in nitty-gritty detail with headlines and everything in order to give them structure then I put the paper on on the big desk and then I only look at the headlines typically
on the rarest occasion i need to look at the formula again i get confused but i essentially really think a
What i cannot freely develop after having thought about in the morning again and of course it's a big thing a whole lecture course is then one just one lecture of those right so everything needs to make sense in the end what i can't lecture freely and precisely and convincingly and step by step on how can i expect the students at the end of the term. To do it.
yes they should be able to do it so i must be able to do it so it's not only it's pride as well i i want to be able to do that but it's a sanity check if i can't do it what am i asking the students to do i ask too much of them okay number one second only if i develop this life does a student can a student follow
it slows me down as opposed to i copy from my paper if i take sometimes i did that on very rare occasion i took the sheet i had there because it was a bit complicated and i started writing what was on the sheet my teaching quality goes down 70 percent
It's not a good thing. It is as if you had sent me your questions before. I would have thought about your questions and would now have paper where I have very intelligent answers to your questions, at least intelligent sounding answers. Okay. Uh, and I would now read them off and I say, Oh yeah, Kurt, that is a very interesting. We wouldn't have a conversation anymore, right? It would feel strange. Now only the best speakers can read from a sheet and speak well.
Okay. And so it's also serves what I want to say is it also serves the communication with the students is a real conversation. It's like a story I tell you over a campfire. It's very real. I might not complete every sentence ideally and so on. But your focus is on it. Yes, that has to do with yet another thing. What do you have to do if you have 200 people sitting there?
And you want them to not open their laptops. They all have laptops. You don't want them to open the laptops. You want them to listen what you do, to write what you write, to see or copy maybe what you write and have their eyes where you want them to have their eyes, where you use a blackboard. And on the blackboard there is a drama developing with actors, my fingers, the chalk. Sometimes I tip on the blackboard as in here and so on.
People look there nobody opens their blackboard i think in the last six or seven years i once had to ask a young lady was probably for very good reasons on her mobile phone i told you please take it away i can't lecture like this and it's really true i have an inability if people don't pay attention it makes me nervous.
okay yeah but of course i can't force people to pay attention i have to play my game such that people don't want to look away and if you go to the cinema and you watch a well-made movie you don't look away so i have to present a well-made movie which has to be scientifically sound as well and and one of the things is use the blackboard speak to the people speak to them in real time and let them participate in your thought
You know roughly speaking so so all of this hc no alternative to using the blackboard Nobody follows a little laser dot on a screen on a you know on a projection
Wall right if you project your and and then you can have your little laser pointer and then you point at things you point at next things Honestly, do you want to follow this little? Jumping red dot you don't it's very difficult to focus but a blackboard lecture is natural the equation evolves and the nicest thing is the lecturer makes mistakes and then a student can say Your second equation. There's something wrong. It must be a minus. I see no
And then I honestly I honestly I'm honestly surprised honestly secure about it now confident about it and then still wrong and shouldn't happen too often right in every lecture you make a mistake in every lecture you make a mistake where the student knows better they think you're a fool maybe that's correct but occasionally.
That's right. Then I look at it and sometimes very, very rarely, but sometimes I spent 20 minutes in a lecture recovering an error, which I made. Oh, that's not how you write it. And then the first thing I say to the student, very honestly, you saw something that I didn't. Very good. Now let's see whether I can save this. And then it's pride and pride. It's also to students a statement like,
You know i don't say i look this up at home and then you will see next time i say i was a little mistake a mistake is a mistake mathematics and our subject in general makes you very humble you know if you have made a mistake you can be the smartest and the cleverest or the most arrogant or whatever if it's a mistake some mistake you better immediately admit it you immediately admit it and try to see whether you can repair it and sometimes you can't.
and so that all of this is only this is the life i think and it's remarkable that in the youtube videos i think some of these things still come through so that students who attended my lectures and watched the videos as well say that still comes through somehow okay good
wouldn't have predicted that, I must say. I thought it needs the immediacy of the classroom. So maybe that's also part of why maybe it might be more than not enjoyable to watch them.
So these are all, you see, these are little ideas, none of them per se is a principle that's set in stone and everybody who does it different does it wrong. I'm not saying this. There are people who give lectures in a very different way. I say, oh, God, I would never do this. I recently had this very excellent colleague, Pim van Toft,
I would never do it like this, but respect, you know, so if as a teacher you can make your method fly,
Wonderful. Wonderful. And I have my method to make it fly.
So what was the bad method or the topic that he had that you wouldn't have taught like that? I think if I remember correctly, we talked about quantum mechanics to high school students, highly talented high school students who every year we have at the university, we invite 100 top talents from Germany and the Netherlands for a talent course, where in three days we teach them quantum theory from nothing up to the teleportation protocol.
But including the foundations, I mean, the axioms and the techniques and all of this. Anyway, let me not talk too much about this cause anyway. And there on the first day we do complex numbers, but we don't say complex numbers, you know, I squared is minus one. We do them as tuple of real numbers with a very special additional multiplication because then they're totally demystified. Okay. Uh, the complex numbers. And, um, and he, uh, said, okay, you add them like this here, a now, you know,
component wise so to speak and then the multiplication of course is not component wise it needs to mix and then he asked them so how would you multiply them and then of course he got them on the wrong track because they would also say component wise you multiply the components of these two pairs of real numbers and I don't do that as a principle because you can't guess how you multiply
Tuples of real numbers if you want to make them into into complex numbers because it's a definition.
and only after you made it you can then start investigating what it is yes okay and and here the point was to define the so i didn't i wouldn't ever do that it's a micro thing you see i thought about all these things very interesting i would never do that i think ah no don't do that because then they they have this bad idea which would then say is wrong and ah no no not this way around but he did it so skillfully the excellent teacher he did it so skillfully
damn well done i'll still not do it but you did well mad i mean i thought i was sitting there yes watching okay and so i want to say these are all for instance another obsession i have is no motivating examples well that sounds very strange right i mean isn't the motivating example a great thing
I mean it in a strict sense. If I say I'm to teach you vector spaces or vectors, never teach you vectors because there's no such thing. They're vector spaces, but vectors. And then people say, well, look, you hear it one and then you can add them up by moving this one like here. And then you have this one. That's the addition. And you can scale them as soon as you start with little arrows or fingers or whatever. Um, uh, you don't have, you have a very special type of vector space, right? Um, um,
And why is addition by moving things around? What the heck are you talking about? If you give people this kind of motivation, which almost every one of us got upon seeing vectors the first time in high school or something, then you get the idea a there are objects that are vectors. And if I see a vector, I recognize a vector. Well, this is all true.
Because the only mathematical object in the game is a vector space is a set with two operations plus and the scaling and for these up in this set together with the operations only if the following eight axioms hold then we call that entire structure a vector space.
And yes, we can then nickname the elements of that set. If the set carries with it as companions, these two operate, we can nickname the elements of such a set vectors, a vector, and we mean an element from that set. But the correct word would be an element from the set that underlies the vector space. The vector space is a triple V plus dot. Okay.
But there is no such thing as a vector. If I write on paper a tuple, one, two, right? One, two as a tuple with brackets. Ask you, is that a vector? You can't answer that question. Do you know that there are others which can be added to this one and scaled by which addition, which scaling? You might think that is clear what it is. No, it isn't. You can make beautiful vector spaces out of, for instance, positive
Yeah, positive real numbers. They can be made to R plus to the end. It's kind of like octane or something. It can be made into an R vector space where the addition is by pointwise multiplication of the components and the scaling is by taking the components to the power of the scaling factor. That vector space, the zero in that vector space, so the neutral element of addition is one, one, one, one, one, one.
You always introduce special situations, special structures that people will never forget and they will always somehow refer to these
maybe in extreme cases only why not instead of giving a motivating example which by its nature is not understandable for anybody who doesn't know the concept yet is made more vague and then you give the definition but the definition doesn't follow from the example of course it doesn't it's a more general thing it cannot follow why not make a little commutation give the definition first
and then give 15 examples afterwards, very, very different examples. That's a much better teaching because that's the object we want to talk about. It's very mathematical thinking. And then I show you what variety of crazy situations are all covered by this general structure. So we better study the general structure than all these crazy examples. You see, so I have obsessions. I want obsessions, no motivating examples.
Sometimes you start a subject, especially in physics, and it's too good. I think it's too good to not give this motivating example. But I always regret it. I always regret it. I mean, I can pull this off. It sounds very good. But ultimately, I always realized it down the line. It can cause confusions in the students. Motivating examples are of the devil.
okay so anyway and you see and whoever skillfully like my colleague i mentioned before on another principle of mine whoever skillfully and masterfully violates these principles bravo
But these are my principles. I try to not do that. So I've thought about many of these things, of course, a lot of experience in trying it this way and trying it this way and being dissatisfied. And the highest judge is always, was it correct what I said or was it mumble jumble? And almost by construction, motivating examples are mumble jumble. Unless it really follows one from what you did before and leads to a question.
not based on the previous lectures I do this calculation or this construction or something and everything can be understood in detail and then I say but here's a question and that motivates this lecture that would be good that would be more a derivation than a motivating example to introduce a new idea now so so so I have probably I don't know whether I have 50 of these principles but many things I think very strongly about none
And they're extremely personal. Of course. That's one of the reasons why many people have asked you, hey, can I interview you about how you teach? And you're not so keen to do so. That's true. I gave some interviews. Usually if my own university asks, I don't want to say no. No, I was once introduced. It's interesting. It's interesting. I think even audio snippet on the Internet where I was asked whether this when these online lectures took off like like crazy internationally.
They asked me from a research center for education in Erlangen whether by doing these videos I also want to promote the new online teaching media or something like this.
And I said very undiplomatically, I said that doesn't interest me one bit, right? So no, I don't want to promote, I don't want to do YouTube videos, I don't want to promote distance teaching, learning, none of this. I want to do good physics. And back then, they actually in Erlang, the students could always choose whose lectures are being recorded. And that's when a number of these Erlang lectures that are on the internet have been recorded by the university.
So I just try, as I said, I try to give students something really valuable and try to make them really good as much as I can. That's my only my only aim. And the other things are side effects. And of course, I like it. Of course, I like it that these lectures are so so well received. Yeah. So I'm confused. You're not a fan of your lectures being online or you're not a fan of distance teaching. What do you mean?
No, I'm not a fan of neither a fan nor an enemy of distance teaching. I know my lectures. Well, first of all, a little anecdote. None of the lectures online have been put online by myself. So there is a video, a YouTube account called Frederick Schuller that features these lectures. That's not me. Somebody took my picture. Somebody took my name and downloaded these lectures, I think mainly from Erlangen University and put them on YouTube.
Great service. I thought, okay, it's a fan. Whatever. Okay. Only a few years later when then there were really views went into the millions and totals on I thought, okay, I got a little bit scared. What if this person one day post something inappropriate, right? I mean, could be anything. And it's my name and
And then I wrote via YouTube to them. I never received a reply. And then meanwhile, then all of a sudden it was a name I didn't recognize. And then it was back my name. And, and I decided, come on, I mean, I could now tell YouTube about this. And then maybe then they take the lectures down as a comma, but people are watching them at the moment. I don't want that. And, you know, so I also, then at some time there was some commercials in between. I thought, okay, somebody is making money of it, but I thought, okay, fine. Okay.
Good for them. So these are not my accounts. The Gravity and Light I gave my OK to, the Gravity and Light lectures, but the others have all been taken from, however public, it's not kind of copyright infringement or anything, public service of the university where they were recorded.
look i think i think of course it's great that there are so many online resources i mean it's the positive side of the internet but we can all look up it's brilliant okay and if people like the stuff and i think it's not wrong or terribly wrong then i i i leave it on everything everything is fine
But I think ultimately I'm psychologists would tell you that you can only be formed children for sure but also young adults in the presence of another human being on whom you can in the weakest sense model yourself. And so this goes back to my teachers in high school at impressive teachers in high school and all these people
Without trying i want to be like him or her but in a way you model you imitate your model yourself so i think we need the personal contact and then of course in the tutorials to all these courses have cost tutorial teachers systems are very good people as well with themselves.
Very good researchers. I go to many of these tutorials and I sit there in the row and if I see the students don't engage enough because they're maybe too shy or too now, I start pushing the tutors on say, well, how can you say this and stuff like this? And that then mixes up the whole atmosphere a little bit, right? And sometimes I confront students, right? I didn't come prepared and I said, Oh, do you play basketball?
Anyway, I pushed him a little bit and I say, well, I mean, it's a professional enterprise here. I mean, you want to become a professional. What do you mean you come unprepared? I don't understand. Did you have a big business running on the side? Because otherwise, I mean, come on, right? Yes.
I try to confront people a little bit. I mean it well. I always mean it well. I try to confront them with what it means to be there and sit there and do things, but not do it seriously. Well, then don't do it at all and face that you're not doing it. Because where does that get you? I try to be nice most of the time. No, I think I'm nice, but I push people. I challenge people sometimes a little bit in the tutorials. All of this is not on the videos.
and but it's also because i believe yeah there's some you see it's like if i was an arts professor i would take my students to the gallery and i would show them the well the picasso's and the all the others and i would discuss with them about these pictures and would say isn't that look at it first of all look at it just look at it okay so it's a little bit like this i say look at classical mechanics
i mean look at this and of course in order to make them look i have to expose the theory right i have to to go step by step and but it's really i think the classical subjects we teach um i show them uh how do you say
Like a masterpiece of an artist, like of a world, justifiably world known art, world known artist. Yeah. Look at this thing, this theory. Look what marvelous cultural achievement this is. I don't use ever these words, right? I just do what I do. I do what you see on the videos, but essentially I do that. I show them and then I showed them a theory.
Which is one of the most developed one of the classical mechanics also in all the theories most developed theories we have how can i expect them to later on make their own theory that's asked a lot or modify liberty if i didn't show them the masterpieces what is how does an end product of research look like if
10 geniuses, saying classical mechanics, let's say 10 geniuses developed it, maybe was five, 10 super geniuses and a thousand almost geniuses who kept shaping it. What you get today is the product of whatever five or 10 geniuses and a thousand almost geniuses who shaped it into this form and this you get. This is my present to you, the thought of genius and you understand it. Is that something? I think that's something.
I think that's something. It's quite different from, oh, I can calculate this. No, it's, it's, it's, it's, it's brilliant. It's a brilliant thing. We have the privilege to have done and others are younger, general relativity, quantum field theory studies, and others are still developing. But we want to make the masterpieces that don't look like the old masterpieces, like a Picasso doesn't look like a Rembrandt, right?
But new masterpieces that stand next to the old masterpieces and all are recognizable as masterpieces, right? And so that's also one part of teaching at a high level in theoretical physics or mathematics, the same logic. But I think you need to be present. So that's your question.
Look, it might be that one day only very few very rich people can afford to go to the remaining few universities who offer in-person teaching and everything else is economized into online teaching. Would that be the worst? I don't think it would be the worst, but it would probably in the long run wouldn't be so good. I think every one of us has some spark of maybe, maybe. I don't know. That's not a good statement.
A little. The tiniest spark of genius, I think, is in everybody. And everybody should go to places where he sees other people participate in lectures. As I said before, students need to see you as a teacher to model themselves on you. They need to see there are many other people in the classroom who struggle with this, but they also see. So I'm not the stupid one, but they also see people who apparently fly through the material and excel. So you say it can't done.
If you can do it, you're apparently very special, but others can't do it either. But some actually make it. I'll give it a try. You know, you need both sides. You need to see it can be done and to see it's not so easy. I'm not stupid because I haven't gotten it yet. So well, you know, all of this only happens in presence. And during Corona, we had beginners starting and I gave, I think it was a lecture, it was a tutorial. I think it was a lecture. I gave lectures and
I didn't see the students, of course not, right? They saw my face and I had some things, they were beginners, right? It didn't work well. It didn't work well. I did my best. I think I gave a good lecture, but it's too remote. I need to see their faces. They need to see mine.
They need to see my gestures. They need to see other human beings doing the same thing. I think they were mainly disoriented because they didn't see who succeeds and doesn't or that there are other people who succeed and don't. We need this. So no, I am not a proponent of online or remote learning, but of course it's not a bad thing as such. But none of that is my intention.
And I'm happy that the people elsewhere who don't have many people wrote to me, it's wrote many positive things. And then they said, it's nice that these lectures are available for free online. I would never have access to such teaching where I live. Okay, I believe that for those people, we write very kind emails. And I'm very happy. It makes me very happy that that they take so much out of it, not only joy, but also maybe future development and so on.
Well, you do your stuff extremely well. Speaking of masterpieces, your lectures are a masterpiece. I'll place a link to all of the lectures, all of your playlists, and they'll be in the description. It's a privilege for me to be able to speak with you. It's a privilege for the audience. The audience is well,
I'm grateful and I'm sure the audience is grateful as well. Thank you so much professor. Thank you very much Kurt for the invitation. It's very pleasurable to talk about this because indeed we talked about many things I usually don't talk about because they're
I think you said this in some places. You like to at least occasionally delve into technical detail or at least pseudo technical detail for people who know more, who know about the real background of things.
Thank you. In parts, I think what it is, it's like overhearing two colleagues in the office talking with the door open. And I think your podcast does this particularly well. Hi there, Kurt here. If you'd like more content from Theories of Everything and the very best listening experience, then be sure to check out my sub stack at KurtGymungle.org.
Some of the top perks are that every week you get brand new episodes ahead of time. You also get bonus written content exclusively for our members. That's C-U-R-T-J-A-I-M-U-N-G-A-L dot org. You can also just search my name and the word sub stack on Google. Since I started that sub stack,
It's somehow already became number two in the science category. Now, Substack for those who are unfamiliar is like a newsletter, one that's beautifully formatted. There's zero spam. This is the best place to follow the content of this channel that isn't anywhere else. It's not on YouTube. It's not on Patreon.
It's exclusive to the Substack. It's free. There are ways for you to support me on Substack if you want, and you'll get special bonuses if you do. Several people ask me like, hey, Kurt, you've spoken to so many people in the field of theoretical physics, of philosophy, of consciousness. What are your thoughts, man? Well, while I remain impartial in interviews, this Substack is a way to peer into my present deliberations on these topics.
And it's the perfect way to support me directly, curtjaymungle.org or search curtjaymungle sub stack on Google. Oh, and I've received several messages, emails and comments from professors and researchers saying that they recommend theories of everything to their students. That's fantastic. If you're a professor or a lecturer or what have you, and there's a particular standout episode that students can benefit from or your friends,
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I know my last name is complicated, so maybe you don't want to type in Jymungle, but you can type in theories of everything and you'll find it. Personally, I gain from rewatching lectures and podcasts. I also read in the comment that toe listeners also gain from replaying. So how about instead you re-listen on one of those platforms like iTunes, Spotify, Google podcasts, whatever podcast catcher you use. I'm there with you. Thank you for listening.
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"text": " And so it's important or it could be important depending on what you want to do to reformulate theories like this well long story short in the classical domain this has been developed over decades by i think it originated with arian fundershaft and bernard maschke and many other people work on this now in germany there's a big"
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"text": " For that you have a Hermitian operator, let's talk finite dimensions, otherwise self-adjoint operator, okay let's think finite dimensions. Quantum information technology justifies us in doing that, right? You have a Hermitian operator and then you find the eigenvalues and of course you can then calculate from the spectral decomposition, you can calculate the probability with which a certain measurement will occur if you measure now. But what do you mean will occur and if you measure now and what does this all mean"
},
{
"end_time": 596.834,
"index": 26,
"start_time": 580.93,
"text": " It's just talk it's talk that works spectacularly well as we know right quantum mechanics in a sense it's work spectacular but much of this talk especially around measurement is not all reflected in the formalism."
},
{
"end_time": 617.329,
"index": 27,
"start_time": 597.176,
"text": " And of course, many people have worked on that. Many very smart people have worked on that, trying to explain measurement, the idea that decoherence may play a role. I guess it does. But is that the whole answer to the measurement problem? No, it is not. You know, all of these things. But this what we're trying to do is very modest."
},
{
"end_time": 645.418,
"index": 28,
"start_time": 617.329,
"text": " But maybe therefore it can be successful we try to give an extended formalism not deviating from quantum mechanics but capturing much of the talk as much as we can in a formalism in this idea of parts but now not energy parts but probability parts play a big role. So it's a natural idea everybody can have it we work for a long time to really get this onto the street because there are many little"
},
{
"end_time": 673.643,
"index": 29,
"start_time": 645.896,
"text": " Things you can trip over and now I think we made some good progress and well once you're convinced we went to a point that it's worth putting it out so that other people can start thinking about too if they like you will hear from it that's it so but that's what I'm thinking about from about quantum mechanics and it's a very thorny issue because you know I mean it's also very easy to talk about the measurement problem because yeah yeah it has been talked a lot about it is a little bit"
},
{
"end_time": 700.384,
"index": 30,
"start_time": 674.019,
"text": " quite dramatically a problem, right? I mean, Roger Penrose talks about it, of course, is true. That's not a secret, so to speak. And we try to have a modest new approach to it. But the claim to fame, well, not fame, but you know what I mean, right? The reason why I think it might be useful, it uses a new technique and a new formalism with a purpose."
},
{
"end_time": 730.265,
"index": 31,
"start_time": 700.879,
"text": " So that's what I'm thinking about on that side. OK, so earlier you said that undergrads, well, you didn't use the word undergrad, but undergrads are taught about kinetic and potential and how you can flow between them as long as energy is conserved. But then you said it was all talk. What do you mean that it's all talk and not reflected in the formalism? And also port, because people keep hearing this word port, port is spelled P-O-R-T and refers to the boundary ports. Yes, the boundary ports, the other ports,"
},
{
"end_time": 756.971,
"index": 32,
"start_time": 730.759,
"text": " It's very easily explained if we write it down. We can't do that right now. They're simple examples. Well, the point is what is not reflected is you have a total energy that's conserved and of course you can define a potential and a kinetic energy and you say it flows between them because the sum of them is preserved, right? So yeah, I mean, I'm not saying it's wrong talk."
},
{
"end_time": 782.142,
"index": 33,
"start_time": 757.295,
"text": " What I mean by it's only talk is, is it built into the formalism that you make use of that insight? Now you're just saying you're looking at two observables, kinetic and potential energy. Yeah, okay. And they change their values as your system evolves classically. You can monitor that classically. But as I said, we're not making use of that in any way."
},
{
"end_time": 790.794,
"index": 34,
"start_time": 782.534,
"text": " We're not now. And then the question is, is really the kinetic energy? Does that constitute a constitute a"
},
{
"end_time": 815.162,
"index": 35,
"start_time": 791.135,
"text": " Conceptual subsystem from which something flows elsewhere, you know, this all sounds good I think this also in some videos that that you talk about where the mathematics One confuses what physically happens with the mathematics and so on it's of this type I think it's really I could now try to explain in words what a port is and it would sound very fancy with dual variables and"
},
{
"end_time": 840.776,
"index": 36,
"start_time": 815.162,
"text": " Note, I'll be placing these notes from this podcast in my sub stack, which you can get by searching my name and the word sub stack or by visiting curtjimongle.com. I know it's a mouthful."
},
{
"end_time": 865.469,
"index": 37,
"start_time": 840.981,
"text": " There are a couple of questions here that I have. You said"
},
{
"end_time": 882.346,
"index": 38,
"start_time": 865.93,
"text": " The phrase, it's a modest proposal, therefore it could be successful. Now that's interesting. Not it's a modest proposal and it could be successful. It's a modest proposal, therefore it could be successful. So I have a stickler for words and I noticed that. Yes, yes, yes. Please tell me what did you mean by that?"
},
{
"end_time": 911.596,
"index": 39,
"start_time": 883.148,
"text": " Why is the modesty connected to the success? Okay, at least for my means, I always think if I have one idea about something, a measurement problem or something else, one idea, you know, ideas are cheap in our field. We can have many, many ideas, right? And we can then find the fifth and the sixth idea. And if we take these 10 ideas together, I believe trying to bring one idea to success,"
},
{
"end_time": 939.718,
"index": 40,
"start_time": 912.09,
"text": " works because you have this one idea and then this idea, if it's any good, will lead you, if you try to implement it, will lead you to more insights. And then the problem dictates you what your next idea would have to be something like that. Okay. Um, uh, I think, look, this is a very, it's a philosophical subject, right? So, um, uh, and I claim no, no truth to this, of course, but"
},
{
"end_time": 963.575,
"index": 41,
"start_time": 941.118,
"text": " If you asked, I don't know, you could view say the whole development up to general relativity starting from Maxwell theory that Einstein stared at the Maxwell equations and the longer he stared and the more he thought about it, he realized there is something at odds with the idea of, you know,"
},
{
"end_time": 993.473,
"index": 42,
"start_time": 963.814,
"text": " the speed of light being in there. I mean, the constant, the C constant by what is an epsilon times times mu is in there. How can that be in that equation? Because if you go to a moving system, shouldn't it be C plus V where we use the moving system? So Einstein looked at Maxwell. In a sense, you can say Einstein took Maxwell theory very seriously. Okay. And taking Maxwell theory very seriously, he was prompted to change"
},
{
"end_time": 1020.401,
"index": 43,
"start_time": 993.865,
"text": " the idea of space and time, or even the separate existence of something like space and something of time, there's only space-time. So it's a very simple idea, it's very modest to say there is a theory that tells you how electromagnetic signals, Heinrich Hertz, I think 1888, he proved that you can actually transmit by electromagnetic waves, you can send signals in the lab and stuff like this."
},
{
"end_time": 1043.37,
"index": 44,
"start_time": 1020.401,
"text": " I think it makes it was something like eighteen fifty eighteen sixty something like this with his equations in eighty eight this was demonstrated so the predicted electromagnetic waves they really exist and it works and so on, send saying what that works and then we have a radio in the radio so it's a modest idea to say let's take mexico theory very very seriously."
},
{
"end_time": 1072.381,
"index": 45,
"start_time": 1043.729,
"text": " And then it leads to special relativity. And then for the inclusion of gravity, by whatever way you want to take there, say the Einstein way, it leads to the curvature of space and time. And if you want to a prediction in that theory and that view to the prediction of the Big Bang. Right. So in a sense, it's very, it's a very modest idea seen through, you see through this idea that you say Maxwell theory is correct. Right."
},
{
"end_time": 1098.37,
"index": 46,
"start_time": 1072.756,
"text": " And so I think seeing through one idea can open doors. Yeah, so that's what I mean by it's a modest idea. One can make many constructions and ideas and intuitions and so on. I always think we need to rely on nature giving us a hint because theory spaces"
},
{
"end_time": 1125.606,
"index": 47,
"start_time": 1098.712,
"text": " Infinite dimensional. And if you tip with your finger somewhere and you say, oh, the metric may be non-symmetric. Einstein did that, right? I mean, Einstein in his later years, he fanatically looked for for the inclusion of of Maxwell theory into the geometric framework of general relativity. And of course, we had to lose the client, all these nice things, all very nice. But ultimately, it doesn't work. So far, we think Einstein didn't find it."
},
{
"end_time": 1145.026,
"index": 48,
"start_time": 1125.998,
"text": " And so once Einstein let's take Einstein also as a counter example in the sense once he started thinking in this formal way and have an idea we could include this here that didn't work so much anymore I think because he didn't have nature on his side like he had before with Maxwell theory. Yes."
},
{
"end_time": 1166.681,
"index": 49,
"start_time": 1146.084,
"text": " I have the advantage that I've gone through your work, so I know that you're presaging constructive gravity."
},
{
"end_time": 1179.923,
"index": 50,
"start_time": 1166.715,
"text": " Yeah and I'll place a link on screen as a preview. We're going to talk about that about how you derive gravity from matter dynamics rather than seeing gravity and matter as separate postulates. We'll talk about that."
},
{
"end_time": 1205.162,
"index": 51,
"start_time": 1180.811,
"text": " Well, right. Yes, yes. So I can tell you where this came from, this whole thing. So absolutely counter to what I just said in the past. I also looked at modified gravity theories for this reason and for that reason. And of course, these are all reasons that are dreamt up. There's a lot of modified gravities ideas out there. And how do we know which one is right?"
},
{
"end_time": 1229.991,
"index": 52,
"start_time": 1205.162,
"text": " And at some point i came to the conclusion for myself of course that doesn't disparate anybody else's attempts in any other direction. It's a little bit hopeless to just try to think that you think up something half formal half motivated and then write down a new lagrangian. That's easy you can do that everybody can write down a lagrangian a modified grid lagrangian for theory."
},
{
"end_time": 1257.466,
"index": 53,
"start_time": 1230.435,
"text": " I thought, what could actually give us a hint at modified gravity if we don't just look at gravity itself? And well, we do a lot of observations about matter, right? We do very precise observations about matter. And the question was, is it actually true that you have to postulate both the dynamics for gravity and the dynamics for the matter?"
},
{
"end_time": 1274.462,
"index": 54,
"start_time": 1258.336,
"text": " At some point we stumbled across this that we thought, no, it's a crazy idea, but maybe if you're given a metal Lagrangian on an assumed background, and I mean just the geometric structure, so to speak, of the background, but not the concrete"
},
{
"end_time": 1301.084,
"index": 55,
"start_time": 1274.804,
"text": " Say you could say on a Lorentzian background on a background that allows for by refringence or something like this, you actually determine from the meta action, how this background has to get its dynamics in order to be compatible with this meta action. And the only connection we saw is that the meta action and the gravity action, they must both have"
},
{
"end_time": 1331.596,
"index": 56,
"start_time": 1301.681,
"text": " They must evolve together. Say if you speak mathematically from the same cushy surfaces, they must take the initial data. Those must be evolved to again a shared cushy surface or a whole family of shared cushy surfaces. This seems to be a minimal requirement if you want a predictive classical theory. Predictive being the key and quantizable, not for the gravity, but for the matter. Yeah."
},
{
"end_time": 1348.695,
"index": 57,
"start_time": 1331.903,
"text": " What are quantized? This is that came in as a technical, but let's let's quantize about for the moment. It became in order to justify an apparently classical condition, technical condition to do that. That's why we let's leave it out for for the clarity of the."
},
{
"end_time": 1378.131,
"index": 58,
"start_time": 1349.206,
"text": " So, and now you might think that's a very weak connection that they have to have the same Cauchy surfaces, so to speak, the meta dynamics on the background you give me and what dynamics the background could get to evolve together with the meta dynamics. And it turns out it's a very strong connection, actually. In fact, you can write down equations that you need to solve in order to get as a result, as a solution to these equations, you get the gravity action."
},
{
"end_time": 1406.817,
"index": 59,
"start_time": 1378.524,
"text": " that you would have to give to that geometric structure. Yes. That is in the background of the meta theory. All right. Sorry, just a moment. I just want to make sure I'm understanding. So let's just make this concrete. How do you go from Maxwell's equations to the action of Einstein and Hilbert? Spell that out. So you know how in physics we like to reduce something that's complex into something that's more elegant, more efficient, more simple. Turns out you can do that"
},
{
"end_time": 1431.22,
"index": 60,
"start_time": 1407.227,
"text": " with dinner. HelloFresh sends you exactly the ingredients you need. They're pre-measured, they're pre-portioned, so you don't have to do this superposition of too much cilantro versus why is there no cilantro or or what have you collapsing in your kitchen every night. They have literally 40 different recipes every week, vegetarian, calorie smart recipes."
},
{
"end_time": 1458.66,
"index": 61,
"start_time": 1431.527,
"text": " protein-heavy recipes, which is my favorite, whatever your diet function looks like. And they all take approximately 15 minutes to a half hour. That's less time than it takes me to figure out whether time is fundamental. I've been using it myself. It's the one experiment that in my life has always had reproducible results. It's delicious. It's easy. It saves me time from living on black coffee while editing episodes at 2 a.m., say."
},
{
"end_time": 1475.162,
"index": 62,
"start_time": 1459.155,
"text": " Personally my favorite part though is that it's an activity I can do with my wife. Thus it not only serves as dinner but as a bonding enterprise. So if you want to make dinner the most predictable part of your day, go to HelloFresh.com"
},
{
"end_time": 1505.213,
"index": 63,
"start_time": 1475.469,
"text": " How do you go from Maxwell's equations?"
},
{
"end_time": 1527.756,
"index": 64,
"start_time": 1505.759,
"text": " To the action of Einstein-Hilbert. Spell that out. Okay, so to ask how does this bigger scheme work in the special case if you would say start with matter that is Maxwell electrodynamics, right? Yes. On some metric background. Let's not even say Lorentzian, any metric, any signature. Well, the first thing you would do, you would find out"
},
{
"end_time": 1557.961,
"index": 65,
"start_time": 1528.114,
"text": " And for what background signature, if you start with a metric like this, would you have a well-defined Cauchy problem for Maxwell theory? And then it turns out immediately only for Lorentzian signature, right? So, but then the question is, aha, so a Lorentzian metric is in the background of this theory, and that's also clear from the phenomenology that we see. Aha, but what is now the dynamics for that background metric? That's the question."
},
{
"end_time": 1584.138,
"index": 66,
"start_time": 1558.131,
"text": " Of course, the textbook answer is Einstein's equation. Why? Because Einstein told us so and there are good reasons and it works out. But in fact, you can derive if you solve these equations, we call them construction equations. You set them up only with information extracted from the matter action. You set up these construction equations, you solve them and their solution give you the action"
},
{
"end_time": 1608.353,
"index": 67,
"start_time": 1584.411,
"text": " That is Einstein-Hilbert with the cosmological constant and of course a gravitational constant undetermined. So you can say, aha, well, we didn't learn anything new and no, we didn't. But we learned new that if you just say Maxwell and you want the background to evolve together with it, it must be Einstein. It must be Einstein-Hilbert."
},
{
"end_time": 1630.674,
"index": 68,
"start_time": 1610.128,
"text": " Now, is that true with other fields, other standard model fields, not just Maxwell? Yes, we also investigated with other standard model fields. Of course, if that hadn't also yielded Einstein theory, there would be something terribly wrong either with our construction or with the physics as we do it. No, indeed,"
},
{
"end_time": 1654.241,
"index": 69,
"start_time": 1631.527,
"text": " Everything works out even if you take nonabilia engaged theories actually had a very good master's student alexander witz but he worked on that and and we figured out and no nothing new comes up we also try to use the same method to break because you see what it is if you say you have the meta action say you keep the background constant like an eta mu nu and minkowski metric right flat space"
},
{
"end_time": 1684.411,
"index": 70,
"start_time": 1654.633,
"text": " Then you could count this as a constant, but the idea of gravity is to make it dynamic. And what we then did is say, okay, but there are other parameters in matter actions. Maybe for them, we can also predict dynamics and that would of course be interesting, right? If some neutrino masses or something like this, but no, these are things we had a lot of hopes for once the actual thing worked, what we'd wanted to do to predict the gravity or to derive the gravity theory from a new matter theory."
},
{
"end_time": 1703.404,
"index": 71,
"start_time": 1685.043,
"text": " okay so look the thing would be as well let me tell you a fantasy story okay okay fantasy story is that tomorrow we look into the universe and we see somewhere either directly or indirectly a light ray split right so like in the birefringent medium well"
},
{
"end_time": 1728.882,
"index": 72,
"start_time": 1703.729,
"text": " again directly indirectly we could see it in the hydrogen spectrum and stuff like this but let's say for simplicity the light ray splits in space as it is bent in space time you know yes before einstein if somebody would have said you the light ray bends around something without there being a lens you would say no in materials this is possible it's called glasses right but without any material how would it happen"
},
{
"end_time": 1754.906,
"index": 73,
"start_time": 1728.882,
"text": " Well, so again, it's a fantasy story assume the light ray would split in vacuum. So one photon is coming. One photon is moving. Let's let's take classical a light ray, a light ray, a laser ray, something like this. You know, I mean, it's fantasy anyway. But if that would be seen directly or indirectly general relativity, and you can ensure it's vacuum and stuff like this, right? General relativity would be dead."
},
{
"end_time": 1767.739,
"index": 74,
"start_time": 1755.742,
"text": " Because a Lorentzian metric does not support the splitting of light rays into different polarizations. So with one observation, you can state the depth of general relativity."
},
{
"end_time": 1790.64,
"index": 75,
"start_time": 1768.183,
"text": " Sure, I mean, with the usual caveats, is there another effect we don't take into account? You're talking to a theorist, right? So I can dream. So let's say something like this, but if something that dramatic happened, or another case, so many years ago when I developed this theory at the Max Planck Institute for Gravitational Physics,"
},
{
"end_time": 1803.046,
"index": 76,
"start_time": 1790.64,
"text": " There was this group in the Gran Sasso laboratory. They ran experiments. So the renowned group is a renowned group, obviously, and they measured faster than speed of light neutrinos."
},
{
"end_time": 1829.718,
"index": 77,
"start_time": 1803.302,
"text": " that was announced and that was exciting and it was a serious group. I think something in the end somebody forgot to unplug something or plug something that that was the reason so there are the end it was clarified but but I mean if that had been true and actually that day Herman Nicolai the director of the Max Planck Institute there at the time and he came into my office said can you do this with the theory you're working on"
},
{
"end_time": 1856.63,
"index": 78,
"start_time": 1829.718,
"text": " And i will of course he was my director says of course you can do it we could do this week we could do this but what we would need is a particle phenomenologist right and like i mean all physics is phenomenology a particle phenomenologist to write down a really good model for it and that good model couldn't be built. On if it was really in documents or couldn't be built on a lorenzo metric."
},
{
"end_time": 1869.684,
"index": 79,
"start_time": 1857.108,
"text": " It needs a more refined structure. For instance, you could take a fourth rank tensor as a geometric background with symmetries like the Riemann tensor, anti-symmetric pairs and stuff like this."
},
{
"end_time": 1895.691,
"index": 80,
"start_time": 1870.196,
"text": " It's just a model. The point is we are prepared for something that hasn't happened yet, right? If somebody sees matter that cannot have due to their behavior, a Lorentzian background, but you would then phenomenologists would pretty quickly figure out what we may be the simplest background that could do that. Then the question comes up, but what's the action for that background? It can't be Einstein, right? Einstein is a for a Lorentzian metric."
},
{
"end_time": 1920.06,
"index": 81,
"start_time": 1896.323,
"text": " Or metric in general, but then you would try to solve our equations and they're hard to solve in the Einstein for the Maxwell case. We can solve them. We get Einstein. They're hard to solve, but the result would be the action for that geometry in the background that could support that new exotic, but the new required matter."
},
{
"end_time": 1938.029,
"index": 82,
"start_time": 1920.52,
"text": " So in a sense we converted the physical question, what's the gravity theory that can support such matter into a mathematical question, solve these equations whose coefficients are constructed in various ways from the properties of the matter action."
},
{
"end_time": 1958.353,
"index": 83,
"start_time": 1938.985,
"text": " That's the idea. That's the idea. And there are many technical issues. Anyway, that was our idea. How can we actually say something about modified gravity that takes seriously some other physical observation we make about matter?"
},
{
"end_time": 1987.21,
"index": 84,
"start_time": 1958.968,
"text": " And it's quite remarkable that this is possible in the first case. Yes. I mean, all of this builds on earlier work by Kukash and Title Boym and ADM. I mean, there's lots of predecessors, but we kind of, in a sense, pushed it, pushed it there because in a sense, I guess before people didn't have the motivation to look at this. But, yeah. I have a quick technical question. So I can see how you can get the signature. You just talked about it with Maxwell. What makes a Lorentzian metric isn't just its"
},
{
"end_time": 1995.759,
"index": 85,
"start_time": 1987.534,
"text": " It's a 02 tensor. It also has a certain signature and then it's non degenerate and so on. But how do you get the condition that it is compatible with the connection?"
},
{
"end_time": 2024.633,
"index": 86,
"start_time": 1996.084,
"text": " Is that a condition from the principle polynomial? Yeah. So this is also something, it is very elegant. Actually, Schrödinger did that, right? Schrödinger had a modified idea. Again, Schrödinger had an idea of modified gravity and he said, no, no, no, Einstein does this non-symmetric matrix, but actually a deeper structural concept than the metric is the connection. And there are connections that come from a metric and they're more general connections, right? So that was,"
},
{
"end_time": 2051.578,
"index": 87,
"start_time": 2024.633,
"text": " Schrodinger's idea, actually a wonderful book by Schrodinger, Space Time Structure, a very beautiful, thin book on general relativity for a beginner. But then he follows this route and it's technically and conceptually wonderful. And then he assigns to this connection a deeper meaning than to the metric, you could argue. And he tries to make a theory for connections rather than for metrics as the fundamental structure."
},
{
"end_time": 2071.903,
"index": 88,
"start_time": 2052.056,
"text": " I think he even announced this in the New York Times or something like this and Einstein was angry. I don't know whether this is historically correct. This is the rumor. Anyway, it didn't work, right? I mean, we would know about it. And you can say, okay, the all the idea with Palatini action, all of these things come from there and relate to this. But it wasn't new physics. So you"
},
{
"end_time": 2098.763,
"index": 89,
"start_time": 2072.398,
"text": " The idea that generalization of relativity goes via a connection, if you go away from a metric, is an old idea by Schrodinger, but it's not the idea here. Here the idea is, why do we talk about a space-time metric in the first place? Well, because of Maxwell. Remember, the pluses and the minuses, say, in the Minkowski metric are the pluses and minuses undergraduate students have to learn in the badly written three plus one decomposed Maxwell equations, right?"
},
{
"end_time": 2120.981,
"index": 90,
"start_time": 2098.763,
"text": " But if we have matter that has a different causality, then the regular cones, it would be cones that are a little bit more folded like this and so on. I'll place an image on screen at this point. Okay. Okay. Okay. Okay. Okay. No. Yeah. Yeah. No. And again, this is all this is all theoretical considerations, right?"
},
{
"end_time": 2147.056,
"index": 91,
"start_time": 2121.357,
"text": " I'm sorry, what did you ask before? Oh, I was saying, okay, so in the principal polynomial, I can imagine how you can get symmetry or anti symmetry conditions, I can imagine how you can get signature, I can imagine how you get that is non degenerate, or that is degenerate. But I don't see how you get compatibility with connection as a condition of the principal polynomial. But but there's no connection at all. So"
},
{
"end_time": 2176.732,
"index": 92,
"start_time": 2147.654,
"text": " So, okay, what we call signature in the metric, if I look at it from the point of Cauchy surfaces, is to say that the theory, the matter theory that has an underlying background of a Lorentzian signature metric, that the theory is hyperbolic, globally hyperbolic. You have a Cauchy surface and so on. For a metric, it translates into this algebraic condition of having a certain signature, 1.3 or Lorentzian signature."
},
{
"end_time": 2191.852,
"index": 93,
"start_time": 2177.312,
"text": " For a non-metric structure, say a fourth rank tensor that could produce as a background to Maxwell theory, it could produce by refringence. There still the global hyperbolicity of the matter theory"
},
{
"end_time": 2220.384,
"index": 94,
"start_time": 2192.193,
"text": " Is the condition we need, but it translates not directly into a signature condition. There are many other algebraic classes. So the point is, well, this is a whole thing when one has to work out, but it's the global hyperbolicity of the matter action. Tells you how to construct. Cauchy surfaces also for the matter action and remarkably also how this matter action must look like."
},
{
"end_time": 2247.807,
"index": 95,
"start_time": 2221.101,
"text": " So at the end of the day, it's a very simple idea, execute, it has some technical hurdles in between, but it's a cute idea. And that's what it is. I mean, we have no claim that it's realized in nature, but in a sense, if really tomorrow somebody discovered something like I said, something that would be faster than like neutrinos."
},
{
"end_time": 2271.527,
"index": 96,
"start_time": 2248.217,
"text": " Yeah, faster light neutrinos could have been a possibility or by refringence in vacuum. Because some people say the whole theory of physics or Einsteinian physics is dead. We don't know what to do tomorrow if we saw faster than light particles. Exactly, exactly. I mean, general relativity couldn't be right, right? I mean, it builds with the Lorentzian metric. This is just not possible."
},
{
"end_time": 2299.428,
"index": 97,
"start_time": 2271.527,
"text": " But if dense again, I'm not saying I couldn't immediately say how the gravity theory looks like. But if some phenomenologist makes a really good model for this matter now, so say standard model grade model, right? So to be incorporated in the standard model, let's fantasize. And then we have a standard model with faster than speed of light neutrinos, say, okay, say, then I would say now is the time to invest the time and money."
},
{
"end_time": 2320.674,
"index": 98,
"start_time": 2299.957,
"text": " to set up our construction equations well that can be done over the weekend so to speak but then to solve them and there you might really i mean you know it's very complicated equations but if you solve them you get the gravity action that would support the new full matter model so so we think we think we showed that"
},
{
"end_time": 2351.169,
"index": 99,
"start_time": 2321.971,
"text": " Okay, I'd like to talk about your mind. When we spoke a couple months ago, off air, we were speaking about how there are toy models in physics, and you were thinking, okay, well, what is it that compels a theorist to go in this direction? That's the question you would ask them. If you're getting too abstract, you just want to say, well, what compels you? Can you please talk about that and how that guides your own research, maybe your teaching, maybe your philosophy? Yes, yes."
},
{
"end_time": 2377.5,
"index": 100,
"start_time": 2351.357,
"text": " Well, you see, in research, we're always tiptoeing the line between the known and the unknown. Right. If we stay firmly in the known, we're not conducting research. We say that's the theory. That's how we look at it. Nothing to change about it. Yes, there are problems, but who knows what that is. Okay. I'm simplifying here, but especially as a theorist, we're tiptoeing on this line. We're always with one foot in the certainty and one foot in the unknown."
},
{
"end_time": 2398.882,
"index": 101,
"start_time": 2378.08,
"text": " And so if you want to do research we need to introduce a new idea into something otherwise at least as a theorist what are you doing there needs to be one new element in it. As i mentioned before i believe if you say oh i have five new ideas how things could be different at once i think it's not manageable."
},
{
"end_time": 2428.575,
"index": 102,
"start_time": 2399.428,
"text": " You have a new idea and you have the old. First of all, are they compatible or not? Well, if they're not really compatible, you have a problem to solve because you have to incorporate this new idea without"
},
{
"end_time": 2453.763,
"index": 103,
"start_time": 2429.002,
"text": " and thereby you typically have to also change the old theory right yes if they're not the new ideas not fully compatible okay and typically this leads to a contradiction in the old theory to a prediction of the modified theory in three lines i exaggerate where you say yeah but late nature isn't like that well what happens then well you throw away your new idea right"
},
{
"end_time": 2472.142,
"index": 104,
"start_time": 2454.155,
"text": " think Verizon the best 5G network is expensive think again bring in your AT&T or T-Mobile bill to a Verizon store"
},
{
"end_time": 2500.162,
"index": 105,
"start_time": 2477.005,
"text": " But if you have a new idea and it"
},
{
"end_time": 2523.831,
"index": 106,
"start_time": 2500.981,
"text": " If you start incorporating or modifying the old theory or aspects of the old theory in that according to this idea or incorporating this idea or incorporating this technique, you get something slightly new, which is not immediately obviously false. And then the question is, what do you do next? And the answer is, well, I hope at least usually it is."
},
{
"end_time": 2552.381,
"index": 107,
"start_time": 2524.172,
"text": " What you're doing there, if you keep looking at it and keep working with it, you will be forced, you will be compelled to maybe to do a next step. For instance, you could have a new idea, let's do this and that. And then it tells you, oh, but unless you choose this object to be of this and that class, rather than the other class it could have, then there's an immediate contradiction. Well, you already have learned you need this other class of object and so on, another algebraic class or whatnot. Yeah."
},
{
"end_time": 2578.643,
"index": 108,
"start_time": 2552.637,
"text": " Can you be more concrete? Can you give a specific example? Maybe you're trying to tiptoe and be diplomatic and non offensive. No, no, no. No, not really. You see that that's the problem of this. All I say are vague ideas of how to not run away in a theoretical direction that doesn't lead nowhere. Right. It's very easy. You see, and I think a lot of physics maybe always has been maybe is"
},
{
"end_time": 2597.483,
"index": 109,
"start_time": 2579.241,
"text": " including some of my own work in the past is having an idea and going here and going there and trying to implement it here and here it's a little bit we need what guides us what is the guiding principles we use right and yeah more concrete"
},
{
"end_time": 2616.698,
"index": 110,
"start_time": 2597.961,
"text": " Let's say what i said in the beginning with this port hamiltonian series where you reformulate classical theories such that you have the energy flow the fundamental variables. Immediately relate to the energy flow between subsystems is a reformulation of hamiltonian mechanics."
},
{
"end_time": 2636.869,
"index": 111,
"start_time": 2617.193,
"text": " and i said let's apply to quantum mechanics okay okay but then we played around for a few months with energy flows in quantum mechanics in the end we discarded the idea well essentially because in quantum mechanics you don't have a continuous energy variable that describes the system you have a hamiltonian"
},
{
"end_time": 2651.766,
"index": 112,
"start_time": 2637.108,
"text": " But you see, if you have Hamiltonian, let's say you take two states that are two different eigenstates of that Hamiltonian, right, two different energy eigenstates, and you take their superposition. Well, then you have a new state, right? The superposition of two states is a new state."
},
{
"end_time": 2674.77,
"index": 113,
"start_time": 2652.875,
"text": " But for this Hamiltonian upon measurement, you would get either one or the other value, right? You would get one eigenvalue or the other one. You wouldn't get the average of the eigenvalues, right? So this state itself, the superposition state of two different energy eigenstates, I don't know how we would say it has this and that energy. It doesn't."
},
{
"end_time": 2692.551,
"index": 114,
"start_time": 2675.981,
"text": " So that means most states, almost all states in a Hilbert space, let's say a finite dimensional one, almost all states in a finite dimensional Hilbert space do not have an energy with respect to a given Hamiltonian operator, right?"
},
{
"end_time": 2718.865,
"index": 115,
"start_time": 2693.353,
"text": " Yes, that that that that that's a fact. So and then this whole idea of construction of ports for reasons that are not clear now, but fails because you would need a continuous continuously in time evolving or even differentially in time evolving. Of quantity, whatever it's supposed to be, you would would need in order to create these ports. But energy is not the right thing."
},
{
"end_time": 2736.101,
"index": 116,
"start_time": 2719.428,
"text": " While energy plays in quantum theory also the role of the generator of the time evolution like in classical theory energies generator of time evolution it is not the right quantity to introduce these parts in in quantum theory."
},
{
"end_time": 2758.234,
"index": 117,
"start_time": 2736.749,
"text": " Right. So you what I say you need to you can't just push an idea. I want energy flows. I want to study energy flows. You need to react what the theory reports back to you if you try to modify it like that. That's that's the rough idea. Look, I think we're talking a little bit too much about"
},
{
"end_time": 2781.834,
"index": 118,
"start_time": 2758.49,
"text": " How i think one could could constrain oneself to make good progress without running away uncontrollably but this is very personal you see if i thought this had deep philosophical value what i say i would have written it up and published it. Okay but it's something i discuss a lot with my with my research students i tell them what ideas are cheap."
},
{
"end_time": 2806.425,
"index": 119,
"start_time": 2782.363,
"text": " very easy to"
},
{
"end_time": 2832.261,
"index": 120,
"start_time": 2806.971,
"text": " I want to qualify what I say. It's not offending anybody, but I think it's the truth. These are basic ideas of how to orient one's own research, but that's very personal. These are yours. You're not advocating that if people aren't following it, then they're doing something incorrectly? No. How do you say?"
},
{
"end_time": 2854.275,
"index": 121,
"start_time": 2833.951,
"text": " I mean look at the history of physics in the 20th century, right? I mean the revolutions that were there and what people predicted about it before it would be totally absurd to say because it's not on my radar right now or I can't imagine this to be a good way to say nobody should do this, of course not. I tell it to my students though."
},
{
"end_time": 2870.247,
"index": 122,
"start_time": 2854.718,
"text": " I put this on my students and my justification is well they don't have to listen to me right and they can take it as one element of what one could think about and hopefully they add something else to it or they rejected or they take it over."
},
{
"end_time": 2892.346,
"index": 123,
"start_time": 2870.247,
"text": " I learned from other colleagues to from other sources to say i think we should speak out about these things these are subtle things you know probably somebody not doing research doesn't know the hell what i'm talking about here and but these ideas and we should put them on our research students but not to force them to take them but just as."
},
{
"end_time": 2912.995,
"index": 124,
"start_time": 2893.592,
"text": " Because otherwise we can't teach them. You can teach people by telling them your own ideas about something and they are less attached to them. They might change them a little and have more success, for instance. Speaking of teaching, you're a world-class teacher. You've won several awards, some of the most prestigious awards."
},
{
"end_time": 2940.93,
"index": 125,
"start_time": 2913.234,
"text": " Yeah, no, I was very lucky because I was in sort of history, I tell you the history of one of these awards. I was very lucky to have been invited by the German Physical Society. They have a youth organization. Actually, the German Physical Society is, I think, the biggest physical society in the world. It's a little bit funny, but they have many, many members and they have a youth organization. And they invited me in 2015 to give a big lecture series on general relativity."
},
{
"end_time": 2959.804,
"index": 126,
"start_time": 2941.578,
"text": " And so I did and we did this in Austria and they gave us a fantastic place to do that and out of that came these gravity and light lectures on YouTube and we put them on YouTube and we didn't think anything of it and they took off quite a bit."
},
{
"end_time": 2975.145,
"index": 127,
"start_time": 2960.145,
"text": " and then there were other lectures taken in Erlangen University on the geometric anatomy of fundamental physics or whatever I call it, geometric anatomy of theoretical physics. Yes, it's about differential geometry."
},
{
"end_time": 2994.036,
"index": 128,
"start_time": 2975.145,
"text": " Yeah yeah it was one of these things that that they do in germany which is fantastic every now and then you can give a lecture that you want to give a lecture course right you give of course lecture courses that need to be given they're part of the curriculum but then there are optional courses where if you have an idea and you want to do it you do it and i just wanted to teach people"
},
{
"end_time": 3023.968,
"index": 129,
"start_time": 2994.275,
"text": " differential geometry from the ground up as it's then used in theoretical physics and so it's more of a applied mathematics course than it's a theoretical physics course and that kind of took off once the university put this on youtube or first on itunes or something like this and yeah that gave me some international followership and also national followership and then at some point i was proposed for the ars legendi prize"
},
{
"end_time": 3047.978,
"index": 130,
"start_time": 3024.36,
"text": " which is the top German teaching prize for university teachers. They were so kind to find that in that year to meet the best candidate. They like the best at least. So you have this Geometric Anatomy course? Yes. And that didn't have a curriculum before you came up with that? That's right. Do you have other ideas for courses?"
},
{
"end_time": 3075.964,
"index": 131,
"start_time": 3050.572,
"text": " Yeah, all the time, all the time, but the question is whether you can give them, right? Whether the university gives the opportunity to give these courses or give these courses or when they say, no, we are already busy with the curriculum, right? But what's in your mind? I'm curious. So for instance, for people who understand differential geometry, what's extremely interesting about your course is you started in the first lecture with propositional logic."
},
{
"end_time": 3098.729,
"index": 132,
"start_time": 3076.527,
"text": " Right, right. And then you built up to the empty set. I think in the second or third lecture. Yeah, yeah. No course on differential geometry starts with the empty set, let alone propositional logic. You started from the ground up. That was extremely interesting. You're exceptionally clear, exceptionally clear. I absolutely love that. Yeah, I think I've rewatched those. I may have rewatched that"
},
{
"end_time": 3115.828,
"index": 133,
"start_time": 3099.292,
"text": " As many times as I've rewatched Seinfeld, which is many times. Yes, yes. Well, I mean, look, it was a course because it was an extracurricular course. I had some mathematicians in it, some physicists and so on."
},
{
"end_time": 3139.206,
"index": 134,
"start_time": 3115.828,
"text": " I can tell you the reason was very simple. If you want to tell people what a manifold is, you need to tell them what the topological manifold is. They need to know what a topological space is. A topological space is a very simple thing. If you know that you have a set and then the set has a power set, how do you know the set has a power set? How do you know the power set is a power set? You need to have some set theory."
},
{
"end_time": 3164.701,
"index": 135,
"start_time": 3139.497,
"text": " Now, if you do naive set theory, you have all kinds of contradictions in two lines. If you say a set is a collection of elements, that sounds good, but that doesn't make any sense. First of all, I didn't tell you what a collection is. Second, I didn't tell you what an element is. So to define a set as a collection of elements is not particularly insightful. And in fact, as we as well known, I mean, this is naive set theories is contradictory in line two."
},
{
"end_time": 3185.555,
"index": 136,
"start_time": 3165.179,
"text": " And so ultimately, if I want to tell people from a broader range of backgrounds, also in physics and mathematics, what are we actually talking about here? I have to tell them also about the axioms of set theory. Now that's a thorny issue. It's a very kind of complicated issue if you really go deeply into this. But if you want to do it, you can do it."
},
{
"end_time": 3203.797,
"index": 137,
"start_time": 3185.811,
"text": " Actually, if you wanted to explain what set theory is, you need to write down the axioms. If you want to write down the axioms, you need a formalism in which you formulate these axioms, because if I then formulate them with other flowery words, I'm as bad as I was before. And so there was the idea, okay, we have to do some quantours and so on."
},
{
"end_time": 3227.056,
"index": 138,
"start_time": 3203.797,
"text": " some propositional logic before. Well that can actually be pushed even deeper and I didn't do that in this course to some first order logic and so on. So there are many steps. Ultimately, I mean it's now known it was Hilbert's dream but it's now known ultimately it's very difficult to find a really foundational beginning from nothing even if you say you have an alphabet and symbols and so on."
},
{
"end_time": 3254.002,
"index": 139,
"start_time": 3227.056,
"text": " but what i wanted to do at least i wanted to go beyond the usual undergrad or even master level idea about what a set is for these students they're all very excellent students in in erlang back then they had also this elite graduate program and so on i mean super students top top top students so i could could deliver that to them it was an attempt at at"
},
{
"end_time": 3284.036,
"index": 140,
"start_time": 3255.128,
"text": " some type of completeness of the presentation starting virtually from nothing. And then you see rigor in mathematics, of course, extremely important. But for me, the best rigor is the conceptual rigor. I mean, of course, you can write down things with epsilons and deltas and can make it very, very, very, very rigorous. Before that, actually, you need to be conceptually rigorous. If I say set,"
},
{
"end_time": 3302.295,
"index": 141,
"start_time": 3284.155,
"text": " We just have a vague idea about it and i build a big edifice on it and then at every other junk shaft to say well now you can show that whatever that a vector space always has a basis in an infinite dimensional one well how do we know that will ultimately this comes from the action of choice right."
},
{
"end_time": 3326.271,
"index": 142,
"start_time": 3302.295,
"text": " Well why do you have the action of choice because at some point i required it you see so i wanted to give it the full picture without claiming that this is at the same time the foundation logic cause of foundation set theory cause because you could probably spend your life if you want to fill in all the details at least i want to be a bit more clear about what all the assumptions are."
},
{
"end_time": 3351.032,
"index": 143,
"start_time": 3326.271,
"text": " And this is a general because you're asked about teaching. This is something that's very important in teaching. And I always joke with people when they ask me, I say my assumptions in teaching, the foundational assumptions are two. A, students, no matter who comes to you, beginners, master students, they know nothing, nothing at all. And second, they're infinitely intelligent."
},
{
"end_time": 3368.66,
"index": 144,
"start_time": 3351.22,
"text": " Okay. Okay. So both assumptions are slightly wrong, right? Students know things and they're not infinitely intelligent. But I present my courses a little bit like that. And I like to develop things from the beginning because I don't know what they know and I don't know in which way they know it."
},
{
"end_time": 3398.643,
"index": 145,
"start_time": 3369.155,
"text": " So I like to start from scratch. Yes. You even told me that instead of starting with a textbook, you'll go into a room, a blank room with blank paper and think, how can I teach the subject? Right. Right. Well, I mean, I think that that's so that's another thing I think was all not my original ideas, a very old idea, you know, unity of research and teaching. I think at university, only people who bring to the table some research grade"
},
{
"end_time": 3417.602,
"index": 146,
"start_time": 3399.48,
"text": " Thinking should actually teach the important lectures, at least for the students who take the subject very seriously. Let's say it like this. Also, if some biology student has a physics course that can be excellently taught without"
},
{
"end_time": 3436.578,
"index": 147,
"start_time": 3418.404,
"text": " Much do but if you say educate the next generation of theoretical physics and maybe you hope that some of them might make groundbreaking discoveries or something well we better we better give them our best and don't just repeat what what in the how we learned it right."
},
{
"end_time": 3465.333,
"index": 148,
"start_time": 3436.988,
"text": " And so how do you do this? And how do you not just follow what is written in the textbook? I think you say this in one of your videos where you say, oh, yeah, we just often just repeat what we have heard. Was it you who said that? Yes. Somebody else you interviewed. And you can recognize this if you would never use this phrase somewhere else. Exactly. On an equal footing, I think it was. There are many such phrases. I keep a catalog of them."
},
{
"end_time": 3489.599,
"index": 149,
"start_time": 3465.333,
"text": " All possible paths seems to be echoed due to doctrinal inheritance without thinking, just like the word equal footing. Time and space are relative and treated on equal footing. Time and space are supposed to enter on equal footing. We should think of space and time on the same footing. What is equal footing? Have you seen a mathematical definition of equal footing? We're supposed to be rigorous. Yeah, yeah, yeah, space and time on an equal footing. Oh, yeah, indeed. What the heck is that supposed to mean? Okay."
},
{
"end_time": 3509.582,
"index": 150,
"start_time": 3489.599,
"text": " Nevertheless we all do that but indeed i would say one way to make a research much better is to try to detect where you using such phrases in order to justify something well there of course placeholders for. A better explanation."
},
{
"end_time": 3539.326,
"index": 151,
"start_time": 3510.196,
"text": " Interesting. Sometimes you have a much better explanation. Everybody knows the better explanation and then you refer to it on an equal footing and then everybody, however, if pushed would give you a brilliant explanation to it, then you're allowed to use this short term. Yes. But if it's just used to gloss over your own ignorance consciously or unconsciously, one should eliminate it. But we all do this. So first of all, if people ask me, how do I teach better?"
},
{
"end_time": 3544.718,
"index": 152,
"start_time": 3539.753,
"text": " very well i say something like that right and then say i"
},
{
"end_time": 3572.91,
"index": 153,
"start_time": 3545.128,
"text": " I mean, general relativity is one of my expertise. So if I teach a course in general relativity, I can teach this in any number, in two or three different ways. Okay, not any number, in two or three different ways. And then I first of all think, what is the best way for this group? And for instance, I once had the task to teach physics to material scientists."
},
{
"end_time": 3589.087,
"index": 154,
"start_time": 3573.114,
"text": " They're not hardcore physicists, but they need some good quantum mechanics and it was quantum mechanics course. And I decided that because they need the energy bands, you know, in solids and so on. I teach them a tempered distribution theory."
},
{
"end_time": 3619.036,
"index": 155,
"start_time": 3589.445,
"text": " right? Schwartz spaces, tempered distributions and so on a distribution theory, which you would say is a very advanced subject. I mean, most physicists don't hear this in the undergraduate studies, right? Right. But I decided before for the applications we want to do, we just need this. I taught this to them. It's not that difficult after all. They all did pretty well. Right. So sometimes we must not shy away from using very advanced methods, of course, explained very well from the bottom up."
},
{
"end_time": 3646.527,
"index": 156,
"start_time": 3619.411,
"text": " Also to people where you say oh normally they wouldn't use this theory but I think they should right so and then I usually textbooks many textbooks don't offer them precisely the line you want to take and I think it's also good for for the lecturing style if I don't take a particular textbook certainly in a subject I know very well yeah I take a stack of paper in the summer break"
},
{
"end_time": 3666.681,
"index": 157,
"start_time": 3646.988,
"text": " And I start sketching what is a good storyline, but I mean, scientifically conceptually rigorous storyline as today one would have to present it in order to get it accepted in a very good journal. If this was a discovery, so to speak. Right. So, um, yeah."
},
{
"end_time": 3696.459,
"index": 158,
"start_time": 3667.363,
"text": " So I try to apply research-grade thinking to the design or redesign, that's the better word, the redesign of also very established courses. And very often you change the order in which you teach subjects. What you think is an advanced subject is typically something you learned later. And a less advanced subject or topic is one you yourself learned earlier. But that's not a particularly meaningful"
},
{
"end_time": 3725.742,
"index": 159,
"start_time": 3697.005,
"text": " This episode is brought to you by State Farm. Listening to this podcast? Smart move. Being financially savvy? Smart move. Another smart move? Having State Farm help you create a competitive price when you choose to bundle home and auto. Bundling. Just another way to save with a personal price plan. Like a good neighbor, State Farm is there. Prices are based on rating plans that vary by state. Coverage options are selected by the customer. Availability, amount of discounts and savings, and eligibility vary by state."
},
{
"end_time": 3747.363,
"index": 160,
"start_time": 3726.305,
"text": " Classification of advanced not advanced, right? For instance, in Erlangen, I taught the classical mechanics course, I decided to teach it using half of the semester to develop differential geometry. Then I did the mechanics. And in the last lecture, I could tell them what general relativity is."
},
{
"end_time": 3776.118,
"index": 161,
"start_time": 3747.892,
"text": " Okay. Um, uh, that worked pretty well. Colleagues said you're crazy, right? I mean, you have bad passing rates. Not true. We have excellent passing rates or very good passes, at least the usual ones. Uh, and, and, and some of these students to just absolutely spectacularly, because once you do it properly, you see, you should never do something because it looks fancy. Oh, we did it with differential geometry. No, I need to tell you what the cove vector is. If I want to talk about momenta."
},
{
"end_time": 3791.817,
"index": 162,
"start_time": 3776.459,
"text": " right because momenta canonical momenta are covectors they're not vectors how do i tell you do i tell you about this in in vector space i could but then people think about the position vector but position is not a vector and and you can't get away from this"
},
{
"end_time": 3818.063,
"index": 163,
"start_time": 3792.346,
"text": " Structurally, conceptually wrong idea unless you immediately put it in the setting of a manifold. And then, of course, if you do then Lagrangian mechanics or something, you anyway generalize coordinates are nothing than what the differential geometry calls coordinates. They are generalized. They are coordinates. It's actually Cartesian coordinates, which are very, very special. Coordinates is existing under very special circumstances. And then you don't have to choose them necessarily. Right."
},
{
"end_time": 3847.841,
"index": 164,
"start_time": 3818.063,
"text": " So you put the whole conceptual basis properly rather than giving people the wrong idea. Because once you taught something in a way that is ultimately not correct, ultimately doesn't carry you far and you have to replace it later on anyway, you shouldn't teach people in the wrong way. And that's why it's important to be a researcher because you know where it's going to be carried. Whereas if you're just a general teacher, you don't know the forefront of the field."
},
{
"end_time": 3871.015,
"index": 165,
"start_time": 3848.473,
"text": " i think many both somehow yes it's because you need to know where you where you want to go and no but the other thing is you see in research you learn this oh could i explain this this other way oh this is a new take on let's let's explain it that way and but what if it's almost only slightly wrong"
},
{
"end_time": 3887.978,
"index": 166,
"start_time": 3871.817,
"text": " If you do something in a new way you need to apply the criticism of research to it to say is this really a valid derivation and is it really as general as the one that you get otherwise you know."
},
{
"end_time": 3916.101,
"index": 167,
"start_time": 3888.746,
"text": " So I'm a big skeptic of teaching methods as a one-size-fits-all method of how you teach better, whether you teach the piano or you teach general relativity. I do not believe that is true. I would never dare to recommend to a piano teacher my teaching methods because I think, oh boy, I mean, you're a concert pianist. I mean, the really good piano teachers that people study with, they're concert pianists."
},
{
"end_time": 3945.077,
"index": 168,
"start_time": 3916.613,
"text": " They don't have just a fancy teaching method. They can play it at a really great level. And then they have methods to teach them, which you can't come up from general considerations. So in physics is also like this teaching. I think good teaching always springs from a deep understanding of the subject coupled with an awareness of what you already explained and what you didn't."
},
{
"end_time": 3967.398,
"index": 169,
"start_time": 3946.903,
"text": " Sometimes people say, oh, that person is a really brilliant scientist, but he doesn't teach well. That's often the case in the University of Toronto. It's infamous for having great researchers, but they don't care about the teaching. Maybe they would be great if they okay. Okay. That's of course one possibility. You don't care about it or you hate your students."
},
{
"end_time": 3990.811,
"index": 170,
"start_time": 3967.398,
"text": " I think a more benevolent view could be they want to explain it well. Let's take those hypothetical ones who are really great, who really know their subject and who really want to explain well but don't. I think the most likely cause in those cases, and I know such cases, but not many actually."
},
{
"end_time": 4017.705,
"index": 171,
"start_time": 3991.34,
"text": " I think they're not fully aware of what they already explained. They explain some things. Oh, I forgot this. And then, okay, you forgot. Okay, I put this as an aside. That happens to all of us. But it's the next thing. Oh, and I did this. And as we know, and as you could show, but you know, then it's a mess. Then it's all over the place. Left as a homework exercise. There's a homework exercise. Yeah, yeah, yeah, yeah, yeah. Well, that's that's an easy opt out. Nice. Say you show this young man or young lady. Yeah."
},
{
"end_time": 4034.36,
"index": 172,
"start_time": 4018.131,
"text": " No, seriously, it's I believe it's certainly the implication error goes in one direction. I think you need to know your subject really well, really deep, really far in order to design a really nice lecture course on it. It's a necessary condition."
},
{
"end_time": 4060.964,
"index": 173,
"start_time": 4034.923,
"text": " the necessary condition. And yeah, and we all are fallible, right? I mean, I think I eradicated these and those problems from this subject and teaching it and how it's strangely taught and things like this. But then do I know, right? I mean, then somebody else must come and do it better. But at least we do better and better. I think if I can improve 5% of how I learned a subject,"
},
{
"end_time": 4091.015,
"index": 174,
"start_time": 4061.442,
"text": " Um, uh, and it's really solid, a solid 5% improvement. I think we, yeah, we can tap our own shoulders, right. And say, you know, but that's what we owe our students. So it's what we owe our students to, to, to really improve it because otherwise they must have a better starting point than we did. Although our, my starting point was excellent. I had brilliant teachers everywhere. Some of the privileges in life. Well, for me, I think for anyone is running water."
},
{
"end_time": 4115.947,
"index": 175,
"start_time": 4092.005,
"text": " Air conditioning and if you're a physics student, it's taking one of your courses. Oh, wow. Immediately after what an air conditioner. I'm not even kidding. It's an absolute joy. I don't know. So why do you care so much? Why do you care so much about teaching? That's a very good question. You see, I think and then I think it's a good lesson to to maybe young people out there."
},
{
"end_time": 4136.51,
"index": 176,
"start_time": 4118.063,
"text": " When I went to study to university, I was just so wanting to understand physics and to also make new discoveries in mathematics as well. I studied both in parallel. That was my aim. And if I now look back,"
},
{
"end_time": 4164.258,
"index": 177,
"start_time": 4136.886,
"text": " Even before that, when I was a younger man, I did lots of sports and I actually started working as a trainer already at a very early time, myself being active, but also teaching youth groups and so on. And if I look back in my life, I think from the age of 15 onwards, I have always in one or the other capacity in sports or elsewhere, I have been teaching, I have been teaching and"
},
{
"end_time": 4192.278,
"index": 178,
"start_time": 4165.657,
"text": " More or less what I told you is my philosophy about teaching today was my teaching back then I wanted to make them really good I wanted to make them really good competition sportsmen and women and things like that and I had this idea and I had myself good teachers in all of these fields and I passed this on but not out of a reflected moral imperative or something it just in retrospect I saw this."
},
{
"end_time": 4208.319,
"index": 179,
"start_time": 4192.773,
"text": " When I went to university in the first semester I had little meetings in the library where I told my fellow students things that we were currently discussing and that I understood before and I taught them on the blackboard in the library in the university."
},
{
"end_time": 4227.346,
"index": 180,
"start_time": 4208.319,
"text": " I always did this was not sure when i was at university and research institutes i was also invited well i am driving has a very sophisticated talent promotion program we have something called the scholarship foundation is the state"
},
{
"end_time": 4249.189,
"index": 181,
"start_time": 4227.346,
"text": " Organization the select point one percent of the best high school university students in any subject and they are they get special summer schools by top professors and so on and we have a similar thing for last year high school students where every high school in germany can send their one best student."
},
{
"end_time": 4260.606,
"index": 182,
"start_time": 4249.462,
"text": " What did I do?"
},
{
"end_time": 4289.65,
"index": 183,
"start_time": 4260.845,
"text": " Well, told them differential geometry, told them general relativity, right? Wow. So I have always done that and my aim is always to make the people as good as can be. So I'm a little bit of an elitist this way. I think, look, you come here to study, I give you the real thing, but the real thing is hard. And I do my very best that I deliver to you so that you can live up to the demands I put on you."
},
{
"end_time": 4319.428,
"index": 184,
"start_time": 4290.93,
"text": " Right. So I put high demands, but at the same time, I know I'm responsible for teaching them. And in the end, if it fails, if not a significant proportion of them takes a big benefit, which from your kind words, I take it many people do. Right. It's now more obvious through YouTube than I'm at university to, of course, I got always good evaluations or very good evaluations. Not a doubt. But then I think I succeeded. I succeeded."
},
{
"end_time": 4347.056,
"index": 185,
"start_time": 4320.299,
"text": " I once had a student who I met in Erlangen on the street years after he took my classical mechanics course I told you about that started with differential geometry and he stopped me and he was very kind and he said because of you I stopped physics and I thought oh really he said no no it was the best thing ever your course was great but I just realized I'm not good enough and I said maybe you should have tried more no no no absolutely not I'm so grateful to you because I realized"
},
{
"end_time": 4368.114,
"index": 186,
"start_time": 4347.466,
"text": " i should have understood it so many in my course said it was great i thought it was great but i just couldn't do it so it's it's a weird uh how do you say compliment but but it was genuine i think it was genuine he meant it and i said again apologized and i say i hope i didn't do anything wrong and so on and said no no no no he's very happy now with what he's doing and so on"
},
{
"end_time": 4391.237,
"index": 187,
"start_time": 4368.114,
"text": " Today we have a lot of talk in teaching circles about people being demotivated by high demand. I think high demand, if it's justified from what you yourself as a teacher deliver,"
},
{
"end_time": 4418.353,
"index": 188,
"start_time": 4391.63,
"text": " is the biggest motivator of all because the good students are pushed beyond what would be their comfort zone and the not so good students see that a good number of students succeed very well so it is possible yes maybe they need to up their game maybe they need to spend more time on it or be more courageous or be less disheartened or you know"
},
{
"end_time": 4439.104,
"index": 189,
"start_time": 4418.916,
"text": " Anyway, that's my view. Maybe that's the nicest outcome or conclusion for me from all these awards. I got others and the many, many, many thousands of emails I got. Of course, not of course, but I got kindly and many I couldn't even read."
},
{
"end_time": 4462.159,
"index": 190,
"start_time": 4439.104,
"text": " Because it was just too much at some time. One year I got 6,000 emails on these YouTube lectures. It was impossible for me to read. They all go to some folder, but I feel very guilty about it because some people write very nice things. I just can't cope with these masses of emails. So maybe hear my thank you to everybody who wrote and addressed very kind words to me."
},
{
"end_time": 4491.203,
"index": 191,
"start_time": 4462.159,
"text": " But the nicest conclusion of that for me is I think my method is at least justified. So to high demands and trying to deliver what it takes to satisfy them. One of the reasons I resonate with you and your lectures is that I care about mathematical rigor. Although you don't just care about rigor for rigor's sake or formality for formality's sake. You care about it because what is required to understand subject X, you have to drill down to"
},
{
"end_time": 4513.2,
"index": 192,
"start_time": 4491.561,
"text": " point y. So you don't care about point z and a, b, c, you care about point y as it relates to x, not just what's around y. Yes. Yes. Although also you see the coherence is actually what we're saying. Well, true is, is it really conclusive what we're saying? Is it compelling?"
},
{
"end_time": 4530.145,
"index": 193,
"start_time": 4513.814,
"text": " Right so we set up a theory we start with assumptions that could be wrong or false as far as physics is concerned wrong or false true or false physics is concerned but then once we set down our assumptions is everything else we say."
},
{
"end_time": 4551.647,
"index": 194,
"start_time": 4530.538,
"text": " Is it actually conclusive is that actually at least compatible with what we said and then you need to be very careful because many things are plausible but just not correct and if we start hand waving it's always very cool right it's a little bit sometimes I blame it on Feynman who was cause quite a charismatic character right and and and and and fill system."
},
{
"end_time": 4580.247,
"index": 195,
"start_time": 4552.022,
"text": " Yes, why don't you be concrete? Why don't you give an example of what ordinarily is hand wavy, but then when you examine it, at least to something wrong?"
},
{
"end_time": 4603.404,
"index": 196,
"start_time": 4582.159,
"text": " Oh God, a million things, a million things. It's very easy to, for instance, talk about the center of mass of two particles, right? Two particles are flying around center of mass. Now think of it relativistically and blah, blah, blah. For instance, relativistically, there is no center of mass."
},
{
"end_time": 4622.346,
"index": 197,
"start_time": 4604.002,
"text": " of mass of course requires you to take the positions of it says they spent flat space are not even curved space flat space you need to take the positions of the two particles same in koski space they could be position vectors in quotation marks okay and and then"
},
{
"end_time": 4647.398,
"index": 198,
"start_time": 4622.517,
"text": " you find the middle point right but for parties at the same time you find the middle point right the position positions at the same time but we know there is no simultaneity in objective simultaneity in special relativity even so in special relativity there is no center of mass that's a concept that cant i think is interesting because cant"
},
{
"end_time": 4669.377,
"index": 199,
"start_time": 4647.705,
"text": " Says this is a what is it a synthetic a priori or something like this something like this or even analytic and analytic truth. No it's just not true in nature isn't like this nature doesn't have simultaneously as a foundational thing that you can talk about that makes sense right."
},
{
"end_time": 4689.087,
"index": 200,
"start_time": 4669.377,
"text": " So it's very easy to give arguments, hand waving arguments, if you don't define it very precisely and then check whether it's well defined under whatever. Yeah, you got to be very careful now. So the hand wavy stuff is very, very dangerous."
},
{
"end_time": 4718.439,
"index": 201,
"start_time": 4689.462,
"text": " I mean, even the written down, the rigorous stuff is very dangerous. We all know this, right? We call it a side error or some other conceptual error. So it's not like because it's written in mathematics is necessarily conceptually coherent or consistent. Of course, then there is ultimately a mistake somewhere, but it becomes mere talk if we start hand waving. Of course, if you do formalism and you don't occasionally bring it to life, say to the students,"
},
{
"end_time": 4748.439,
"index": 202,
"start_time": 4718.797,
"text": " I understand we don't have a blackboard and we don't have the ability for you to draw right now, but if you were to explain to the audience and they're educated in physics and math, what is the problem with quantum gravity? How would you say it? Oh, well, that's why is this so difficult to make gravity into a quantum theory? Should gravity be a quantum theory? Exactly, exactly."
},
{
"end_time": 4759.94,
"index": 203,
"start_time": 4748.831,
"text": " Exactly. I want to hear your viewpoint. Well, I mean, okay, I don't think I have anything new to add, but I think if you ask me as a little examination, I'm happy to oblige. Yes, it's a PhD defense."
},
{
"end_time": 4789.087,
"index": 204,
"start_time": 4760.674,
"text": " Okay, we have a nice theory of gravity. General relativity is the best one we have. We use it. It's subject to the interpretation of the data we get and so on. It has the following form. G mu nu is T mu nu and G mu nu is the space-time curvature and T mu nu is the annoyingly metric containing energy momentum tensor of the matter. So the metric is also in the T mu nu. But very roughly speaking, the T mu nu"
},
{
"end_time": 4816.152,
"index": 205,
"start_time": 4789.599,
"text": " Of course, it's mainly determined by the matter content and distribution in the universe, say. Now, there are many issues to be discussed. Well, this is already a godlike view on all of space time. You would actually have to go to three plus one to talk about evolution and so on. But let's leave this all out. The problem is on the matter side, as long as you have classical fields like Maxwell feels classical. This team you knew is a classical field, a tensor on a smooth manifold."
},
{
"end_time": 4840.896,
"index": 206,
"start_time": 4816.152,
"text": " It can be beautifully equated to the G mu nu Einstein curvature tensor on the manifold. This is mathematically meaningful. And then you solve that there's a big elephant there, but you solve these equations and you get the prediction of how the gravity and the matter in the end work together. You also need the matter field equations. But"
},
{
"end_time": 4869.497,
"index": 207,
"start_time": 4841.544,
"text": " Unfortunately Planck got us the idea and then people said oh yeah that's true there seems to be no classical matter all the matter light and particles and so on they're all quantum. I don't think this is to be doubted that that seems to be the case at least the way we look at it fine but then how do you build this T mu nu tensor on the right hand side of this equation g mu nu is T mu nu"
},
{
"end_time": 4897.773,
"index": 208,
"start_time": 4870.111,
"text": " Because now all of a sudden there are quantum fields there. Okay, big question. And then the easiest, so then you can say also in a sense, this team you knew is also more like an operator operating on some vector space here, but so Hilbert space Fox space was not no matter how you there are many, many issues with perturbative theory. And so anyway, you have this on the team you knew side."
},
{
"end_time": 4926.323,
"index": 209,
"start_time": 4898.353,
"text": " And then you say that doesn't fit. You can't equate a classical tensor to some operator. The equal sign makes no sense anymore. Right. The matter you want to put on the right hand side is quantum, but the right hand side is formulated only for classical fields and many things you can try. Oh, we take the expectation value. All of this doesn't work. Right. All of this doesn't work. Obviously. So then the, in a sense, laziest idea, and I'm"
},
{
"end_time": 4956.152,
"index": 210,
"start_time": 4926.903,
"text": " Close your eyes, exhale, feel your body relax, and let go of whatever you're carrying today. Well, I'm letting go of the worry that I wouldn't get my new contacts in time for this class. I got them delivered free from 1-800-CONTACTS. Oh my gosh, they're so fast. And breathe. Oh, sorry. I almost couldn't breathe when I saw the discount they gave me on my first order. Oh, sorry. Namaste. Visit 1-800-CONTACTS.COM today to save on your first order."
},
{
"end_time": 4978.677,
"index": 211,
"start_time": 4957.278,
"text": " unnecessarily provocative but the laziest ideas to say why don't we make the left hand side also an operator or bit more seriously formulated maybe gravity should also be quantized then we have both theories matter and gravity in the same formalism and then we can"
},
{
"end_time": 5003.302,
"index": 212,
"start_time": 4979.07,
"text": " Write down a new equation roughly speaking in this new formalism where now the matter and the space-time speak the same language or we speak the same language in looking at them and that's the origin of the idea we should quantize gravity at least from a formal point of view there are other good reasons what happens with black holes what's with singularities"
},
{
"end_time": 5025.162,
"index": 213,
"start_time": 5004.241,
"text": " Big Bang. Was there a Big Bang? Is the theory actually to be extrapolated up down to the Big Bang? Many questions. There's Heisenberg's idea. What does it actually mean to talk about space-time as a smooth manifold and the metric measuring so precisely? How would you measure? He would use higher and higher frequency to be more precise."
},
{
"end_time": 5052.841,
"index": 214,
"start_time": 5025.162,
"text": " Say photons to check something, but then that would disturb the space time, the very space time you'd like to measure. There are many, many reasons that you can concoct a whole bouquet of reasons why you think quantum gravity, quantum formulation of gravity might address, solve, enlighten us concerning all these problems. Okay."
},
{
"end_time": 5080.913,
"index": 215,
"start_time": 5054.582,
"text": " But this comes ultimately from the way we look at things in the first place. And I think there is no really compelling reason why gravity has to be quantized in the first place. Maybe something very different is going on. So that's the first thing. Do I know? No, I don't know. I don't know better than anybody else."
},
{
"end_time": 5110.316,
"index": 216,
"start_time": 5081.271,
"text": " But it's not so clear that we want to quantize gravity. Look, I mean, there are many things, many questions one could ask and probably none of them is original. If you do quantum theory, say ordinary quantum three and three dimensional, say in Euclidean space and you do, I don't know, quantum information or deal with qubits. What your quantum systems are, at least the constituents of it, the opposite, they must come from"
},
{
"end_time": 5124.36,
"index": 217,
"start_time": 5110.742,
"text": " representations if it's elementary irreducible representations of the universal covering group of the symmetry group of the classical space in which you think about this quantum system."
},
{
"end_time": 5147.363,
"index": 218,
"start_time": 5124.94,
"text": " This is how you get the spin one halves in three dimension. They come from the three dimension Euclidean group and you look at all the projective unitary representations of the group of this Euclidean group or technically you can also look at the universal covering group that would be then something like"
},
{
"end_time": 5175.435,
"index": 219,
"start_time": 5148.029,
"text": " So if you just take SO3, universal covering group is SU2, you find the unitary representations of those and then you know how you can build your quantum systems that live in such a space. And the same then works in with the Poincare group and Wigner figured that out. What are actually the possible representations of the SL2C?"
},
{
"end_time": 5205.503,
"index": 220,
"start_time": 5175.964,
"text": " of this universal covering group of the symmetry group of physical space. Why do I say this? Well, the whole standard model is built on this. It has very clear conceptual reasons why it must be done like this. It's not an abstract thing. But that means physical classical space, be it space time or space, you need to have a concept of classical space in order to talk about quantum matter in the way we do it."
},
{
"end_time": 5227.466,
"index": 221,
"start_time": 5206.032,
"text": " yes aha if you now say i want to quantize this classical geometry or you know whatever ideas you might get the dynamics of it the drum well in a sense undermining the very foundation of what brought you to the quantum matter right you see so"
},
{
"end_time": 5257.449,
"index": 222,
"start_time": 5227.927,
"text": " That's not immediately plausible to me. Of course, you can always say, yeah, that was just the ladder we used to get up to the theory. And in the end, it all works out. And then we throw away the original idea of this. But you know, the point is, I don't know, probably nobody knows. But these are also, I think probably to most of the ideas, why gravity should be quantized, one could at least make intelligent counter arguments, why that is a funny idea."
},
{
"end_time": 5288.456,
"index": 223,
"start_time": 5258.712,
"text": " Okay, so maybe something else is at work. There were these proposals by Oppenheim and collaborators on this idea that that gravity is not to be quantized, but rather it's to be treated as a stochastic theory, classical stochastic theory, interacting with the matter. That's an interesting idea, I find, because the quantum axioms and"
},
{
"end_time": 5312.756,
"index": 224,
"start_time": 5288.985,
"text": " Never. Yeah, the quantum axioms say something like this. You say you can't measure, you can't predict what the measurement outcome is, but you can give a probability distribution, a classical probability distribution. So the axioms tell you classically, you're not connecting to a classical theory in a pure state. You connect into a classical probability distribution."
},
{
"end_time": 5328.985,
"index": 225,
"start_time": 5313.08,
"text": " And i think that's a little bit the idea they have i hope i don't misrepresent that you should ask them but you see this is a priori also a very plausible way whether this works out and whether what they work that's not the question the question is there many other."
},
{
"end_time": 5353.626,
"index": 226,
"start_time": 5329.36,
"text": " i don't know many that that for instance is a plausible thing we see from the quantum axis the quantum axioms at no point instruct us to quantize the space time behind it yes right and maybe this uh representation theory construction accepted construction uh speaks against it say no no you need this classical space idea otherwise we don't know what we're talking about the quantum theory either and so"
},
{
"end_time": 5382.073,
"index": 227,
"start_time": 5353.626,
"text": " But the quantum axioms talk about the contact to the classical world as a kind of a stochastic system contact. Maybe there's something in the idea. You know, so the and I mean, it has failed for so long to bring this idea to quantize gravity to success. But I mean, who knows? I mean, there's a lot of criticism of string theory these days and hey, I share it. But you know what? Maybe they pull it off."
},
{
"end_time": 5403.285,
"index": 228,
"start_time": 5382.585,
"text": " You know we don't know we should be not very not so judgmental about I mean very clever people spend a lot of time and very clever people in the past were wrong about what they wanted to do although they were very clever and sometimes people are lucky I also wouldn't discard the string theorists who keep pursuing it."
},
{
"end_time": 5424.172,
"index": 229,
"start_time": 5403.985,
"text": " I wouldn't but who am i to say who's anybody to say i think that's the good thing about science that everybody can and should do what what they think is right and it is enough if one of us at some point is right about something and that's progress."
},
{
"end_time": 5455.077,
"index": 230,
"start_time": 5425.299,
"text": " The project of science is fantastic. Everybody does what they think they should do. I mean, in a sense, that has changed a little bit. There are also some commentators of that, also in the German speaking area, I think Sabine Hosenfelder and so on."
},
{
"end_time": 5483.609,
"index": 231,
"start_time": 5455.452,
"text": " She brings some very strong criticism of how the scientific system works these days and so on. And some of these points are just valid. Yes, absolutely valid. Well, the old idea is freedom of teaching and research. There's a Humboldtian idea. Humboldt had this idea when he was asked to, I think, to create a educational system for Prussia."
},
{
"end_time": 5513.114,
"index": 232,
"start_time": 5484.206,
"text": " or got my history, but I think something like that. Okay. And, and he said, education at university is not vocational training. It's not for you to find a job. It's for you to learn to think. And if you learn to think, and if you dig deep, well, I don't know whether he said it like this, let me say what he wanted to say if he was alive today. Okay. If, if, if, if you dig deep in physics,"
},
{
"end_time": 5524.531,
"index": 233,
"start_time": 5513.763,
"text": " And you become a really good physicist and then you talk to a lawyer and legal scholar who really dig deep on legal thinking you recognize a good thinker."
},
{
"end_time": 5553.899,
"index": 234,
"start_time": 5525.196,
"text": " because you learned thinking well in your subject and the other way around and if you can do that and you go out in the world you're infinitely more useful for a company who has a good thinker with a lot of skill and has learned to think deeply to think critically in the long run that produces growth for the company right at least on average the idea that we educate people to conform with the expectations of current employers well"
},
{
"end_time": 5575.52,
"index": 235,
"start_time": 5554.224,
"text": " The current employers do not know how the world looks like in ten or twenty years when thirty years i don't know. Nobody knows right but for eight hundred years universities have actually provided us with thinkers who then took on the problems of that time."
},
{
"end_time": 5596.852,
"index": 236,
"start_time": 5576.254,
"text": " you have to be educated to do that and what is not going well it's what there is the idea of freedom of teaching and research and the diversity to use that trigger word but there it's actually appropriate the diversity of different thinkers because we're all naturally diverse we're all different um"
},
{
"end_time": 5625.657,
"index": 237,
"start_time": 5597.415,
"text": " We should be allowed to do what we want to do and then society has to decide to whose people to people this privilege to which people this privilege is given. What is however happening at the moment? Say if you're in the in the European Union universities, of course they want you to gain grants and the biggest grants are the European grants from the European Union and they decide on topics"
},
{
"end_time": 5651.544,
"index": 238,
"start_time": 5626.032,
"text": " They are open grants to be fair. They are open grants. You can bring your topic, but some very big grants, they decide on topics what it would be important to have scientific research on and they are decided politically. How does that work? Well, would you think that in the current situation, energy situations on energy would be such a topic? Of course, such a energy is such a topic. Energy is such a topic. Okay."
},
{
"end_time": 5681.852,
"index": 239,
"start_time": 5651.886,
"text": " That means if you do energy research, you're good. You can apply for these big grants. I mean, I'm caricaturing the whole thing a little bit, but that's what is ultimately what we do research on is decided by bureaucrats and politicians who thinks that is plausible. And of course it's plausible to do energy research. But even if we look in the past, did nuclear power be invented by government programs looking for energy research? It came out of blue sky research."
},
{
"end_time": 5707.671,
"index": 240,
"start_time": 5682.875,
"text": " Right. So, so it, if you look at the financial situation is no longer true, uh, that researchers really decide entirely freely on what they do research. That's a fact. It's a fact. And the problem with that is a monoculture explained. Well, well, if, if, if people go for the big grants,"
},
{
"end_time": 5730.23,
"index": 241,
"start_time": 5708.183,
"text": " Either they're already famous they've already done fantastic things and i would also say give them another grant very high probability they keep doing very good work. But new ideas that a little bit out of the box and again they're also funded i'm just giving the general idea it's much harder because."
},
{
"end_time": 5758.592,
"index": 242,
"start_time": 5730.52,
"text": " One look research doesn't work by you telling me I need you to research this in this it works if I have to research a travel journey for you I can do that for you I can deliver that but if you say I need you to find the solution to the problem of quantum gravity it's nice that you think it's important or anybody thinks it's important I think it's important it's a good research field but but that doesn't mean that that is where the next breakthrough will be"
},
{
"end_time": 5787.346,
"index": 243,
"start_time": 5759.172,
"text": " So you think that the academics should be more free? Oh, yeah. Oh, yeah. Oh, yeah. Of course. Freedom. Look, look, it's yeah. Look, it's the same. Let's go back to teaching because the similar argument. I think every professor who has the right background, educated in it and specialist in it and so on, who should be given total freedom on how he teaches a, say, quantum theory course."
},
{
"end_time": 5817.449,
"index": 244,
"start_time": 5788.404,
"text": " for audience x total freedom this principle gets you some of the worst lecture courses you have ever attended well that's unfortunate but i also believe it gives you the most brilliant lecture courses you have ever attended and i think it's better to have in your student life two or three or four or five would be luxury brilliant lecture courses i think i had as many brilliant ones thank you to my teachers right"
},
{
"end_time": 5842.671,
"index": 245,
"start_time": 5818.439,
"text": " But then there's some that are not that good that also comes from the freedom but the freedom is necessary to develop new things to do it better to do it differently. Not that that's what is no general commission that can decide i mean should we very simple curriculum should we teach momentum vectors of course we should we need it."
},
{
"end_time": 5866.869,
"index": 246,
"start_time": 5843.183,
"text": " There's no momentum vector. It's a covector. So, you know, even if a committee agrees this is important stuff, what if you say, yeah, but that doesn't really fit together at a deeper level of analysis. Should I teach it because the committee decided it, you know, the accreditation committee for the courses or whatever? I don't think so. I don't think so. Huh? Look,"
},
{
"end_time": 5893.404,
"index": 247,
"start_time": 5867.193,
"text": " If we had a wild west of teaching and everybody would give terrible lectures and everybody did what they wanted and nothing would ever fit together, I would advocate for some structure. At the moment we have, at least in Europe, the tendency of more and more structure of more and more ideas of centrally accredited courses and core systems and so on. And what you get is an average good thing."
},
{
"end_time": 5924.275,
"index": 248,
"start_time": 5894.309,
"text": " But if you want to get something really good, you need to give freedom. It's a belief, I admit, but it's an old Humboldt idea. And certainly it served Germany very, very well for very long in educating an extremely broad part of the society, educating them very, very excellently in engineering and also in mathematics and physics and so on."
},
{
"end_time": 5949.462,
"index": 249,
"start_time": 5924.684,
"text": " Early 20th century, Germany was quite the powerhouse of all these fields. Can I state this with sociological, how do you say, scientific certainty? No, but I think it's an outflow of the humble principles of how you teach at high level, at university level. Don't look at the vocational use first."
},
{
"end_time": 5978.626,
"index": 250,
"start_time": 5950.162,
"text": " the vocational use and that companies and the economy profits from these people. This is doubtless afterwards. Don't be too short-sighted. And so, yeah, the diversity of the approach is important and you have only diversity with freedom. I restrict this statement really to what I'm talking about here. Different researchers should follow their way. And then it's a question, who do you make a researcher? Right. So fair question."
},
{
"end_time": 6002.244,
"index": 251,
"start_time": 5979.002,
"text": " Well, a teacher at university. Yeah. So let me ask you, I've already asked you about what you're pursuing, but I'm curious also, there are some fashionable subjects, the subjects that are in vogue, like ADS, CFT, or quantum information or black hole information, string theory, and so on. Why are you not pursuing the more fashionable ones? If it merely is just you're not interested in it?"
},
{
"end_time": 6031.596,
"index": 252,
"start_time": 6002.927,
"text": " What is it? That's not true. And some of them are interest with some of them, I have some contact, some of them I understand others I didn't look into, I mean, it's a lot of stuff out there. I like to follow the ideas I my collaborators have, and I try to make my contribution that way. So I mainstream subjects on which already 1000s of people work, will I make the difference? Well, maybe I would. But"
},
{
"end_time": 6059.787,
"index": 253,
"start_time": 6031.886,
"text": " I think it neither takes justification to work on a mainstream subject or on a more on a sideline. I was educated at Cambridge University by excellent people, Michael Green and Peter Goddard, John Stewart, Gary Gibbons, all prominent people, obviously string theory people and general relativity people."
},
{
"end_time": 6087.961,
"index": 254,
"start_time": 6060.23,
"text": " I know certainly the foundations of many of these things quite well, and some attracted me more than others. So, string theory didn't attract me so much. At the time, there was the saying, all the best students go to string theory, and it was true. The best students went to string theory. I think I was a reasonably good student there, but I kind of didn't really feel it. I didn't really feel it."
},
{
"end_time": 6106.903,
"index": 255,
"start_time": 6088.285,
"text": " I'm not saying I was prescient and I knew it was not going to work. Of course not, of course not. You know, you make a pick. It's also emotional to make it, not when you say, I thought that I find interesting this direction I would go on. And you weren't feeling it? I wasn't feeling it. No, no, no."
},
{
"end_time": 6122.705,
"index": 256,
"start_time": 6107.517,
"text": " Well, I didn't understand one thing. Actually, I once discussed with I think with Peter Goddard for a short while and I asked him, so why do we take the Minkowski metric in our what was the 26 dimensional space? I mean, basic strength."
},
{
"end_time": 6149.462,
"index": 257,
"start_time": 6123.08,
"text": " And he told us, he told me, well, because Einstein told us so. And I say, yeah, but he told us for four dimensional space and didn't, isn't the reason for using it that you have point particles that move there. And he want to get the clock postulate by the length of the curve and stuff like this. But this is a point particle based idea. But now if you think about strings being the fundamental objects,"
},
{
"end_time": 6171.561,
"index": 258,
"start_time": 6149.462,
"text": " Rather than point particles wouldn't you rather have something that measures area fundamentally rather than length much later wrote a paper about these things and setting up a plausible idea okay finds plausible idea i also did something i don't think it solves anything but you see the point is i did the set up i found it to at hock in a way."
},
{
"end_time": 6196.886,
"index": 259,
"start_time": 6172.432,
"text": " In a sense, the only idea, at least as it was communicated to us back then, later on, of course, people change perspective. I'm not a specialist. It's like, let's rather start from little strings close to open and quantize them difficult enough, quantize them rather than point particles as a first quantization. And let's see what happens. And there were some remarkable results. And"
},
{
"end_time": 6222.534,
"index": 260,
"start_time": 6197.363,
"text": " At least at the time I thought it was remarkable that the Einstein action kind of drops out if you look at it in a certain way and so on. Later on I thought well it's not so remarkable because if you didn't do anything wrong from a differential geometry point of view or from a calculation point of view what else would you get but in lowest order general relativity maybe the factor could be zero in front of the Ricci scalar or something right."
},
{
"end_time": 6240.145,
"index": 261,
"start_time": 6222.534,
"text": " So look, I mean, were these mature reasons to reject it? Of course not. I was a student, right? But I wasn't pulled in that direction. And I'm happy that many other people did, right?"
},
{
"end_time": 6265.862,
"index": 262,
"start_time": 6240.657,
"text": " so far it wasn't successful, which is maybe just very unfortunate. I would much rather have that the people who did it were successful and would have an exciting new discovery in theory and that I would say look fool me. We don't know, right? It's like investing in the stock market. Will the stock go up and down? Nobody knows. Nobody knows, right?"
},
{
"end_time": 6289.838,
"index": 263,
"start_time": 6265.862,
"text": " And then it's the same here we can just try to do our best and i think it's good in academic life you do research you really try to push something and to do something and but then on the side you educate the next generation if you don't educate them to a higher level to improve it by five percent what you present them with we also did a great thing."
},
{
"end_time": 6311.561,
"index": 264,
"start_time": 6290.282,
"text": " So that's the nice thing about the academic job, right? I mean, you're not only relying on winning or doing Nobel or similar worthy work, of course, would be nice. But we have another very, very important task in society, because if we don't at least pass on what we have and make it a little bit better so that more can be passed on,"
},
{
"end_time": 6339.753,
"index": 265,
"start_time": 6312.005,
"text": " was more efficient, then we lose that knowledge. That would be also catastrophic. So I sleep very well. I sleep very well. Passing on stuff is very important. And trying to do new things. Yeah, trying to new things is an audible thing. And this is exciting. And it's also training for students to for them to do research. I mean, you can do research, which goes that far, but maybe a student learned many things"
},
{
"end_time": 6368.575,
"index": 266,
"start_time": 6340.077,
"text": " contents wise and and method wise and they bring something else to success right so so so i mean that that's that's the life of an academic no we're often talking about the the the the holiest grail right there is the big open questions and um uh uh yeah that's important i'm also thinking about some of these things um uh um but i think the the the path there is is is more modest steps uh more modest steps"
},
{
"end_time": 6397.79,
"index": 267,
"start_time": 6368.575,
"text": " So you just did something psychologically interesting with the string theory case when they were extending to 26 or 10 dimensions with the Minkowski metric. They said, it's because Einstein told us. And then you said, well, what was the motivation for Einstein? It was point particles in four dimensions and light clocks. Okay. Even in your constructive gravity approach, where you were saying Einstein tried to anti-symmetrize the metric or at least not make it symmetric, metric symmetric."
},
{
"end_time": 6427.961,
"index": 268,
"start_time": 6398.302,
"text": " that if you're doing so then raising and lowering isn't going to be the same but you can only see that from your approach because there's a gauss map and there's a legendre map if i recall correctly oh yeah that's right well okay that's one of the okay okay we can get into the technicalities of that i would like to at some point but yeah but the point is that what you just did there was extremely interesting you said look we don't willy-nilly modify up here without understanding the reason from which here came from"
},
{
"end_time": 6455.196,
"index": 269,
"start_time": 6427.961,
"text": " because if you modify here maybe you don't have to modify just this you think you do but it's all of this oh yeah i mean or it's only this why don't you talk on that then well i mean that's that's that's so so what you're describing there is one could summarize it abstractly as follows formal generalizations typically fail that's what i understand it i have a symmetric metric"
},
{
"end_time": 6478.353,
"index": 270,
"start_time": 6455.845,
"text": " Now I do a non-symmetric one there's a motivation because F mu nu is not symmetric right today of course we we smile a little bit at that because the F mu nu is the field strength and not the potential stuff like that but we had some reason for making it non-symmetric right but then if you formally say we generalized this formally"
},
{
"end_time": 6507.773,
"index": 271,
"start_time": 6478.882,
"text": " Then you don't know what you're doing. You need to generalize conceptually. So you have to ask why was it symmetric there? Why was it the metric? And then you might have a starting point to say under what circumstances with the same why question have a different answer. Yes. All right. So, so, so yeah, you have to think conceptually, not formally. Formal is good. Once, once look, I mean, every equation in physics,"
},
{
"end_time": 6532.108,
"index": 272,
"start_time": 6508.148,
"text": " is only a secondary product. Let's take the first thing. So what is energy? What does Einstein do? Einstein said energy is what is it MC squared plus and then all the higher order terms in the P nice the square root of them. You have all these and you can say Einstein Newton wrote the P squared over two M term for say kinetic energy."
},
{
"end_time": 6562.568,
"index": 273,
"start_time": 6532.585,
"text": " But if you do relativity, you have also a P cubed, a P, well, at least a P square, a P quarter, the fourth power to the sixth power, you have this whole expansion coming from the square roots, right? In relativity. So you say, ah, look here, Newton didn't see or didn't consider the higher order terms in P. That's correct, right? They're there in relativity, if you write it in this form. But Newton also didn't see the zero order term."
},
{
"end_time": 6592.312,
"index": 274,
"start_time": 6563.524,
"text": " The MC squared. You see what I mean? So the point is, if you say energy, it's a different concept in relativity than it is in classical physics. And if you think you come from one theory to the next by adding higher order terms, because that is the only thing that could happen measurement wise or something, you make, I don't know whether it's a category error, but something like this, you want a new"
},
{
"end_time": 6616.323,
"index": 275,
"start_time": 6592.875,
"text": " Idea of energy then you have to first have a concept for that and don't do it purely formally. You see what i mean that's why you need to think conceptually and once you have the conception right. I'm simply fine a little bit then the equation flows out of the idea. It's not the equation first."
},
{
"end_time": 6643.473,
"index": 276,
"start_time": 6617.892,
"text": " It's the concept for us. Yes. Yes. Okay. Cause otherwise the ambitious undergraduate would say, well, maybe there's a fifth order term in energy. Let me try that. But then you're wondering, well, where did that fifth order, where was the impetus for the second order coming from? Something like that. Something like that. You always in order to generalize a theory, you must understand the to be generalized theory first at a deeper conceptual level."
},
{
"end_time": 6670.265,
"index": 277,
"start_time": 6644.189,
"text": " And that's already ambiguous because you can look at things at different conceptual levels, right? You can describe, take gravity. Okay. High school question. High school teacher asks the student here, final fail or pass will be decided on your correct answer to the following question. Student says, okay, is gravity a force? And we mean Newtonian gravity because high school only Newtonian gravity. Is Newtonian gravity a force?"
},
{
"end_time": 6693.507,
"index": 278,
"start_time": 6670.896,
"text": " a student will say yes it's a force and he says excellent you passed but if the student had said no it's not a force he should also pass because you can rewrite newtonian gravity as a curvature of space and of newtonian space time not relative is newtonian space time is also curved in the time direction which there is now a unique time direction and"
},
{
"end_time": 6722.415,
"index": 279,
"start_time": 6693.968,
"text": " fully equivalently fully different conceptualization of what gravity is not a force but a curvature of the space and you know freefall is geodesics auto-parallel in that context because you have to do it with a with a connection in Newtonian space-time. So that means the answer to the question is is gravity Newtonian gravity a force yes or no both answers are correct if you conceptualize differently predictions are the same."
},
{
"end_time": 6745.452,
"index": 280,
"start_time": 6723.08,
"text": " What does that tell us? Well, gravity is gravity, what it does. And our formalism for it could come in many different guises, and it could give the same result. So we shouldn't confuse the formalism for the physics or the objects in the form is I mean, force is a concept in Newtonian mechanics."
},
{
"end_time": 6775.623,
"index": 281,
"start_time": 6745.981,
"text": " And gravitational force is then also there, but you could argue, well, gravity also Newtonian theory should be made a curvature of Newtonian space time. And then the first axiom starts making sense. The first axiom sense says a particle under the influence of no force moves along a straight line. Okay. So you can say, do you know an example for that? No force. And you would say, well, at least where we live on earth,"
},
{
"end_time": 6795.691,
"index": 282,
"start_time": 6776.049,
"text": " The first axiom is out of work, right? It's unemployed because there's always the gravitational force. It's just there. So what do you mean a particle under the influence of no force? If you ever say no, gravity, also Newtonian theory, is the curvature of Newtonian space-time, then it would mean any particle"
},
{
"end_time": 6820.759,
"index": 283,
"start_time": 6795.998,
"text": " on which no force other than gravity which we no longer consider a force acts moves along a straight line that defines straight line in an operational way and then the second axiom says and should you ever see a particle not move along the lines that particles on which no force acts then those are those other particles are force acted yes otherwise the first axioms a special case of the second"
},
{
"end_time": 6839.343,
"index": 284,
"start_time": 6820.845,
"text": " Exactly that makes no sense. Newton wasn't stupid. He doesn't say I first do it for the beginners. I say no force, then do it with the force for people who can't set the right hand side of MA double dot or MA equals F to zero, right? I mean, no, no, no, right? He wasn't silly. No, the first one defines what a straight line is."
},
{
"end_time": 6860.828,
"index": 285,
"start_time": 6839.991,
"text": " Hi everyone, hope you're enjoying today's episode. If you're hungry for deeper dives into physics, AI, consciousness, philosophy, along with my personal reflections, you'll find it all on my sub stack. Subscribers get first access to new episodes, new posts as well, behind the scenes insights, and the chance to be a part of a thriving community of like-minded pilgrimers."
},
{
"end_time": 6881.152,
"index": 286,
"start_time": 6860.828,
"text": " By joining you'll directly be supporting my work and helping keep these conversations at the cutting edge so click the link on screen here hit subscribe and let's keep pushing the boundaries of knowledge together thank you and enjoy the show just so you know if you're listening it's c u r t j a i m u n g a l dot org kurt jaimangal dot org."
},
{
"end_time": 6911.476,
"index": 287,
"start_time": 6881.988,
"text": " How is it that you get to learn a subject? How is it that you, Frederick Schuler, learn a subject? Now, you said you had great teachers and so on, but let's remove that self-studying. How is it that you learn a subject so well? What is it that you do to learn a subject conceptually well? Well, if you're an absolute beginner, you do need a teacher because in the flood of textbooks and lectures, you need a guide. You need a good guide."
},
{
"end_time": 6938.882,
"index": 288,
"start_time": 6911.92,
"text": " But if you now say forget about the teachers, how do you learn it? Well, it's different at different times. As a student, I learned the lecture notes, I learned the textbook in the sense I've tried to understand every equal sign. I still tell this my student, every implication arrow, I must be able to say why precisely this is a valid step. It's a passive approach, right?"
},
{
"end_time": 6968.78,
"index": 289,
"start_time": 6939.206,
"text": " Great people set this up. If it's properly presented, I can check. I can check that what is said makes sense, fits together. This is very far away from finding it, right? And then the quality of material reveals itself. If you can start on page one and you're properly equipped, you know, if you can start on page one and you really try hard to understand it,"
},
{
"end_time": 6997.312,
"index": 290,
"start_time": 6969.224,
"text": " But again and again, there are jumps and gaps and things you don't understand. It might be you, but I always, yeah, but actually good material goes step by step. And I always tell my students, my quality guarantee or my hope is that if you don't understand something in lecture 23, then the answer should be in lectures one to 22. Otherwise I need to up my game. Look,"
},
{
"end_time": 7028.08,
"index": 291,
"start_time": 6998.541,
"text": " Do I satisfy this in the strictest sense? Of course not. I'm human like everybody is human, right? We all make mistakes. As we said before, we all use ways to think about it, which one could would better think about twice when this is really a good argument and so on. But at least we should try to eliminate that as much as possible. But as you ask the question from a student side, I judge I judged material. Is it can I understand every step in detail?"
},
{
"end_time": 7054.428,
"index": 292,
"start_time": 7028.473,
"text": " Okay. And then you have a lot to do this as a student. Now, of course, with so many years of experience, I look at things, I read over them, I read the gist of them and I say, okay, what do they actually do? And then I apply all my my knowledge as far as it's existent. And I try to redevelop it. As I think what they actually wanted to say, but might not have said."
},
{
"end_time": 7078.131,
"index": 293,
"start_time": 7055.179,
"text": " and half of"
},
{
"end_time": 7104.565,
"index": 294,
"start_time": 7078.882,
"text": " No, no, no, no, no, that's more like and then I tried to set it up new. And so in some cases I really succeed in this and then I bring this into my lectures and I redevelop a course entirely from there. There's of course a difference of how I did it as a student and how I did it later. However, what I did as a graduate student, as a PhD student, I often sat in the cafeteria on Fridays and I also took only white paper. So that's"
},
{
"end_time": 7134.258,
"index": 295,
"start_time": 7105.009,
"text": " I think that started there. And I thought, okay, now I'm here doing my PhD in theoretical physics. Let me write down for myself, what is actually the basic subjects, quantum mechanics, classical mechanics, quantum mechanics, Maxwell electromagnetism. What is it really? How would I write it down now if I had to write some summary of it? And then I realized all my gaps and all my lack of understanding. And sometimes this lack of understanding was simply because it wasn't properly said."
},
{
"end_time": 7160.572,
"index": 296,
"start_time": 7134.565,
"text": " and taught. I confronted myself with what happens if I have no textbook with me and I'm supposed to write up a subject, a defined subject, a lecture course type subject, as we know classical mechanics, Lagrangian mechanics, from scratch, including its justification, the whole setting, what is the scope of it and so on."
},
{
"end_time": 7170.811,
"index": 297,
"start_time": 7161.101,
"text": " That's very humbling. It's very humbling, but it's a very good training. And I think meanwhile I can make more out of it. I can then make it better."
},
{
"end_time": 7197.381,
"index": 298,
"start_time": 7171.374,
"text": " Okay, so let me see if I can formalize that. You are in a room, you're alone, you have blank paper, and you're thinking you pick a subject arbitrarily, or is it just whatever is next up? Back then, no. Back then, I thought, let me go through the four elementary things, something like classical mechanics, electronics, quantum mechanics, statistical physics. You know, these are standard big lecture courses, say in Germany, but anywhere, right? In theory, theoretical thinking."
},
{
"end_time": 7217.415,
"index": 299,
"start_time": 7197.381,
"text": " What is the formalism? How does it start? What are the concepts? And how do I bring this into an order that makes sense? A, B, C, D, E, not in another order, right?"
},
{
"end_time": 7243.66,
"index": 300,
"start_time": 7218.097,
"text": " So, and if one really tries this, and even as a very good student and very good graduate student, I realized, oh my gosh, I mean, there's more holes than anything, right? And then you will recognize the holes, then you can start to fill them. And in a sense, I'm still filling them on some points, right? I also noticed that when you're lecturing, sometimes you'll pause at the blackboard,"
},
{
"end_time": 7272.756,
"index": 301,
"start_time": 7243.968,
"text": " And you'll derive, you'll make sure that you can derive it right then and there, even in front of the students. Oh, yeah. I wasn't sure if that was for you, for your own pride that you need to be able to derive it or for your own intellectual satisfaction or if it's to role model for the students, because it seemed clear to me you have lecture notes behind you. You could actually look, well, what's the final formula? Where am I trying to get to and use that as a hint? But then you don't. Yeah. Well, the reason is all of the above plus a sanity check"
},
{
"end_time": 7302.705,
"index": 302,
"start_time": 7273.029,
"text": " that what I with all my experience of doing this for what 30 years can't do freely after I of course had the think about thought about it for four hours in the morning I always prepare my lectures four hours earlier in the morning and then I go and I write them up in nitty-gritty detail with headlines and everything in order to give them structure then I put the paper on on the big desk and then I only look at the headlines typically"
},
{
"end_time": 7315.828,
"index": 303,
"start_time": 7303.592,
"text": " on the rarest occasion i need to look at the formula again i get confused but i essentially really think a"
},
{
"end_time": 7338.131,
"index": 304,
"start_time": 7316.186,
"text": " What i cannot freely develop after having thought about in the morning again and of course it's a big thing a whole lecture course is then one just one lecture of those right so everything needs to make sense in the end what i can't lecture freely and precisely and convincingly and step by step on how can i expect the students at the end of the term. To do it."
},
{
"end_time": 7362.739,
"index": 305,
"start_time": 7338.643,
"text": " yes they should be able to do it so i must be able to do it so it's not only it's pride as well i i want to be able to do that but it's a sanity check if i can't do it what am i asking the students to do i ask too much of them okay number one second only if i develop this life does a student can a student follow"
},
{
"end_time": 7380.828,
"index": 306,
"start_time": 7363.217,
"text": " it slows me down as opposed to i copy from my paper if i take sometimes i did that on very rare occasion i took the sheet i had there because it was a bit complicated and i started writing what was on the sheet my teaching quality goes down 70 percent"
},
{
"end_time": 7410.367,
"index": 307,
"start_time": 7381.22,
"text": " It's not a good thing. It is as if you had sent me your questions before. I would have thought about your questions and would now have paper where I have very intelligent answers to your questions, at least intelligent sounding answers. Okay. Uh, and I would now read them off and I say, Oh yeah, Kurt, that is a very interesting. We wouldn't have a conversation anymore, right? It would feel strange. Now only the best speakers can read from a sheet and speak well."
},
{
"end_time": 7435.162,
"index": 308,
"start_time": 7410.845,
"text": " Okay. And so it's also serves what I want to say is it also serves the communication with the students is a real conversation. It's like a story I tell you over a campfire. It's very real. I might not complete every sentence ideally and so on. But your focus is on it. Yes, that has to do with yet another thing. What do you have to do if you have 200 people sitting there?"
},
{
"end_time": 7464.838,
"index": 309,
"start_time": 7435.828,
"text": " And you want them to not open their laptops. They all have laptops. You don't want them to open the laptops. You want them to listen what you do, to write what you write, to see or copy maybe what you write and have their eyes where you want them to have their eyes, where you use a blackboard. And on the blackboard there is a drama developing with actors, my fingers, the chalk. Sometimes I tip on the blackboard as in here and so on."
},
{
"end_time": 7483.353,
"index": 310,
"start_time": 7465.196,
"text": " People look there nobody opens their blackboard i think in the last six or seven years i once had to ask a young lady was probably for very good reasons on her mobile phone i told you please take it away i can't lecture like this and it's really true i have an inability if people don't pay attention it makes me nervous."
},
{
"end_time": 7511.493,
"index": 311,
"start_time": 7483.831,
"text": " okay yeah but of course i can't force people to pay attention i have to play my game such that people don't want to look away and if you go to the cinema and you watch a well-made movie you don't look away so i have to present a well-made movie which has to be scientifically sound as well and and one of the things is use the blackboard speak to the people speak to them in real time and let them participate in your thought"
},
{
"end_time": 7524.684,
"index": 312,
"start_time": 7512.534,
"text": " You know roughly speaking so so all of this hc no alternative to using the blackboard Nobody follows a little laser dot on a screen on a you know on a projection"
},
{
"end_time": 7553.899,
"index": 313,
"start_time": 7524.906,
"text": " Wall right if you project your and and then you can have your little laser pointer and then you point at things you point at next things Honestly, do you want to follow this little? Jumping red dot you don't it's very difficult to focus but a blackboard lecture is natural the equation evolves and the nicest thing is the lecturer makes mistakes and then a student can say Your second equation. There's something wrong. It must be a minus. I see no"
},
{
"end_time": 7574.531,
"index": 314,
"start_time": 7556.271,
"text": " And then I honestly I honestly I'm honestly surprised honestly secure about it now confident about it and then still wrong and shouldn't happen too often right in every lecture you make a mistake in every lecture you make a mistake where the student knows better they think you're a fool maybe that's correct but occasionally."
},
{
"end_time": 7604.906,
"index": 315,
"start_time": 7575.316,
"text": " That's right. Then I look at it and sometimes very, very rarely, but sometimes I spent 20 minutes in a lecture recovering an error, which I made. Oh, that's not how you write it. And then the first thing I say to the student, very honestly, you saw something that I didn't. Very good. Now let's see whether I can save this. And then it's pride and pride. It's also to students a statement like,"
},
{
"end_time": 7629.855,
"index": 316,
"start_time": 7605.179,
"text": " You know i don't say i look this up at home and then you will see next time i say i was a little mistake a mistake is a mistake mathematics and our subject in general makes you very humble you know if you have made a mistake you can be the smartest and the cleverest or the most arrogant or whatever if it's a mistake some mistake you better immediately admit it you immediately admit it and try to see whether you can repair it and sometimes you can't."
},
{
"end_time": 7648.387,
"index": 317,
"start_time": 7630.282,
"text": " and so that all of this is only this is the life i think and it's remarkable that in the youtube videos i think some of these things still come through so that students who attended my lectures and watched the videos as well say that still comes through somehow okay good"
},
{
"end_time": 7664.718,
"index": 318,
"start_time": 7649.189,
"text": " wouldn't have predicted that, I must say. I thought it needs the immediacy of the classroom. So maybe that's also part of why maybe it might be more than not enjoyable to watch them."
},
{
"end_time": 7684.155,
"index": 319,
"start_time": 7665.179,
"text": " So these are all, you see, these are little ideas, none of them per se is a principle that's set in stone and everybody who does it different does it wrong. I'm not saying this. There are people who give lectures in a very different way. I say, oh, God, I would never do this. I recently had this very excellent colleague, Pim van Toft,"
},
{
"end_time": 7713.899,
"index": 320,
"start_time": 7684.497,
"text": " I would never do it like this, but respect, you know, so if as a teacher you can make your method fly,"
},
{
"end_time": 7720.128,
"index": 321,
"start_time": 7714.48,
"text": " Wonderful. Wonderful. And I have my method to make it fly."
},
{
"end_time": 7746.732,
"index": 322,
"start_time": 7720.435,
"text": " So what was the bad method or the topic that he had that you wouldn't have taught like that? I think if I remember correctly, we talked about quantum mechanics to high school students, highly talented high school students who every year we have at the university, we invite 100 top talents from Germany and the Netherlands for a talent course, where in three days we teach them quantum theory from nothing up to the teleportation protocol."
},
{
"end_time": 7774.394,
"index": 323,
"start_time": 7746.732,
"text": " But including the foundations, I mean, the axioms and the techniques and all of this. Anyway, let me not talk too much about this cause anyway. And there on the first day we do complex numbers, but we don't say complex numbers, you know, I squared is minus one. We do them as tuple of real numbers with a very special additional multiplication because then they're totally demystified. Okay. Uh, the complex numbers. And, um, and he, uh, said, okay, you add them like this here, a now, you know,"
},
{
"end_time": 7800.862,
"index": 324,
"start_time": 7774.974,
"text": " component wise so to speak and then the multiplication of course is not component wise it needs to mix and then he asked them so how would you multiply them and then of course he got them on the wrong track because they would also say component wise you multiply the components of these two pairs of real numbers and I don't do that as a principle because you can't guess how you multiply"
},
{
"end_time": 7807.807,
"index": 325,
"start_time": 7801.493,
"text": " Tuples of real numbers if you want to make them into into complex numbers because it's a definition."
},
{
"end_time": 7835.435,
"index": 326,
"start_time": 7808.2,
"text": " and only after you made it you can then start investigating what it is yes okay and and here the point was to define the so i didn't i wouldn't ever do that it's a micro thing you see i thought about all these things very interesting i would never do that i think ah no don't do that because then they they have this bad idea which would then say is wrong and ah no no not this way around but he did it so skillfully the excellent teacher he did it so skillfully"
},
{
"end_time": 7854.753,
"index": 327,
"start_time": 7836.169,
"text": " damn well done i'll still not do it but you did well mad i mean i thought i was sitting there yes watching okay and so i want to say these are all for instance another obsession i have is no motivating examples well that sounds very strange right i mean isn't the motivating example a great thing"
},
{
"end_time": 7884.753,
"index": 328,
"start_time": 7855.401,
"text": " I mean it in a strict sense. If I say I'm to teach you vector spaces or vectors, never teach you vectors because there's no such thing. They're vector spaces, but vectors. And then people say, well, look, you hear it one and then you can add them up by moving this one like here. And then you have this one. That's the addition. And you can scale them as soon as you start with little arrows or fingers or whatever. Um, uh, you don't have, you have a very special type of vector space, right? Um, um,"
},
{
"end_time": 7909.036,
"index": 329,
"start_time": 7885.52,
"text": " And why is addition by moving things around? What the heck are you talking about? If you give people this kind of motivation, which almost every one of us got upon seeing vectors the first time in high school or something, then you get the idea a there are objects that are vectors. And if I see a vector, I recognize a vector. Well, this is all true."
},
{
"end_time": 7930.555,
"index": 330,
"start_time": 7909.394,
"text": " Because the only mathematical object in the game is a vector space is a set with two operations plus and the scaling and for these up in this set together with the operations only if the following eight axioms hold then we call that entire structure a vector space."
},
{
"end_time": 7958.439,
"index": 331,
"start_time": 7931.578,
"text": " And yes, we can then nickname the elements of that set. If the set carries with it as companions, these two operate, we can nickname the elements of such a set vectors, a vector, and we mean an element from that set. But the correct word would be an element from the set that underlies the vector space. The vector space is a triple V plus dot. Okay."
},
{
"end_time": 7984.684,
"index": 332,
"start_time": 7958.746,
"text": " But there is no such thing as a vector. If I write on paper a tuple, one, two, right? One, two as a tuple with brackets. Ask you, is that a vector? You can't answer that question. Do you know that there are others which can be added to this one and scaled by which addition, which scaling? You might think that is clear what it is. No, it isn't. You can make beautiful vector spaces out of, for instance, positive"
},
{
"end_time": 8012.858,
"index": 333,
"start_time": 7984.684,
"text": " Yeah, positive real numbers. They can be made to R plus to the end. It's kind of like octane or something. It can be made into an R vector space where the addition is by pointwise multiplication of the components and the scaling is by taking the components to the power of the scaling factor. That vector space, the zero in that vector space, so the neutral element of addition is one, one, one, one, one, one."
},
{
"end_time": 8033.097,
"index": 334,
"start_time": 8013.456,
"text": " You always introduce special situations, special structures that people will never forget and they will always somehow refer to these"
},
{
"end_time": 8059.906,
"index": 335,
"start_time": 8033.677,
"text": " maybe in extreme cases only why not instead of giving a motivating example which by its nature is not understandable for anybody who doesn't know the concept yet is made more vague and then you give the definition but the definition doesn't follow from the example of course it doesn't it's a more general thing it cannot follow why not make a little commutation give the definition first"
},
{
"end_time": 8088.183,
"index": 336,
"start_time": 8061.305,
"text": " and then give 15 examples afterwards, very, very different examples. That's a much better teaching because that's the object we want to talk about. It's very mathematical thinking. And then I show you what variety of crazy situations are all covered by this general structure. So we better study the general structure than all these crazy examples. You see, so I have obsessions. I want obsessions, no motivating examples."
},
{
"end_time": 8112.944,
"index": 337,
"start_time": 8088.609,
"text": " Sometimes you start a subject, especially in physics, and it's too good. I think it's too good to not give this motivating example. But I always regret it. I always regret it. I mean, I can pull this off. It sounds very good. But ultimately, I always realized it down the line. It can cause confusions in the students. Motivating examples are of the devil."
},
{
"end_time": 8127.363,
"index": 338,
"start_time": 8113.848,
"text": " okay so anyway and you see and whoever skillfully like my colleague i mentioned before on another principle of mine whoever skillfully and masterfully violates these principles bravo"
},
{
"end_time": 8155.52,
"index": 339,
"start_time": 8128.387,
"text": " But these are my principles. I try to not do that. So I've thought about many of these things, of course, a lot of experience in trying it this way and trying it this way and being dissatisfied. And the highest judge is always, was it correct what I said or was it mumble jumble? And almost by construction, motivating examples are mumble jumble. Unless it really follows one from what you did before and leads to a question."
},
{
"end_time": 8183.899,
"index": 340,
"start_time": 8155.93,
"text": " not based on the previous lectures I do this calculation or this construction or something and everything can be understood in detail and then I say but here's a question and that motivates this lecture that would be good that would be more a derivation than a motivating example to introduce a new idea now so so so I have probably I don't know whether I have 50 of these principles but many things I think very strongly about none"
},
{
"end_time": 8213.933,
"index": 341,
"start_time": 8184.497,
"text": " And they're extremely personal. Of course. That's one of the reasons why many people have asked you, hey, can I interview you about how you teach? And you're not so keen to do so. That's true. I gave some interviews. Usually if my own university asks, I don't want to say no. No, I was once introduced. It's interesting. It's interesting. I think even audio snippet on the Internet where I was asked whether this when these online lectures took off like like crazy internationally."
},
{
"end_time": 8227.398,
"index": 342,
"start_time": 8213.933,
"text": " They asked me from a research center for education in Erlangen whether by doing these videos I also want to promote the new online teaching media or something like this."
},
{
"end_time": 8255.657,
"index": 343,
"start_time": 8227.5,
"text": " And I said very undiplomatically, I said that doesn't interest me one bit, right? So no, I don't want to promote, I don't want to do YouTube videos, I don't want to promote distance teaching, learning, none of this. I want to do good physics. And back then, they actually in Erlang, the students could always choose whose lectures are being recorded. And that's when a number of these Erlang lectures that are on the internet have been recorded by the university."
},
{
"end_time": 8282.91,
"index": 344,
"start_time": 8255.657,
"text": " So I just try, as I said, I try to give students something really valuable and try to make them really good as much as I can. That's my only my only aim. And the other things are side effects. And of course, I like it. Of course, I like it that these lectures are so so well received. Yeah. So I'm confused. You're not a fan of your lectures being online or you're not a fan of distance teaching. What do you mean?"
},
{
"end_time": 8309.684,
"index": 345,
"start_time": 8283.592,
"text": " No, I'm not a fan of neither a fan nor an enemy of distance teaching. I know my lectures. Well, first of all, a little anecdote. None of the lectures online have been put online by myself. So there is a video, a YouTube account called Frederick Schuller that features these lectures. That's not me. Somebody took my picture. Somebody took my name and downloaded these lectures, I think mainly from Erlangen University and put them on YouTube."
},
{
"end_time": 8330.384,
"index": 346,
"start_time": 8310.077,
"text": " Great service. I thought, okay, it's a fan. Whatever. Okay. Only a few years later when then there were really views went into the millions and totals on I thought, okay, I got a little bit scared. What if this person one day post something inappropriate, right? I mean, could be anything. And it's my name and"
},
{
"end_time": 8360.384,
"index": 347,
"start_time": 8330.384,
"text": " And then I wrote via YouTube to them. I never received a reply. And then meanwhile, then all of a sudden it was a name I didn't recognize. And then it was back my name. And, and I decided, come on, I mean, I could now tell YouTube about this. And then maybe then they take the lectures down as a comma, but people are watching them at the moment. I don't want that. And, you know, so I also, then at some time there was some commercials in between. I thought, okay, somebody is making money of it, but I thought, okay, fine. Okay."
},
{
"end_time": 8383.353,
"index": 348,
"start_time": 8360.384,
"text": " Good for them. So these are not my accounts. The Gravity and Light I gave my OK to, the Gravity and Light lectures, but the others have all been taken from, however public, it's not kind of copyright infringement or anything, public service of the university where they were recorded."
},
{
"end_time": 8401.92,
"index": 349,
"start_time": 8383.592,
"text": " look i think i think of course it's great that there are so many online resources i mean it's the positive side of the internet but we can all look up it's brilliant okay and if people like the stuff and i think it's not wrong or terribly wrong then i i i leave it on everything everything is fine"
},
{
"end_time": 8428.882,
"index": 350,
"start_time": 8402.227,
"text": " But I think ultimately I'm psychologists would tell you that you can only be formed children for sure but also young adults in the presence of another human being on whom you can in the weakest sense model yourself. And so this goes back to my teachers in high school at impressive teachers in high school and all these people"
},
{
"end_time": 8448.353,
"index": 351,
"start_time": 8429.548,
"text": " Without trying i want to be like him or her but in a way you model you imitate your model yourself so i think we need the personal contact and then of course in the tutorials to all these courses have cost tutorial teachers systems are very good people as well with themselves."
},
{
"end_time": 8472.722,
"index": 352,
"start_time": 8448.78,
"text": " Very good researchers. I go to many of these tutorials and I sit there in the row and if I see the students don't engage enough because they're maybe too shy or too now, I start pushing the tutors on say, well, how can you say this and stuff like this? And that then mixes up the whole atmosphere a little bit, right? And sometimes I confront students, right? I didn't come prepared and I said, Oh, do you play basketball?"
},
{
"end_time": 8488.2,
"index": 353,
"start_time": 8472.722,
"text": " Anyway, I pushed him a little bit and I say, well, I mean, it's a professional enterprise here. I mean, you want to become a professional. What do you mean you come unprepared? I don't understand. Did you have a big business running on the side? Because otherwise, I mean, come on, right? Yes."
},
{
"end_time": 8517.688,
"index": 354,
"start_time": 8488.2,
"text": " I try to confront people a little bit. I mean it well. I always mean it well. I try to confront them with what it means to be there and sit there and do things, but not do it seriously. Well, then don't do it at all and face that you're not doing it. Because where does that get you? I try to be nice most of the time. No, I think I'm nice, but I push people. I challenge people sometimes a little bit in the tutorials. All of this is not on the videos."
},
{
"end_time": 8542.449,
"index": 355,
"start_time": 8518.08,
"text": " and but it's also because i believe yeah there's some you see it's like if i was an arts professor i would take my students to the gallery and i would show them the well the picasso's and the all the others and i would discuss with them about these pictures and would say isn't that look at it first of all look at it just look at it okay so it's a little bit like this i say look at classical mechanics"
},
{
"end_time": 8561.493,
"index": 356,
"start_time": 8542.79,
"text": " i mean look at this and of course in order to make them look i have to expose the theory right i have to to go step by step and but it's really i think the classical subjects we teach um i show them uh how do you say"
},
{
"end_time": 8588.404,
"index": 357,
"start_time": 8562.602,
"text": " Like a masterpiece of an artist, like of a world, justifiably world known art, world known artist. Yeah. Look at this thing, this theory. Look what marvelous cultural achievement this is. I don't use ever these words, right? I just do what I do. I do what you see on the videos, but essentially I do that. I show them and then I showed them a theory."
},
{
"end_time": 8612.21,
"index": 358,
"start_time": 8589.053,
"text": " Which is one of the most developed one of the classical mechanics also in all the theories most developed theories we have how can i expect them to later on make their own theory that's asked a lot or modify liberty if i didn't show them the masterpieces what is how does an end product of research look like if"
},
{
"end_time": 8641.34,
"index": 359,
"start_time": 8612.978,
"text": " 10 geniuses, saying classical mechanics, let's say 10 geniuses developed it, maybe was five, 10 super geniuses and a thousand almost geniuses who kept shaping it. What you get today is the product of whatever five or 10 geniuses and a thousand almost geniuses who shaped it into this form and this you get. This is my present to you, the thought of genius and you understand it. Is that something? I think that's something."
},
{
"end_time": 8666.869,
"index": 360,
"start_time": 8641.937,
"text": " I think that's something. It's quite different from, oh, I can calculate this. No, it's, it's, it's, it's, it's brilliant. It's a brilliant thing. We have the privilege to have done and others are younger, general relativity, quantum field theory studies, and others are still developing. But we want to make the masterpieces that don't look like the old masterpieces, like a Picasso doesn't look like a Rembrandt, right?"
},
{
"end_time": 8690.145,
"index": 361,
"start_time": 8667.654,
"text": " But new masterpieces that stand next to the old masterpieces and all are recognizable as masterpieces, right? And so that's also one part of teaching at a high level in theoretical physics or mathematics, the same logic. But I think you need to be present. So that's your question."
},
{
"end_time": 8720.452,
"index": 362,
"start_time": 8690.845,
"text": " Look, it might be that one day only very few very rich people can afford to go to the remaining few universities who offer in-person teaching and everything else is economized into online teaching. Would that be the worst? I don't think it would be the worst, but it would probably in the long run wouldn't be so good. I think every one of us has some spark of maybe, maybe. I don't know. That's not a good statement."
},
{
"end_time": 8751.937,
"index": 363,
"start_time": 8721.937,
"text": " A little. The tiniest spark of genius, I think, is in everybody. And everybody should go to places where he sees other people participate in lectures. As I said before, students need to see you as a teacher to model themselves on you. They need to see there are many other people in the classroom who struggle with this, but they also see. So I'm not the stupid one, but they also see people who apparently fly through the material and excel. So you say it can't done."
},
{
"end_time": 8781.203,
"index": 364,
"start_time": 8751.937,
"text": " If you can do it, you're apparently very special, but others can't do it either. But some actually make it. I'll give it a try. You know, you need both sides. You need to see it can be done and to see it's not so easy. I'm not stupid because I haven't gotten it yet. So well, you know, all of this only happens in presence. And during Corona, we had beginners starting and I gave, I think it was a lecture, it was a tutorial. I think it was a lecture. I gave lectures and"
},
{
"end_time": 8801.323,
"index": 365,
"start_time": 8781.766,
"text": " I didn't see the students, of course not, right? They saw my face and I had some things, they were beginners, right? It didn't work well. It didn't work well. I did my best. I think I gave a good lecture, but it's too remote. I need to see their faces. They need to see mine."
},
{
"end_time": 8827.312,
"index": 366,
"start_time": 8801.954,
"text": " They need to see my gestures. They need to see other human beings doing the same thing. I think they were mainly disoriented because they didn't see who succeeds and doesn't or that there are other people who succeed and don't. We need this. So no, I am not a proponent of online or remote learning, but of course it's not a bad thing as such. But none of that is my intention."
},
{
"end_time": 8853.916,
"index": 367,
"start_time": 8827.415,
"text": " And I'm happy that the people elsewhere who don't have many people wrote to me, it's wrote many positive things. And then they said, it's nice that these lectures are available for free online. I would never have access to such teaching where I live. Okay, I believe that for those people, we write very kind emails. And I'm very happy. It makes me very happy that that they take so much out of it, not only joy, but also maybe future development and so on."
},
{
"end_time": 8882.892,
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"start_time": 8854.36,
"text": " Well, you do your stuff extremely well. Speaking of masterpieces, your lectures are a masterpiece. I'll place a link to all of the lectures, all of your playlists, and they'll be in the description. It's a privilege for me to be able to speak with you. It's a privilege for the audience. The audience is well,"
},
{
"end_time": 8894.889,
"index": 369,
"start_time": 8883.302,
"text": " I'm grateful and I'm sure the audience is grateful as well. Thank you so much professor. Thank you very much Kurt for the invitation. It's very pleasurable to talk about this because indeed we talked about many things I usually don't talk about because they're"
},
{
"end_time": 8924.855,
"index": 370,
"start_time": 8895.401,
"text": " I think you said this in some places. You like to at least occasionally delve into technical detail or at least pseudo technical detail for people who know more, who know about the real background of things."
},
{
"end_time": 8950.162,
"index": 371,
"start_time": 8925.623,
"text": " Thank you. In parts, I think what it is, it's like overhearing two colleagues in the office talking with the door open. And I think your podcast does this particularly well. Hi there, Kurt here. If you'd like more content from Theories of Everything and the very best listening experience, then be sure to check out my sub stack at KurtGymungle.org."
},
{
"end_time": 8972.91,
"index": 372,
"start_time": 8950.435,
"text": " Some of the top perks are that every week you get brand new episodes ahead of time. You also get bonus written content exclusively for our members. That's C-U-R-T-J-A-I-M-U-N-G-A-L dot org. You can also just search my name and the word sub stack on Google. Since I started that sub stack,"
},
{
"end_time": 8993.029,
"index": 373,
"start_time": 8973.183,
"text": " It's somehow already became number two in the science category. Now, Substack for those who are unfamiliar is like a newsletter, one that's beautifully formatted. There's zero spam. This is the best place to follow the content of this channel that isn't anywhere else. It's not on YouTube. It's not on Patreon."
},
{
"end_time": 9022.125,
"index": 374,
"start_time": 8993.268,
"text": " It's exclusive to the Substack. It's free. There are ways for you to support me on Substack if you want, and you'll get special bonuses if you do. Several people ask me like, hey, Kurt, you've spoken to so many people in the field of theoretical physics, of philosophy, of consciousness. What are your thoughts, man? Well, while I remain impartial in interviews, this Substack is a way to peer into my present deliberations on these topics."
},
{
"end_time": 9051.817,
"index": 375,
"start_time": 9022.381,
"text": " And it's the perfect way to support me directly, curtjaymungle.org or search curtjaymungle sub stack on Google. Oh, and I've received several messages, emails and comments from professors and researchers saying that they recommend theories of everything to their students. That's fantastic. If you're a professor or a lecturer or what have you, and there's a particular standout episode that students can benefit from or your friends,"
},
{
"end_time": 9081.92,
"index": 376,
"start_time": 9052.159,
"text": " Please do share. And of course, a huge thank you to our advertising sponsor, The Economist. Visit Economist.com slash Toe T-O-E to get a massive discount on their annual subscription. I subscribe to The Economist and you'll love it as well. Toe is actually the only podcast that they currently partner with. So it's a huge honor for me. And for you, you're getting an exclusive discount. That's Economist.com slash Toe T-O-E."
},
{
"end_time": 9093.166,
"index": 377,
"start_time": 9082.176,
"text": " And finally, you should know this podcast is on iTunes, it's on Spotify, it's on all the audio platforms. All you have to do is type in theories of everything and you'll find it."
},
{
"end_time": 9118.746,
"index": 378,
"start_time": 9093.473,
"text": " I know my last name is complicated, so maybe you don't want to type in Jymungle, but you can type in theories of everything and you'll find it. Personally, I gain from rewatching lectures and podcasts. I also read in the comment that toe listeners also gain from replaying. So how about instead you re-listen on one of those platforms like iTunes, Spotify, Google podcasts, whatever podcast catcher you use. I'm there with you. Thank you for listening."
}
]
}No transcript available.