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Intro to Modern Physics in 13m (Primer for Noobs 2023)
January 10, 2023
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The Economist covers math, physics, philosophy, and AI in a manner that shows how different countries perceive developments and how they impact markets. They recently published a piece on China's new neutrino detector. They cover extending life via mitochondrial transplants, creating an entirely new field of medicine. But it's also not just science they analyze.
Culture, they analyze finance, economics, business, international affairs across every region. I'm particularly liking their new insider feature. It was just launched this month. It gives you, it gives me, a front row access to The Economist's internal editorial debates.
Where senior editors argue through the news with world leaders and policy makers in twice weekly long format shows. Basically an extremely high quality podcast. Whether it's scientific innovation or shifting global politics, The Economist provides comprehensive coverage beyond headlines. As a toe listener, you get a special discount. Head over to economist.com slash TOE to subscribe. That's economist.com slash TOE for your discount.
Given that you're listening to this on audio, you should know that the YouTube version of this podcast is the best version because of the visuals being referenced. Either way, thank you and enjoy. 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?
It's operational. 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 says here, the second is equal to the duration of nine 192631 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 French. 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. And 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. There's some controversy with what's considered natural because when someone comes to you with a
some dish and they say this is a natural dish and that's unnatural well what do you mean that that those Doritos that 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 that 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. 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. Let's say slash ratios.
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 did your craft weigh? And they say, oh, it weighs four Garvars. And then you're like, what the heck is a Garvar? And they say, well, that's how much liquid we release from our Borbans every two Farcals.
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.
Hear that sound? 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.
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. 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 Brooklyn. 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 slash theories, all lowercase.
go to shopify.com slash theories now to grow your business no matter what stage you're in shopify.com slash theories 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
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, 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. 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. 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 one c equals one what they actually mean is that we are now using units where we've taken that two nine nine seven nine two four five eight 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 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 that 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 an 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 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. 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 now let's say we want to measure someone else let's say some let's say Goku so what is Goku 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, prices 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 say is
0.00000000005 I'm making this up of these speed of light units. That's what it means. Okay, 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 C 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
Welcome to the Theories of Everything podcast. You just watched a clip from a much larger two-hour video lesson including what to do with these natural units, such as how to calculate the radius of a black hole in five seconds. No joke. As well as the vacuum energy of the universe, as well as the pressure inside a neutron star, some facts about extra dimensions and quantum gravity. To watch it, click here. Think Verizon, the best 5G network is expensive? Think again. Bring in your AT&T or T-Mobile bill to a Verizon store
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"text": " 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. Now look, this is actually what C is. C refers to all of this."
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"text": " c doesn't just refer to the magnitude c refers to the entirety of it including the units so when someone says c equals one c equals one what they actually mean is that we are now using units where we've taken that two nine nine seven nine two four five eight 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 this is not ordinarily explained and it's because"
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"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 that 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"
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"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 an 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"
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"end_time": 820.964,
"index": 33,
"start_time": 798.626,
"text": " 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": 846.834,
"index": 34,
"start_time": 821.22,
"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. 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": 876.834,
"index": 35,
"start_time": 847.568,
"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": 905.896,
"index": 36,
"start_time": 877.346,
"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 now let's say we want to measure someone else let's say some let's say Goku so what is Goku Goku"
},
{
"end_time": 918.592,
"index": 37,
"start_time": 906.664,
"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? Well, that's let's say two Lady Gaga's."
},
{
"end_time": 937.21,
"index": 38,
"start_time": 918.882,
"text": " 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, prices 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": 954.224,
"index": 39,
"start_time": 937.21,
"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": 978.353,
"index": 40,
"start_time": 954.224,
"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 say is"
},
{
"end_time": 994.974,
"index": 41,
"start_time": 978.677,
"text": " 0.00000000005 I'm making this up of these speed of light units. That's what it means. Okay, so this is all including By the way this right here. This is all foolish"
},
{
"end_time": 1023.456,
"index": 42,
"start_time": 997.193,
"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": 1036.749,
"index": 43,
"start_time": 1023.456,
"text": " and that's where this is misleading because it's just showing you the magnitude how the heck can C 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"
},
{
"end_time": 1062.995,
"index": 44,
"start_time": 1037.619,
"text": " Welcome to the Theories of Everything podcast. You just watched a clip from a much larger two-hour video lesson including what to do with these natural units, such as how to calculate the radius of a black hole in five seconds. No joke. As well as the vacuum energy of the universe, as well as the pressure inside a neutron star, some facts about extra dimensions and quantum gravity. To watch it, click here. Think Verizon, the best 5G network is expensive? Think again. Bring in your AT&T or T-Mobile bill to a Verizon store"
},
{
"end_time": 1087.159,
"index": 45,
"start_time": 1067.449,
"text": " . . . . . . . . ."
}
]
}No transcript available.