The Interesting Physics of Robert Oppenheimer (not the bomb) - Sixty Symbols
The Interesting Physics of Robert Oppenheimer (not the bomb) - Sixty Symbols
Transcript
00:00 Oppenheimer, right? I thought it was amazing. I got serious
00:02 physics fanboy vibes. I loved it.
00:05 So I thought it'd be nice to sort of talk a little bit about Oppenheimer.
00:08 But I didn't- I didn't see any point in talking about the whole atomic bomb project, the Manhattan Project, because obviously that's
00:13 big in the film.
00:14 I thought I'd talk about some of Oppenheimer's great physics prior to that, of which there is some really great physics.
00:20 So I picked out four papers that I think are probably his four most important papers in my view. And
00:28 the funny thing about them is, is that I think every single one of these papers- now Oppenheimer never won a Nobel Prize, right?
00:34 But I think every single one of these four papers has led to somebody else getting a Nobel Prize.
00:39 This just sort of demonstrates, you know, Oppenheimer wasn't just about the Manhattan Project and the leadership he showed there,
00:45 whatever you think about that, it- he- he was- he was a great physicist.
00:50 And so I think we should talk about that. First paper, right, first paper. Now they do mention his paper in the film, his paper
00:56 with Max Born in 1927. So Max Born was one of the
00:59 great physicists, won the Nobel Prize in I think 1954
01:03 for his work on the foundations of quantum mechanics. But do you know whose granddaughter was?
01:08 - Was it Olivia Newton-John? - It is Olivia Newton-John, yeah.
01:12 Exactly, yeah. Olivia Newton-John is his granddaughter. Anyway, we're not here to talk about Max Born, we're here to talk about Oppenheimer.
01:18 Well, we're here to talk about this paper. Okay, so what is this paper about? This is their 1927 paper on
01:24 basically molecular quantum mechanics. As I said, they talk about it in the film, but briefly. So what- what is it-
01:30 what does it do? What even is this?
01:32 Okay, so what they're doing is- so this is right at the beginning of quantum mechanics, and people are using this new theory to try
01:39 to describe, say, atoms and understand this sort of spectrum of these atoms, you know, the locations of their energy levels and so on.
01:45 So these guys wanted to apply that to molecules. They're a much more complicated problem.
01:52 But they wanted to essentially try to figure things out for molecules.
01:55 How did- so I wanted to sort of demonstrate kind of what they did.
01:59 So I'm gonna- I've got some- I'm gonna make a molecule, right, to try and illustrate what- what
02:04 Born and Oppenheimer did. The molecules have gone bloody everywhere.
02:09 Okay, so these- these are not molecules, these are gonna be my nuclei. So I've got some big molecule,
02:14 it's got- well, a big molecule has lots of nuclei and lots of electrons floating around.
02:18 So these are the nuclei, these are gonna be the nuclei. Imagine there's loads of these guys, right?
02:22 You know, different nuclei in this molecule. And I've also got a bunch of electrons
02:27 floating around them. These are my brother's old marbles. I don't know why I've got them, but anyway.
02:33 So you've got a load of electrons. - (You're gonna regret that.) - I am regretting it already.
02:41 I got a load of electrons floating around these nuclei, very complex, loads of-
02:47 there's loads of electrons, there's loads of nuclei. It's a very complex problem, mathematically.
02:51 So what- what's- what the- these guys were trying to do is they were trying to apply
02:54 Schrodinger's equation to this- to this problem. Schrodinger's equation is this sort of- it's the equation-
03:00 one of the main equations of quantum mechanics developed a few years earlier by- by Eben Schrodinger.
03:05 And it allows you to sort of calculate those- those energy levels, those- you know, the spectral lines of these-
03:11 whatever you're interested in, an atom, or in this case a molecule. For a molecule, it's complicated.
03:16 Why? Because you've got all these electrons with all their different positions,
03:19 you've got all these nuclei with all their different positions. It's a really complicated equation to try to solve.
03:24 So Oppenheimer and Born, they said, well, okay, we need- this is too hard.
03:28 We can't- we can't possibly handle this this way. So they- they came up with a really clever approximation scheme to try to solve it.
03:34 So you've got to remember that in reality all these things are whizzing around, right?
03:39 They're moving about and so on and so forth, right? But- but what
03:43 Born and Oppenheimer realized was this, that actually these nuclei, right, these guys, are actually much heavier than these electrons.
03:50 Okay, so nuclei are much heavier.
03:53 So,
03:54 there's an approximation which works really well where you can assume that these guys are not moving,
03:58 okay, whereas the electrons are. So you assume- so some approximation that these guys are not moving.
04:04 So you do the calculation assuming that these guys are fixed.
04:06 They're fixed in space and you allow all the electrons to whiz around.
04:10 And you solve for the electronic energy levels, the energy levels from the electronic system,
04:15 the electrons themselves. You solve that and you get an answer.
04:18 And it's a number, it's an energy that depends on where you put these.
04:23 Okay, so if you put them in a slightly different place, you might get a slightly different answer.
04:27 But whatever the answer- but they're still fixed,
04:29 but the answer that you get for the energies and levels of these- this electronic system is coming- depends on the locations of these things.
04:37 Okay, so that's the first pass.
04:41 Then what they do is they feed that answer for the electronic energy levels
04:44 into the full system again, and they start allowing these nuclei to move.
04:49 Okay.
04:51 But they move in a potential set up by the electrons that he's just calculated.
04:55 And then they use that to then go again with Schrodinger's equation and solve for the full system and get the full
05:01 set of energy levels for the- for the whole molecule.
05:04 In a really- really reducing the complexity of the problem and getting a really good approximation.
05:10 -What are you getting an approximation of? The final answer that spits out at the end
05:14 is
05:15 energy levels. -It's the energy levels, it's the spectrum of the molecule.
05:19 So the different energy levels that it can have, right?
05:21 So that's what you're doing when you're doing quantum physics, this kind of thing you're interested in.
05:24 So yeah, that's what they were after. -In much the same way atoms have energy levels, molecules have energy levels. -Exactly, exactly.
05:31 But it's a much more mathematically complicated problem to solve in the case of molecules because it's just- just- look at the mess!
05:38 There's so much stuff here. And I've only got three nuclei here, in reality you're gonna have a lot more.
05:43 Okay, so it's a very complicated problem, but they managed to find- it's a classic physicist technique. Let's look at a problem.
05:48 Okay, this is way too complicated to solve. I've got the right equation,
05:52 but I can't solve that equation as it is. I need to figure out
05:55 what is the physics that allows me to sort of get to an answer that I can use.
05:59 And the physics here is that the nuclei are actually just a lot- a lot heavier than the electrons.
06:04 So interestingly this- so this is
06:07 a really, really important result in chemistry. So I decided to ask Martin about it. You know, Martin Polyakov, who does your periodic videos.
06:15 I asked him, you know, what's-
06:18 give me a flavour of the impact of this. And Martin told me that- he said, yeah, Born-Oppenheimer approximation,
06:23 it's really, really important in chemistry. He said- but he hadn't realised until
06:27 watching the film that it was the same guy who did the atomic bomb.
06:31 I was like, Martin, come on! So the 2013 Nobel Prize for chemistry was basically really using Born-Oppenheimer approximation
06:38 in what it did. And there's even- the Born-Oppenheimer approximation is so important in chemistry
06:43 that there's even a branch of chemistry which is not doing the Born-Oppenheimer approximation. That's how sort of
06:49 embedded it is with it for chemists. So next paper, Oppenheimer on his own.
06:54 Really short paper, not mentioned in the film at all.
06:59 It's part of- it's only two pages long, as you can see.
07:02 I think this is his Annus Mirabilis, right? You know, people talk about Einstein 1905.
07:07 I think 1930 was a really impressive year for Oppenheimer, some great papers that year. This is one of them.
07:12 This is where he essentially predicts the existence of positrons.
07:16 Just almost, right? It's- so just a bit of history. So a couple years earlier,
07:23 Dirac had- we talked about Schrodinger's equation describing quantum mechanics. The thing about Schrodinger's equation
07:29 is it's not a relativistic equation. It doesn't deal with- it doesn't include the symmetries of Einstein's theory of relativity.
07:36 It's a non-relativistic equation.
07:38 So people wanted to extend those ideas to include Einstein's theory of relativity.
07:43 So that's what Dirac did, Paul Dirac, you know, the British physicist.
07:46 And he came up with an equation which was a relativistic equation, a version essentially of
07:52 quantum mechanics.
07:54 And
07:55 that equation was used to describe the electron.
07:58 But one of the weird things, to make it relativistic, it came at a catch. There were extra solutions to the equation.
08:05 So the equations didn't just describe an electron. It predicted that there had to be some other ingredient there, another type of particle
08:12 that actually had the opposite charge to the electron, so positive charge.
08:16 So everyone's like, well, it's not like
08:19 it's another state of the electron, because it's not like the- there's no transition which takes the electron to a positive,
08:25 the, you know, something with positive charge. That's not a thing that exists.
08:28 So they really thought that this extra solution to Dirac's equation had to be,
08:32 you know,
08:34 another particle.
08:36 There should be a particle that's with positive charge that we can identify with the other solution to Dirac's equation.
08:40 And of course everybody at the time was screaming, well, it's the proton, right? Obviously it's the proton, right?
08:45 Well, Oppenheimer wasn't so sure.
08:48 So he looked at the arguments in favor of people saying it had to be the proton.
08:52 Dirac himself was pushing for it to be the proton.
08:55 Oppenheimer said no, and basically it's very- really, really simple argument.
08:59 So he said, if you think this guy's the proton, and this is the theory describing both the proton and the electron,
09:04 then when you scatter light
09:07 against an electron, it should pretty much behave in the same way as when you scatter light against a proton.
09:13 And we know that it doesn't. The scattering is slightly different. And the difference is weighted by the difference in their masses, by the way.
09:20 And so what Oppenheimer said is actually,
09:23 this other solution to Dirac's equation is not the proton. It's got to be a- it must be another particle
09:30 with positive charge that has the same mass as the electron.
09:33 Okay? That is the property of the positron.
09:37 But he stopped short of predicting that it should exist, because he didn't quite- his interpretation was he didn't quite buy Dirac's theory.
09:44 It wasn't 100% taken by it. There were some other calculations he'd done which he thought were not quite agreeing with experiments.
09:50 So he wasn't quite convinced by it at that stage. Now Dirac's equation is basically right.
09:55 Dirac himself then took what Oppenheimer and
09:59 Hermann Weyl as well had said afterwards and said, right, okay, this is- this is really predicting another particle. And he predicted the
10:06 positron, essentially, which was then discovered a few years later. Incidentally discovered, it was discovered by Anderson, but
10:12 that- he gets the credit for it. Anderson gets the credit for discovering the positron. But actually,
10:17 Blackett, who- people who've seen the film will know, Blackett features in the film.
10:21 He's the Cambridge professor at the start of the film, right? He actually discovered it first, but he published it after.
10:26 So there's a little bit of another connection to the film there. But anyway, yeah, positrons,
10:30 essentially predicted by- by Oppenheimer, but he never got the credit for it. Next one. Okay, another 1930 paper, right?
10:37 So as I said, is- is Anis Mirabilis in my view. Okay, so what's he doing here?
10:41 Again, he's playing- this is when he was working with Wolfgang Pauli, by the way.
10:46 Wolfgang Pauli, great physicist, one of the fathers of quantum mechanics.
10:50 Probably heard of the Pauli exclusion principle, which named after him. Very much a sort of, you know,
10:55 no-nonsense physicist as well, actually. But he really respected Oppenheimer. In fact, this is what he said about Oppenheimer.
11:00 He said, "Oppenheimer's physics is always interesting,
11:04 but his calculations are always wrong."
11:07 So, but actually this is a calculation that- that-
11:10 that- that Pauli had sort of nudged Oppenheimer towards, that actually I think he got the calculation right.
11:15 Anyway, so what was it about? Well again, they were- they were thinking about
11:19 Pauli in particular being worried about- about the electron, and in particular something called the self-energy. So what's that?
11:25 So you think about an electron as a- people talk about the electron as a point particle, and they were talking about it as a
11:30 point particle then. A particle, a charged particle moves, you know, it responds to an electromagnetic field, right?
11:36 It moves within it. What Pauli realized was that the electron itself
11:40 was creating its own
11:43 electromagnetic field.
11:45 So it should have- it should respond to its own electromagnetic field. And you can think about this as it-
11:50 it sort of- it gives the- the electron an energy.
11:53 But the problem is
11:56 the-
11:57 the energy that you get from its electromagnetic- its own electromagnetic field, if you do this calculation classically,
12:03 because the electromagnetic field blows up to infinity at the point of the electron itself,
12:07 so does the energy it wants to endow the electron with, this self-energy. It blows up, it becomes infinite.
12:13 So Pauli realized this can't- can't be right. Okay, the electron doesn't behave as if it's got infinite energy,
12:19 which is the same as infinite mass. It doesn't behave like that. So this had to be wrong.
12:23 So he said, well maybe the solution to this, which we're treating this problem classically,
12:27 maybe if we think about it quantum mechanically, using Dirac's theory, we can take care of this. We can fix this problem.
12:33 So he set Oppenheimer on it.
12:36 So Oppenheimer did the calculation. Now he started to do the calculation,
12:40 not in a- in a sort of obscure setting, but in this- he wanted to look at the calculation in a physically meaningful setting.
12:47 So something where- where the quantities you're actually calculating are physically measurable.
12:51 So he decided to look at the- at the energy levels of hydrogen- of the hydrogen atom,
12:55 and the- and you know, and the electrons in- in- in orbit around it. So- so he calculated this.
13:01 And indeed he found
13:04 that when he went to sort of higher order in his approximations, that indeed an infinite contribution
13:10 was always there.
13:13 So this energy of the electron was always getting this infinite contribution.
13:17 You have to go- it didn't happen at first order approximation,
13:20 but when you get to next order, higher order in its approximations, this infinite contribution appeared.
13:24 Now again,
13:27 his interpretation of this was, the theory's probably just wrong, right?
13:32 The- the electron doesn't have this infinite energy. It doesn't have infinite mass. Well, this is obviously just wrong.
13:37 But no,
13:39 it wasn't wrong, it was right. It took about 15 years later, eight or so,
13:43 Feynman, for example, Schwinger, Tominaga, they came up with the theory of renormalization, which we- we should probably do a video out,
13:50 but it's a whole other story.
13:52 But essentially what- what you do there is you realize you can add an infinite correction to this,
13:56 and come out with a final answer. And you can do this in a consistent way that all makes sense, and you can make
14:02 concrete predictions. Okay, so Oppenheimer missed that, but he was- his calculation was really the seed
14:08 for trying to understand what was really going on. - (He sowed a lot of seeds!)
14:12 He did sow a lot of seeds. Should we do his final seed? - (Yeah.) Okay, his final seed.
14:16 Again, this final one is-
14:19 is alluded to in the film.
14:22 It's his work on black holes.
14:24 And probably nowadays this is, you know, well, it's hard to say which is the most important, but this is really important. So
14:30 there's actually a few papers this year in 1939 that he'd started working on sort of more asteroid type stuff.
14:36 He started looking, for example, at the structure of neutron stars and trying to find equilibrium solutions,
14:42 solutions to general relativity that could describe a neutron star. And one of the things he realized there was,
14:48 was that- that the- there was a maximum mass that a neutron star could have
14:52 for it to be stable and in equilibrium. If you went beyond a certain mass, in his case he said it was 0.7 solar masses,
15:00 actually
15:02 that calc- that's a bit of an underestimate based on how he modelled the star, but the ideas were right. - (His physics was interesting.)
15:08 His physics was interesting. - (His calculations were.) Yeah, exactly, exactly.
15:11 So, so,
15:13 it's probably close. It's a high- slightly higher number than that.
15:15 But, but the fact is true. There is a maximum size that a neutron star can have and be stable,
15:21 okay, and be in equilibrium. So he'd realised this, right? He said, okay, well, what if I go to higher masses? What happens then?
15:28 Well, like we know it can't be a neutron star. We know it can't be stable.
15:31 Okay, so what happens? And he was the first person to really start to think about this.
15:36 And he realised, he started studying, he realised that actually these things were going to collapse into black holes.
15:41 He was the first person to really sort of model on it in anything like a realistic scenario.
15:46 And it's really cool actually. Now with the sort of modern eye,
15:49 you can really understand this paper in a kind of a much deeper way. And this is essentially what he had.
15:53 So he set up a problem. Oppenheimer was a great physicist in that he had this knack for sort of
15:58 cutting through to, cutting out all the guff,
16:01 and zooming in on the real problem and doing the right, the interesting approximation that captured all the really essential physics.
16:07 So in this case, he just took a spherically symmetric star, okay, that's an approximation clearly,
16:12 and he just assumed constant density. Again, an approximation, not realistic, but enough to capture the really important physics.
16:19 And he realised that outside the star,
16:23 it would have a solution which was Schwarzschild's solution, which is the solution for a spherically symmetric
16:28 distribution of anything in vacuum, in general relativity. It's the solution that if you
16:35 take it to its extreme, you will get a black hole. But
16:38 he had this star sitting there. So it was only the exterior solution which sort of
16:42 fed into Schwarzschild, right? So it wasn't a black hole yet.
16:46 Inside the star, he realised that the geometry,
16:49 inside the star, was that of a
16:53 basically a universe, a section of a cosmological space-time that
16:58 had constant density,
17:01 but actually it was a contracting universe.
17:03 And so this model is a model of a star which where you have this distribution of
17:08 mass,
17:11 spherically symmetric distribution of mass. It won't be stable, it will shrink, it will collapse. Eventually that star will collapse
17:20 to within its event horizon,
17:22 okay, and then it now becomes a black hole.
17:25 And he was the first person to really realise that process could happen. And the other thing is
17:30 he also talked about what it would look like. And it's again the first time I think anybody ever discussed this.
17:35 He realised that if you were riding on the edge of the star as it was, as it was collapsing,
17:40 then, you know, let's say you take something like the sun and it was collapsing to form a black hole. Take a few hours, right?
17:48 Eventually it falls behind the event horizon and then there is no return after that.
17:53 But, you know, it takes a few hours for that to happen say.
17:56 In the case, but for somebody watching far away,
17:59 Oppenheimer realised it would actually take an infinite amount of time for that to happen.
18:03 This is, this is something, this is one of these weird quirks of when you look at a black hole, you
18:07 see somebody fall into a black hole. You actually, if you're watching from far away, you never see them fall in.
18:12 That guy falls in and he's pretty, pretty quickly ends up
18:16 turned to spaghetti. But you watching him, you never actually see him cross the event horizon of the black hole.
18:21 So Oppenheimer realised all this. And this was, this was really a forerunner to, to
18:26 very early days. People weren't taking black holes seriously, but Oppenheimer really started to do that.
18:31 And Roger Penrose, when he got his 2020 Nobel Prize, really cited this paper as the real inspiration
18:38 for his work in the 1960s with Stephen Hawking on, on black holes being, well, black holes basically.
18:45 So yeah, his final paper. Oh, by the way, this is really quite amazing actually.
18:49 This paper, this is the last of the ones that, that we, that we've talked about. The date it was published,
18:56 I always forgot to say this, the date it was published, September the 1st, 1939.
19:00 Do you know what else happened that day?
19:02 - 1939.
19:05 - Was it the, was it the start of the war? - That was the day Hitler invaded Poland.
19:08 It's an amazing coincidence, right? And that was, that's the,
19:12 and this is really the last really significant paper that, that Oppenheimer wrote, published on the day that Hitler invaded Poland.
19:19 Check out the video description for some links relating to this video, to other videos we've done with Tony,
19:26 and his book, Fantastic Numbers and Where to Find Them, A Journey to the Edge of Physics.
19:32 Anyone who's seen Tony's Numberphile videos will be unsurprised to learn
19:36 there are all sorts of huge numbers in this book, plus some fascinating and curious physics.
19:42 As I said, links in the description.