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Crash Course in Theoretical Physics (How To Solve Every Physics Problem)
May 9, 2022
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You may want to watch this on YouTube, the link's in the description, as I'm referencing plenty of images and formulae. However, there are enough digressions here, at a high level, to make listening an additive exercise. If you want more information, there are links in the description to videos that have heavily inspired this one, including Andrew Dotson, PrettyMuchPhysics, Nima Arkani Hamid's talk, and Sabine Haassenfelder's wonderful and short video on natural units. I highly recommend each of those channels, slash people, if you're serious about physics.
Okay, this video will outline how and why to use natural units to determine a numerical value, place a numerical value to almost any physical observable that's macroscopic that you would like. In my opinion, this should be taught first in physics, but for whatever reason, there's no single lesson, there's no single chapter in a book, there's no single lecture in a lecture series on this. Instead, it's strewn across several and you start to intuit it. You start to understand it implicitly as a physics student.
rather than it being made explicit which it is being made explicit here and that's because it can serve you in the beginning of your understanding of physics and even in the middle of your misunderstanding of physics which is where we all are generally this video is meant to change the way that you view physics and even the world and that's the point the point of view shift this perspective shift is the point of this video while it's outwardly about calculations it's truly about
Developing a different stance on nature. For those of you who are unfamiliar with me, my name is Kurt Jaimungal. I'm a filmmaker with a background in mathematical physics, and I run this channel called theories of everything, which is a podcast. It's a podcast first and foremost. So don't subscribe to this if you're not interested in the rest of the content.
And the rest of the content is about making comprehensible the different toes that exist, the different theories of everything. So for example, Wolfram's theory of everything or geometric unity that's coming up or quantum gravity. Well, that's the seedlings of a toe.
string theory etc etc we even cover the more larger philosophical ones because i'm interested in consciousness what role does that have to play with physics or can it be derived from physics what about free will what about god so you can think of this is largely what is reality.
Okay, let's contextualize the rest of this video, because much of the misapprehension in learning comes generally from not understanding the context of what's being presented, or worse, the context isn't given to you at all. There are timestamps here in every one of the Toll videos, and they're meticulously written, so you can skip around if you like. By the end of this, you'll be able to calculate virtually any phenomenon, as well as have some understanding of it, specifically by the end of the next, let's say, 60 minutes, with just high school mathematics,
You'll be able to answer the following without memorization, in fact, with derivation, which is superior. Why is there only time? So why is it that only time exists? I could have said only energy exists, or I could have said only seconds, or only length exists. I just didn't want to come out of the gate sounding like a Buddhist by saying, hey, all that exists is energy. But you can equally replace that there. What is the vacuum energy expectation? I'm sure you've heard that this is the worst prediction in physics, et cetera.
What are the bounds on extra dimensions? Why saying gravity is weak is worse than a false statement. It's meaningless statement. That deserves a bolded exclamation point. Great. The neutron star pressure. What is the pressure inside a neutron star? By the end of this video, you'll be able to answer that in almost a second.
Microtubules for consciousness. We'll delve a little bit into that. That's Penrose's theory. Why was magnetism understood so late? That's a historical fact, but you can actually derive it from fundamental principles. We'll explain what that means. What is the size of the Earth? Yes, you can derive the size of the Earth approximately. Napkin calculations.
Chasmier pressure. I'm sure you've heard that, hey, if you take some plates and then there's some mode that goes in between, there are more modes outside and so the plates come together in a vacuum. We'll also be covering knots and quantum gravity, at least the modicum. We'll also cover the Schwinger limit and Salvatore Pius' super force, or the Planck force. We'll also talk about black holes. Now, all of these facts look like they belong under the umbrella of physics, except perhaps maybe the consciousness one.
Penrose disagrees, but all of them belong to physics and disparate fields. And you would need to apply completely different frameworks to properly understand them. That's true. If you want to make a precise calculation, then yes. But if what you want is an estimate, a napkin calculation, then you don't need this. You can use natural units. Now, this video is akin to an introduction to the next video, which is coming out perhaps a few months from now. I don't plan on doing these lecture type videos. Like I mentioned, this is a podcast channel. I don't plan on doing these much.
The next video will be about how to analyze and comprehend a physics paper theoretical physics paper that lies at least currently far beyond your current level of understanding. So I'll be going through geometric unity and giving tips on learning physics and mathematics in general. Now let's get on to the approach of this video. So number one, what's different about this? Number one is that there will be
quite a few digressions because it will be about how to think that is how to think about physics problems in general rather than how to just solve certain ones with natural units number two this is great for theory yes but and it's also great because it's practical
The reason is that whenever you're dealing with numbers, whenever you're dealing with units, it's akin to a choice of a basis. In the theoretical end, you should try to construct whatever you're doing without reference to a choice of basis. Much of your existence in physics so far has taken place with
an implicit choice of a basis when you're talking about some transpiration let's say you say it's well it's three meters to the left and two meters up but then the question is well three meters to the left from where two meters up from where and then also what is up what is left what are those directions per se now the real world
In theoretical physics, there's a saying that there's nothing noble in choosing a basis. True nobility.
is being coordinate free. Number three, it will be important for us to be precise. So the reason is that otherwise you'll be confused and you won't realize where your confusion lies. Much of the time when you're a student and you're going to a professor or a lecturer or your tutor and they say well what is it that you don't understand? Sometimes you don't know where your misunderstanding is and so it's difficult to learn a subject and much of the time that comes from the subject not being explained specifically to you.
Throughout this video, I'll be throwing out tidbits, perhaps different pieces of terminology that you don't understand. That's okay. It's for those who want to learn.
slightly more, and I'll also be going through the specific steps. I won't skip a step as often as I can, and that's because I don't want you to be as confused as myself when I was learning much of this. Often steps are glossed over because the presenter is so familiar with them that they've forgotten what it's like to not understand a subject. So for me, when it's delineated specifically, you go from here to A to B to C, rather than from B to D, let's say. Then because the logical progression is made painstakingly clear, you understand it better.
for example we will not be using this symbol what the heck is this what the heck is this now that deserves a bolded exclamation point the reason is that well is zero approximately one
is one approximately 10 ask the person who's teaching you please define this guy specifically what the heck is that this is not a mathematically well-defined symbol this quote-unquote approximately symbol so instead what we'll use is this
which means on the order of so 10 is on the order of 90 they have the same amount of digits 102 is on the same order of 999 for example in the interest of being precise technically this video should be titled how to approximately solve every physics question regarding observables but that's unwieldy and doesn't fit the title character count number four is will be as chewing exercises in favor of a point of view shift
Generally when I watch videos online, they're generally given by lecturers to university students, and then they say, okay, we'll leave this as an exercise to you. If you want to learn more, do this as an exercise. However, even highly, highly motivated people don't do those exercises.
generally you're trying to get an overview and the lecturer is used to assigning problems to students so they think that the viewer is going to actually do them but they don't and it's tedious and so it's more nursing is to instead provide a point-of-view shift so that when you're going about your life you can convert all these measurements that you see to energy for example rather than assigning exercises which almost no one does anyway so as chewing exercises
in favor of point-of-view shit. Firstly, it's easier to get this shift of perspective, and number two, it's more enjoyable, it's fun. Number three, it's more practical. The fifth point is that it will be extremely lean, and what I mean by that is that there will be little fat, there will be little that's extraneous. This is meant to be a video that you can watch, you can re-watch, not only when you've forgotten about natural units and you want to get some understanding, get some handle on how to calculate with them, do napkin calculations, but also
When you've lost some motivation to learn mathematics or physics, there will be myriad points throughout about how to think about mathematics and physics in terms of a general approach to learning. Like I mentioned before, this latter point will be expanded upon in some video that I'll release in a few months about going through a physics paper that you currently don't understand, some theoretical physics one, and I believe I'll be doing geometric unity. Number six, now this one's more for you. If you don't understand
a part of this video that's fine keep pushing this comes from Wheeler the point is not to drink from the fire hose that's what we think we're supposed to do but instead you're simply supposed to get wet
Same with watching the podcasts on this channel. Sometimes they're extremely technical. People say, well, I can't understand so-and-so. That's fine. Just keep watching. The first pass is generally to just know where are you going so that you can contextualize the understanding that comes earlier. Much of the time we're told, look, physics and mathematics, you build upon it and you have to know the foundations, otherwise the top will be shaky. And that's true, but it's
It's often useful to keep going even when you don't understand simply so that you can know where are you going because your misapprehension about the fundamental steps come from not being able to contextualize it. So it's fine. Keep going. Don't feel like I can't drink quote unquote from the firehose. The point is simply get soaked and trust that the learning will occur.
Alright, let's get into this. What are natural units? In order to understand what natural units are, we want to know what are units. So for example, what is a meter? Or if you're being Canadian, a meter. I'm based in Toronto, if that wasn't clear already. What is a second? What is a pound?
Now you'll get fairly frenzied if you think about this for quite some time as I have. That is metaphysically, what the heck is a second? What is a meter? What is length? Science actually doesn't answer what is questions. And this is something that's not taught to you. Science isn't materialistic. Science isn't immaterialistic. It's operational. And this is a point that
Many people don't seem to understand, including scientists. Science is metaphysically agnostic, meaning that it doesn't actually make a claim onto ontology. It doesn't tell you what is. Instead, science gives operational meanings. So what is a second? It's something like 9, 192, I don't know those three, 770. It's one of those numbers you memorize as a child to show how clever you are. Let's look it up on Wikipedia. So let's do this. Wikipedia second.
It says here, the second is equal to the duration of 9192631, that's what I forgot, 631770 periods of the radiation corresponding to the transition between hyperfine levels of the unperturbed ground state of a cesium atom, a certain isotope of a cesium atom. Okay, so then the natural question that comes up is why this number? So why this and not some other number?
And the reason is because in London many decades ago, someone in some back alley took methamphetamine on a Tuesday night and came up with that number. Now, I'm not kidding. It may as well be that to someone studying high-energy physics in the same way that, well, what the heck is a kilogram? What is a kilogram? It means you go to Paris, you go outside Paris actually, it's on the borders of Paris, you go to some vault,
and you deal with people being condescending to you because you don't speak English. Then you duplicate this little metal slab that's in Paris. You duplicate it 67 times so that you have 68 of them in total. I'm just being quick with my writing. 68 of them is in total. Then you measure yourself on a scale and these two numbers will coincide. That's what it means. It's an operational definition. Now, physicists like to use units that appear in nature. So units that appear
and those we call natural units. Now there is some, at least with me, there's some controversy with what's considered natural because when someone comes to you with some dish and they say this is a natural dish and that's unnatural, well what do you mean that those Doritos are unnatural? Did they come from outside this universe from some void? Because isn't everything in this universe natural? Aren't we a product of nature and so what we create is natural?
Okay, what a physicist means by natural is that it's invariant across the universe, as far as we can tell. To be extremely precise, what we mean when we say natural units, natural in the natural units, is natural with respect to our current understanding in order to make certain equations simpler and remove arbitrary human qualities. Why do I say arbitrary human qualities and not just human qualities? Well, in some sense, even an electron is a human construct in the sense that it's there because it
Nature doesn't parse itself out into these elements. I mean, you can say elementary. Elementary seems to be an objective quality because of the way that we define what an elementary particle is. It's an irreducible representation of something. So the fact that it's irreducible means if it could be reduced in this block matrix form, then we can just decompose it and we'd say those elements are elementary. But the reason why we set aside some special canonical place for the electron is because it's useful for us. It makes
are models easier to understand, simpler outcomes, razor, etc. There's plenty of philosophy that undergirds natural. Again, this is not usually explained and you'll be led astray if you don't understand that point. Now here's another point that's ordinarily not explained. Observables have no units. They're dimensionless.
Okay, now what's meant by that? Again, when you say that you weigh 68 kilograms, it means you take 68 of some other reference quantity, some other reference object, and then you stack 68 of them and then you get yourself. It's actually 68. It's not 68 kilograms per se. You can also think of this in another way. If you wanted to speak to aliens, which by the way is another
Topic on this channel not speaking to aliens per se but UFOs then it would be foolish to say I weigh 68 of some product from France now you can reverse this and imagine an alien is speaking to you and you say well how much does your craft weigh and they say oh it weighs four gar bars and then you're like what the heck is a gar bar then they say well that's how much liquid we release from our borbons every two farkles
it doesn't provide much information so instead we do what you see colloquially which is c equals h bar equals one okay let's get to some myths about natural units before exploring exactly what that means so firstly one of the myths is that we just simply set c to equal one to equal h bar this is a meaningless statement as it's written and the reason is it doesn't they can't equal one it means we're now using
the speed of light and h bar as a reference for some other quantity that we're trying to develop. If you're confused about this now, then that means you're thinking about this correctly because it's not ordinarily explained. It's left ambiguous. Let's look at this. Let's imagine what is the speed of, let's say, some car on the highway. So the speed of a car on a highway equals, we would say, 100 kilometers per hour. These are the units.
And that's the magnitude with respect to those units. So if I wanted to say, what is the speed? Sorry, that's already speed. What is the speed of light? What we mean is 2, 9, 9, 7, 9, 2, 4, 5, 8. Again, it's one of those numbers you try to show how clever you are when you're a child by memorizing meters per second.
Now look, this is actually what C is. C refers to all of this. C doesn't just refer to the magnitude. C refers to the entirety of it, including the units. So when someone says C equals 1, what they actually mean is that we are now using units where we've taken that 2, 9, 9, 7, 9, 2, 4, 5,
8 meters per second and we've placed it in here so we've taken this guy and we've placed it in here see all of this is not ordinarily explained and it's because
As an undergraduate, you're especially used to writing with reference to a coordinate basis, which is why I said try to do everything you can coordinate free. If you have an instructor, you're lucky enough to have an instructor, you always ask, how can you represent these equations coordinate free? Another way of thinking about this is that we have graphs in physics and math constantly plot, and those etchings are akin to choosing a unit. The fact that we put lines with etchings
means we've chosen a coordinate so these etchings outward are it implicitly a choice of coordinates but nature but if you look again like I mentioned there's no detector that can detect the coordinates much like if you take a picture with your phone and you then look at it on the screen and you zoom in you see pixels the pixels are an artifact of you taking a picture and trying to manipulate it in some manner the world itself is not pixelated unless you're
to believe Thomas Campbell or Donald Hoffman. Another reason to think coordinate free is you'll start to construct constructions that actually depend on your coordinates when they in fact don't in nature and then you'll wonder why are you getting an incorrect answer. So for example in physics and so on we often use let's say this and then we represent it in some symmetry. This is how theoretical physicists generally reference matrices.
they don't like them so they call them cemeteries these rows and columns but then you also would reference this same object with numbers in a similar manner however they transform completely differently so one is an endomorphism and then the other is a two-form or a bilinear form and they transform completely differently and which is why you have transpose which is it's not ill-defined object but it's a strangely defined object the inverse of a matrix is more
Copacetic, but the transpose is a strange one. So this one is a two-form, a bilinear form. The metric in the Einstein equations is a two-form, is a bilinear form.
And also the determinants of endomorphism is a completely different object, it's invariant, compared to the determinants of a two-form or a bilinear form. And then as you start to understand this coordinate-free, you'll realize that there's a special place in hell for the person who developed the transpose. It's an unwieldy object. Another one that will confuse you if you think in terms of coordinates is that the wave function, you ordinarily think of the wave function as going from some RD or some subset of RD
to to the complex numbers but actually this guy is a section
on a c line bundle and you need to understand bundles in order to understand it coordinate free so that you can do not only polar coordinates and you wonder why the heck does the derivative change well that makes sense when you understand it in terms of a principal bundle and then the associated bundle but also in terms of no longer staying in rd what if you want to move to a curved space for quantum mechanics what if you want to do quantum mechanics on a curved space this is why one should try their best
to understand what the heck is going on without reference to coordinates and then go to coordinates when you're actually making a calculation. So that's why this is a myth. We just simply set c to equal 1 to equal h-bar. By the way, what is h-bar? Well, that's a bit more abstract. You don't need to understand that for the sake of this video. But this is an ill-defined equation. There's actually a caveat here that will come into play later. Another way of thinking about it is imagine you have one USD, one US dollar.
sometimes you would say it equals 127 yen it doesn't actually equal 127 yen otherwise when you have a US dollar it would just be 127 yen what it means is that there's something called value or some monetary equivalent that's another way of thinking about it conversion what it means that you go here with some mapping let's say M and then here with some mapping that's called let's say M prime what it means is that you do let's say M prime inverse
We have to make all these constructions now, and then that's after you've already done M. So you've gone from here, and then you go back up there. They're not the same. So another way of thinking about this is imagine you want to change lengths. Instead of using meters, because you think meters are strange for some reason, you want to measure everyone in terms of Lady Gaga. So you have Lady Gaga here, which I'm going to call LG. So then let's say we want to measure someone else. Let's say Goku. So what is Goku?
equals maybe one and a half Lady Gaga's in length. So you take half of Lady Gaga and you stack that again on Lady Gaga and you get a Goku in terms of length. How about Tony Robbins?
Well, that's let's say two Lady Gaga's now what we're doing here is we're saying I'm going to make all my future length measurements in terms of Lady Gaga for whatever reason in the same way that generally speaking, the prices on the internet can be made in reference to the US dollar and then you do some conversion to find out its equivalent monetary value in some other currency.
In the same way, what we're doing right here is we're referencing everyone's height in terms of Lady Gaga's height. And it's just as foolish as it would be to say Lady Gaga equals 1 equals the USD. Just as foolish as this equation is, it's tantamount to saying C equals 1 equals h-bar. There's so much that goes into a statement like that.
that's just seeing that gives the impression oh physicists are just setting it equal to one so no this statement is foolish and what's underneath that is saying hey I'm going to now measure everything in terms of the speed of light so I want to measure my car maybe it's a millionth of the speed of light I don't know I can don't want to do the calculation right now but let's say it's a millionth of a speed of light so then I say well the speed of walking let's see is 0.000000005
I'm making this up of these speed of light units. That's what it means. OK, so this is all including, by the way, this right here. This is all foolish.
You have to understand what's lurking underneath. So in this example, the value is what's being referenced. When I say the real world, that's what I mean, is that there's something else that's tangible that I'm trying to represent my quantity in reference to. So from now on, we're going to no longer say that this is moving at 500 meters per second. We're going to say that this is moving at a fraction of the speed of light. By the way, this should be a definition, and that refers to the entire object there, not just this. This is just the magnitude.
and that's where this is misleading because it's just showing you the magnitude how the heck can see equal this in the same way how the heck can Lady Gaga equal the US equals one that is myth number one now myth number two is that the advantage of natural units by the way doesn't matter whether you capitalize it or not the advantage of natural units is that it makes
equations simpler. Where is the myth here? The myth is one of these words. It's an article. It's the definite article of the V advantage. That's one should actually be a advantage or an advantage.
The primary advantage is that it allows you to understand the world in a much more elegant manner that allows you to grasp, to understand physical quantities much more intuitively with these napkin calculations. And by the way, I say napkin calculations and not back of the envelope calculations because when you're outside and you're doing one of these, why, where are you going to find an envelope? I don't think I've written on an envelope or the back of one in my entire life. And then, okay, so you take a napkin and you do your calculation on it. What the heck is the front of a napkin versus the back?
It's not like you choose the front or the back or you can even tell most of the time. So it's a napkin calculation. Now let's think about what did I say over here, which is that it allows you to have only time or only energy, et cetera, et cetera. Well, there's some conversion equations. It's best to think of them in terms of conversion, just like money. These are the central equations that allow you to convert. So let's give them a special symbol, a special kind of one.
Number one is E equals, you can guess this, E equals MC squared. Number two, and then let's also make it special, is XP. Well, now I'm going to use this, which means on the order of, so actually let's get rid of this guy, put him on the order of. There's also the Compton wavelength, which will give another fancy symbol, which is
Lambda again, I'm going to say on the order of and notice right now, what have we done? We've already set C to equal one. Look, I'm, I'm making the mistake. Notice what have we done already? We're already going to be using units where C of light is expressed in those units as one. So we're only making reference to C of light to speed of light.
That means that right here we can remove that because that equals one. Right here we can change that to one. Right here we can change that to one and then we can get rid of that because it's the same. A zero with order equation is, well, the speed of light equals some spatial amount over this. Now, since we're setting this to equal one, this means that any time that you have a distance we can express it in terms of a speed.
For example, you can let's imagine that's the earth and then we're going to one light year away or one light second, one light second away.
I can either say, hey, that's two, nine, nine, seven, nine, two, four, five, eight meters away, or I can say that's one light second. That means that it's now converting distance into time. Any distance measure that you give me, I can give you an equivalent time measure. It's not the same. It's a conversion, but you can convert it to time. So this allows a conversion of length to time.
and back because you can do the same thing forward or backward and then this one also allows a conversion of energy to mass so I can tell you this is one gram or I can give you its energy equivalent or you can give me some energy and I can tell you well that what makes up that energy is the equivalent of a certain amount of mass now this one is also interesting because it gives a conversion of length to momentum
I noticed that I didn't explain where this one comes from, and it's the famous Heisenberg uncertainty equation, where you're told that the objects of space and momentum don't commute. However, even this is a misnomer, since it makes no sense to say, quote unquote, objects don't commute. It should be stated precisely that the operations with those objects or operations on those objects don't commute.
How can an object be commutative or not without the extra structure of the group operation? Again, I'm being pedantic because I was extremely confused learning all of this, and you may be as well, and it's best these imprecise statements are made clear. Clearly it's inversed, and then this one gives a conversion of length to mass.
Now how many different types of units do we have here? We have length, one, two, time, three, mass, four, energy, five, momentum, and we have four equations. Which means that we have five unknowns and four equations, which means that we can represent, we only actually have one unknown. So we can represent any of these in terms of any quantity that we like. And thus, we can represent
All of our quantities, mass, time, length, energy, in terms of one or the other. There are many reasons why a high energy physicist just chooses energy, though they equivalently could have chosen time, could have chosen length, etc. It's just for the purposes of this video and for you to have a different point of view on the world, it's better to think in terms of energy because of a series of accidents. The unit that they like to use is giga electron volts, GEV. And that's the units we'll be using.
are the units we will use. So why is this useful at all? Why does one want to convert to GeV constantly? Because if you were to give me the mass of this in grams, I don't know what that means. But if you were to give me it in terms of GeV, I can tell you how many nucleons are in here. So what does that mean? Firstly, notice this accident. Again, it's perhaps an accident, but perhaps not. One proton mass
Equivalent remember it's not just this is something else that needs to be emphasized. It's not the mass of a proton It's its energy equivalent. So once proton masses energy equivalent is Let's say I think it's zero point nine three eight. I have to look that up Okay, we go to Wikipedia and we see What is the mass of a proton? So then we look at the protons mass and it's this right here
And that's the same as 0.93 GeV, if you just know what giga means versus mega. And why is this useful at all? Because it's almost equal to 1. So if I want it to be sloppy, I would say equals to 1. But instead, I will say on the order of 1 GeV. Now we want to know what is a GeV. So firstly, what is an Ev?
Well, you can look all of these up and I'm going to be giving you these practical steps by searching because that's actually what it's like to do physics or any research in general. You go to Wikipedia as one of your first sources. So it says here, EV means electron volt is a measure of an amount of kinetic energy gained by a single electron accelerating through an electric potential difference of one volt. What that means is that let's imagine we have some potential difference here. This is one volt.
And here's an electron, it's at rest. Then it will accelerate a certain amount. Once it gets here, it will have a new speed because the first speed was zero. It will have a new speed and associated with that speed is an energy. And then that energy now that it has, well, let me just do this, it converts to energy. Then the energy, the kinetic energy of it is one eV, is one electron volt.
Why is this useful at all? The reason is that we have now made a connection between one proton, one proton's mass energy, let's say mass energy equivalent. Remember, that's important. It's not its energy per se, it's its energy equivalent.
We've made an association between this and one giga electron volt, and then there's this connection, which is implicit, but I'm making it explicit. This is what NEMA didn't emphasize. The connection isn't actually here. The connection is that this is, well, I'm going to be sloppy and say approximately because it's truly this. The connection is that this number, one, is readily
cognitively graspable, meaning that we can chunk it. It's easier for me to think in terms of one lip balm than it is for me to think in terms of 0.825 lip balms. The reason why this latter point is important is that you'll see in physics constantly
there's an effort to reduce some convoluted equation into linear algebra. And that's because linear algebra is extremely cognitively graspable. It's understood. It's one of the few areas of math, if not the only area of math, that's well understood. That means anytime you have a complex equation, if you can linearize it, you understand it much better. In the same way that anytime we have some complicated phenomenon, we can put it to something that's in terms of GeV, means we understand it in terms of protons.
It's akin to Feynman saying that the number one lesson for some future civilization, if you had to impart one piece of knowledge to them, the best knowledge, the best bang for your buck in terms of facts, would be to tell them that the world comprises atoms and from that fact many other laws of nature come. Now I don't know about that because to me that would imply that you would have some fact like let's say the atom fact and then we have the space of all facts
and then you have to have some measure on the space of all facts in order for you to say that this is this one fact implies the most facts and that's somewhat dubious but you at least understand informally what Feynman meant it's one of the reasons why in the theories of everything podcast what I'm trying to do constantly you'll see me asking the professor who has some extremely intricate Baroque equation or concept
I'm frequently saying, okay, what does it mean in terms of billiard balls? So let's imagine that this has a charge and this one does too. What's going on there? It's the same, trying to reduce down to some fundamentals that you understand in order to properly understand it. Then there's another somewhat of an accident. Maybe it's not. Heisenberg said there was isospin. So that one neutron has similar mass.
to a proton. And it's these that all work together that allow one to make use of natural units for these napkin calculations. I'm being extremely specific and somewhat pedantic because much of this is glossed over and then you'll start, at least if you're like me, you'll start to be confused at a much later point and you won't realize that some of these fundamentals weren't explained specifically. Now let's go through a conversion chart. Conversion.
chart. Here we go. One meter is the equivalent of on the order of 10 to the 16 GeV inverse. Ah, now I haven't explained what the inverses mean. Here at our equation bolded number one and then bolded number three we have an equivalence between energy and mass so you say one giga electron volt and that can mean
a certain amount of mass. Okay, you can convert between them. But you can also convert between the mass and then the length. But this is an inverse relationship. So that means that length actually has inverse energy units. So anytime you give a length, you can also have given the same quantity in inverse energy. Anytime you have a second, you could do the same. You can give that in terms of inverse energy. Anytime you have a mass, this one's simple, you can give it in terms of energy. Now this mp is the Planck mass.
Not the proton mass. Remember, proton mass is 1 GeV. Just for fun, you can do the calculation of a gram, and it's this much. You can do Hertz, which is inverse time. And by the way, because you're in inverse time, you have regular energy units, which means frequency is actually a unit of energy. Anytime someone gives you a frequency, you can just convert that straight to energy. We're going to be doing these. By the way, I didn't actually do this, but for entropy,
You can see that this is a dimensionless quantity. It's information. It should be dimensionless. Because it's dimensionless, then from the Boltzmann constant, you can get that Kelvin is also a unit of energy. So temperature is a unit of energy, which somewhat makes sense because you've heard that temperature is some function of the average kinetic energy of the molecules in a room or in a box. But that statement alone isn't enough to say that it's units of energy, because just because it's a function of energy doesn't necessarily mean the units of it are energy.
However, it does turn out to be the case. This means you can convert from energy to temperature and vice versa. All of these are vice versa. And then one we may use later is nanometers equals this. By the way, if any of these are incorrect, well, then please just write the correct one in the comments section. When you look at these conversion charts online, some of them have a plus or minus one in the units. And that's because we're using this symbol, which means we don't actually care too much about rounding errors.
Remember that this is all about napkin calculations, NCs, we're just doing NCs. To be extremely concrete, you can say your desk in front of you is one meter, approximately, let's say approximately one meter long, or you can give it in terms of GEV, it's 10 to the 16 GEV inverses. And that means that if you stacked, stack 10 to the 16 protons, so you get proton, proton, proton, proton, 10 to the 16 times,
Then you get your desk. So it gives you an extremely concrete way of understanding what your desk is. Your desk is 10 to the 16 protons stacked one after the other. And by the way, you may say, well, Kurt, isn't GEV also arbitrary? Wasn't the whole point of natural units to get away from this arbitrariness? Well, yes, that's true. Except that the other part here, which is a great confluence, is that this coincides
with how engineers think. Engineers think in terms of electron volts, well they think in terms of volts. So now you've found a connection between protons, between something that is cognitively graspable, between a neutron, and between what you can communicate with with others. So engineers, now throughout the rest of the video you'll see that many different quantities, physical, macroscopic, sometimes even microscopic, physical, observable quantities, are expressed in terms of these fundamental
Now notice I didn't say fundamental constants, and that's because I'm trying to emphasize the fact that they're dimensionless. Let's analyze Newton's constant and others. Here's what you do in general. Firstly you go to Wikipedia, so let's do that right now.
and you type in newton's constant so it's also known as the gravitational constant you've seen it before it's this g then we take a look at what are the units here we go we get newton's meters squared so on and so on so let's write this down the units of g and even here i noticed i made a mistake because often you'll see online m which means meters which means it's actually a length
And this is a common mistake when you're initially doing this. So this is actually mass and this is length squared.
You'll see it here that it says Newtons meter squared, so length squared, then a mass squared is what it's being divided by. Then you wonder, well, what the heck is a Newton? So what we do is we go into it because all of these are derived from something that's much simpler, usually mass, length or time. So we go here and we see that is equal to a kilogram. So mass times length over time squared. So let's do that.
Okay, now it's as simple as doing some cancellations. Well, we can remove one of these masses and we go mass. All right, now we want to reduce this even further. Remember, there's only length or there's only time or only energy. Let's see if we can place this in terms of only energy.
we go to our conversion equations there's a correspondence between length and time between energy and mass between length and momentum actually this correspondence is between length and inverse momentum and this is between length and inverse mass you can see that just from the fact that there's a one over and obviously that can go one over there there's also another equation that will come in handy let's give it a bolded four which is the energy time uncertainty and this gives a correspondence between
Energy and time. However, looking at the equation, you can see that it's inverse time. That means that inverse time is energy. Inverse energy is time. Let's now make some substitutions. Mass is the same as energy, so I'm going to call it GeV. Time is the same as GeV inverse. Length is the same as GeV inverse.
Well, length is the same as mass, but mass is the same as energy, so you can make that substitution. Making all of these substitutions, you then get that G, the units of newtons, is actually 1 over GeV squared, or, as we'll be writing it, simply GeV to the power of negative 2. It's all simple. We look and we see that it's newtons times kilograms times
Length, etc. actually reduces down to this. So let's underline that in red. How about entropy? Well, entropy, as we've noted above, is given by a formula, which looks like it's actually minus what I wrote before. And these are probabilities, which is dimensionless.
Again, extremely simple. Now much of this is made complicated, but if you look at it through the lens of natural units as well as these conversion equations, all of the quantities that you know and that you love and that you want to work with become units of energy raised to some integer power. How about pressure? Again, let's just look that up on Wikipedia. That's usually the first step.
It says here Newtons per meter squared. That makes sense because it's Newton, which is a force unit over some area. And then luckily they've decomposed it further for us. So let's write that down. That is a mass over a length. And then we have time squared, which then becomes, which we can now do in our head, but we won't do that right now because we're trying to not skip any steps. Mass becomes GeV.
Length becomes GeV inverse, so it goes to the top. Time is also GeV inverse, so it's GeV squared, and that is the same as GeV to the fourth.
This tells you an extremely important property of pressure. It's an extensive property of space-time itself. This is one of the reasons why it's much easier or much more useful to think in terms of pressure rather than force, because pressure is a property of space-time itself, whereas force is some derived quantity that usually isn't useful in fundamental physics. Now let's do a fun one. How about speed? Well, we think of it as length over time.
And then because time and length are the same in our conversion chart, this just becomes dimensionless. That deserves a bolded exclamation point.
Then you think, well, how the heck is speed dimensionless? Isn't it the case that you said over here, Kurt, C equals one, you can't simply say C equals one. Yes, that's true, except there was a caveat. And the caveat is that there are these conversion equations because we're placing it in terms of C, which is invariant. It means that we can tell time in terms of length and we can tell length in terms of time.
And that means that this equation is correct, but only when you take into account the fact that C is invariant and these other conversion equations.
It's usually just glossed over, so plenty of preamble goes into making a statement as seemingly simple as C equals 1 equals h-bar. So C equals 1 is a meaningless statement unless you're specifying that you're using some of these as conversions. And then you're also emphasizing the invariance of the speed of light. If the speed of light depends on something else, you can't actually use that. All of this needs to be explained unequivocally first.
It's usually not, and then there's an abundance of befuddlement that occurs, much like with the Brachetta notation, which looks graceful. However, there's plenty of assumptions that go into it, which make it not terribly useful.
Let's use this to calculate a practical quantity. So how many protons are there in you? At first, if you were to just say, well, I weigh 70 kilograms, that doesn't give much information. What we can do is we can use our conversion chart over here and say, okay, well, look, one gram is this much energy. So how about a kilogram? So a kilogram must be 10 to the 26 GeV. Using this, we then get that 70 kilograms becomes 70
times 10 to the 26 GeV, which is on the order of 10 to the 28 GeV. That means that what comprises you is 10 to the 28 protons. And that's a much more physically meaningful quantity. Now you have some physical intuition given to you by your weight. Whereas if it was just kilograms, then you have to go to Paris, etc.
Then you may wonder, well Kurt, don't neutrons come with protons, so shouldn't you times 2 the above? Yes, except because of this. We're saying on the order of. So we can say there are 10 to the 28 nucleons that comprise you. Protons and neutrons bound. There we go. Simple and powerful because it allows these napkin calculations. Let's do one that you may think requires plenty of work, but it's actually extremely quick. You can do it in a second. So what is the pressure inside a neutron star?
The pressure inside a neutron star, well firstly you have to think what is happening. There are neutrons as far as you can see and recall that neutrons are the same as protons in terms of their radius and mass approximately.
Then as far as you can see, all you see are neutrons. Think about what have you learned about a neutron star. It's that the neutrons are packed so close together that they can't be packed any further. Then you think, well, what is the units of pressure? And it's GeV to the fourth. So we have GeV times GeV times GeV times GeV, one, one, one, one, one. And we get pressure in a neutron star is simply GeV to the fourth.
Okay, that's it. It's just GeV to the fourth. And this is something that you can verify yourself if you look up what it is in Pascals and then do the conversion. And just keep in mind that some conversion charts have a plus or minus one on the order because sometimes people round up, sometimes people round down.
Now let's get through this much more quickly because I'm re-recording constantly. There are many errors and my facial hair is growing. I've renamed this for reasons that will become clear later. A neutron star's pressure is much more copacetic. So proportionate strength of the forces. So you know from perhaps around high school that it's something like the first charge times the second charge, so on and so on and so on.
Let's look at this in terms of the electron charge. So Q1 will equal Q2 will equal E. V is energy. We know that. That's potential energy. R is inverse energy, which means this equation has this guy here, which means that this guy here, which I'll rewrite, is dimensionless.
And this is what is usually denoted as alpha, which I'm sure you've heard is 1, 3, 7 inverse. This is the reason why the strength of the electromagnetic force or the electromagnetic interaction is quantifiable, it's dimensionless. However, if we were to look up here, notice this, this G newton
has negative mass dimension, which means that saying that gravity is weak is actually a meaningless statement because you need test masses. You need two test masses in order to say that. Usually what's done in fundamental physics is one takes the most massive of all the particles, the fundamental particles, and says, well, look, compared to the weak force, which is the weakest of all the standard model forces, the gauge fields, gravity is so-and-so times weaker. So that's what's meant specifically by gravity is weak.
But all of that needs to be stated. There are assumptions that go into that. You need a test mass. And by the way, this guy here, this negative square mass dimension of the coupling of gravity, plays an extremely important role in the non-renormalizability of gravity. Let's calculate the average speed of an electron. So later, we're going to calculate the radius of an electron, and that's going to turn out to be this. But this right now just looks like junk because we haven't derived any of this. However, from this, we know that one of our equations over here,
says that we can figure out the momentum based on a length so then what is the momentum of the average electron and it's hear that sound
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And that means that this is the average speed of an electron. Think Verizon, the best 5G network is expensive? Think again. Bring in your AT&T or T-Mobile bill to a Verizon store today and we'll give you a better deal. Now what to do with your unwanted bills? Ever seen an origami version of the Miami Bull?
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And this number is the reason why magnetism was discovered so much later, because electrons are moving relatively slowly, and we know that magnetism has to do with the speed, it has to do with current changes. Thus, from relatively fundamental principles, you can derive a historic fact. Why was it that magnetism was discovered much later? Well, it's because of this guy.
And by the way, you'll notice that I spend quite a bit of time writing and rewriting painstakingly almost. And that's because I know that clarity of thought leads to this clarity of writing and vice versa for myself and for you. And if you're lucky enough to have a lecturer who's blessed in that area, in this notational refinement area, then it will translate directly to higher comprehension for you. It's a
It's a neglected part of pedagogy, I find. The logical placement of the words in the formula matter, and many of you are trying to create your own theory of everything, you're advancing your own, you're not simply learning about others. It's one of the reasons why I try to be specific in the podcast in general, and then also here as much as I can be, given the time constraints, because generally you're told
have truths so for example that a wave function is a member of a square integrable Hilbert space okay but then if you derive it is a square integrable function necessarily square integrable itself okay so then you limit it to Schwartz functions and then you say well perhaps Gelfand triples and so on and then you realize well that only works for pure states that a general quantum mechanical state is actually endomorphism on a Hilbert space and even then when it's a pure state it's not a unique you can't assign a unique member of a Hilbert space you have to take a
The reason for me to be extremely detailed is because many of you are trying to advance your own toes, and if you're going to build them based on some shaky foundation, then you're going to derive fantastic formula and fantastic theories based on
half truths and based on what's misleading you can it's akin to dividing by zero you can prove the entire universe from scratch if you divide by zero what I found is that the popularizers of science have generally spent a significant amount of time on let's say the wave particle duality instead of telling you it's a quantum mechanical object that behaves in this manner well mainly for for a few reasons and one of the reasons is because they want to evoke awe in you and show you how unimaginably intelligent these
Esoteric Physicists
Gelfand triple, you're wondering what the heck is that? Well now you can at least look that up on Wikipedia and you can gain a far better understanding of what a quantum mechanical object is rather than simply saying that it's both a wave and a particle at the same time and who knows what the collapse means and so on. By the way, I talk about this here in the quantum gravity section of the Salvatore Pius interview. If you want, I'll leave a link in the description. This is why quantizing gravity is so difficult and it's explained in somewhat pedantic mathematical detail
mainly because then you can see, okay, this is why it's so difficult and it's not necessarily because you're trying to mix the jittery with the smooth and so on. What does that mean? Let's get to knots and extra dimensions. The whole point of this is to get familiar with the different length scales and the different energy scales. So let's take a look at this. The mass of the pion, which you can look up online, is about 10 to the minus 1 GeV. The mass of the electron, which I think we've used, is about 10 to the minus 3 GeV.
Thinking of physics in the manner of natural units and GEVs, etc., gives you concrete ways of thinking about some phenomenon in different respects. So, for example, length scales here. These automatically imply that, for example, chemistry becomes important at what scale? Well, 10 to the 3 GEV inverse. We simply take the inverse of this, and then same with
And by the way, that's because the electron is what's responsible for chemistry, largely speaking. And for the strong force, we expect the scale that it becomes relevant is 10 GeV inverse. And then we can simply do our conversion over here to find out the relevant length scale in terms of meters. Let's now have a quick detour into extra dimensions.
Extraspacial dimensions are called universal extra dimensions. And usually we're dealing with one temporal time dimension. So you'll hear three plus one or four plus one, that plus one usually means the time. At some point in the Toe podcast, I may do a single episode just on extra dimensions. If you're interested, let me know as well as extra temporal dimensions. What we're doing is looking here. So we're seeing that usually what you've heard is that you compactify the dimensions.
Sometimes, I think in the string theory episode, which I'll link over here, we talked about a Kaluza-Klein compactification of 10-dimensional super Yang-Mills theory. So that's what's being referenced here when you hear about a Kaluza-Klein resonance. And then you may wonder, well, look, it says that we have put some bounds on the extra dimensions, which is 1 TeV. But if we take a look at what the LHC, the largest energy of the LHC is, it says here it's 6.8 times 2, so it's 13.6 TeV.
TeV is just a thousand GeV. So then you wonder, well, how is it that we've put a bound of an extra dimension only at one TeV? Shouldn't it be at 13 TeV? Well, strangely, some of the theories of extra dimensions have it such that the standard model fields stay within our three spatial dimensions and then they leak out. Well, gravity mainly leaks out into another dimension. That's the ADD model, not attention deficit disorder, but Arkani Hamed and
hear that sound?
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It's actually not, it's somewhat comparable, it's just that it goes into another dimension. And because we're confined here, this is where we're confined, it's not as simple as looking for an extra dimension like you can see it just like you can see a DNA molecule.
What we're looking for are deviations in the inverse square law and this number 2 here is actually can be generalized to higher dimensions dim minus 2 where I'm including time here to make this simple so for us it's 4 minus 2 which is what gives rise to this inverse square law but if we're in higher dimensions then we'll see a different number here this becomes 1 over the dimension of the manifold that you're on minus 2 and in the manifold I'm including time just to make it simple
As for how we derive this, don't worry about that. You can just think of the flow through a surface. If we're in R3, then a sphere around us is like a shell, and that's a two-dimensional surface. So if you're in R3, you go one dimension down. If you're in R4, you go one dimension down, so it's R3 and so on and so on. Technically, to be rigorous, you need to show that the potential of some Laplacian vanishes, but we can leave that. Let's get to looking at some of the papers on extra dimensions.
Here we go. So firstly, notice this, this is inverse R, which is related to an energy. And so this makes sense because you know, length is inverse energy. Now you're starting to get a handle on all of this. Let's take a look at another paper, which I'll link in the description. This is actually a section from a book, I believe. And you can take a look. Well, here, what this is saying is that if we have extra dimension, see here is four plus the extra spatial dimensions right there. That's Delta.
You have the Einstein-Hilbert action. This we know if we remove this d delta y. This is just the standard action that leads to the Einstein equations. And we trivially add some more spatial dimensions right here. And then here's some matter fields. You want to couple some matter to it. And notice that it's four dimensional here, whereas this one is four plus delta. And that's saying, hey, let's restrict our standard model matter fields to this four dimensional manifold. And that explains why we see them as fairly strong, but then gravity is allowed to
leak out into the extra delta dimensions. If we take a look at this, this also gives us some bounds on the extra dimensions. Now there are large extra dimensions as well. The ADD model I mentioned before isn't a compactification, and you can similarly find bounds on them, which are found here. Now that you're becoming more and more familiar with TEVs and GEVs and so on, you can at least skim this paper and get an idea of what's being said.
Notice here, another number you should recognize is the Planck scale, which is 10 to the 16 TeV. We have it written down as 10 to the 19 GeV, but those are the same numbers. Now let's have a quick aside on knots if I have enough room here. What is a knot? A knot is an embedding of a circle into R3. Let's take an example. Right there is a knot. And this what we're actually seeing, this is not a knot. This is an embedding of a knot. Technically, these should be modded out by isotopic equivalence.
I'll include a link to a podcast where we go into more about knots and quantum field theory. Each one of these guys can directly translate to a Feynman diagram in two plus one dimensions. Now you may ask, well, why is it that we're going from a circle to R3 but not to RD? Well, there are extensions, except you can't have S1
You cannot have S1 into R4. You can, except that every single knot can be trivially unknotted. So it can be morphed into a circle. So that's why you'll have to have S2 if you're going into R4, and then S3 into R5, et cetera, if you want to have higher dimensional generalization of knots. But then their connection to Feynman diagrams are more complicated, and I believe it's current research. So this is only the unknot.
Additionally, whenever you hear about the Planck length, that will come up, the Planck length, it can't be that space is, quote unquote, trivially made up into some lattice of discrete lattice of Planck lengths, Planck cubed, and so on. And the reason is that that concept is not Lorentz invariant. Because what if you're zooming past it, then do you get smaller than the Planck length? What if you make this room into the Planck length? And should this room exist from another perspective? You get into plenty of paradoxes, and that's because we don't have an understanding as to what happens around that scale.
Another way that extra dimensions can be tested is if you collide particles. So let's say they look like this. And then who knows what happens here? No one actually knows their Feynman diagrams and so on. But whether or not that corresponds to something physical, who knows? Imagine they come out like this. Well, what happened here?
This is the same as this, but then this is less than this, which means we have a, if they're the same particles, we don't have a conservation of momentum. And then we can say that perhaps what happened was some of the momentum leaked into another dimension. So this is also being looked for. This is called discrepancies in transverse momentum.
Now let's take a dive into Penrose's theory, the microtubules of consciousness. Because this is meant to be an overview, and each one of these could be its own two-hour, three-hour, four-hour podcast on its own at least, let's simply go to Wikipedia and get familiar with using these conversion equations and natural units, the whole point of this video. The founders of this theory are Penrose and Stuart Hameroff.
So if we take a look, we're just looking for equations right now. We're scrolling through. I'm not concerned too much with the background. Notice this. This looks extremely similar to this. And it is. It's called Penrose's indeterminacy principle, much like Heisenberg's uncertainty principle. What Penrose is saying is that imagine we have one particle and then it's in a superposition. So let's imagine it's a superposition of just two states, which can be left or right. Let's call this
and let's call this option B. Along with option A and option B, they have their own warping of spacetime, so gravity. Anytime you hear about a gravitational field, usually when you hear the term gravitational field, it's the metric, the spacetime metric in general relativity. However, technically speaking, the gravitational field tensor is the Riemannian tensor and the gravitational potential is the metric. Regardless, we take a look here and we say that there are different
Warpings of space time associated with each of the options so a may have some warping that looks like this as you go outward and then B may look like let's say this and then you wonder well is this the superposition so ordinarily be denoted this plus this well are we to have a superposition of space times
What Penrose is saying is that once the particles are of a sufficient distance from one another in metric space, so over here it says EG is the gravitational self-energy and the degree of spacetime separation. So the degree of spacetime separation is a bit of a misnomer here. What's meant is that there's a symplectic measure on the metric of spacetimes and then from that you assign a number to the metric of A and then to the metric of B and you see the difference once that difference is large enough.
then there's a collapse. So this is a mechanism that merges gravity as well as the quantum collapse as well as consciousness. So like three mysteries in one. There's an episode with Stuart Hamarov if you want to see more about that. Over here it says one kilogram of an object will reach its objective reduction within 10 to the minus 37 sec. I believe this is incorrect on Wikipedia because when you take a look at the reference here it actually doesn't make a
it only has one reference to kilograms and it's 10 kilograms not one and then it says 10 to the minus 43 so I'm unsure where Wikipedia gets their number from and here is the better diagram that I was trying to draw before of the different space times and you can see let's see yes that's correct there's technically a symplectic measure on the space of four metrics that's right and Penrose is not going into extra dimensions here okay so let's write down that equation it's the gravitational self-energy one over
What is the gravitational self energy? One may guess naively. Hear that sound?
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That it is M1 M2 and then G over R and that would be correct because of this. However, if you look it up online, there's about a there's a correction of about five thirds or so. That doesn't matter because we're using this
Then what I'm unclear about is that there's still an r here, so we have an extra factor and I'm unsure of how he's deriving this number when there should be one more factor. To me this r should be a function of t and this should be related to the measure that we had here, the measure that's generated from the metrics. However, I'm unsure of this and I'm going to be speaking to
An essential feature of Penrose's theory is that when there's a wave function collapse, where it collapses to is chosen neither randomly nor algorithmically. This is outlined in his book called The Emperor's New Mind, where Penrose makes an analogy between something called non-recursively enumerable sets and
You may wonder why is it that we're using one GEV instead of
Well, it just makes some of the napkin calculations easier, so this is all about NCs, napkin calculations, as well as it gives you a much more concrete physical intuition. Later we'll derive the radius of an atom, but for now you can see that this is the radius of a proton, it's also the energy of a proton, the mass of a proton,
Which, as we mentioned earlier, this means my desk is 10 to the 16 protons long. If you take 10 to the 16 protons and stack them, you get the length of my desk. And I said desk, so don't get excited. Okay, now let's get to vacuum energy. Okay, you've heard the story that the universe is expanding, and because it's expanding, it has a positive cosmological constant, and much fervor is expressed to the disdain of the word prediction, the worst prediction of physics I'm sure you've heard. Worst prediction.
And many people dislike this word prediction because it's not as if a specific theory was said to be false because of this prediction. However, that gives the impression of discounting the calculation completely. It wasn't a prediction per se, it was a comportment. Namely, if lambda was to comport with the standard model,
That is, if it was to be a consequence of absolute energy from the vacuum fluctuations from the Planck scale upward, then it should be of order, let's say, x. We're going to calculate that. It was a comportment test rather than a prediction. The mechanism could have been the vacuum fluctuations of QED. I believe Weinberg calculated this, but it turns out to be vastly, vastly incorrect. So let's take a look. There are three main sources of vacuum energy.
And this is just from the standard model. Forget about general relativity. So number one, QCD. And these are these little quark bilinears. Number two, it's the Higgs field. And number three, it would be the zero point. These are called the zero point fluctuations. And this one is of order 10 to the minus one, GEV.
And what power goes here? It's a pressure. It's dark energy. It's a property of space time itself. So four. Simple. Then what is the Higgs field's contribution? 10 squared GeV. And what power goes here? Well, what else could it be? Number four. Let's get to the calculation of the zero point fluctuations. What this means is that at each space time volume space time. So now we're dealing with four, not just three volumes, but I'll draw it as a cube.
at each space time volume of length, let's say L. So L cubed in this case, but actually it's truly L4. So let's just place L4 here. That corresponding to this length is some frequency omega. The reason why is that we have this relation that energy is related to
Frequency, which means there's a tight relationship between frequency and energy. You can convert between the two. We're going to do that later once we analyze the Sun. From each space-time volume of length L, there's a contribution of a certain mode that happens within here. So let's call that frequency, well, whatever, it's omega in this case. So we constantly get these omegas associated with length 1 plus an omega associated with length 2.
So on and so on. And because of this relation here, the shorter the length, the larger the energy. Firstly, that means that it's infinite. Technically, the zero point fluctuation yields an infinite energy, but that doesn't mean that it's literally true. It means technically it's true with our theories, which already break down.
And where do they break down? At the Planck scale, this is what you've heard. So how about we simply cut it off at the Planck scale. So we let this be the Planck length, which by the way is what? Well, it's the inverse of the Planck mass. Because we're taking an inverse of an inverse, we simply get that the energy contribution from the vacuum,
is the plank mass to the four.
The one where it's the plank length. So this is the only one that meaningfully contributes. This is why this NC or this napkin calculation, which is contingent on this, on the order of symbol, this tilde here is so vital. This is what allows you to do this quickly without thinking eventually. This gives an NC of what a napkin calculation of 10 to the 18 GEV to the fourth.
Well, this should be that. And then that means that this is 10 to the 72 GEV to the fourth. Now, what is observed? What's observed is what you can get online because this is what's calculated by data. You'll see these strange units and then you'll have to look up on some other conversion site. So, for example, let's take a look here. Here's some conversion table.
You can find online, they've set the Boltzmann constant to one as well. And here's another one. I'll leave these links in the description because these can be helpful. You'll notice that some of them defer at the last digits. And the reason is, again, I mentioned this, some places round up, some places round down. This then becomes 10 to the minus 48 GeV.
You may wonder, why am I not placing square brackets here? Well, you can. It doesn't matter because you know that this is the only unit anyway. You may wonder, well, where does this observation come from? Like I mentioned, people look at data and then they have some assumptions like homogeneity and an isotropic universe. And then you get the Friedmann equations, which you can look up, which relates the acceleration to the cosmological constant and thus the pressure and density.
The above then yields slash implies that our napkin calculation is the same as the observed times 10 to the 120. And now you know about the vacuum energy expectation.
Now let's get on to calculating with the Schwinger limit. If you watched the Salvatore Pius interview, you'll notice that one coulomb of charge was brought up. So firstly, let's talk about what is one coulomb of charge. Let's get a handle on it. Let's go to Wikipedia, our friend. We take a look and we see that the elementary charge was assigned to this exact value in 2019. So this is the exact value of one elementary charge. It turns out that elementary charge is a dimensionless quantity. Let's write this down here.
elementary charge is on the order of 10 to the minus 19 coulombs. This means that one coulomb, which I'm going to denote as C, one coulomb is the same as 10 to the 19 charges. So proton charges, electron charges, they're the same, they're just the reverse of one another plus or minus
Let's deal with protons. 10 to the 19 protons. That's 10 to the 19 GeV. Let's get a handle on that number. If we were to stack protons one after the other, 10 to the 19 times, then going up to our conversion chart, that is 10 to the 3 meters.
That's the definition of one kilometer. That means if you were to take protons and stack them, stack them, stack them without any gap in between, it would be a strip of one proton wide and then one kilometer high. That's an extreme amount of charge. Great. Now we've gotten out of the way. What is one coulomb? Let's get to the Schwinger limit.
The Schwinger limit here, it says, is the scale above which the electromagnetic field is expected to become nonlinear. So we haven't observed this because this is an extreme amount. We're going to actually deal with what the heck does this mean in our manageable units. The limit is typically reported as some maximum electric field or magnetic field before some nonlinear effects kick in. If we take a look here, we see this. Firstly, let's just analyze this.
We notice there's a C. We notice there's an H bar. We set those to 1. That means that all that's left over is mass over charge. Charge is dimensionless. Mass squared. That means energy squared. That means that this is energy squared. This is a force. And then this has the same units. This is also a force. So Tesla has the units of force. Energy squared. E has this volts over meter has the units energy squared. You can get that right now just by looking at this for three seconds. Let's just deal with E.
So e is on the order of 10 to the 18 volts per meter. This is also, as defined here, m e squared c to the 3 over h bar, the charge of the electron. That is, in our units, m e, so the mass of the electron, those become 1, this becomes 1, and then we get this.
Now the charge of the electron is just one. Let's get a handle on this number. So firstly, what is a volt? We don't have to do much work because a volt, well, a GeV is 10 to the 9 volts. And that means that we can just take 9 from inside there and it becomes 10 to the 9, so 9 plus 9, GeV over meters. And then we can go upstairs to this and see that a meter is 10 to the 16.
Using our formula from above, we get that a meter is this, and I will just put some clouds around this as well. Because we have an inverse meter here, we take the inverses of this. So we take one here minus that becomes a plus one. This then implies that we take the nine, we plus 16 to it. So we get 10 to the 25 GeV squared. This is, by the way, a unit of force like we mentioned before.
Ah, and those again who have watched the Salvatore Pius interview, you know that he mentions the super force, and what the super force is, is this. It's simply the Planck force. Now you should have more of an intuition as to what this actually means. So this is 1, so it's 1 over g, which is what we've calculated before, the square of the Planck mass.
And you can see that makes sense in terms of units because mass squared is the same as energy squared is the same as force. Now, as I've mentioned before, I don't think force is a particularly useful concept in fundamental physics. I think pressure is. So there should be a plank pressure.
And it turns out there is and it's called a plank density. I call it the plank pressure. It doesn't seem like anyone else calls it that. But anyway, how do you get the plank pressure? Well, you take some energy and you divide it by volume. What's the energy that we have? We have the mass, the plank mass, and we divide it by some volume. What's the volume that we have? We have the plank length and we just cube that.
And that's how you derive the Planck pressure. At least that's what I think it should be called. Now at first I was going to draw some picture to give some interesting ideas to what the Schwinger limit is in some fundamental manner, but actually force isn't a particularly interesting concept because it requires extra structure. So for example, we know that we have these inverse squared laws that characterize the Coulomb force and gravity, which technically means that you can get however
large of a force you'd like depending on how close you are to the original source, to the point source, if it's a point source. This, to me, demonstrates a flaw in Newtonian mechanics from the get-go, and yet it works so well, thus if a particular theory has a major flaw, perhaps give it a chance to breathe before dismissing it as patently broken.
See, all of this is decidedly simple, and often you'll be confused but not know where your confusion is. Often what will happen is you'll ask someone to explain or re-explain some phenomenon or some mathematical trick, and then they'll say, well, what part of it did you not understand? And you won't be able to give an account because your confusion is such that you're unable to see where your confusion is.
that is to say you don't know the aspects of the technique or the mathematical trick or formula or structure etc that you don't understand so asking someone to explain a particular part because you just chosen some party say I don't understand this somewhat fruitless because that was arbitrarily chosen by you this is one of the reasons why it's great to read from multiple sources so watch multiple videos on the same phenomenon the same trick the same formula you'll see professors when they're being interviewed or when you go to their office they'll often have
a plethora of books and then you think well they're extremely bright and they are they're extremely extremely extremely bright hard-working people but then you wonder why do you have five books on linear algebra and it's because even Ed Whitten needs to read from multiple sources on the same topic in order to truly understand it you need to see it from multiple perspectives actually I spoke to Jordan Peterson about this exact topic I'll leave the podcast in the description so if you feel like some concept is far beyond you perhaps it's not perhaps you need to re-watch the video so you can re-watch this one if you like
Or you can watch from multiple sources and then it will slowly start to make sense. You'll start to see this baroque, intricate, complex object from multiple perspectives. You can only see a projection of it and then you start to build a shape of it. Seeing it from one source generally doesn't help. To sum up, learn from multiple sources, read multiple sources, watch multiple sources. Sometimes you don't need to know where your confusion is because at least you don't consciously need to know because it will unconsciously resolve itself after learning from different perspectives.
Okay, now let's get to number eight, which is annihilating positron electron pairs and quantum gravity. We got to get through this quick. I'm likely going to turn this screen off. I'm making way too many mistakes. I'm recording this over and over and different parts aren't working. So if there are any errors here, obviously leave them in the comments. It's great if you unceremoniously point them out. I don't mind. I'll highlight them. Annihilating pairs of positron electrons and quantum gravity. So firstly, what happens when you look at the vacuum? You simply look.
Well, we know this relation, which is E, is the inverse of time. And let's imagine that we wanted to create particles that were on the order of an electron, so electron-positron. Then we just replace this E with the mass of an electron. Technically it's 2, but it doesn't matter because we're saying this is on the order of. This means that for a small amount of time,
an electron-positron pair can be created. And then you can also ask, this is a unit of length, which means that if you were to probe the vacuum, if you were to look close enough, and exactly how close enough? Well, what is Me? Me, remember, it's akin to 1 MeV, which is the same as
This means looking at empty space itself. If you look close enough, just the act of looking close enough will create the electron-positron pairs. Now this is something you know from quantum field theory. And by the way, when people say quantum field theory, there's not the quantum field theory, there are multiple.
It's more like a framework. So there's five, four, and then there are different. Well, string theory itself can be thought of as a generalization of quantum field theory. So when people say quantum field theory, you should ask them, well, which quantum field theory are you referring to? Now let's talk about quantum gravity. Forget about field theory. When it comes to quantum gravity, there are several conceptual infinities that pop up. So for example,
So firstly, if you're going to be infinitely accurate about let's say where an electron is, you have to measure it an infinite amount of time or prepare something and then measure that an infinite amount of time because there's an error, an uncertainty associated with the measurement. And then another infinity comes in when you're having to store all of those bits somewhere.
And then you also need to make your apparatus size infinitely large because you want to make sure that there's no quantum fluctuations that make an error in one of your bits, as well as, well, decoherence, etc. So there are many antinomies that crop up, which imply that however we're ordinarily viewing our laws or viewing space-time, it must be some approximation. Also, interestingly enough, when it comes to higher energies, it doesn't mean lower distances when it comes to quantum gravity.
Ordinarily we think, well, you just place in plenty of energy to probe a smaller and smaller distance. Well, that's true, except at some point you create a black hole.
That is to say, if you want to measure a small distance, well, you put in more energy. But if you want to measure an even smaller distance, you put in more energy, at some point you just create a black hole, and then the more energy you put in, the larger the radius of the black hole. So at some point, larger energy actually means larger distance.
And then even more fundamental than that, the black hole will start to evaporate and let out Hawking radiation, which is low energy particles, even though what you inputted was high energy particles. So you get a strange intermingling of high and low and the reversal of it from what you'd expect from our ordinary calculations.
Okay, now let's talk about black holes. So how much density is required to create a black hole? Turns out that's an ill-defined question because we need to pick a test mass. Much like with gravity and the coupling constant, it's dependent upon mass, same with black holes. You can get whatever density you like, so let's just choose a mass and then ask a different question.
How small of a region, what is the radius called the Schwarzschild radius? What is the radius that we can take this mass and squeeze it into such that it will produce a black hole? I'm going to call this Schwarzschild radius capital R and first we need to choose a mass, so let's choose a copacetic one, perhaps the Planck mass.
And then think, well, what region of space, how small do we have to squeeze the Planck mass to create a black hole? We'll do this in a variety of ways. Number one, naively, it's simple. The standard physics folklore says what we do is we take a Planck mass and we stuff it into a Planck length and that creates a black hole. Then we wonder, well, what is a Planck length? What's a Planck length but an inverse Planck mass?
So let's say Planck length is inverse Planck mass. We've used this answer many times and we're done. That's the answer in one line. We've derived the Schwarzschild radius of a mass Planck, of a Planck mass. Another way of calculating this, again this is also naive, is to think, okay what does it involve? It involves gravity, so Newton's constant, and it involves some mass. Let's give it a variable name for now, mu. So it involves g and it involves mu, which is a mass.
We then use these quantities to come up with a radius, which is length. Now how do we combine g and mu, so Newton and a mass, to make the units match up? Well, it's as simple as combining it in this manner. Because, recall, this is of units inverse mass squared, and this is of units mass, and so we have an inverse mass in total, and this is an inverse mass unit as well. Keep in mind that there are no alphas here, and the reason is that we're not referencing electric charge at all.
Now we know that g is mass Planck squared inverse, and we know that we can set mu, in this case, to be mass Planck, and then we recover the same formula. Let's do another naive calculation. What would the density of such a black hole be? We know that it only involves the Planck mass, and we know the units of density, and so we would imagine that the density would be mass Planck to the fourth, and that's actually correct.
And then for a final way of calculating this, we go to Wikipedia. What is the Schwarzschild radius? And we see that it is R2GM over C squared. Now for us, this 2 drops out because of this symbol here, this on the order of symbol. The C becomes 1, and we then recover GM, which you'll notice is the exact same as this formula that we have here, except we just called it mu, and they called it capital M.
Note one needs to be a bit prudent here because the volume inside a horizon is dependent on the coordinate system and so the densities are also dependent on the observer. If you don't have a lesson on this then it will appear as if this is magic or that it requires years and years of training but it's not either of those two. The popularizers of science have an incentive to mystify these subjects for you unless you're in the universities
However, it's fairly effortless if it's explained by belaboring these technical details and being extremely precise. Now, you may also say, hey, Kurt, well, I could have come up with any first attempt at a formula G to the power of five and M to the power of two and so on and so on.
or square root of so on and so on. And yes, that's correct, which is why it requires a certain amount of physical intuition as well. However, in this case, the dimensional analysis would make all of this trivial because you have to have inverse square mass as the left and the right side dimension anyway. The left hand side of the radius, the Schwarzschild radius, which is a length, has to match with whatever the units are on the right hand side, which severely limits the amount of formulas you can generate.
Also, keep in mind that some of these formulas depend on the fact that we're in fairly low dimensions. We're in, let's say, dim of our manifold is 4. Well, it's 3 plus 1, so that's space. That's when we're calculating the density of a neutron star and we said, hey, what we do is we look to our left, look up, look down, look toward and backward and all we see are neutrons and thus we get GeV to the fourth.
This actually depends on sphere packing because the atoms act like spheres and in higher dimensions this doesn't work because spheres don't act like cubes in higher dimensions they become less and less of the space and thus over here we're drastically overestimating or underestimating our quantity and this by the way is assuming flat space if we're in hyperbolic space well then it becomes even different there's no limit to the amount of spheres that can surround another sphere and the concept of average quote-unquote density becomes
One of the reasons for being over-scrupulous is because
There are enthememes, what are called enthememes, which are unstated data, unstated assumptions that go into an argument. And the reason they're unstated is because they're so simple, they're so familiar. Many people, like even Nima or Connie Hamed, don't go through each of these assumptions. One, it would just take too long. But two is that they're so familiar, they are generally glossed over. But I like to make as much of what's ordinarily below the earth, I'd like to unearth it,
Because then perhaps you won't be as confused as myself when I was learning these subjects. If you'd like to learn a little bit more about enthememes, some example of them in physics, then you can check out this clip with Luis Elizondo, linked in the description. Okay, so that was a quick detour into quantum gravity. If you want to learn more, like I mentioned, there's an extremely detailed episode on quantum gravity with Salvatore Pius, and that's linked in the description. Now we should get on to the sponsor message. Just so you know, anytime there's a sponsor message on the Toe channel, there's usually a
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You should also know that it's the patrons as well that allow this to happen. I was supposed to spend about
Two hours on a video like this. It's been almost two weeks at this point because of different errors and so on But I'm able to do this because of the patrons So if you want to support content like this, then please do consider going to patreon.com slash Kurt Jaimungal My wife is also extremely thankful too as now she's full-time with me responding to the community and helping me plan the direction of tow and she's Extremely extremely grateful every time we get a new patron. She's like, oh my gosh, that's so sweet. Oh
So both my wife and myself, thank you so much. Okay, let's get back to these NCs, these napkin calculations, with one about the length of an atom, the radius of an atom. We'll start to move quick from this point. Let's determine the Bohr radius. We have a model here with the electron on the outside and then the proton in the center. So how do we determine the radius of an atom? Let's call that rA.
Firstly, what do we know? The energy has a contribution that looks like this. This is what we've derived earlier. And we have another contribution, which comes from a kinetic term. And this we can use equation number two, the bolded number two, to change this P square into an R square.
Which mass is this? This is the mass of an electron and for our purposes we can get rid of these factors here and just say well what minimizes this? The graph of this looks like this and then there's a minimum point and then it starts to look like 1 over r in the long run yes it looks like 1 over r and then in the short run it looks like this guy over here
We want to know what is the minimum point right here. You can differentiate this to get the answer or you can guess and then you get that. The star equation implies. This is the Bohr radius and we were able to derive that and maybe two or three lines with napkin calculations. We can go back over here where I should have said this was the radius of an atom.
And now we get that from equation number star. And by the way, because this is the average speed of the electron of the atom, this is the reason why Schrodinger's equation works because Schrodinger's equation is non relativistic. And you can see that just from the factor alpha, which means Schrodinger got lucky.
Let's skip forward because we're going to need this for our next napkin calculation. I realized that the size of the earth comes first. How would we go about calculating the size of the earth? Well, that occurs when the gravitational pressure is counterbalanced by the atomic pressure. So this is unlike the neutron star, it requires a bit more work. So what is the gravitational pressure? Let's call it capital P and it's going to be some energy over some volume. What energy? Well, the gravitational energy, some M. We don't know what M yet. We'll figure this out.
over r, and then over some volume, so r cubed. However, recall that g, g newton, so the gravitational constant, is the Planck mass squared, inverse. And also, let's make a density. So a density is what? It's some mass over some volume, which is, let's say, mass over r cubed. Then these two combine to help make this and
That is from one and two, which go into this. Now we would like to know what the atomic pressure is. So this atomic pressure, which I should denote these differently, let's say the pressure due to gravity and the pressure due to the atoms, this atomic pressure is going to be, again, some energy over some volume. So what is the energy? Well, it's going to be the energy associated with the atom, which we have over here. So let's call this EA. EA, and this is going to be over RA to the third.
After substituting, we get... Then we want to know, well, what is this density here, this row? This row is going to be some mass over some volume, because that's what a density is. And what mass? Well, a proton mass over what volume? Making in substitutions, we get one over the Planck mass. This is different. I should have used different notation, but this is the proton mass. This is the Planck mass.
squared alpha sixth m proton squared of the electron and then r squared and this implies that the radius of the earth
This implies that the radius of the Earth is this. So this is in general for rocky planets. Now this means that alpha factors in, the mass of the electron, the Planck mass, well g factors in, the mass of the proton, all of this comes into play to derive the size of the Earth or the size of rocky planets in general like Mars and Venus and so on. This is what's extremely powerful about this napkin calculation technique and natural units, etc. This was perhaps six or seven lines of derivation that you do in a closet to figure out the radius of the Earth.
By the way, for fun, if you want to calculate what is the weight of the world, you can do so in a second. So we have some guy here, and he is some angry fellow, so let's make him angry. And let's just make the rest of his body a stick figure. And he's holding the world.
Well, what is the weight of the world? The weight of the world, not the mass of the world. Well, you can get the mass from this, but the weight of the world is actually zero. So when you hear that, and the reason is because it's all pointing toward the center, you're experiencing the weight of the world. Actually, the weight of the world, if you want to be Atlas, you just do a handstand.
Because the weight of the world is, well, it's technically zero because it's pointing from every single direction. Zero. Now, the reason why I say technically zero is because then you may say, well, okay, let's imagine that we're here on Earth. So we want the gravitational force of the Earth to hold up another gravitational force. Well, let's say you place some mass here. Yes, it's heavy. Let's say you increase it, you increase it, you increase it to the size of another Earth. Then actually the weight is zero because you're in the in between points of the same masses. So in some sense, the weight of the world is fairly manageable.
Alright, now let's get to cutting a solid. Now, by the way, I left out some factors here, which I've corrected here, and the reason it's written in this manner is because you can then relate the size of the Earth to the size of an atom, and the fact that gravity is quote-unquote weak is what plays into the largeness of a planet, or the smallness of a planet. As for cutting a solid, what we want is just this equation. All we have to do
is exceed the atomic pressure. All we have to do is just place what is greater than this equation. There we go. Extremely, extremely simple. Notice this. This is the most important aspect of this video is that there's a perspective shift. You can now carry this around with you and do napkin calculations, NCs. You can even leave them in the comments and derive what ordinarily you would think you would need
nuclear physics or special relativity by the way about special relativity many people talk about time dilation and so on but to me what's most interesting about special relativity is that it messes with what you think existence is it places you in an unhinged manner so let's take a look over here if there's some event that occurs outside your light cone then what's considered simultaneous
is a dubious concept. The reason being that if you were to say, for example, the corner store, the store on your corner doesn't exist anymore, well, why are you saying that? It's because now it is no longer there. It is now bought by someone else or it is now demolished. Well, there exists another perspective where it does exist. This is explored in the Carlo Rovelli interview, and this is because the notion of simultaneity is placed on an unassured grounding.
Let's get to a laconic derivation of the Casimir falloff. So all you need to know about it is what you've heard from popular science, which is that it's a demonstration of the vacuum fluctuations because there are certain modes that are allowed and not allowed in between the plates. There are more outside than inside, and thus they come together.
You know that it's a pressure, and we have that it falls off as some r to the n. What is the n? What could it be but pressure? So it's r to the 4th. There we go. We get that the Casimir pressure falls off, and it's a minus because it's an attractive force, as 1 over r to the 4. Ordinarily, this is an extremely tedious calculation. We can go to Wikipedia right now just to check.
you can see from Wikipedia that it requires quantum field theory and you go through plenty and plenty of rigmarole just to arrive at this which is the a to the fourth minus that we're referring to these factors are what we firstly these are set to one this is what we didn't derive but you were able to get an estimate now you may wonder why is it that we go through so much pedantic palaver just to arrive at a small correction when we could have done this in one laconic line the reason is that sometimes often you want to be precise for example you don't want a surgeon that
Approximately operates on you. Thus, in mathematics, one goes through great pains to make explicit each axiom and line of reasoning. Now, there are other reasons for being axiomatic and specific. For example, you may wonder why does it take 100 pages to arrive at 1 plus 1 equals 2. So there are a couple of reasons. So one of the reasons is that
we don't derive that one plus one equals two we validate the axiomatic system by seeing one plus one equals two as a valid target and knowing we need to hit it seeing we hit it validates the axiomatic system that produced it number two is because now that we have axioms
and then we saw that something is constructed in this manner because we've set it to be then that means that we can set it differently we could have constructed it differently so for example setting the curvature to zero gives euclidean geometry and then we wonder well what happens if we don't set it to zero then we get more general spaces like non-euclidean geometry which as you know has a crucial role to play in general relativity all right now let's get to analyzing the Sun this one is a simple one we firstly go to
our friend Google and we search for the sunlight spectrum and we see it looks something like this we see okay this peaks approximately at let's say 500 so it's 500 nanometers is the wavelength we then go to our conversion charts and we see okay we can use equation number three and we're going to use equation number three and we're going to use this and we're going to use this
to get a temperature this gives a temperature on the order of 5,000 or so, well let's say on the order of it's about 5,000 Kelvin if you want to work it out specifically or you can simply say it's on the order of so and so and we can search what is the temperature of the sun and we see that it's approximately correct
By the way, it's from this fact that you can look at LEDs that come from your lights or your cell phone screen and determine what temperature it would have if it were a blackbody radiator and note that your cell phone isn't thousands of degrees hot
Thus allowing you to infer just from a napkin calculation that LEDs that characterize your phone screen don't produce light as blackbody radiators in the same way that, for example, incandescents do. Now let's intuit the radius of the electron. As you know, the radius of the electron is, well, it's a point particle. However, let's think about it classically. So here's how Lorenz and others thought about it classically. We have this electron here. Let's call it E.
and it's emitting some electric field here. What we want is that the energy of the electron, so alpha over Re, which we have before, so the energy of the electron, we don't want that to be much greater than mc squared of the electron. So in our units, mc squared is just m, which implies that Re is simply this.
And there we go. We have a classical derivation of the radius of the electron. It turns out that, and by the way, Lawrence and others thought that, okay, the classical laws have to break down somewhat here. Something strange has to occur at that radius. And they were trying to analyze it and they didn't get the right answers. And that's because quantum mechanics comes in and they had no idea about quantum mechanics, which says actually around the electron is positron-electron pairs and so on.
And so it's cloudy, and the radius of this, if we go in here, the radius of one of these, what is it? What do you think it may be? Well, it's an electron-positron pair, so it's this much. Well, it's two of that, but it doesn't matter. The point is that the law started breaking down at a distance 137 times greater than where they thought it would have broken down.
If we extrapolate this line of reasoning to our current models, that is the standard model in general relativity, while they suggest that there's some breakdown that occurs at the Planck scale, my money would be that new laws would be required far before we get to the Planck scale. Maybe not 130 times before the Planck scale, but many, many more orders of magnitude prior to that energy.
Alright, now we're on to solids and x-rays. If we want to find out the number density, that is the number of atoms in a solid per unit volume, what does it look like? Well, number density. Firstly, let's think about the units. It's GeV to some n. What is n? Is it minus 3? It's plus 3. And what information do we have? We have the radius of the atom, and so it's that cubed, and we can use this equation from before.
alpha times the mass of the electron is the radius which means we have which is KeV to the third and this is one of the reasons why it's much better to work with GeVs and so on because this gives you an actual tangible amount you understand what a KeV is and by the way KeV what is its relationship to light that is to say if we're on the order of a length that is let's say just one KeV
Then we'll need to shine a light whose wavelength is at least 1 keV in order to resolve this distance. I'll explain exactly what that means to resolve it. And then you can wonder, well, what is 1 keV of light? You can look that up online. Let's do that right now. So you can see from this napkin calculation that an x-ray is what allows you to probe solids.
That's why we use x-rays, because their wavelength is just short enough to resolve the distance of the atoms within a solid. And when we talk about a certain wavelength as what's needed to resolve a certain distance, that was never explained, at least not to me, properly. I always heard of it in terms of balls. You take some large ball and you try and throw it and you try and resolve. You need smaller and smaller balls in order to get higher resolution. But I think a better way of understanding this, understanding why we need x-rays or whatever UV rays, whatever the light is,
to resolve a certain distance. I think it's better explained like this. If we zoom in here, so let's zoom in. This is, let's see, how many pixels wide? Maybe this is one, two, three. Maybe this is on the order of 50. Who knows? But then if I say, let's pixelate this, let's put it in a mosaic.
See, if we make the cell size, the cell size, by the way, is equivalent to a wavelength. So we want the wavelength small in order to resolve shorter and shorter distances. If we make the cell size
fairly large like 200 then we can just make out that there exists some substructure here we cannot make out that there was any structure above and as soon as we start reducing it we're resolving with higher and higher frequencies you can think of it like that so if this is let's say on the order of a cell and then we want to get to the order of an atom well we need to shoot smaller and smaller wavelengths of light this corresponds to the wavelength and all the sudden now you can resolve that distance
I'm placing that as an aside here because the way that it's ordinarily explained is a bit confusing. By the way, based on this number density, you can now get a actual density. So what do you do is you times it by the proton mass, because the proton slash the neutron are what hold the most, well, the largest contribution to the mass. And then you get the density of solids.
Okay, now we're on the last one, the scales of the universe, in particular the Higgs boson, which is extremely easy now that we've gone through
plenty of these exercises and you're so familiar with natural units and GEVs and so on. What is the scale that you should find the Higgs boson? How far should you zoom in to find it? Well firstly let's go on Google and we see look they give you the mass in terms of GEV. Now this C we set to 1 so this GEV it's 125 GEV 125 GEV Higgs boson
From the above conversion chart or we can go to a website and see what does that correspond to in terms of length. Now you can see how far do you have to zoom in in order for you to find the Higgs boson. You can convert that or you can use another chart. They're all approximately the same. Remember, we only care about the order. We can also type in, well, what is the LHC?
What is the highest energy of the particles that have been collided? It's 13 TeV. We covered this earlier. That tells you something concrete about how small the distances are. Now these numbers are no longer foreign to you. You're extremely familiar with manipulating them. You can get a handle on them.
By the way, another reason why they're afraid that black holes could be created, I didn't mention this in the extra dimensions part, but it's because if gravity is leaking in to some other dimension, then that means that gravity is in fact stronger than we think somewhere else. So it's weaker here, but it's stronger somewhere else. And so what we think of what would ordinarily create a black hole, the conditions may be much smaller because gravity is much stronger than we think. Though luckily the Earth hasn't been enveloped by a black hole, at least not yet.
Okay, great. You should congratulate yourself because in about two hours or an hour and a half, however long this video is, you've now covered quite a significant amount of work. We've gone through Newton's constant and seeing that it's actually mass dependent or energy is proportional to the mass to the inverse square of a mass and pressure and speed is dimensionless.
The pressure in a neutron star, the proportionate strength of forces, knots and extra dimensions, calculating the Schwinger limit, just getting a handle on it, the size of the Earth, analyzing the Sun, the Casimir effect, how it falls off, a vacuum expectation energy, the length of an atom, microtubules, the Higgs boson, the God particle. You even learned about deriving the Schwarzschild radius and black holes. And by the way, for fun, these acrostically spell out napkin calculations.
All of this becomes virtually child's play once you use natural units and then some physical intuition. Alright, now continue watching for the next couple of minutes because this will help you contextualize what came before and so it will stick more readily. Recall, unlike giving viewer exercises, which is par for the course in most courses and lectures and so on,
People almost never do exercises, including myself, and I'm extremely motivated to do so. The most nourishing approach is to provide a point of view shift. And that's what you now have. There are a variety of phenomenon that you can now do an NC to so a napkin calculation. And if you find a particularly inventive one, then share it in the comment section, but delineate each step.
Don't skip when explaining to people. Now, as you go through life and you want to develop a bit more of a physical intuition, then constantly think about what you're seeing and the numbers that you're hearing and the lengths and the times and the quantities, etc. in terms of GEV. And also think about how you can derive them from these somewhat fundamental principles. A last note on learning. Every time that you hear someone describe some object in a different way,
So for example, you may hear me refer to fields in some other video as a group twice over. And what's meant by that? What do I mean by that? It's that you have these field axioms. So commutative, associative, neutral elements, so on, so on, so on. And it's two of them. Whereas one of these is like a group, a commutative group. And so it's somewhat like a twice over group. This is false because there's an interplay between these. Like you need to exclude the neutral element here for the multiplicative inverse and so on.
However, the point is that when you hear someone explain something that you think you know, but explained in a different way, it's useful to write that down in some reference document, and then eventually go back and think, how are all these disparate lessons or views the same? Another one may be, how are all the exponentials, the definitions of exponentials, the same? So we know that an exponential map goes from TEG, so the Lie algebra, to the group itself.
Well, how is that related to what we know as e to the e squared, for example, equals so and so on as a number? By the way, almost no one will do this exercise. That is, you write down the disparate lessons and teachings and then you try to relate them. There's about n choose two of them. So how is this related to that? How is this related to that? How is this related to that? How is this related to that? And so on. Almost no one will do that because it's extremely tedious, which means if you do this, then you'll garner far more insight than your peers. Maybe that
That competitive edge will tickle your rivalrous nature. If it does, then you can use it as motivation. And for myself, I may be doing a video at some point. I'm not don't hold me to this on how the various definitions of entropy are all related. So there's Shannon, there's thermal, there's neg entropy, there's residual entropy, and so on and so on.
As I mentioned before, this video will be akin to an introduction to another video that I plan on releasing at some point. Now this one has taken way, way, way too long. So perhaps I thought I was going to do it in a few months. This going through a theoretical physics paper you don't currently understand. I was
Going to go through geometric unity. Perhaps I won't do that in a few months. Perhaps it will be the winter time now because this is way, way, way more difficult than I thought it would be. Regardless, you can expect that at some point. So the question is, is this leading anywhere? This lecture is series and I don't plan on releasing more content like this as this is not my forte. I'm interested in what I call explicating the landscape of theories of everything, which means to intensely investigate each toe. Geometric unity Wolframs. So there's a thumbnail here you can click on or in the description.
Thomas Campbell's, there's theories on consciousness. There's Veltan Shaung's like Ian McGilchrist and John Vervecky I mentioned before. There's interpretations of quantum theory like Carlo Rovelli and Nicholas Gisson. There's even how to go about learning mathematics with Norman Wildberger and Richard Borchardt. I highly recommend both of their YouTube channels by the way. Norman in particular is great at making whatever is complex seems so elementary that it's criminally humiliating.
Now most people have a subscriber request, but I have a request for you to not subscribe unless you are interested in podcasts about the above, as this channel's bread and butter are those podcasts. You will be sorely disappointed if you expect more videos like this, so check out some of the other podcasts on this channel. Here's a playlist for you to get started. Also it's linked in the description.
Again, if you have an interesting NC about some napkin calculation, about some observable that ordinarily is a tedious calculation that you can arrive at simply from this new natural unit point of view, then make sure to leave it in the comments and make it clear what each step is. Don't skip any steps. I'll also place a thread in the subreddit reddit.com slash r slash theories of everything and I'll try to comment on the most interesting ones.
If you want to share or get feedback on your NC or on your theory of everything, let's imagine you have one, then or some ideas to one, then go to the Discord. That's also linked in the subreddit below. Again, like I mentioned, there's no one source on this. It's strewn generally across several lectures and you start to intuit it as a physics student. However, videos that served as inspiration to this one are that of Nima Arkani Hamed, Andrew Dotson,
Pretty much physics and Sabine Hassenfelder. I recommend you check out all of those channels. The links to their work are in the description. Thank you and take care.
The podcast is now finished. If you'd like to support conversations like this, then do consider going to patreon.com slash C-U-R-T-J-A-I-M-U-N-G-A-L. That is Kurt Jaimungal. It's support from the patrons and from the sponsors that allow me to do this full time. Every dollar helps tremendously. Thank you.
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"text": " 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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"text": " This is Martian Beast Mode Lynch. Prize pick is making sports season even more fun. On prize picks, whether you're a football fan, a basketball fan, you'll always feel good to be ranked. Right now, new users get $50 instantly in lineups when you play your first $5. The app is simple to use. Pick two or more players. Pick more or less on their stat projections. Anything from touchdown to threes. And if you're right, you can win big. Mix and match players from"
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"text": " You may want to watch this on YouTube, the link's in the description, as I'm referencing plenty of images and formulae. However, there are enough digressions here, at a high level, to make listening an additive exercise. If you want more information, there are links in the description to videos that have heavily inspired this one, including Andrew Dotson, PrettyMuchPhysics, Nima Arkani Hamid's talk, and Sabine Haassenfelder's wonderful and short video on natural units. I highly recommend each of those channels, slash people, if you're serious about physics."
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"text": " Okay, this video will outline how and why to use natural units to determine a numerical value, place a numerical value to almost any physical observable that's macroscopic that you would like. In my opinion, this should be taught first in physics, but for whatever reason, there's no single lesson, there's no single chapter in a book, there's no single lecture in a lecture series on this. Instead, it's strewn across several and you start to intuit it. You start to understand it implicitly as a physics student."
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"text": " rather than it being made explicit which it is being made explicit here and that's because it can serve you in the beginning of your understanding of physics and even in the middle of your misunderstanding of physics which is where we all are generally this video is meant to change the way that you view physics and even the world and that's the point the point of view shift this perspective shift is the point of this video while it's outwardly about calculations it's truly about"
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"text": " Developing a different stance on nature. For those of you who are unfamiliar with me, my name is Kurt Jaimungal. I'm a filmmaker with a background in mathematical physics, and I run this channel called theories of everything, which is a podcast. It's a podcast first and foremost. So don't subscribe to this if you're not interested in the rest of the content."
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"text": " And the rest of the content is about making comprehensible the different toes that exist, the different theories of everything. So for example, Wolfram's theory of everything or geometric unity that's coming up or quantum gravity. Well, that's the seedlings of a toe."
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"text": " string theory etc etc we even cover the more larger philosophical ones because i'm interested in consciousness what role does that have to play with physics or can it be derived from physics what about free will what about god so you can think of this is largely what is reality."
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"text": " Okay, let's contextualize the rest of this video, because much of the misapprehension in learning comes generally from not understanding the context of what's being presented, or worse, the context isn't given to you at all. There are timestamps here in every one of the Toll videos, and they're meticulously written, so you can skip around if you like. By the end of this, you'll be able to calculate virtually any phenomenon, as well as have some understanding of it, specifically by the end of the next, let's say, 60 minutes, with just high school mathematics,"
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"text": " You'll be able to answer the following without memorization, in fact, with derivation, which is superior. Why is there only time? So why is it that only time exists? I could have said only energy exists, or I could have said only seconds, or only length exists. I just didn't want to come out of the gate sounding like a Buddhist by saying, hey, all that exists is energy. But you can equally replace that there. What is the vacuum energy expectation? I'm sure you've heard that this is the worst prediction in physics, et cetera."
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"text": " What are the bounds on extra dimensions? Why saying gravity is weak is worse than a false statement. It's meaningless statement. That deserves a bolded exclamation point. Great. The neutron star pressure. What is the pressure inside a neutron star? By the end of this video, you'll be able to answer that in almost a second."
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"text": " Microtubules for consciousness. We'll delve a little bit into that. That's Penrose's theory. Why was magnetism understood so late? That's a historical fact, but you can actually derive it from fundamental principles. We'll explain what that means. What is the size of the Earth? Yes, you can derive the size of the Earth approximately. Napkin calculations."
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"text": " Chasmier pressure. I'm sure you've heard that, hey, if you take some plates and then there's some mode that goes in between, there are more modes outside and so the plates come together in a vacuum. We'll also be covering knots and quantum gravity, at least the modicum. We'll also cover the Schwinger limit and Salvatore Pius' super force, or the Planck force. We'll also talk about black holes. Now, all of these facts look like they belong under the umbrella of physics, except perhaps maybe the consciousness one."
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"text": " Penrose disagrees, but all of them belong to physics and disparate fields. And you would need to apply completely different frameworks to properly understand them. That's true. If you want to make a precise calculation, then yes. But if what you want is an estimate, a napkin calculation, then you don't need this. You can use natural units. Now, this video is akin to an introduction to the next video, which is coming out perhaps a few months from now. I don't plan on doing these lecture type videos. Like I mentioned, this is a podcast channel. I don't plan on doing these much."
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"text": " The next video will be about how to analyze and comprehend a physics paper theoretical physics paper that lies at least currently far beyond your current level of understanding. So I'll be going through geometric unity and giving tips on learning physics and mathematics in general. Now let's get on to the approach of this video. So number one, what's different about this? Number one is that there will be"
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"text": " quite a few digressions because it will be about how to think that is how to think about physics problems in general rather than how to just solve certain ones with natural units number two this is great for theory yes but and it's also great because it's practical"
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"text": " The reason is that whenever you're dealing with numbers, whenever you're dealing with units, it's akin to a choice of a basis. In the theoretical end, you should try to construct whatever you're doing without reference to a choice of basis. Much of your existence in physics so far has taken place with"
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"text": " an implicit choice of a basis when you're talking about some transpiration let's say you say it's well it's three meters to the left and two meters up but then the question is well three meters to the left from where two meters up from where and then also what is up what is left what are those directions per se now the real world"
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"text": " In theoretical physics, there's a saying that there's nothing noble in choosing a basis. True nobility."
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"text": " is being coordinate free. Number three, it will be important for us to be precise. So the reason is that otherwise you'll be confused and you won't realize where your confusion lies. Much of the time when you're a student and you're going to a professor or a lecturer or your tutor and they say well what is it that you don't understand? Sometimes you don't know where your misunderstanding is and so it's difficult to learn a subject and much of the time that comes from the subject not being explained specifically to you."
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"text": " Throughout this video, I'll be throwing out tidbits, perhaps different pieces of terminology that you don't understand. That's okay. It's for those who want to learn."
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"text": " slightly more, and I'll also be going through the specific steps. I won't skip a step as often as I can, and that's because I don't want you to be as confused as myself when I was learning much of this. Often steps are glossed over because the presenter is so familiar with them that they've forgotten what it's like to not understand a subject. So for me, when it's delineated specifically, you go from here to A to B to C, rather than from B to D, let's say. Then because the logical progression is made painstakingly clear, you understand it better."
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"text": " for example we will not be using this symbol what the heck is this what the heck is this now that deserves a bolded exclamation point the reason is that well is zero approximately one"
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"text": " is one approximately 10 ask the person who's teaching you please define this guy specifically what the heck is that this is not a mathematically well-defined symbol this quote-unquote approximately symbol so instead what we'll use is this"
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"text": " which means on the order of so 10 is on the order of 90 they have the same amount of digits 102 is on the same order of 999 for example in the interest of being precise technically this video should be titled how to approximately solve every physics question regarding observables but that's unwieldy and doesn't fit the title character count number four is will be as chewing exercises in favor of a point of view shift"
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"text": " Generally when I watch videos online, they're generally given by lecturers to university students, and then they say, okay, we'll leave this as an exercise to you. If you want to learn more, do this as an exercise. However, even highly, highly motivated people don't do those exercises."
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"text": " generally you're trying to get an overview and the lecturer is used to assigning problems to students so they think that the viewer is going to actually do them but they don't and it's tedious and so it's more nursing is to instead provide a point-of-view shift so that when you're going about your life you can convert all these measurements that you see to energy for example rather than assigning exercises which almost no one does anyway so as chewing exercises"
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"text": " in favor of point-of-view shit. Firstly, it's easier to get this shift of perspective, and number two, it's more enjoyable, it's fun. Number three, it's more practical. The fifth point is that it will be extremely lean, and what I mean by that is that there will be little fat, there will be little that's extraneous. This is meant to be a video that you can watch, you can re-watch, not only when you've forgotten about natural units and you want to get some understanding, get some handle on how to calculate with them, do napkin calculations, but also"
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"text": " When you've lost some motivation to learn mathematics or physics, there will be myriad points throughout about how to think about mathematics and physics in terms of a general approach to learning. Like I mentioned before, this latter point will be expanded upon in some video that I'll release in a few months about going through a physics paper that you currently don't understand, some theoretical physics one, and I believe I'll be doing geometric unity. Number six, now this one's more for you. If you don't understand"
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"text": " a part of this video that's fine keep pushing this comes from Wheeler the point is not to drink from the fire hose that's what we think we're supposed to do but instead you're simply supposed to get wet"
},
{
"end_time": 769.906,
"index": 34,
"start_time": 745.845,
"text": " Same with watching the podcasts on this channel. Sometimes they're extremely technical. People say, well, I can't understand so-and-so. That's fine. Just keep watching. The first pass is generally to just know where are you going so that you can contextualize the understanding that comes earlier. Much of the time we're told, look, physics and mathematics, you build upon it and you have to know the foundations, otherwise the top will be shaky. And that's true, but it's"
},
{
"end_time": 791.715,
"index": 35,
"start_time": 770.998,
"text": " It's often useful to keep going even when you don't understand simply so that you can know where are you going because your misapprehension about the fundamental steps come from not being able to contextualize it. So it's fine. Keep going. Don't feel like I can't drink quote unquote from the firehose. The point is simply get soaked and trust that the learning will occur."
},
{
"end_time": 815.606,
"index": 36,
"start_time": 792.278,
"text": " Alright, let's get into this. What are natural units? In order to understand what natural units are, we want to know what are units. So for example, what is a meter? Or if you're being Canadian, a meter. I'm based in Toronto, if that wasn't clear already. What is a second? What is a pound?"
},
{
"end_time": 840.879,
"index": 37,
"start_time": 818.012,
"text": " Now you'll get fairly frenzied if you think about this for quite some time as I have. That is metaphysically, what the heck is a second? What is a meter? What is length? Science actually doesn't answer what is questions. And this is something that's not taught to you. Science isn't materialistic. Science isn't immaterialistic. It's operational. And this is a point that"
},
{
"end_time": 868.439,
"index": 38,
"start_time": 841.527,
"text": " Many people don't seem to understand, including scientists. Science is metaphysically agnostic, meaning that it doesn't actually make a claim onto ontology. It doesn't tell you what is. Instead, science gives operational meanings. So what is a second? It's something like 9, 192, I don't know those three, 770. It's one of those numbers you memorize as a child to show how clever you are. Let's look it up on Wikipedia. So let's do this. Wikipedia second."
},
{
"end_time": 894.121,
"index": 39,
"start_time": 869.582,
"text": " It says here, the second is equal to the duration of 9192631, that's what I forgot, 631770 periods of the radiation corresponding to the transition between hyperfine levels of the unperturbed ground state of a cesium atom, a certain isotope of a cesium atom. Okay, so then the natural question that comes up is why this number? So why this and not some other number?"
},
{
"end_time": 918.131,
"index": 40,
"start_time": 894.599,
"text": " And the reason is because in London many decades ago, someone in some back alley took methamphetamine on a Tuesday night and came up with that number. Now, I'm not kidding. It may as well be that to someone studying high-energy physics in the same way that, well, what the heck is a kilogram? What is a kilogram? It means you go to Paris, you go outside Paris actually, it's on the borders of Paris, you go to some vault,"
},
{
"end_time": 949.206,
"index": 41,
"start_time": 920.862,
"text": " and you deal with people being condescending to you because you don't speak English. Then you duplicate this little metal slab that's in Paris. You duplicate it 67 times so that you have 68 of them in total. I'm just being quick with my writing. 68 of them is in total. Then you measure yourself on a scale and these two numbers will coincide. That's what it means. It's an operational definition. Now, physicists like to use units that appear in nature. So units that appear"
},
{
"end_time": 976.988,
"index": 42,
"start_time": 949.906,
"text": " and those we call natural units. Now there is some, at least with me, there's some controversy with what's considered natural because when someone comes to you with some dish and they say this is a natural dish and that's unnatural, well what do you mean that those Doritos are unnatural? Did they come from outside this universe from some void? Because isn't everything in this universe natural? Aren't we a product of nature and so what we create is natural?"
},
{
"end_time": 1006.305,
"index": 43,
"start_time": 977.449,
"text": " Okay, what a physicist means by natural is that it's invariant across the universe, as far as we can tell. To be extremely precise, what we mean when we say natural units, natural in the natural units, is natural with respect to our current understanding in order to make certain equations simpler and remove arbitrary human qualities. Why do I say arbitrary human qualities and not just human qualities? Well, in some sense, even an electron is a human construct in the sense that it's there because it"
},
{
"end_time": 1034.019,
"index": 44,
"start_time": 1006.971,
"text": " Nature doesn't parse itself out into these elements. I mean, you can say elementary. Elementary seems to be an objective quality because of the way that we define what an elementary particle is. It's an irreducible representation of something. So the fact that it's irreducible means if it could be reduced in this block matrix form, then we can just decompose it and we'd say those elements are elementary. But the reason why we set aside some special canonical place for the electron is because it's useful for us. It makes"
},
{
"end_time": 1059.667,
"index": 45,
"start_time": 1034.514,
"text": " are models easier to understand, simpler outcomes, razor, etc. There's plenty of philosophy that undergirds natural. Again, this is not usually explained and you'll be led astray if you don't understand that point. Now here's another point that's ordinarily not explained. Observables have no units. They're dimensionless."
},
{
"end_time": 1087.961,
"index": 46,
"start_time": 1063.524,
"text": " Okay, now what's meant by that? Again, when you say that you weigh 68 kilograms, it means you take 68 of some other reference quantity, some other reference object, and then you stack 68 of them and then you get yourself. It's actually 68. It's not 68 kilograms per se. You can also think of this in another way. If you wanted to speak to aliens, which by the way is another"
},
{
"end_time": 1112.517,
"index": 47,
"start_time": 1088.336,
"text": " Topic on this channel not speaking to aliens per se but UFOs then it would be foolish to say I weigh 68 of some product from France now you can reverse this and imagine an alien is speaking to you and you say well how much does your craft weigh and they say oh it weighs four gar bars and then you're like what the heck is a gar bar then they say well that's how much liquid we release from our borbons every two farkles"
},
{
"end_time": 1138.985,
"index": 48,
"start_time": 1112.841,
"text": " it doesn't provide much information so instead we do what you see colloquially which is c equals h bar equals one okay let's get to some myths about natural units before exploring exactly what that means so firstly one of the myths is that we just simply set c to equal one to equal h bar this is a meaningless statement as it's written and the reason is it doesn't they can't equal one it means we're now using"
},
{
"end_time": 1169.531,
"index": 49,
"start_time": 1139.753,
"text": " the speed of light and h bar as a reference for some other quantity that we're trying to develop. If you're confused about this now, then that means you're thinking about this correctly because it's not ordinarily explained. It's left ambiguous. Let's look at this. Let's imagine what is the speed of, let's say, some car on the highway. So the speed of a car on a highway equals, we would say, 100 kilometers per hour. These are the units."
},
{
"end_time": 1192.381,
"index": 50,
"start_time": 1170.213,
"text": " And that's the magnitude with respect to those units. So if I wanted to say, what is the speed? Sorry, that's already speed. What is the speed of light? What we mean is 2, 9, 9, 7, 9, 2, 4, 5, 8. Again, it's one of those numbers you try to show how clever you are when you're a child by memorizing meters per second."
},
{
"end_time": 1216.852,
"index": 51,
"start_time": 1193.882,
"text": " Now look, this is actually what C is. C refers to all of this. C doesn't just refer to the magnitude. C refers to the entirety of it, including the units. So when someone says C equals 1, what they actually mean is that we are now using units where we've taken that 2, 9, 9, 7, 9, 2, 4, 5,"
},
{
"end_time": 1228.114,
"index": 52,
"start_time": 1216.852,
"text": " 8 meters per second and we've placed it in here so we've taken this guy and we've placed it in here see all of this is not ordinarily explained and it's because"
},
{
"end_time": 1254.838,
"index": 53,
"start_time": 1229.087,
"text": " As an undergraduate, you're especially used to writing with reference to a coordinate basis, which is why I said try to do everything you can coordinate free. If you have an instructor, you're lucky enough to have an instructor, you always ask, how can you represent these equations coordinate free? Another way of thinking about this is that we have graphs in physics and math constantly plot, and those etchings are akin to choosing a unit. The fact that we put lines with etchings"
},
{
"end_time": 1279.48,
"index": 54,
"start_time": 1254.838,
"text": " means we've chosen a coordinate so these etchings outward are it implicitly a choice of coordinates but nature but if you look again like I mentioned there's no detector that can detect the coordinates much like if you take a picture with your phone and you then look at it on the screen and you zoom in you see pixels the pixels are an artifact of you taking a picture and trying to manipulate it in some manner the world itself is not pixelated unless you're"
},
{
"end_time": 1304.497,
"index": 55,
"start_time": 1279.889,
"text": " to believe Thomas Campbell or Donald Hoffman. Another reason to think coordinate free is you'll start to construct constructions that actually depend on your coordinates when they in fact don't in nature and then you'll wonder why are you getting an incorrect answer. So for example in physics and so on we often use let's say this and then we represent it in some symmetry. This is how theoretical physicists generally reference matrices."
},
{
"end_time": 1331.459,
"index": 56,
"start_time": 1304.753,
"text": " they don't like them so they call them cemeteries these rows and columns but then you also would reference this same object with numbers in a similar manner however they transform completely differently so one is an endomorphism and then the other is a two-form or a bilinear form and they transform completely differently and which is why you have transpose which is it's not ill-defined object but it's a strangely defined object the inverse of a matrix is more"
},
{
"end_time": 1344.991,
"index": 57,
"start_time": 1331.971,
"text": " Copacetic, but the transpose is a strange one. So this one is a two-form, a bilinear form. The metric in the Einstein equations is a two-form, is a bilinear form."
},
{
"end_time": 1372.039,
"index": 58,
"start_time": 1345.333,
"text": " And also the determinants of endomorphism is a completely different object, it's invariant, compared to the determinants of a two-form or a bilinear form. And then as you start to understand this coordinate-free, you'll realize that there's a special place in hell for the person who developed the transpose. It's an unwieldy object. Another one that will confuse you if you think in terms of coordinates is that the wave function, you ordinarily think of the wave function as going from some RD or some subset of RD"
},
{
"end_time": 1381.527,
"index": 59,
"start_time": 1375.094,
"text": " to to the complex numbers but actually this guy is a section"
},
{
"end_time": 1407.585,
"index": 60,
"start_time": 1383.148,
"text": " on a c line bundle and you need to understand bundles in order to understand it coordinate free so that you can do not only polar coordinates and you wonder why the heck does the derivative change well that makes sense when you understand it in terms of a principal bundle and then the associated bundle but also in terms of no longer staying in rd what if you want to move to a curved space for quantum mechanics what if you want to do quantum mechanics on a curved space this is why one should try their best"
},
{
"end_time": 1433.951,
"index": 61,
"start_time": 1407.875,
"text": " to understand what the heck is going on without reference to coordinates and then go to coordinates when you're actually making a calculation. So that's why this is a myth. We just simply set c to equal 1 to equal h-bar. By the way, what is h-bar? Well, that's a bit more abstract. You don't need to understand that for the sake of this video. But this is an ill-defined equation. There's actually a caveat here that will come into play later. Another way of thinking about it is imagine you have one USD, one US dollar."
},
{
"end_time": 1464.445,
"index": 62,
"start_time": 1434.667,
"text": " sometimes you would say it equals 127 yen it doesn't actually equal 127 yen otherwise when you have a US dollar it would just be 127 yen what it means is that there's something called value or some monetary equivalent that's another way of thinking about it conversion what it means that you go here with some mapping let's say M and then here with some mapping that's called let's say M prime what it means is that you do let's say M prime inverse"
},
{
"end_time": 1493.865,
"index": 63,
"start_time": 1464.957,
"text": " We have to make all these constructions now, and then that's after you've already done M. So you've gone from here, and then you go back up there. They're not the same. So another way of thinking about this is imagine you want to change lengths. Instead of using meters, because you think meters are strange for some reason, you want to measure everyone in terms of Lady Gaga. So you have Lady Gaga here, which I'm going to call LG. So then let's say we want to measure someone else. Let's say Goku. So what is Goku?"
},
{
"end_time": 1504.258,
"index": 64,
"start_time": 1494.684,
"text": " equals maybe one and a half Lady Gaga's in length. So you take half of Lady Gaga and you stack that again on Lady Gaga and you get a Goku in terms of length. How about Tony Robbins?"
},
{
"end_time": 1526.732,
"index": 65,
"start_time": 1504.514,
"text": " Well, that's let's say two Lady Gaga's now what we're doing here is we're saying I'm going to make all my future length measurements in terms of Lady Gaga for whatever reason in the same way that generally speaking, the prices on the internet can be made in reference to the US dollar and then you do some conversion to find out its equivalent monetary value in some other currency."
},
{
"end_time": 1544.104,
"index": 66,
"start_time": 1526.732,
"text": " In the same way, what we're doing right here is we're referencing everyone's height in terms of Lady Gaga's height. And it's just as foolish as it would be to say Lady Gaga equals 1 equals the USD. Just as foolish as this equation is, it's tantamount to saying C equals 1 equals h-bar. There's so much that goes into a statement like that."
},
{
"end_time": 1573.814,
"index": 67,
"start_time": 1544.104,
"text": " that's just seeing that gives the impression oh physicists are just setting it equal to one so no this statement is foolish and what's underneath that is saying hey I'm going to now measure everything in terms of the speed of light so I want to measure my car maybe it's a millionth of the speed of light I don't know I can don't want to do the calculation right now but let's say it's a millionth of a speed of light so then I say well the speed of walking let's see is 0.000000005"
},
{
"end_time": 1585.606,
"index": 68,
"start_time": 1574.189,
"text": " I'm making this up of these speed of light units. That's what it means. OK, so this is all including, by the way, this right here. This is all foolish."
},
{
"end_time": 1614.411,
"index": 69,
"start_time": 1587.739,
"text": " You have to understand what's lurking underneath. So in this example, the value is what's being referenced. When I say the real world, that's what I mean, is that there's something else that's tangible that I'm trying to represent my quantity in reference to. So from now on, we're going to no longer say that this is moving at 500 meters per second. We're going to say that this is moving at a fraction of the speed of light. By the way, this should be a definition, and that refers to the entire object there, not just this. This is just the magnitude."
},
{
"end_time": 1642.09,
"index": 70,
"start_time": 1614.411,
"text": " and that's where this is misleading because it's just showing you the magnitude how the heck can see equal this in the same way how the heck can Lady Gaga equal the US equals one that is myth number one now myth number two is that the advantage of natural units by the way doesn't matter whether you capitalize it or not the advantage of natural units is that it makes"
},
{
"end_time": 1662.261,
"index": 71,
"start_time": 1644.224,
"text": " equations simpler. Where is the myth here? The myth is one of these words. It's an article. It's the definite article of the V advantage. That's one should actually be a advantage or an advantage."
},
{
"end_time": 1691.681,
"index": 72,
"start_time": 1662.671,
"text": " The primary advantage is that it allows you to understand the world in a much more elegant manner that allows you to grasp, to understand physical quantities much more intuitively with these napkin calculations. And by the way, I say napkin calculations and not back of the envelope calculations because when you're outside and you're doing one of these, why, where are you going to find an envelope? I don't think I've written on an envelope or the back of one in my entire life. And then, okay, so you take a napkin and you do your calculation on it. What the heck is the front of a napkin versus the back?"
},
{
"end_time": 1716.749,
"index": 73,
"start_time": 1692.056,
"text": " It's not like you choose the front or the back or you can even tell most of the time. So it's a napkin calculation. Now let's think about what did I say over here, which is that it allows you to have only time or only energy, et cetera, et cetera. Well, there's some conversion equations. It's best to think of them in terms of conversion, just like money. These are the central equations that allow you to convert. So let's give them a special symbol, a special kind of one."
},
{
"end_time": 1746.63,
"index": 74,
"start_time": 1717.056,
"text": " Number one is E equals, you can guess this, E equals MC squared. Number two, and then let's also make it special, is XP. Well, now I'm going to use this, which means on the order of, so actually let's get rid of this guy, put him on the order of. There's also the Compton wavelength, which will give another fancy symbol, which is"
},
{
"end_time": 1769.053,
"index": 75,
"start_time": 1747.056,
"text": " Lambda again, I'm going to say on the order of and notice right now, what have we done? We've already set C to equal one. Look, I'm, I'm making the mistake. Notice what have we done already? We're already going to be using units where C of light is expressed in those units as one. So we're only making reference to C of light to speed of light."
},
{
"end_time": 1797.21,
"index": 76,
"start_time": 1770.111,
"text": " That means that right here we can remove that because that equals one. Right here we can change that to one. Right here we can change that to one and then we can get rid of that because it's the same. A zero with order equation is, well, the speed of light equals some spatial amount over this. Now, since we're setting this to equal one, this means that any time that you have a distance we can express it in terms of a speed."
},
{
"end_time": 1806.186,
"index": 77,
"start_time": 1797.654,
"text": " For example, you can let's imagine that's the earth and then we're going to one light year away or one light second, one light second away."
},
{
"end_time": 1839.002,
"index": 78,
"start_time": 1809.599,
"text": " I can either say, hey, that's two, nine, nine, seven, nine, two, four, five, eight meters away, or I can say that's one light second. That means that it's now converting distance into time. Any distance measure that you give me, I can give you an equivalent time measure. It's not the same. It's a conversion, but you can convert it to time. So this allows a conversion of length to time."
},
{
"end_time": 1869.735,
"index": 79,
"start_time": 1840.128,
"text": " and back because you can do the same thing forward or backward and then this one also allows a conversion of energy to mass so I can tell you this is one gram or I can give you its energy equivalent or you can give me some energy and I can tell you well that what makes up that energy is the equivalent of a certain amount of mass now this one is also interesting because it gives a conversion of length to momentum"
},
{
"end_time": 1893.507,
"index": 80,
"start_time": 1872.824,
"text": " I noticed that I didn't explain where this one comes from, and it's the famous Heisenberg uncertainty equation, where you're told that the objects of space and momentum don't commute. However, even this is a misnomer, since it makes no sense to say, quote unquote, objects don't commute. It should be stated precisely that the operations with those objects or operations on those objects don't commute."
},
{
"end_time": 1919.206,
"index": 81,
"start_time": 1893.831,
"text": " How can an object be commutative or not without the extra structure of the group operation? Again, I'm being pedantic because I was extremely confused learning all of this, and you may be as well, and it's best these imprecise statements are made clear. Clearly it's inversed, and then this one gives a conversion of length to mass."
},
{
"end_time": 1940.998,
"index": 82,
"start_time": 1920.213,
"text": " Now how many different types of units do we have here? We have length, one, two, time, three, mass, four, energy, five, momentum, and we have four equations. Which means that we have five unknowns and four equations, which means that we can represent, we only actually have one unknown. So we can represent any of these in terms of any quantity that we like. And thus, we can represent"
},
{
"end_time": 1969.804,
"index": 83,
"start_time": 1941.323,
"text": " All of our quantities, mass, time, length, energy, in terms of one or the other. There are many reasons why a high energy physicist just chooses energy, though they equivalently could have chosen time, could have chosen length, etc. It's just for the purposes of this video and for you to have a different point of view on the world, it's better to think in terms of energy because of a series of accidents. The unit that they like to use is giga electron volts, GEV. And that's the units we'll be using."
},
{
"end_time": 1999.411,
"index": 84,
"start_time": 1970.282,
"text": " are the units we will use. So why is this useful at all? Why does one want to convert to GeV constantly? Because if you were to give me the mass of this in grams, I don't know what that means. But if you were to give me it in terms of GeV, I can tell you how many nucleons are in here. So what does that mean? Firstly, notice this accident. Again, it's perhaps an accident, but perhaps not. One proton mass"
},
{
"end_time": 2029.326,
"index": 85,
"start_time": 2000.316,
"text": " Equivalent remember it's not just this is something else that needs to be emphasized. It's not the mass of a proton It's its energy equivalent. So once proton masses energy equivalent is Let's say I think it's zero point nine three eight. I have to look that up Okay, we go to Wikipedia and we see What is the mass of a proton? So then we look at the protons mass and it's this right here"
},
{
"end_time": 2053.831,
"index": 86,
"start_time": 2030.111,
"text": " And that's the same as 0.93 GeV, if you just know what giga means versus mega. And why is this useful at all? Because it's almost equal to 1. So if I want it to be sloppy, I would say equals to 1. But instead, I will say on the order of 1 GeV. Now we want to know what is a GeV. So firstly, what is an Ev?"
},
{
"end_time": 2085.418,
"index": 87,
"start_time": 2055.896,
"text": " Well, you can look all of these up and I'm going to be giving you these practical steps by searching because that's actually what it's like to do physics or any research in general. You go to Wikipedia as one of your first sources. So it says here, EV means electron volt is a measure of an amount of kinetic energy gained by a single electron accelerating through an electric potential difference of one volt. What that means is that let's imagine we have some potential difference here. This is one volt."
},
{
"end_time": 2110.094,
"index": 88,
"start_time": 2086.459,
"text": " And here's an electron, it's at rest. Then it will accelerate a certain amount. Once it gets here, it will have a new speed because the first speed was zero. It will have a new speed and associated with that speed is an energy. And then that energy now that it has, well, let me just do this, it converts to energy. Then the energy, the kinetic energy of it is one eV, is one electron volt."
},
{
"end_time": 2130.265,
"index": 89,
"start_time": 2110.828,
"text": " Why is this useful at all? The reason is that we have now made a connection between one proton, one proton's mass energy, let's say mass energy equivalent. Remember, that's important. It's not its energy per se, it's its energy equivalent."
},
{
"end_time": 2157.995,
"index": 90,
"start_time": 2130.776,
"text": " We've made an association between this and one giga electron volt, and then there's this connection, which is implicit, but I'm making it explicit. This is what NEMA didn't emphasize. The connection isn't actually here. The connection is that this is, well, I'm going to be sloppy and say approximately because it's truly this. The connection is that this number, one, is readily"
},
{
"end_time": 2174.309,
"index": 91,
"start_time": 2158.285,
"text": " cognitively graspable, meaning that we can chunk it. It's easier for me to think in terms of one lip balm than it is for me to think in terms of 0.825 lip balms. The reason why this latter point is important is that you'll see in physics constantly"
},
{
"end_time": 2202.739,
"index": 92,
"start_time": 2174.309,
"text": " there's an effort to reduce some convoluted equation into linear algebra. And that's because linear algebra is extremely cognitively graspable. It's understood. It's one of the few areas of math, if not the only area of math, that's well understood. That means anytime you have a complex equation, if you can linearize it, you understand it much better. In the same way that anytime we have some complicated phenomenon, we can put it to something that's in terms of GeV, means we understand it in terms of protons."
},
{
"end_time": 2226.578,
"index": 93,
"start_time": 2203.148,
"text": " It's akin to Feynman saying that the number one lesson for some future civilization, if you had to impart one piece of knowledge to them, the best knowledge, the best bang for your buck in terms of facts, would be to tell them that the world comprises atoms and from that fact many other laws of nature come. Now I don't know about that because to me that would imply that you would have some fact like let's say the atom fact and then we have the space of all facts"
},
{
"end_time": 2252.415,
"index": 94,
"start_time": 2226.954,
"text": " and then you have to have some measure on the space of all facts in order for you to say that this is this one fact implies the most facts and that's somewhat dubious but you at least understand informally what Feynman meant it's one of the reasons why in the theories of everything podcast what I'm trying to do constantly you'll see me asking the professor who has some extremely intricate Baroque equation or concept"
},
{
"end_time": 2279.838,
"index": 95,
"start_time": 2252.944,
"text": " I'm frequently saying, okay, what does it mean in terms of billiard balls? So let's imagine that this has a charge and this one does too. What's going on there? It's the same, trying to reduce down to some fundamentals that you understand in order to properly understand it. Then there's another somewhat of an accident. Maybe it's not. Heisenberg said there was isospin. So that one neutron has similar mass."
},
{
"end_time": 2309.548,
"index": 96,
"start_time": 2280.794,
"text": " to a proton. And it's these that all work together that allow one to make use of natural units for these napkin calculations. I'm being extremely specific and somewhat pedantic because much of this is glossed over and then you'll start, at least if you're like me, you'll start to be confused at a much later point and you won't realize that some of these fundamentals weren't explained specifically. Now let's go through a conversion chart. Conversion."
},
{
"end_time": 2338.114,
"index": 97,
"start_time": 2310.896,
"text": " chart. Here we go. One meter is the equivalent of on the order of 10 to the 16 GeV inverse. Ah, now I haven't explained what the inverses mean. Here at our equation bolded number one and then bolded number three we have an equivalence between energy and mass so you say one giga electron volt and that can mean"
},
{
"end_time": 2366.869,
"index": 98,
"start_time": 2338.592,
"text": " a certain amount of mass. Okay, you can convert between them. But you can also convert between the mass and then the length. But this is an inverse relationship. So that means that length actually has inverse energy units. So anytime you give a length, you can also have given the same quantity in inverse energy. Anytime you have a second, you could do the same. You can give that in terms of inverse energy. Anytime you have a mass, this one's simple, you can give it in terms of energy. Now this mp is the Planck mass."
},
{
"end_time": 2393.78,
"index": 99,
"start_time": 2367.125,
"text": " Not the proton mass. Remember, proton mass is 1 GeV. Just for fun, you can do the calculation of a gram, and it's this much. You can do Hertz, which is inverse time. And by the way, because you're in inverse time, you have regular energy units, which means frequency is actually a unit of energy. Anytime someone gives you a frequency, you can just convert that straight to energy. We're going to be doing these. By the way, I didn't actually do this, but for entropy,"
},
{
"end_time": 2424.94,
"index": 100,
"start_time": 2395.947,
"text": " You can see that this is a dimensionless quantity. It's information. It should be dimensionless. Because it's dimensionless, then from the Boltzmann constant, you can get that Kelvin is also a unit of energy. So temperature is a unit of energy, which somewhat makes sense because you've heard that temperature is some function of the average kinetic energy of the molecules in a room or in a box. But that statement alone isn't enough to say that it's units of energy, because just because it's a function of energy doesn't necessarily mean the units of it are energy."
},
{
"end_time": 2453.029,
"index": 101,
"start_time": 2426.254,
"text": " However, it does turn out to be the case. This means you can convert from energy to temperature and vice versa. All of these are vice versa. And then one we may use later is nanometers equals this. By the way, if any of these are incorrect, well, then please just write the correct one in the comments section. When you look at these conversion charts online, some of them have a plus or minus one in the units. And that's because we're using this symbol, which means we don't actually care too much about rounding errors."
},
{
"end_time": 2485.196,
"index": 102,
"start_time": 2455.247,
"text": " Remember that this is all about napkin calculations, NCs, we're just doing NCs. To be extremely concrete, you can say your desk in front of you is one meter, approximately, let's say approximately one meter long, or you can give it in terms of GEV, it's 10 to the 16 GEV inverses. And that means that if you stacked, stack 10 to the 16 protons, so you get proton, proton, proton, proton, 10 to the 16 times,"
},
{
"end_time": 2514.633,
"index": 103,
"start_time": 2489.77,
"text": " Then you get your desk. So it gives you an extremely concrete way of understanding what your desk is. Your desk is 10 to the 16 protons stacked one after the other. And by the way, you may say, well, Kurt, isn't GEV also arbitrary? Wasn't the whole point of natural units to get away from this arbitrariness? Well, yes, that's true. Except that the other part here, which is a great confluence, is that this coincides"
},
{
"end_time": 2541.92,
"index": 104,
"start_time": 2515.009,
"text": " with how engineers think. Engineers think in terms of electron volts, well they think in terms of volts. So now you've found a connection between protons, between something that is cognitively graspable, between a neutron, and between what you can communicate with with others. So engineers, now throughout the rest of the video you'll see that many different quantities, physical, macroscopic, sometimes even microscopic, physical, observable quantities, are expressed in terms of these fundamental"
},
{
"end_time": 2561.237,
"index": 105,
"start_time": 2542.346,
"text": " Now notice I didn't say fundamental constants, and that's because I'm trying to emphasize the fact that they're dimensionless. Let's analyze Newton's constant and others. Here's what you do in general. Firstly you go to Wikipedia, so let's do that right now."
},
{
"end_time": 2588.097,
"index": 106,
"start_time": 2562.483,
"text": " and you type in newton's constant so it's also known as the gravitational constant you've seen it before it's this g then we take a look at what are the units here we go we get newton's meters squared so on and so on so let's write this down the units of g and even here i noticed i made a mistake because often you'll see online m which means meters which means it's actually a length"
},
{
"end_time": 2596.561,
"index": 107,
"start_time": 2589.599,
"text": " And this is a common mistake when you're initially doing this. So this is actually mass and this is length squared."
},
{
"end_time": 2620.828,
"index": 108,
"start_time": 2597.688,
"text": " You'll see it here that it says Newtons meter squared, so length squared, then a mass squared is what it's being divided by. Then you wonder, well, what the heck is a Newton? So what we do is we go into it because all of these are derived from something that's much simpler, usually mass, length or time. So we go here and we see that is equal to a kilogram. So mass times length over time squared. So let's do that."
},
{
"end_time": 2645.947,
"index": 109,
"start_time": 2625.947,
"text": " Okay, now it's as simple as doing some cancellations. Well, we can remove one of these masses and we go mass. All right, now we want to reduce this even further. Remember, there's only length or there's only time or only energy. Let's see if we can place this in terms of only energy."
},
{
"end_time": 2677.363,
"index": 110,
"start_time": 2647.773,
"text": " we go to our conversion equations there's a correspondence between length and time between energy and mass between length and momentum actually this correspondence is between length and inverse momentum and this is between length and inverse mass you can see that just from the fact that there's a one over and obviously that can go one over there there's also another equation that will come in handy let's give it a bolded four which is the energy time uncertainty and this gives a correspondence between"
},
{
"end_time": 2705.213,
"index": 111,
"start_time": 2678.729,
"text": " Energy and time. However, looking at the equation, you can see that it's inverse time. That means that inverse time is energy. Inverse energy is time. Let's now make some substitutions. Mass is the same as energy, so I'm going to call it GeV. Time is the same as GeV inverse. Length is the same as GeV inverse."
},
{
"end_time": 2731.357,
"index": 112,
"start_time": 2705.435,
"text": " Well, length is the same as mass, but mass is the same as energy, so you can make that substitution. Making all of these substitutions, you then get that G, the units of newtons, is actually 1 over GeV squared, or, as we'll be writing it, simply GeV to the power of negative 2. It's all simple. We look and we see that it's newtons times kilograms times"
},
{
"end_time": 2753.848,
"index": 113,
"start_time": 2731.561,
"text": " Length, etc. actually reduces down to this. So let's underline that in red. How about entropy? Well, entropy, as we've noted above, is given by a formula, which looks like it's actually minus what I wrote before. And these are probabilities, which is dimensionless."
},
{
"end_time": 2778.473,
"index": 114,
"start_time": 2756.613,
"text": " Again, extremely simple. Now much of this is made complicated, but if you look at it through the lens of natural units as well as these conversion equations, all of the quantities that you know and that you love and that you want to work with become units of energy raised to some integer power. How about pressure? Again, let's just look that up on Wikipedia. That's usually the first step."
},
{
"end_time": 2808.251,
"index": 115,
"start_time": 2779.599,
"text": " It says here Newtons per meter squared. That makes sense because it's Newton, which is a force unit over some area. And then luckily they've decomposed it further for us. So let's write that down. That is a mass over a length. And then we have time squared, which then becomes, which we can now do in our head, but we won't do that right now because we're trying to not skip any steps. Mass becomes GeV."
},
{
"end_time": 2823.251,
"index": 116,
"start_time": 2809.497,
"text": " Length becomes GeV inverse, so it goes to the top. Time is also GeV inverse, so it's GeV squared, and that is the same as GeV to the fourth."
},
{
"end_time": 2855.589,
"index": 117,
"start_time": 2827.91,
"text": " This tells you an extremely important property of pressure. It's an extensive property of space-time itself. This is one of the reasons why it's much easier or much more useful to think in terms of pressure rather than force, because pressure is a property of space-time itself, whereas force is some derived quantity that usually isn't useful in fundamental physics. Now let's do a fun one. How about speed? Well, we think of it as length over time."
},
{
"end_time": 2869.701,
"index": 118,
"start_time": 2856.834,
"text": " And then because time and length are the same in our conversion chart, this just becomes dimensionless. That deserves a bolded exclamation point."
},
{
"end_time": 2893.882,
"index": 119,
"start_time": 2871.493,
"text": " Then you think, well, how the heck is speed dimensionless? Isn't it the case that you said over here, Kurt, C equals one, you can't simply say C equals one. Yes, that's true, except there was a caveat. And the caveat is that there are these conversion equations because we're placing it in terms of C, which is invariant. It means that we can tell time in terms of length and we can tell length in terms of time."
},
{
"end_time": 2902.039,
"index": 120,
"start_time": 2893.882,
"text": " And that means that this equation is correct, but only when you take into account the fact that C is invariant and these other conversion equations."
},
{
"end_time": 2928.183,
"index": 121,
"start_time": 2903.865,
"text": " It's usually just glossed over, so plenty of preamble goes into making a statement as seemingly simple as C equals 1 equals h-bar. So C equals 1 is a meaningless statement unless you're specifying that you're using some of these as conversions. And then you're also emphasizing the invariance of the speed of light. If the speed of light depends on something else, you can't actually use that. All of this needs to be explained unequivocally first."
},
{
"end_time": 2941.305,
"index": 122,
"start_time": 2928.695,
"text": " It's usually not, and then there's an abundance of befuddlement that occurs, much like with the Brachetta notation, which looks graceful. However, there's plenty of assumptions that go into it, which make it not terribly useful."
},
{
"end_time": 2972.056,
"index": 123,
"start_time": 2942.159,
"text": " Let's use this to calculate a practical quantity. So how many protons are there in you? At first, if you were to just say, well, I weigh 70 kilograms, that doesn't give much information. What we can do is we can use our conversion chart over here and say, okay, well, look, one gram is this much energy. So how about a kilogram? So a kilogram must be 10 to the 26 GeV. Using this, we then get that 70 kilograms becomes 70"
},
{
"end_time": 2995.657,
"index": 124,
"start_time": 2972.534,
"text": " times 10 to the 26 GeV, which is on the order of 10 to the 28 GeV. That means that what comprises you is 10 to the 28 protons. And that's a much more physically meaningful quantity. Now you have some physical intuition given to you by your weight. Whereas if it was just kilograms, then you have to go to Paris, etc."
},
{
"end_time": 3025.316,
"index": 125,
"start_time": 2996.135,
"text": " Then you may wonder, well Kurt, don't neutrons come with protons, so shouldn't you times 2 the above? Yes, except because of this. We're saying on the order of. So we can say there are 10 to the 28 nucleons that comprise you. Protons and neutrons bound. There we go. Simple and powerful because it allows these napkin calculations. Let's do one that you may think requires plenty of work, but it's actually extremely quick. You can do it in a second. So what is the pressure inside a neutron star?"
},
{
"end_time": 3038.456,
"index": 126,
"start_time": 3026.852,
"text": " The pressure inside a neutron star, well firstly you have to think what is happening. There are neutrons as far as you can see and recall that neutrons are the same as protons in terms of their radius and mass approximately."
},
{
"end_time": 3067.858,
"index": 127,
"start_time": 3040.179,
"text": " Then as far as you can see, all you see are neutrons. Think about what have you learned about a neutron star. It's that the neutrons are packed so close together that they can't be packed any further. Then you think, well, what is the units of pressure? And it's GeV to the fourth. So we have GeV times GeV times GeV times GeV, one, one, one, one, one. And we get pressure in a neutron star is simply GeV to the fourth."
},
{
"end_time": 3085.623,
"index": 128,
"start_time": 3068.456,
"text": " Okay, that's it. It's just GeV to the fourth. And this is something that you can verify yourself if you look up what it is in Pascals and then do the conversion. And just keep in mind that some conversion charts have a plus or minus one on the order because sometimes people round up, sometimes people round down."
},
{
"end_time": 3104.957,
"index": 129,
"start_time": 3086.032,
"text": " Now let's get through this much more quickly because I'm re-recording constantly. There are many errors and my facial hair is growing. I've renamed this for reasons that will become clear later. A neutron star's pressure is much more copacetic. So proportionate strength of the forces. So you know from perhaps around high school that it's something like the first charge times the second charge, so on and so on and so on."
},
{
"end_time": 3127.619,
"index": 130,
"start_time": 3105.247,
"text": " Let's look at this in terms of the electron charge. So Q1 will equal Q2 will equal E. V is energy. We know that. That's potential energy. R is inverse energy, which means this equation has this guy here, which means that this guy here, which I'll rewrite, is dimensionless."
},
{
"end_time": 3152.432,
"index": 131,
"start_time": 3130.794,
"text": " And this is what is usually denoted as alpha, which I'm sure you've heard is 1, 3, 7 inverse. This is the reason why the strength of the electromagnetic force or the electromagnetic interaction is quantifiable, it's dimensionless. However, if we were to look up here, notice this, this G newton"
},
{
"end_time": 3181.169,
"index": 132,
"start_time": 3152.858,
"text": " has negative mass dimension, which means that saying that gravity is weak is actually a meaningless statement because you need test masses. You need two test masses in order to say that. Usually what's done in fundamental physics is one takes the most massive of all the particles, the fundamental particles, and says, well, look, compared to the weak force, which is the weakest of all the standard model forces, the gauge fields, gravity is so-and-so times weaker. So that's what's meant specifically by gravity is weak."
},
{
"end_time": 3209.94,
"index": 133,
"start_time": 3181.169,
"text": " But all of that needs to be stated. There are assumptions that go into that. You need a test mass. And by the way, this guy here, this negative square mass dimension of the coupling of gravity, plays an extremely important role in the non-renormalizability of gravity. Let's calculate the average speed of an electron. So later, we're going to calculate the radius of an electron, and that's going to turn out to be this. But this right now just looks like junk because we haven't derived any of this. However, from this, we know that one of our equations over here,"
},
{
"end_time": 3222.517,
"index": 134,
"start_time": 3212.585,
"text": " says that we can figure out the momentum based on a length so then what is the momentum of the average electron and it's hear that sound"
},
{
"end_time": 3249.514,
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"start_time": 3223.439,
"text": " That's the sweet sound of success with Shopify. Shopify is the all-encompassing commerce platform that's with you from the first flicker of an idea to the moment you realize you're running a global enterprise. Whether it's handcrafted jewelry or high-tech gadgets, Shopify supports you at every point of sale, both online and in person. They streamline the process with the internet's best converting checkout, making it 36% more effective than other leading platforms."
},
{
"end_time": 3269.411,
"index": 136,
"start_time": 3249.514,
"text": " There's also something called Shopify Magic, your AI powered assistant that's like an all-star team member working tirelessly behind the scenes. What I find fascinating about Shopify is how it scales with your ambition. No matter how big you want to grow, Shopify gives you everything you need to take control and take your business to the next level."
},
{
"end_time": 3299.019,
"index": 137,
"start_time": 3269.411,
"text": " Join the ranks of businesses in 175 countries that have made Shopify the backbone of their commerce. Shopify, by the way, powers 10% of all e-commerce in the United States, including huge names like Allbirds, Rothy's, and Brooklynin. If you ever need help, their award-winning support is like having a mentor that's just a click away. Now, are you ready to start your own success story? Sign up for a $1 per month trial period at Shopify.com"
},
{
"end_time": 3309.292,
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"start_time": 3299.019,
"text": " go to shopify.com slash theories now to grow your business no matter what stage you're in shopify.com slash theories"
},
{
"end_time": 3330.299,
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"start_time": 3312.517,
"text": " Razor blades are like diving boards. The longer the board, the more the wobble, the more the wobble, the more nicks, cuts, scrapes. A bad shave isn't a blade problem, it's an extension problem. Henson is a family owned aerospace parts manufacturer that's made parts for the International Space Station and the Mars Rover."
},
{
"end_time": 3352.142,
"index": 140,
"start_time": 3330.299,
"text": " Now they're bringing that precision engineering to your shaving experience. By using aerospace-grade CNC machines, Henson makes razors that extend less than the thickness of a human hair. The razor also has built-in channels that evacuates hair and cream, which make clogging virtually impossible. Henson Shaving wants to produce the best razors, not the best razor business,"
},
{
"end_time": 3372.125,
"index": 141,
"start_time": 3352.142,
"text": " So that means no plastics, no subscriptions, no proprietary blades and no planned obsolescence. It's also extremely affordable. The Henson razor works with the standard dual edge blades that give you that old school shave with the benefits of this new school tech. It's time to say no to subscriptions and yes to a razor that'll last you a lifetime."
},
{
"end_time": 3392.108,
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"start_time": 3372.125,
"text": " Visit HensonShaving.com slash everything. If you use that code, you'll get two years worth of blades for free. Just make sure to add them to the cart. Plus 100 free blades when you head to H-E-N-S-O-N-S-H-A-V-I-N-G dot com slash everything and use the code everything."
},
{
"end_time": 3412.005,
"index": 143,
"start_time": 3396.305,
"text": " And that means that this is the average speed of an electron. Think Verizon, the best 5G network is expensive? Think again. Bring in your AT&T or T-Mobile bill to a Verizon store today and we'll give you a better deal. Now what to do with your unwanted bills? Ever seen an origami version of the Miami Bull?"
},
{
"end_time": 3430.196,
"index": 144,
"start_time": 3412.483,
"text": " Jokes aside, Verizon has the most ways to save on phones and plans where you can get a single line with everything you need. So bring in your bill to your local Miami Verizon store today and we'll give you a better deal."
},
{
"end_time": 3455.247,
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"start_time": 3436.783,
"text": " And this number is the reason why magnetism was discovered so much later, because electrons are moving relatively slowly, and we know that magnetism has to do with the speed, it has to do with current changes. Thus, from relatively fundamental principles, you can derive a historic fact. Why was it that magnetism was discovered much later? Well, it's because of this guy."
},
{
"end_time": 3478.541,
"index": 146,
"start_time": 3456.664,
"text": " And by the way, you'll notice that I spend quite a bit of time writing and rewriting painstakingly almost. And that's because I know that clarity of thought leads to this clarity of writing and vice versa for myself and for you. And if you're lucky enough to have a lecturer who's blessed in that area, in this notational refinement area, then it will translate directly to higher comprehension for you. It's a"
},
{
"end_time": 3498.217,
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"start_time": 3479.36,
"text": " It's a neglected part of pedagogy, I find. The logical placement of the words in the formula matter, and many of you are trying to create your own theory of everything, you're advancing your own, you're not simply learning about others. It's one of the reasons why I try to be specific in the podcast in general, and then also here as much as I can be, given the time constraints, because generally you're told"
},
{
"end_time": 3526.681,
"index": 148,
"start_time": 3498.217,
"text": " have truths so for example that a wave function is a member of a square integrable Hilbert space okay but then if you derive it is a square integrable function necessarily square integrable itself okay so then you limit it to Schwartz functions and then you say well perhaps Gelfand triples and so on and then you realize well that only works for pure states that a general quantum mechanical state is actually endomorphism on a Hilbert space and even then when it's a pure state it's not a unique you can't assign a unique member of a Hilbert space you have to take a"
},
{
"end_time": 3545.043,
"index": 149,
"start_time": 3527.056,
"text": " The reason for me to be extremely detailed is because many of you are trying to advance your own toes, and if you're going to build them based on some shaky foundation, then you're going to derive fantastic formula and fantastic theories based on"
},
{
"end_time": 3575.23,
"index": 150,
"start_time": 3546.186,
"text": " half truths and based on what's misleading you can it's akin to dividing by zero you can prove the entire universe from scratch if you divide by zero what I found is that the popularizers of science have generally spent a significant amount of time on let's say the wave particle duality instead of telling you it's a quantum mechanical object that behaves in this manner well mainly for for a few reasons and one of the reasons is because they want to evoke awe in you and show you how unimaginably intelligent these"
},
{
"end_time": 3588.609,
"index": 151,
"start_time": 3575.759,
"text": " Esoteric Physicists"
},
{
"end_time": 3616.51,
"index": 152,
"start_time": 3589.394,
"text": " Gelfand triple, you're wondering what the heck is that? Well now you can at least look that up on Wikipedia and you can gain a far better understanding of what a quantum mechanical object is rather than simply saying that it's both a wave and a particle at the same time and who knows what the collapse means and so on. By the way, I talk about this here in the quantum gravity section of the Salvatore Pius interview. If you want, I'll leave a link in the description. This is why quantizing gravity is so difficult and it's explained in somewhat pedantic mathematical detail"
},
{
"end_time": 3645.64,
"index": 153,
"start_time": 3616.51,
"text": " mainly because then you can see, okay, this is why it's so difficult and it's not necessarily because you're trying to mix the jittery with the smooth and so on. What does that mean? Let's get to knots and extra dimensions. The whole point of this is to get familiar with the different length scales and the different energy scales. So let's take a look at this. The mass of the pion, which you can look up online, is about 10 to the minus 1 GeV. The mass of the electron, which I think we've used, is about 10 to the minus 3 GeV."
},
{
"end_time": 3671.442,
"index": 154,
"start_time": 3646.067,
"text": " Thinking of physics in the manner of natural units and GEVs, etc., gives you concrete ways of thinking about some phenomenon in different respects. So, for example, length scales here. These automatically imply that, for example, chemistry becomes important at what scale? Well, 10 to the 3 GEV inverse. We simply take the inverse of this, and then same with"
},
{
"end_time": 3695.964,
"index": 155,
"start_time": 3671.732,
"text": " And by the way, that's because the electron is what's responsible for chemistry, largely speaking. And for the strong force, we expect the scale that it becomes relevant is 10 GeV inverse. And then we can simply do our conversion over here to find out the relevant length scale in terms of meters. Let's now have a quick detour into extra dimensions."
},
{
"end_time": 3722.193,
"index": 156,
"start_time": 3696.681,
"text": " Extraspacial dimensions are called universal extra dimensions. And usually we're dealing with one temporal time dimension. So you'll hear three plus one or four plus one, that plus one usually means the time. At some point in the Toe podcast, I may do a single episode just on extra dimensions. If you're interested, let me know as well as extra temporal dimensions. What we're doing is looking here. So we're seeing that usually what you've heard is that you compactify the dimensions."
},
{
"end_time": 3751.288,
"index": 157,
"start_time": 3722.193,
"text": " Sometimes, I think in the string theory episode, which I'll link over here, we talked about a Kaluza-Klein compactification of 10-dimensional super Yang-Mills theory. So that's what's being referenced here when you hear about a Kaluza-Klein resonance. And then you may wonder, well, look, it says that we have put some bounds on the extra dimensions, which is 1 TeV. But if we take a look at what the LHC, the largest energy of the LHC is, it says here it's 6.8 times 2, so it's 13.6 TeV."
},
{
"end_time": 3779.616,
"index": 158,
"start_time": 3752.005,
"text": " TeV is just a thousand GeV. So then you wonder, well, how is it that we've put a bound of an extra dimension only at one TeV? Shouldn't it be at 13 TeV? Well, strangely, some of the theories of extra dimensions have it such that the standard model fields stay within our three spatial dimensions and then they leak out. Well, gravity mainly leaks out into another dimension. That's the ADD model, not attention deficit disorder, but Arkani Hamed and"
},
{
"end_time": 3806.476,
"index": 159,
"start_time": 3780.708,
"text": " hear that sound?"
},
{
"end_time": 3833.609,
"index": 160,
"start_time": 3807.483,
"text": " That's the sweet sound of success with Shopify. Shopify is the all-encompassing commerce platform that's with you from the first flicker of an idea to the moment you realize you're running a global enterprise. Whether it's handcrafted jewelry or high-tech gadgets, Shopify supports you at every point of sale, both online and in person. They streamline the process with the internet's best converting checkout, making it 36% more effective than other leading platforms."
},
{
"end_time": 3853.422,
"index": 161,
"start_time": 3833.609,
"text": " There's also something called Shopify Magic, your AI powered assistant that's like an all-star team member working tirelessly behind the scenes. What I find fascinating about Shopify is how it scales with your ambition. No matter how big you want to grow, Shopify gives you everything you need to take control and take your business to the next level."
},
{
"end_time": 3883.046,
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"text": " Join the ranks of businesses in 175 countries that have made Shopify the backbone of their commerce. Shopify, by the way, powers 10% of all e-commerce in the United States, including huge names like Allbirds, Rothy's, and Brooklynin. If you ever need help, their award-winning support is like having a mentor that's just a click away. Now, are you ready to start your own success story? Sign up for a $1 per month trial period at Shopify.com"
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"text": " It's actually not, it's somewhat comparable, it's just that it goes into another dimension. And because we're confined here, this is where we're confined, it's not as simple as looking for an extra dimension like you can see it just like you can see a DNA molecule."
},
{
"end_time": 3937.278,
"index": 164,
"start_time": 3910.401,
"text": " What we're looking for are deviations in the inverse square law and this number 2 here is actually can be generalized to higher dimensions dim minus 2 where I'm including time here to make this simple so for us it's 4 minus 2 which is what gives rise to this inverse square law but if we're in higher dimensions then we'll see a different number here this becomes 1 over the dimension of the manifold that you're on minus 2 and in the manifold I'm including time just to make it simple"
},
{
"end_time": 3963.114,
"index": 165,
"start_time": 3938.046,
"text": " As for how we derive this, don't worry about that. You can just think of the flow through a surface. If we're in R3, then a sphere around us is like a shell, and that's a two-dimensional surface. So if you're in R3, you go one dimension down. If you're in R4, you go one dimension down, so it's R3 and so on and so on. Technically, to be rigorous, you need to show that the potential of some Laplacian vanishes, but we can leave that. Let's get to looking at some of the papers on extra dimensions."
},
{
"end_time": 3988.353,
"index": 166,
"start_time": 3963.387,
"text": " Here we go. So firstly, notice this, this is inverse R, which is related to an energy. And so this makes sense because you know, length is inverse energy. Now you're starting to get a handle on all of this. Let's take a look at another paper, which I'll link in the description. This is actually a section from a book, I believe. And you can take a look. Well, here, what this is saying is that if we have extra dimension, see here is four plus the extra spatial dimensions right there. That's Delta."
},
{
"end_time": 4016.937,
"index": 167,
"start_time": 3988.814,
"text": " You have the Einstein-Hilbert action. This we know if we remove this d delta y. This is just the standard action that leads to the Einstein equations. And we trivially add some more spatial dimensions right here. And then here's some matter fields. You want to couple some matter to it. And notice that it's four dimensional here, whereas this one is four plus delta. And that's saying, hey, let's restrict our standard model matter fields to this four dimensional manifold. And that explains why we see them as fairly strong, but then gravity is allowed to"
},
{
"end_time": 4039.633,
"index": 168,
"start_time": 4017.449,
"text": " leak out into the extra delta dimensions. If we take a look at this, this also gives us some bounds on the extra dimensions. Now there are large extra dimensions as well. The ADD model I mentioned before isn't a compactification, and you can similarly find bounds on them, which are found here. Now that you're becoming more and more familiar with TEVs and GEVs and so on, you can at least skim this paper and get an idea of what's being said."
},
{
"end_time": 4069.258,
"index": 169,
"start_time": 4040.026,
"text": " Notice here, another number you should recognize is the Planck scale, which is 10 to the 16 TeV. We have it written down as 10 to the 19 GeV, but those are the same numbers. Now let's have a quick aside on knots if I have enough room here. What is a knot? A knot is an embedding of a circle into R3. Let's take an example. Right there is a knot. And this what we're actually seeing, this is not a knot. This is an embedding of a knot. Technically, these should be modded out by isotopic equivalence."
},
{
"end_time": 4093.285,
"index": 170,
"start_time": 4069.633,
"text": " I'll include a link to a podcast where we go into more about knots and quantum field theory. Each one of these guys can directly translate to a Feynman diagram in two plus one dimensions. Now you may ask, well, why is it that we're going from a circle to R3 but not to RD? Well, there are extensions, except you can't have S1"
},
{
"end_time": 4122.142,
"index": 171,
"start_time": 4094.036,
"text": " You cannot have S1 into R4. You can, except that every single knot can be trivially unknotted. So it can be morphed into a circle. So that's why you'll have to have S2 if you're going into R4, and then S3 into R5, et cetera, if you want to have higher dimensional generalization of knots. But then their connection to Feynman diagrams are more complicated, and I believe it's current research. So this is only the unknot."
},
{
"end_time": 4154.77,
"index": 172,
"start_time": 4125.282,
"text": " Additionally, whenever you hear about the Planck length, that will come up, the Planck length, it can't be that space is, quote unquote, trivially made up into some lattice of discrete lattice of Planck lengths, Planck cubed, and so on. And the reason is that that concept is not Lorentz invariant. Because what if you're zooming past it, then do you get smaller than the Planck length? What if you make this room into the Planck length? And should this room exist from another perspective? You get into plenty of paradoxes, and that's because we don't have an understanding as to what happens around that scale."
},
{
"end_time": 4175.026,
"index": 173,
"start_time": 4155.06,
"text": " Another way that extra dimensions can be tested is if you collide particles. So let's say they look like this. And then who knows what happens here? No one actually knows their Feynman diagrams and so on. But whether or not that corresponds to something physical, who knows? Imagine they come out like this. Well, what happened here?"
},
{
"end_time": 4191.305,
"index": 174,
"start_time": 4175.64,
"text": " This is the same as this, but then this is less than this, which means we have a, if they're the same particles, we don't have a conservation of momentum. And then we can say that perhaps what happened was some of the momentum leaked into another dimension. So this is also being looked for. This is called discrepancies in transverse momentum."
},
{
"end_time": 4221.766,
"index": 175,
"start_time": 4198.712,
"text": " Now let's take a dive into Penrose's theory, the microtubules of consciousness. Because this is meant to be an overview, and each one of these could be its own two-hour, three-hour, four-hour podcast on its own at least, let's simply go to Wikipedia and get familiar with using these conversion equations and natural units, the whole point of this video. The founders of this theory are Penrose and Stuart Hameroff."
},
{
"end_time": 4249.241,
"index": 176,
"start_time": 4222.841,
"text": " So if we take a look, we're just looking for equations right now. We're scrolling through. I'm not concerned too much with the background. Notice this. This looks extremely similar to this. And it is. It's called Penrose's indeterminacy principle, much like Heisenberg's uncertainty principle. What Penrose is saying is that imagine we have one particle and then it's in a superposition. So let's imagine it's a superposition of just two states, which can be left or right. Let's call this"
},
{
"end_time": 4276.459,
"index": 177,
"start_time": 4250.196,
"text": " and let's call this option B. Along with option A and option B, they have their own warping of spacetime, so gravity. Anytime you hear about a gravitational field, usually when you hear the term gravitational field, it's the metric, the spacetime metric in general relativity. However, technically speaking, the gravitational field tensor is the Riemannian tensor and the gravitational potential is the metric. Regardless, we take a look here and we say that there are different"
},
{
"end_time": 4293.712,
"index": 178,
"start_time": 4276.459,
"text": " Warpings of space time associated with each of the options so a may have some warping that looks like this as you go outward and then B may look like let's say this and then you wonder well is this the superposition so ordinarily be denoted this plus this well are we to have a superposition of space times"
},
{
"end_time": 4318.848,
"index": 179,
"start_time": 4294.053,
"text": " What Penrose is saying is that once the particles are of a sufficient distance from one another in metric space, so over here it says EG is the gravitational self-energy and the degree of spacetime separation. So the degree of spacetime separation is a bit of a misnomer here. What's meant is that there's a symplectic measure on the metric of spacetimes and then from that you assign a number to the metric of A and then to the metric of B and you see the difference once that difference is large enough."
},
{
"end_time": 4346.288,
"index": 180,
"start_time": 4318.848,
"text": " then there's a collapse. So this is a mechanism that merges gravity as well as the quantum collapse as well as consciousness. So like three mysteries in one. There's an episode with Stuart Hamarov if you want to see more about that. Over here it says one kilogram of an object will reach its objective reduction within 10 to the minus 37 sec. I believe this is incorrect on Wikipedia because when you take a look at the reference here it actually doesn't make a"
},
{
"end_time": 4374.821,
"index": 181,
"start_time": 4348.285,
"text": " it only has one reference to kilograms and it's 10 kilograms not one and then it says 10 to the minus 43 so I'm unsure where Wikipedia gets their number from and here is the better diagram that I was trying to draw before of the different space times and you can see let's see yes that's correct there's technically a symplectic measure on the space of four metrics that's right and Penrose is not going into extra dimensions here okay so let's write down that equation it's the gravitational self-energy one over"
},
{
"end_time": 4389.445,
"index": 182,
"start_time": 4375.452,
"text": " What is the gravitational self energy? One may guess naively. Hear that sound?"
},
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"start_time": 4390.418,
"text": " That's the sweet sound of success with Shopify. Shopify is the all-encompassing commerce platform that's with you from the first flicker of an idea to the moment you realize you're running a global enterprise. Whether it's handcrafted jewelry or high-tech gadgets, Shopify supports you at every point of sale, both online and in person. They streamline the process with the internet's best converting checkout, making it 36% more effective than other leading platforms."
},
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"text": " There's also something called Shopify Magic, your AI powered assistant that's like an all-star team member working tirelessly behind the scenes. What I find fascinating about Shopify is how it scales with your ambition. No matter how big you want to grow, Shopify gives you everything you need to take control and take your business to the next level."
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"text": " Join the ranks of businesses in 175 countries that have made Shopify the backbone of their commerce. Shopify, by the way, powers 10% of all e-commerce in the United States, including huge names like Allbirds, Rothy's, and Brooklynin. If you ever need help, their award-winning support is like having a mentor that's just a click away. Now, are you ready to start your own success story? Sign up for a $1 per month trial period at Shopify.com"
},
{
"end_time": 4492.21,
"index": 186,
"start_time": 4465.981,
"text": " That it is M1 M2 and then G over R and that would be correct because of this. However, if you look it up online, there's about a there's a correction of about five thirds or so. That doesn't matter because we're using this"
},
{
"end_time": 4513.865,
"index": 187,
"start_time": 4492.841,
"text": " Then what I'm unclear about is that there's still an r here, so we have an extra factor and I'm unsure of how he's deriving this number when there should be one more factor. To me this r should be a function of t and this should be related to the measure that we had here, the measure that's generated from the metrics. However, I'm unsure of this and I'm going to be speaking to"
},
{
"end_time": 4538.626,
"index": 188,
"start_time": 4514.275,
"text": " An essential feature of Penrose's theory is that when there's a wave function collapse, where it collapses to is chosen neither randomly nor algorithmically. This is outlined in his book called The Emperor's New Mind, where Penrose makes an analogy between something called non-recursively enumerable sets and"
},
{
"end_time": 4564.241,
"index": 189,
"start_time": 4538.814,
"text": " You may wonder why is it that we're using one GEV instead of"
},
{
"end_time": 4587.722,
"index": 190,
"start_time": 4564.838,
"text": " Well, it just makes some of the napkin calculations easier, so this is all about NCs, napkin calculations, as well as it gives you a much more concrete physical intuition. Later we'll derive the radius of an atom, but for now you can see that this is the radius of a proton, it's also the energy of a proton, the mass of a proton,"
},
{
"end_time": 4617.602,
"index": 191,
"start_time": 4587.961,
"text": " Which, as we mentioned earlier, this means my desk is 10 to the 16 protons long. If you take 10 to the 16 protons and stack them, you get the length of my desk. And I said desk, so don't get excited. Okay, now let's get to vacuum energy. Okay, you've heard the story that the universe is expanding, and because it's expanding, it has a positive cosmological constant, and much fervor is expressed to the disdain of the word prediction, the worst prediction of physics I'm sure you've heard. Worst prediction."
},
{
"end_time": 4642.21,
"index": 192,
"start_time": 4620.145,
"text": " And many people dislike this word prediction because it's not as if a specific theory was said to be false because of this prediction. However, that gives the impression of discounting the calculation completely. It wasn't a prediction per se, it was a comportment. Namely, if lambda was to comport with the standard model,"
},
{
"end_time": 4669.172,
"index": 193,
"start_time": 4643.746,
"text": " That is, if it was to be a consequence of absolute energy from the vacuum fluctuations from the Planck scale upward, then it should be of order, let's say, x. We're going to calculate that. It was a comportment test rather than a prediction. The mechanism could have been the vacuum fluctuations of QED. I believe Weinberg calculated this, but it turns out to be vastly, vastly incorrect. So let's take a look. There are three main sources of vacuum energy."
},
{
"end_time": 4699.906,
"index": 194,
"start_time": 4671.374,
"text": " And this is just from the standard model. Forget about general relativity. So number one, QCD. And these are these little quark bilinears. Number two, it's the Higgs field. And number three, it would be the zero point. These are called the zero point fluctuations. And this one is of order 10 to the minus one, GEV."
},
{
"end_time": 4729.889,
"index": 195,
"start_time": 4700.862,
"text": " And what power goes here? It's a pressure. It's dark energy. It's a property of space time itself. So four. Simple. Then what is the Higgs field's contribution? 10 squared GeV. And what power goes here? Well, what else could it be? Number four. Let's get to the calculation of the zero point fluctuations. What this means is that at each space time volume space time. So now we're dealing with four, not just three volumes, but I'll draw it as a cube."
},
{
"end_time": 4752.261,
"index": 196,
"start_time": 4730.179,
"text": " at each space time volume of length, let's say L. So L cubed in this case, but actually it's truly L4. So let's just place L4 here. That corresponding to this length is some frequency omega. The reason why is that we have this relation that energy is related to"
},
{
"end_time": 4778.899,
"index": 197,
"start_time": 4752.892,
"text": " Frequency, which means there's a tight relationship between frequency and energy. You can convert between the two. We're going to do that later once we analyze the Sun. From each space-time volume of length L, there's a contribution of a certain mode that happens within here. So let's call that frequency, well, whatever, it's omega in this case. So we constantly get these omegas associated with length 1 plus an omega associated with length 2."
},
{
"end_time": 4798.592,
"index": 198,
"start_time": 4779.48,
"text": " So on and so on. And because of this relation here, the shorter the length, the larger the energy. Firstly, that means that it's infinite. Technically, the zero point fluctuation yields an infinite energy, but that doesn't mean that it's literally true. It means technically it's true with our theories, which already break down."
},
{
"end_time": 4826.288,
"index": 199,
"start_time": 4799.104,
"text": " And where do they break down? At the Planck scale, this is what you've heard. So how about we simply cut it off at the Planck scale. So we let this be the Planck length, which by the way is what? Well, it's the inverse of the Planck mass. Because we're taking an inverse of an inverse, we simply get that the energy contribution from the vacuum,"
},
{
"end_time": 4841.596,
"index": 200,
"start_time": 4827.244,
"text": " is the plank mass to the four."
},
{
"end_time": 4869.48,
"index": 201,
"start_time": 4841.852,
"text": " The one where it's the plank length. So this is the only one that meaningfully contributes. This is why this NC or this napkin calculation, which is contingent on this, on the order of symbol, this tilde here is so vital. This is what allows you to do this quickly without thinking eventually. This gives an NC of what a napkin calculation of 10 to the 18 GEV to the fourth."
},
{
"end_time": 4897.995,
"index": 202,
"start_time": 4870.009,
"text": " Well, this should be that. And then that means that this is 10 to the 72 GEV to the fourth. Now, what is observed? What's observed is what you can get online because this is what's calculated by data. You'll see these strange units and then you'll have to look up on some other conversion site. So, for example, let's take a look here. Here's some conversion table."
},
{
"end_time": 4920.64,
"index": 203,
"start_time": 4899.189,
"text": " You can find online, they've set the Boltzmann constant to one as well. And here's another one. I'll leave these links in the description because these can be helpful. You'll notice that some of them defer at the last digits. And the reason is, again, I mentioned this, some places round up, some places round down. This then becomes 10 to the minus 48 GeV."
},
{
"end_time": 4948.49,
"index": 204,
"start_time": 4923.456,
"text": " You may wonder, why am I not placing square brackets here? Well, you can. It doesn't matter because you know that this is the only unit anyway. You may wonder, well, where does this observation come from? Like I mentioned, people look at data and then they have some assumptions like homogeneity and an isotropic universe. And then you get the Friedmann equations, which you can look up, which relates the acceleration to the cosmological constant and thus the pressure and density."
},
{
"end_time": 4965.879,
"index": 205,
"start_time": 4950.094,
"text": " The above then yields slash implies that our napkin calculation is the same as the observed times 10 to the 120. And now you know about the vacuum energy expectation."
},
{
"end_time": 4997.875,
"index": 206,
"start_time": 4968.285,
"text": " Now let's get on to calculating with the Schwinger limit. If you watched the Salvatore Pius interview, you'll notice that one coulomb of charge was brought up. So firstly, let's talk about what is one coulomb of charge. Let's get a handle on it. Let's go to Wikipedia, our friend. We take a look and we see that the elementary charge was assigned to this exact value in 2019. So this is the exact value of one elementary charge. It turns out that elementary charge is a dimensionless quantity. Let's write this down here."
},
{
"end_time": 5024.718,
"index": 207,
"start_time": 5000.384,
"text": " elementary charge is on the order of 10 to the minus 19 coulombs. This means that one coulomb, which I'm going to denote as C, one coulomb is the same as 10 to the 19 charges. So proton charges, electron charges, they're the same, they're just the reverse of one another plus or minus"
},
{
"end_time": 5050.998,
"index": 208,
"start_time": 5024.957,
"text": " Let's deal with protons. 10 to the 19 protons. That's 10 to the 19 GeV. Let's get a handle on that number. If we were to stack protons one after the other, 10 to the 19 times, then going up to our conversion chart, that is 10 to the 3 meters."
},
{
"end_time": 5073.763,
"index": 209,
"start_time": 5055.64,
"text": " That's the definition of one kilometer. That means if you were to take protons and stack them, stack them, stack them without any gap in between, it would be a strip of one proton wide and then one kilometer high. That's an extreme amount of charge. Great. Now we've gotten out of the way. What is one coulomb? Let's get to the Schwinger limit."
},
{
"end_time": 5097.125,
"index": 210,
"start_time": 5074.735,
"text": " The Schwinger limit here, it says, is the scale above which the electromagnetic field is expected to become nonlinear. So we haven't observed this because this is an extreme amount. We're going to actually deal with what the heck does this mean in our manageable units. The limit is typically reported as some maximum electric field or magnetic field before some nonlinear effects kick in. If we take a look here, we see this. Firstly, let's just analyze this."
},
{
"end_time": 5125.913,
"index": 211,
"start_time": 5098.336,
"text": " We notice there's a C. We notice there's an H bar. We set those to 1. That means that all that's left over is mass over charge. Charge is dimensionless. Mass squared. That means energy squared. That means that this is energy squared. This is a force. And then this has the same units. This is also a force. So Tesla has the units of force. Energy squared. E has this volts over meter has the units energy squared. You can get that right now just by looking at this for three seconds. Let's just deal with E."
},
{
"end_time": 5148.353,
"index": 212,
"start_time": 5128.251,
"text": " So e is on the order of 10 to the 18 volts per meter. This is also, as defined here, m e squared c to the 3 over h bar, the charge of the electron. That is, in our units, m e, so the mass of the electron, those become 1, this becomes 1, and then we get this."
},
{
"end_time": 5176.869,
"index": 213,
"start_time": 5148.933,
"text": " Now the charge of the electron is just one. Let's get a handle on this number. So firstly, what is a volt? We don't have to do much work because a volt, well, a GeV is 10 to the 9 volts. And that means that we can just take 9 from inside there and it becomes 10 to the 9, so 9 plus 9, GeV over meters. And then we can go upstairs to this and see that a meter is 10 to the 16."
},
{
"end_time": 5206.886,
"index": 214,
"start_time": 5178.166,
"text": " Using our formula from above, we get that a meter is this, and I will just put some clouds around this as well. Because we have an inverse meter here, we take the inverses of this. So we take one here minus that becomes a plus one. This then implies that we take the nine, we plus 16 to it. So we get 10 to the 25 GeV squared. This is, by the way, a unit of force like we mentioned before."
},
{
"end_time": 5231.049,
"index": 215,
"start_time": 5207.415,
"text": " Ah, and those again who have watched the Salvatore Pius interview, you know that he mentions the super force, and what the super force is, is this. It's simply the Planck force. Now you should have more of an intuition as to what this actually means. So this is 1, so it's 1 over g, which is what we've calculated before, the square of the Planck mass."
},
{
"end_time": 5247.756,
"index": 216,
"start_time": 5233.217,
"text": " And you can see that makes sense in terms of units because mass squared is the same as energy squared is the same as force. Now, as I've mentioned before, I don't think force is a particularly useful concept in fundamental physics. I think pressure is. So there should be a plank pressure."
},
{
"end_time": 5268.439,
"index": 217,
"start_time": 5248.114,
"text": " And it turns out there is and it's called a plank density. I call it the plank pressure. It doesn't seem like anyone else calls it that. But anyway, how do you get the plank pressure? Well, you take some energy and you divide it by volume. What's the energy that we have? We have the mass, the plank mass, and we divide it by some volume. What's the volume that we have? We have the plank length and we just cube that."
},
{
"end_time": 5296.954,
"index": 218,
"start_time": 5269.582,
"text": " And that's how you derive the Planck pressure. At least that's what I think it should be called. Now at first I was going to draw some picture to give some interesting ideas to what the Schwinger limit is in some fundamental manner, but actually force isn't a particularly interesting concept because it requires extra structure. So for example, we know that we have these inverse squared laws that characterize the Coulomb force and gravity, which technically means that you can get however"
},
{
"end_time": 5321.203,
"index": 219,
"start_time": 5297.5,
"text": " large of a force you'd like depending on how close you are to the original source, to the point source, if it's a point source. This, to me, demonstrates a flaw in Newtonian mechanics from the get-go, and yet it works so well, thus if a particular theory has a major flaw, perhaps give it a chance to breathe before dismissing it as patently broken."
},
{
"end_time": 5343.131,
"index": 220,
"start_time": 5322.142,
"text": " See, all of this is decidedly simple, and often you'll be confused but not know where your confusion is. Often what will happen is you'll ask someone to explain or re-explain some phenomenon or some mathematical trick, and then they'll say, well, what part of it did you not understand? And you won't be able to give an account because your confusion is such that you're unable to see where your confusion is."
},
{
"end_time": 5370.299,
"index": 221,
"start_time": 5343.131,
"text": " that is to say you don't know the aspects of the technique or the mathematical trick or formula or structure etc that you don't understand so asking someone to explain a particular part because you just chosen some party say I don't understand this somewhat fruitless because that was arbitrarily chosen by you this is one of the reasons why it's great to read from multiple sources so watch multiple videos on the same phenomenon the same trick the same formula you'll see professors when they're being interviewed or when you go to their office they'll often have"
},
{
"end_time": 5399.667,
"index": 222,
"start_time": 5370.964,
"text": " a plethora of books and then you think well they're extremely bright and they are they're extremely extremely extremely bright hard-working people but then you wonder why do you have five books on linear algebra and it's because even Ed Whitten needs to read from multiple sources on the same topic in order to truly understand it you need to see it from multiple perspectives actually I spoke to Jordan Peterson about this exact topic I'll leave the podcast in the description so if you feel like some concept is far beyond you perhaps it's not perhaps you need to re-watch the video so you can re-watch this one if you like"
},
{
"end_time": 5427.602,
"index": 223,
"start_time": 5399.667,
"text": " Or you can watch from multiple sources and then it will slowly start to make sense. You'll start to see this baroque, intricate, complex object from multiple perspectives. You can only see a projection of it and then you start to build a shape of it. Seeing it from one source generally doesn't help. To sum up, learn from multiple sources, read multiple sources, watch multiple sources. Sometimes you don't need to know where your confusion is because at least you don't consciously need to know because it will unconsciously resolve itself after learning from different perspectives."
},
{
"end_time": 5456.732,
"index": 224,
"start_time": 5428.456,
"text": " Okay, now let's get to number eight, which is annihilating positron electron pairs and quantum gravity. We got to get through this quick. I'm likely going to turn this screen off. I'm making way too many mistakes. I'm recording this over and over and different parts aren't working. So if there are any errors here, obviously leave them in the comments. It's great if you unceremoniously point them out. I don't mind. I'll highlight them. Annihilating pairs of positron electrons and quantum gravity. So firstly, what happens when you look at the vacuum? You simply look."
},
{
"end_time": 5483.148,
"index": 225,
"start_time": 5457.261,
"text": " Well, we know this relation, which is E, is the inverse of time. And let's imagine that we wanted to create particles that were on the order of an electron, so electron-positron. Then we just replace this E with the mass of an electron. Technically it's 2, but it doesn't matter because we're saying this is on the order of. This means that for a small amount of time,"
},
{
"end_time": 5501.271,
"index": 226,
"start_time": 5483.814,
"text": " an electron-positron pair can be created. And then you can also ask, this is a unit of length, which means that if you were to probe the vacuum, if you were to look close enough, and exactly how close enough? Well, what is Me? Me, remember, it's akin to 1 MeV, which is the same as"
},
{
"end_time": 5521.664,
"index": 227,
"start_time": 5501.527,
"text": " This means looking at empty space itself. If you look close enough, just the act of looking close enough will create the electron-positron pairs. Now this is something you know from quantum field theory. And by the way, when people say quantum field theory, there's not the quantum field theory, there are multiple."
},
{
"end_time": 5542.807,
"index": 228,
"start_time": 5521.664,
"text": " It's more like a framework. So there's five, four, and then there are different. Well, string theory itself can be thought of as a generalization of quantum field theory. So when people say quantum field theory, you should ask them, well, which quantum field theory are you referring to? Now let's talk about quantum gravity. Forget about field theory. When it comes to quantum gravity, there are several conceptual infinities that pop up. So for example,"
},
{
"end_time": 5568.2,
"index": 229,
"start_time": 5550.503,
"text": " So firstly, if you're going to be infinitely accurate about let's say where an electron is, you have to measure it an infinite amount of time or prepare something and then measure that an infinite amount of time because there's an error, an uncertainty associated with the measurement. And then another infinity comes in when you're having to store all of those bits somewhere."
},
{
"end_time": 5594.753,
"index": 230,
"start_time": 5568.2,
"text": " And then you also need to make your apparatus size infinitely large because you want to make sure that there's no quantum fluctuations that make an error in one of your bits, as well as, well, decoherence, etc. So there are many antinomies that crop up, which imply that however we're ordinarily viewing our laws or viewing space-time, it must be some approximation. Also, interestingly enough, when it comes to higher energies, it doesn't mean lower distances when it comes to quantum gravity."
},
{
"end_time": 5604.206,
"index": 231,
"start_time": 5595.23,
"text": " Ordinarily we think, well, you just place in plenty of energy to probe a smaller and smaller distance. Well, that's true, except at some point you create a black hole."
},
{
"end_time": 5626.852,
"index": 232,
"start_time": 5610.196,
"text": " That is to say, if you want to measure a small distance, well, you put in more energy. But if you want to measure an even smaller distance, you put in more energy, at some point you just create a black hole, and then the more energy you put in, the larger the radius of the black hole. So at some point, larger energy actually means larger distance."
},
{
"end_time": 5645.282,
"index": 233,
"start_time": 5626.852,
"text": " And then even more fundamental than that, the black hole will start to evaporate and let out Hawking radiation, which is low energy particles, even though what you inputted was high energy particles. So you get a strange intermingling of high and low and the reversal of it from what you'd expect from our ordinary calculations."
},
{
"end_time": 5665.52,
"index": 234,
"start_time": 5645.316,
"text": " Okay, now let's talk about black holes. So how much density is required to create a black hole? Turns out that's an ill-defined question because we need to pick a test mass. Much like with gravity and the coupling constant, it's dependent upon mass, same with black holes. You can get whatever density you like, so let's just choose a mass and then ask a different question."
},
{
"end_time": 5683.985,
"index": 235,
"start_time": 5665.913,
"text": " How small of a region, what is the radius called the Schwarzschild radius? What is the radius that we can take this mass and squeeze it into such that it will produce a black hole? I'm going to call this Schwarzschild radius capital R and first we need to choose a mass, so let's choose a copacetic one, perhaps the Planck mass."
},
{
"end_time": 5706.305,
"index": 236,
"start_time": 5684.036,
"text": " And then think, well, what region of space, how small do we have to squeeze the Planck mass to create a black hole? We'll do this in a variety of ways. Number one, naively, it's simple. The standard physics folklore says what we do is we take a Planck mass and we stuff it into a Planck length and that creates a black hole. Then we wonder, well, what is a Planck length? What's a Planck length but an inverse Planck mass?"
},
{
"end_time": 5738.712,
"index": 237,
"start_time": 5708.797,
"text": " So let's say Planck length is inverse Planck mass. We've used this answer many times and we're done. That's the answer in one line. We've derived the Schwarzschild radius of a mass Planck, of a Planck mass. Another way of calculating this, again this is also naive, is to think, okay what does it involve? It involves gravity, so Newton's constant, and it involves some mass. Let's give it a variable name for now, mu. So it involves g and it involves mu, which is a mass."
},
{
"end_time": 5769.36,
"index": 238,
"start_time": 5739.411,
"text": " We then use these quantities to come up with a radius, which is length. Now how do we combine g and mu, so Newton and a mass, to make the units match up? Well, it's as simple as combining it in this manner. Because, recall, this is of units inverse mass squared, and this is of units mass, and so we have an inverse mass in total, and this is an inverse mass unit as well. Keep in mind that there are no alphas here, and the reason is that we're not referencing electric charge at all."
},
{
"end_time": 5799.565,
"index": 239,
"start_time": 5770.026,
"text": " Now we know that g is mass Planck squared inverse, and we know that we can set mu, in this case, to be mass Planck, and then we recover the same formula. Let's do another naive calculation. What would the density of such a black hole be? We know that it only involves the Planck mass, and we know the units of density, and so we would imagine that the density would be mass Planck to the fourth, and that's actually correct."
},
{
"end_time": 5830.247,
"index": 240,
"start_time": 5800.367,
"text": " And then for a final way of calculating this, we go to Wikipedia. What is the Schwarzschild radius? And we see that it is R2GM over C squared. Now for us, this 2 drops out because of this symbol here, this on the order of symbol. The C becomes 1, and we then recover GM, which you'll notice is the exact same as this formula that we have here, except we just called it mu, and they called it capital M."
},
{
"end_time": 5857.039,
"index": 241,
"start_time": 5830.64,
"text": " Note one needs to be a bit prudent here because the volume inside a horizon is dependent on the coordinate system and so the densities are also dependent on the observer. If you don't have a lesson on this then it will appear as if this is magic or that it requires years and years of training but it's not either of those two. The popularizers of science have an incentive to mystify these subjects for you unless you're in the universities"
},
{
"end_time": 5875.486,
"index": 242,
"start_time": 5858.131,
"text": " However, it's fairly effortless if it's explained by belaboring these technical details and being extremely precise. Now, you may also say, hey, Kurt, well, I could have come up with any first attempt at a formula G to the power of five and M to the power of two and so on and so on."
},
{
"end_time": 5901.067,
"index": 243,
"start_time": 5876.357,
"text": " or square root of so on and so on. And yes, that's correct, which is why it requires a certain amount of physical intuition as well. However, in this case, the dimensional analysis would make all of this trivial because you have to have inverse square mass as the left and the right side dimension anyway. The left hand side of the radius, the Schwarzschild radius, which is a length, has to match with whatever the units are on the right hand side, which severely limits the amount of formulas you can generate."
},
{
"end_time": 5929.77,
"index": 244,
"start_time": 5901.493,
"text": " Also, keep in mind that some of these formulas depend on the fact that we're in fairly low dimensions. We're in, let's say, dim of our manifold is 4. Well, it's 3 plus 1, so that's space. That's when we're calculating the density of a neutron star and we said, hey, what we do is we look to our left, look up, look down, look toward and backward and all we see are neutrons and thus we get GeV to the fourth."
},
{
"end_time": 5959.753,
"index": 245,
"start_time": 5930.145,
"text": " This actually depends on sphere packing because the atoms act like spheres and in higher dimensions this doesn't work because spheres don't act like cubes in higher dimensions they become less and less of the space and thus over here we're drastically overestimating or underestimating our quantity and this by the way is assuming flat space if we're in hyperbolic space well then it becomes even different there's no limit to the amount of spheres that can surround another sphere and the concept of average quote-unquote density becomes"
},
{
"end_time": 5970.213,
"index": 246,
"start_time": 5960.009,
"text": " One of the reasons for being over-scrupulous is because"
},
{
"end_time": 5994.599,
"index": 247,
"start_time": 5970.913,
"text": " There are enthememes, what are called enthememes, which are unstated data, unstated assumptions that go into an argument. And the reason they're unstated is because they're so simple, they're so familiar. Many people, like even Nima or Connie Hamed, don't go through each of these assumptions. One, it would just take too long. But two is that they're so familiar, they are generally glossed over. But I like to make as much of what's ordinarily below the earth, I'd like to unearth it,"
},
{
"end_time": 6023.66,
"index": 248,
"start_time": 5994.821,
"text": " Because then perhaps you won't be as confused as myself when I was learning these subjects. If you'd like to learn a little bit more about enthememes, some example of them in physics, then you can check out this clip with Luis Elizondo, linked in the description. Okay, so that was a quick detour into quantum gravity. If you want to learn more, like I mentioned, there's an extremely detailed episode on quantum gravity with Salvatore Pius, and that's linked in the description. Now we should get on to the sponsor message. Just so you know, anytime there's a sponsor message on the Toe channel, there's usually a"
},
{
"end_time": 6049.292,
"index": 249,
"start_time": 6024.394,
"text": " Timestamp here that says click on this timestamp. It's somewhere here as well It's in the description because I don't want to manipulate anyone into watching a sponsor message that generally means Because this channel depends on the patrons which we'll talk about and the sponsors That's the only reason I'm able to do this full-time It usually means that the sponsors pay less because people will just click on the timestamp However, I'm hoping and I well, I hope this is the case that in the long run"
},
{
"end_time": 6077.398,
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"start_time": 6049.701,
"text": " the trust that's built between myself and you by seeing you're not being manipulated into a sponsor message you can always click out of them and the sponsors hopefully it's better for everyone the sponsors myself and the audience in the long run now the sponsor for today is brilliant brilliant.org slash toe is where you can visit if you want to get 20% off an annual subscription what brilliant is that it's a website where you can go and you can take courses and they don't feel like courses it makes learning math and science and engineering an extremely"
},
{
"end_time": 6102.654,
"index": 251,
"start_time": 6077.398,
"text": " practical fun enterprise where it's interactive rather than you being told information you can play with the information and speaking of information in a little while from now I hope to speak to Chiara Marletto or David Deutsch on constructor theory and that's heavily based in information theory so I decided to take a course on information theory and from that you find that this formula which I keep referencing over and over"
},
{
"end_time": 6135.265,
"index": 252,
"start_time": 6106.357,
"text": " This formula is an extremely natural formula for entropy and it would be strange to define it in any other manner. Again, visit brilliant.org slash toe to get 20% off your annual subscription. The second sponsor is Algo and Algo is an end to end supply chain optimization software company with software that helps business users optimize sales and operations, planning to avoid stock outs, reduce returns and inventory write downs while reducing inventory investment. It's a supply chain AI that drives smart ROI headed by Amjad Hussain."
},
{
"end_time": 6151.067,
"index": 253,
"start_time": 6135.811,
"text": " You should also know that it's the patrons as well that allow this to happen. I was supposed to spend about"
},
{
"end_time": 6180.179,
"index": 254,
"start_time": 6151.067,
"text": " Two hours on a video like this. It's been almost two weeks at this point because of different errors and so on But I'm able to do this because of the patrons So if you want to support content like this, then please do consider going to patreon.com slash Kurt Jaimungal My wife is also extremely thankful too as now she's full-time with me responding to the community and helping me plan the direction of tow and she's Extremely extremely grateful every time we get a new patron. She's like, oh my gosh, that's so sweet. Oh"
},
{
"end_time": 6207.278,
"index": 255,
"start_time": 6180.179,
"text": " So both my wife and myself, thank you so much. Okay, let's get back to these NCs, these napkin calculations, with one about the length of an atom, the radius of an atom. We'll start to move quick from this point. Let's determine the Bohr radius. We have a model here with the electron on the outside and then the proton in the center. So how do we determine the radius of an atom? Let's call that rA."
},
{
"end_time": 6236.442,
"index": 256,
"start_time": 6211.544,
"text": " Firstly, what do we know? The energy has a contribution that looks like this. This is what we've derived earlier. And we have another contribution, which comes from a kinetic term. And this we can use equation number two, the bolded number two, to change this P square into an R square."
},
{
"end_time": 6269.07,
"index": 257,
"start_time": 6241.852,
"text": " Which mass is this? This is the mass of an electron and for our purposes we can get rid of these factors here and just say well what minimizes this? The graph of this looks like this and then there's a minimum point and then it starts to look like 1 over r in the long run yes it looks like 1 over r and then in the short run it looks like this guy over here"
},
{
"end_time": 6297.159,
"index": 258,
"start_time": 6269.838,
"text": " We want to know what is the minimum point right here. You can differentiate this to get the answer or you can guess and then you get that. The star equation implies. This is the Bohr radius and we were able to derive that and maybe two or three lines with napkin calculations. We can go back over here where I should have said this was the radius of an atom."
},
{
"end_time": 6318.899,
"index": 259,
"start_time": 6299.582,
"text": " And now we get that from equation number star. And by the way, because this is the average speed of the electron of the atom, this is the reason why Schrodinger's equation works because Schrodinger's equation is non relativistic. And you can see that just from the factor alpha, which means Schrodinger got lucky."
},
{
"end_time": 6350.128,
"index": 260,
"start_time": 6321.169,
"text": " Let's skip forward because we're going to need this for our next napkin calculation. I realized that the size of the earth comes first. How would we go about calculating the size of the earth? Well, that occurs when the gravitational pressure is counterbalanced by the atomic pressure. So this is unlike the neutron star, it requires a bit more work. So what is the gravitational pressure? Let's call it capital P and it's going to be some energy over some volume. What energy? Well, the gravitational energy, some M. We don't know what M yet. We'll figure this out."
},
{
"end_time": 6379.65,
"index": 261,
"start_time": 6350.486,
"text": " over r, and then over some volume, so r cubed. However, recall that g, g newton, so the gravitational constant, is the Planck mass squared, inverse. And also, let's make a density. So a density is what? It's some mass over some volume, which is, let's say, mass over r cubed. Then these two combine to help make this and"
},
{
"end_time": 6409.633,
"index": 262,
"start_time": 6380.077,
"text": " That is from one and two, which go into this. Now we would like to know what the atomic pressure is. So this atomic pressure, which I should denote these differently, let's say the pressure due to gravity and the pressure due to the atoms, this atomic pressure is going to be, again, some energy over some volume. So what is the energy? Well, it's going to be the energy associated with the atom, which we have over here. So let's call this EA. EA, and this is going to be over RA to the third."
},
{
"end_time": 6440.299,
"index": 263,
"start_time": 6410.384,
"text": " After substituting, we get... Then we want to know, well, what is this density here, this row? This row is going to be some mass over some volume, because that's what a density is. And what mass? Well, a proton mass over what volume? Making in substitutions, we get one over the Planck mass. This is different. I should have used different notation, but this is the proton mass. This is the Planck mass."
},
{
"end_time": 6461.527,
"index": 264,
"start_time": 6441.305,
"text": " squared alpha sixth m proton squared of the electron and then r squared and this implies that the radius of the earth"
},
{
"end_time": 6502.688,
"index": 265,
"start_time": 6472.79,
"text": " This implies that the radius of the Earth is this. So this is in general for rocky planets. Now this means that alpha factors in, the mass of the electron, the Planck mass, well g factors in, the mass of the proton, all of this comes into play to derive the size of the Earth or the size of rocky planets in general like Mars and Venus and so on. This is what's extremely powerful about this napkin calculation technique and natural units, etc. This was perhaps six or seven lines of derivation that you do in a closet to figure out the radius of the Earth."
},
{
"end_time": 6529.309,
"index": 266,
"start_time": 6503.541,
"text": " By the way, for fun, if you want to calculate what is the weight of the world, you can do so in a second. So we have some guy here, and he is some angry fellow, so let's make him angry. And let's just make the rest of his body a stick figure. And he's holding the world."
},
{
"end_time": 6548.046,
"index": 267,
"start_time": 6532.363,
"text": " Well, what is the weight of the world? The weight of the world, not the mass of the world. Well, you can get the mass from this, but the weight of the world is actually zero. So when you hear that, and the reason is because it's all pointing toward the center, you're experiencing the weight of the world. Actually, the weight of the world, if you want to be Atlas, you just do a handstand."
},
{
"end_time": 6576.92,
"index": 268,
"start_time": 6548.473,
"text": " Because the weight of the world is, well, it's technically zero because it's pointing from every single direction. Zero. Now, the reason why I say technically zero is because then you may say, well, okay, let's imagine that we're here on Earth. So we want the gravitational force of the Earth to hold up another gravitational force. Well, let's say you place some mass here. Yes, it's heavy. Let's say you increase it, you increase it, you increase it to the size of another Earth. Then actually the weight is zero because you're in the in between points of the same masses. So in some sense, the weight of the world is fairly manageable."
},
{
"end_time": 6602.227,
"index": 269,
"start_time": 6577.637,
"text": " Alright, now let's get to cutting a solid. Now, by the way, I left out some factors here, which I've corrected here, and the reason it's written in this manner is because you can then relate the size of the Earth to the size of an atom, and the fact that gravity is quote-unquote weak is what plays into the largeness of a planet, or the smallness of a planet. As for cutting a solid, what we want is just this equation. All we have to do"
},
{
"end_time": 6623.217,
"index": 270,
"start_time": 6602.5,
"text": " is exceed the atomic pressure. All we have to do is just place what is greater than this equation. There we go. Extremely, extremely simple. Notice this. This is the most important aspect of this video is that there's a perspective shift. You can now carry this around with you and do napkin calculations, NCs. You can even leave them in the comments and derive what ordinarily you would think you would need"
},
{
"end_time": 6645.299,
"index": 271,
"start_time": 6623.217,
"text": " nuclear physics or special relativity by the way about special relativity many people talk about time dilation and so on but to me what's most interesting about special relativity is that it messes with what you think existence is it places you in an unhinged manner so let's take a look over here if there's some event that occurs outside your light cone then what's considered simultaneous"
},
{
"end_time": 6673.251,
"index": 272,
"start_time": 6645.776,
"text": " is a dubious concept. The reason being that if you were to say, for example, the corner store, the store on your corner doesn't exist anymore, well, why are you saying that? It's because now it is no longer there. It is now bought by someone else or it is now demolished. Well, there exists another perspective where it does exist. This is explored in the Carlo Rovelli interview, and this is because the notion of simultaneity is placed on an unassured grounding."
},
{
"end_time": 6691.971,
"index": 273,
"start_time": 6674.343,
"text": " Let's get to a laconic derivation of the Casimir falloff. So all you need to know about it is what you've heard from popular science, which is that it's a demonstration of the vacuum fluctuations because there are certain modes that are allowed and not allowed in between the plates. There are more outside than inside, and thus they come together."
},
{
"end_time": 6715.043,
"index": 274,
"start_time": 6692.688,
"text": " You know that it's a pressure, and we have that it falls off as some r to the n. What is the n? What could it be but pressure? So it's r to the 4th. There we go. We get that the Casimir pressure falls off, and it's a minus because it's an attractive force, as 1 over r to the 4. Ordinarily, this is an extremely tedious calculation. We can go to Wikipedia right now just to check."
},
{
"end_time": 6744.735,
"index": 275,
"start_time": 6715.674,
"text": " you can see from Wikipedia that it requires quantum field theory and you go through plenty and plenty of rigmarole just to arrive at this which is the a to the fourth minus that we're referring to these factors are what we firstly these are set to one this is what we didn't derive but you were able to get an estimate now you may wonder why is it that we go through so much pedantic palaver just to arrive at a small correction when we could have done this in one laconic line the reason is that sometimes often you want to be precise for example you don't want a surgeon that"
},
{
"end_time": 6764.292,
"index": 276,
"start_time": 6745.009,
"text": " Approximately operates on you. Thus, in mathematics, one goes through great pains to make explicit each axiom and line of reasoning. Now, there are other reasons for being axiomatic and specific. For example, you may wonder why does it take 100 pages to arrive at 1 plus 1 equals 2. So there are a couple of reasons. So one of the reasons is that"
},
{
"end_time": 6779.616,
"index": 277,
"start_time": 6764.292,
"text": " we don't derive that one plus one equals two we validate the axiomatic system by seeing one plus one equals two as a valid target and knowing we need to hit it seeing we hit it validates the axiomatic system that produced it number two is because now that we have axioms"
},
{
"end_time": 6809.343,
"index": 278,
"start_time": 6779.616,
"text": " and then we saw that something is constructed in this manner because we've set it to be then that means that we can set it differently we could have constructed it differently so for example setting the curvature to zero gives euclidean geometry and then we wonder well what happens if we don't set it to zero then we get more general spaces like non-euclidean geometry which as you know has a crucial role to play in general relativity all right now let's get to analyzing the Sun this one is a simple one we firstly go to"
},
{
"end_time": 6839.667,
"index": 279,
"start_time": 6809.94,
"text": " our friend Google and we search for the sunlight spectrum and we see it looks something like this we see okay this peaks approximately at let's say 500 so it's 500 nanometers is the wavelength we then go to our conversion charts and we see okay we can use equation number three and we're going to use equation number three and we're going to use this and we're going to use this"
},
{
"end_time": 6869.991,
"index": 280,
"start_time": 6841.237,
"text": " to get a temperature this gives a temperature on the order of 5,000 or so, well let's say on the order of it's about 5,000 Kelvin if you want to work it out specifically or you can simply say it's on the order of so and so and we can search what is the temperature of the sun and we see that it's approximately correct"
},
{
"end_time": 6891.476,
"index": 281,
"start_time": 6870.828,
"text": " By the way, it's from this fact that you can look at LEDs that come from your lights or your cell phone screen and determine what temperature it would have if it were a blackbody radiator and note that your cell phone isn't thousands of degrees hot"
},
{
"end_time": 6919.497,
"index": 282,
"start_time": 6891.92,
"text": " Thus allowing you to infer just from a napkin calculation that LEDs that characterize your phone screen don't produce light as blackbody radiators in the same way that, for example, incandescents do. Now let's intuit the radius of the electron. As you know, the radius of the electron is, well, it's a point particle. However, let's think about it classically. So here's how Lorenz and others thought about it classically. We have this electron here. Let's call it E."
},
{
"end_time": 6944.497,
"index": 283,
"start_time": 6919.94,
"text": " and it's emitting some electric field here. What we want is that the energy of the electron, so alpha over Re, which we have before, so the energy of the electron, we don't want that to be much greater than mc squared of the electron. So in our units, mc squared is just m, which implies that Re is simply this."
},
{
"end_time": 6970.196,
"index": 284,
"start_time": 6945.265,
"text": " And there we go. We have a classical derivation of the radius of the electron. It turns out that, and by the way, Lawrence and others thought that, okay, the classical laws have to break down somewhat here. Something strange has to occur at that radius. And they were trying to analyze it and they didn't get the right answers. And that's because quantum mechanics comes in and they had no idea about quantum mechanics, which says actually around the electron is positron-electron pairs and so on."
},
{
"end_time": 6990.452,
"index": 285,
"start_time": 6970.452,
"text": " And so it's cloudy, and the radius of this, if we go in here, the radius of one of these, what is it? What do you think it may be? Well, it's an electron-positron pair, so it's this much. Well, it's two of that, but it doesn't matter. The point is that the law started breaking down at a distance 137 times greater than where they thought it would have broken down."
},
{
"end_time": 7012.927,
"index": 286,
"start_time": 6990.725,
"text": " If we extrapolate this line of reasoning to our current models, that is the standard model in general relativity, while they suggest that there's some breakdown that occurs at the Planck scale, my money would be that new laws would be required far before we get to the Planck scale. Maybe not 130 times before the Planck scale, but many, many more orders of magnitude prior to that energy."
},
{
"end_time": 7043.404,
"index": 287,
"start_time": 7014.565,
"text": " Alright, now we're on to solids and x-rays. If we want to find out the number density, that is the number of atoms in a solid per unit volume, what does it look like? Well, number density. Firstly, let's think about the units. It's GeV to some n. What is n? Is it minus 3? It's plus 3. And what information do we have? We have the radius of the atom, and so it's that cubed, and we can use this equation from before."
},
{
"end_time": 7073.114,
"index": 288,
"start_time": 7044.172,
"text": " alpha times the mass of the electron is the radius which means we have which is KeV to the third and this is one of the reasons why it's much better to work with GeVs and so on because this gives you an actual tangible amount you understand what a KeV is and by the way KeV what is its relationship to light that is to say if we're on the order of a length that is let's say just one KeV"
},
{
"end_time": 7094.189,
"index": 289,
"start_time": 7073.49,
"text": " Then we'll need to shine a light whose wavelength is at least 1 keV in order to resolve this distance. I'll explain exactly what that means to resolve it. And then you can wonder, well, what is 1 keV of light? You can look that up online. Let's do that right now. So you can see from this napkin calculation that an x-ray is what allows you to probe solids."
},
{
"end_time": 7122.807,
"index": 290,
"start_time": 7094.189,
"text": " That's why we use x-rays, because their wavelength is just short enough to resolve the distance of the atoms within a solid. And when we talk about a certain wavelength as what's needed to resolve a certain distance, that was never explained, at least not to me, properly. I always heard of it in terms of balls. You take some large ball and you try and throw it and you try and resolve. You need smaller and smaller balls in order to get higher resolution. But I think a better way of understanding this, understanding why we need x-rays or whatever UV rays, whatever the light is,"
},
{
"end_time": 7141.391,
"index": 291,
"start_time": 7122.807,
"text": " to resolve a certain distance. I think it's better explained like this. If we zoom in here, so let's zoom in. This is, let's see, how many pixels wide? Maybe this is one, two, three. Maybe this is on the order of 50. Who knows? But then if I say, let's pixelate this, let's put it in a mosaic."
},
{
"end_time": 7159.172,
"index": 292,
"start_time": 7145.742,
"text": " See, if we make the cell size, the cell size, by the way, is equivalent to a wavelength. So we want the wavelength small in order to resolve shorter and shorter distances. If we make the cell size"
},
{
"end_time": 7188.985,
"index": 293,
"start_time": 7159.411,
"text": " fairly large like 200 then we can just make out that there exists some substructure here we cannot make out that there was any structure above and as soon as we start reducing it we're resolving with higher and higher frequencies you can think of it like that so if this is let's say on the order of a cell and then we want to get to the order of an atom well we need to shoot smaller and smaller wavelengths of light this corresponds to the wavelength and all the sudden now you can resolve that distance"
},
{
"end_time": 7210.759,
"index": 294,
"start_time": 7189.872,
"text": " I'm placing that as an aside here because the way that it's ordinarily explained is a bit confusing. By the way, based on this number density, you can now get a actual density. So what do you do is you times it by the proton mass, because the proton slash the neutron are what hold the most, well, the largest contribution to the mass. And then you get the density of solids."
},
{
"end_time": 7229.701,
"index": 295,
"start_time": 7211.442,
"text": " Okay, now we're on the last one, the scales of the universe, in particular the Higgs boson, which is extremely easy now that we've gone through"
},
{
"end_time": 7257.688,
"index": 296,
"start_time": 7230.111,
"text": " plenty of these exercises and you're so familiar with natural units and GEVs and so on. What is the scale that you should find the Higgs boson? How far should you zoom in to find it? Well firstly let's go on Google and we see look they give you the mass in terms of GEV. Now this C we set to 1 so this GEV it's 125 GEV 125 GEV Higgs boson"
},
{
"end_time": 7279.565,
"index": 297,
"start_time": 7259.753,
"text": " From the above conversion chart or we can go to a website and see what does that correspond to in terms of length. Now you can see how far do you have to zoom in in order for you to find the Higgs boson. You can convert that or you can use another chart. They're all approximately the same. Remember, we only care about the order. We can also type in, well, what is the LHC?"
},
{
"end_time": 7297.159,
"index": 298,
"start_time": 7279.855,
"text": " What is the highest energy of the particles that have been collided? It's 13 TeV. We covered this earlier. That tells you something concrete about how small the distances are. Now these numbers are no longer foreign to you. You're extremely familiar with manipulating them. You can get a handle on them."
},
{
"end_time": 7324.787,
"index": 299,
"start_time": 7297.602,
"text": " By the way, another reason why they're afraid that black holes could be created, I didn't mention this in the extra dimensions part, but it's because if gravity is leaking in to some other dimension, then that means that gravity is in fact stronger than we think somewhere else. So it's weaker here, but it's stronger somewhere else. And so what we think of what would ordinarily create a black hole, the conditions may be much smaller because gravity is much stronger than we think. Though luckily the Earth hasn't been enveloped by a black hole, at least not yet."
},
{
"end_time": 7352.125,
"index": 300,
"start_time": 7328.831,
"text": " Okay, great. You should congratulate yourself because in about two hours or an hour and a half, however long this video is, you've now covered quite a significant amount of work. We've gone through Newton's constant and seeing that it's actually mass dependent or energy is proportional to the mass to the inverse square of a mass and pressure and speed is dimensionless."
},
{
"end_time": 7381.118,
"index": 301,
"start_time": 7352.654,
"text": " The pressure in a neutron star, the proportionate strength of forces, knots and extra dimensions, calculating the Schwinger limit, just getting a handle on it, the size of the Earth, analyzing the Sun, the Casimir effect, how it falls off, a vacuum expectation energy, the length of an atom, microtubules, the Higgs boson, the God particle. You even learned about deriving the Schwarzschild radius and black holes. And by the way, for fun, these acrostically spell out napkin calculations."
},
{
"end_time": 7405.111,
"index": 302,
"start_time": 7382.346,
"text": " All of this becomes virtually child's play once you use natural units and then some physical intuition. Alright, now continue watching for the next couple of minutes because this will help you contextualize what came before and so it will stick more readily. Recall, unlike giving viewer exercises, which is par for the course in most courses and lectures and so on,"
},
{
"end_time": 7425.538,
"index": 303,
"start_time": 7405.913,
"text": " People almost never do exercises, including myself, and I'm extremely motivated to do so. The most nourishing approach is to provide a point of view shift. And that's what you now have. There are a variety of phenomenon that you can now do an NC to so a napkin calculation. And if you find a particularly inventive one, then share it in the comment section, but delineate each step."
},
{
"end_time": 7449.002,
"index": 304,
"start_time": 7425.538,
"text": " Don't skip when explaining to people. Now, as you go through life and you want to develop a bit more of a physical intuition, then constantly think about what you're seeing and the numbers that you're hearing and the lengths and the times and the quantities, etc. in terms of GEV. And also think about how you can derive them from these somewhat fundamental principles. A last note on learning. Every time that you hear someone describe some object in a different way,"
},
{
"end_time": 7478.353,
"index": 305,
"start_time": 7449.497,
"text": " So for example, you may hear me refer to fields in some other video as a group twice over. And what's meant by that? What do I mean by that? It's that you have these field axioms. So commutative, associative, neutral elements, so on, so on, so on. And it's two of them. Whereas one of these is like a group, a commutative group. And so it's somewhat like a twice over group. This is false because there's an interplay between these. Like you need to exclude the neutral element here for the multiplicative inverse and so on."
},
{
"end_time": 7502.995,
"index": 306,
"start_time": 7478.643,
"text": " However, the point is that when you hear someone explain something that you think you know, but explained in a different way, it's useful to write that down in some reference document, and then eventually go back and think, how are all these disparate lessons or views the same? Another one may be, how are all the exponentials, the definitions of exponentials, the same? So we know that an exponential map goes from TEG, so the Lie algebra, to the group itself."
},
{
"end_time": 7532.756,
"index": 307,
"start_time": 7503.2,
"text": " Well, how is that related to what we know as e to the e squared, for example, equals so and so on as a number? By the way, almost no one will do this exercise. That is, you write down the disparate lessons and teachings and then you try to relate them. There's about n choose two of them. So how is this related to that? How is this related to that? How is this related to that? How is this related to that? And so on. Almost no one will do that because it's extremely tedious, which means if you do this, then you'll garner far more insight than your peers. Maybe that"
},
{
"end_time": 7555.145,
"index": 308,
"start_time": 7533.473,
"text": " That competitive edge will tickle your rivalrous nature. If it does, then you can use it as motivation. And for myself, I may be doing a video at some point. I'm not don't hold me to this on how the various definitions of entropy are all related. So there's Shannon, there's thermal, there's neg entropy, there's residual entropy, and so on and so on."
},
{
"end_time": 7571.391,
"index": 309,
"start_time": 7555.52,
"text": " As I mentioned before, this video will be akin to an introduction to another video that I plan on releasing at some point. Now this one has taken way, way, way too long. So perhaps I thought I was going to do it in a few months. This going through a theoretical physics paper you don't currently understand. I was"
},
{
"end_time": 7600.691,
"index": 310,
"start_time": 7571.63,
"text": " Going to go through geometric unity. Perhaps I won't do that in a few months. Perhaps it will be the winter time now because this is way, way, way more difficult than I thought it would be. Regardless, you can expect that at some point. So the question is, is this leading anywhere? This lecture is series and I don't plan on releasing more content like this as this is not my forte. I'm interested in what I call explicating the landscape of theories of everything, which means to intensely investigate each toe. Geometric unity Wolframs. So there's a thumbnail here you can click on or in the description."
},
{
"end_time": 7627.739,
"index": 311,
"start_time": 7601.015,
"text": " Thomas Campbell's, there's theories on consciousness. There's Veltan Shaung's like Ian McGilchrist and John Vervecky I mentioned before. There's interpretations of quantum theory like Carlo Rovelli and Nicholas Gisson. There's even how to go about learning mathematics with Norman Wildberger and Richard Borchardt. I highly recommend both of their YouTube channels by the way. Norman in particular is great at making whatever is complex seems so elementary that it's criminally humiliating."
},
{
"end_time": 7651.032,
"index": 312,
"start_time": 7628.507,
"text": " Now most people have a subscriber request, but I have a request for you to not subscribe unless you are interested in podcasts about the above, as this channel's bread and butter are those podcasts. You will be sorely disappointed if you expect more videos like this, so check out some of the other podcasts on this channel. Here's a playlist for you to get started. Also it's linked in the description."
},
{
"end_time": 7677.961,
"index": 313,
"start_time": 7651.681,
"text": " Again, if you have an interesting NC about some napkin calculation, about some observable that ordinarily is a tedious calculation that you can arrive at simply from this new natural unit point of view, then make sure to leave it in the comments and make it clear what each step is. Don't skip any steps. I'll also place a thread in the subreddit reddit.com slash r slash theories of everything and I'll try to comment on the most interesting ones."
},
{
"end_time": 7703.712,
"index": 314,
"start_time": 7677.961,
"text": " If you want to share or get feedback on your NC or on your theory of everything, let's imagine you have one, then or some ideas to one, then go to the Discord. That's also linked in the subreddit below. Again, like I mentioned, there's no one source on this. It's strewn generally across several lectures and you start to intuit it as a physics student. However, videos that served as inspiration to this one are that of Nima Arkani Hamed, Andrew Dotson,"
},
{
"end_time": 7712.995,
"index": 315,
"start_time": 7704.497,
"text": " Pretty much physics and Sabine Hassenfelder. I recommend you check out all of those channels. The links to their work are in the description. Thank you and take care."
},
{
"end_time": 7735.316,
"index": 316,
"start_time": 7716.101,
"text": " The podcast is now finished. If you'd like to support conversations like this, then do consider going to patreon.com slash C-U-R-T-J-A-I-M-U-N-G-A-L. That is Kurt Jaimungal. It's support from the patrons and from the sponsors that allow me to do this full time. Every dollar helps tremendously. Thank you."
}
]
}No transcript available.