In Our Time - Paul Dirac

Episode Date: March 5, 2020

Melvyn Bragg and guests discuss the theoretical physicist Dirac (1902-1984), whose achievements far exceed his general fame. To his peers, he was ranked with Einstein and, when he moved to America in his retirement, he was welcomed as if he were Shakespeare. Born in Bristol, he trained as an engineer before developing theories in his twenties that changed the understanding of quantum mechanics, bringing him a Nobel Prize in 1933 which he shared with Erwin Schrödinger. He continued to make deep contributions, bringing abstract maths to physics, beyond predicting anti-particles as he did in his Dirac Equation.With Graham Farmelo Biographer of Dirac and Fellow at Churchill College, CambridgeValerie Gibson Professor of High Energy Physics at the University of Cambridge and Fellow of Trinity CollegeAndDavid Berman Professor of Theoretical Physics at Queen Mary University of LondonProducer: Simon Tillotson

BBC Sounds, music, radio, podcasts. Thanks for downloading this episode of In Our Time. There's a reading list to go with it on our website, and you can get news about our programs if you follow us on Twitter at BBC In Our Time. I hope you enjoy the programs. Hello, Paul Dirac, 1902 to 1984, made some of the greatest discoveries in 20th century physics, second only to Einstein. He used beautiful mathematics to reveal the fundamentals of nature, such as antimatter,

and his ideas have been described as exquisitely carved marble statues falling out of the sky. Yet while there are many statues of Einstein, there are barely any of Dirac, even in his native Bristol, despite his Nobel Prize, his plaque in Westminster Abbey, and Stephen Hawking's claim that Dirac was the greatest British theoretical physicist since Newton. With me to discuss Paul Dirac's work and life are David Berman, Professor of Theoretical Physics at Queen Mary, University of London. Val Gibson, Professor of High Energy Physics at the University of Cambridge and Fellow of Trinity College,

and Graham Farmelow, biographer of Derek and fellow at Churchill College, Cambridge. Graham Faramolo, can you tell us about Dirac's early childhood and his relationship with his parents? Yeah, well, Dirac said that he never had a childhood, and what he meant by that was that it was unlike any typical childhood that he came to know about. He was in an unusual family. His father was Swiss, his mother, Cornish.

He had a brother and a sister. They had almost no family visitors, and the father insisted on speaking to his children only in French. Mother insisted on speaking only in English. So there was this kind of balkanisation where he would sit with his father speaking only in French, while his mother and the other two siblings were speaking only in English. English. This is in Bristol. In Bristol, he was born, as you say, 1902 in North Bristol. His father was a notorious disciplinarian and he brought that ethic, work ethic, so to speak, to his children and drove them very hard. In the case of Dirac's brother and sister, they turned out to be okay academics, but Dirac thrived in this and did very well, learning things quickly. He went to a junior school,

round the corner from their house, Bishop Road School. He was in the same playground as Archibald Leach, later Carrie Grant. And he was starting to shine towards the end of that period. When you come to the First World War, he went to one of the best schools, public schools, public, I don't mean... Independent day schools.

Yeah, he was, it was where with everybody else, the Merchant Venturer School in the centre of Bristol. And that's where he shone. within a few years he was pretty well top of the class in all technical subjects he was seen as unhandleable in mathematics and physics and they'd have to send him his own homework he really was a star but he didn't actually know what to do so he followed this is for his university degree

so he followed his brother Felix into the subject that his father was very keen on which was engineering He was one of HG Wells' scientific samurai, so to speak. He wanted to get a job in that technical field. And you got at first in engineering, then he immediately switched to maths at a very young age. Why did this switch to maths? Well, he'd done brilliantly in engineering, apart from having terrible practical skills.

But he couldn't get a job. This was in the early 1920s. And he was busy doing experiments in the basement of Bristol. university and one of his teachers said, don't mess about with those food-line experiments, you're such a talented mathematician, hitch a ride on the mathematics degree, which you can do in two years. That was absolutely critical because Dirac was a trained engineer and he was going to become a trained mathematician.

And it was then that he developed this remarkable sensibility to pure, beautiful ideas in mathematics. Why do you use the word beautiful? Why did I use the word? you just did. Yeah, well, I used it because he used it. He's his teacher, who, as far as I know, he never wrote a paper, academic paper.

But according to Derek was a wonderful teacher. He thought he was the best teacher he ever had. And he was not a great academic, but he was extremely good at imparting the idea that mathematics wasn't just a subject you bang your head against, but there was something inevitable, something that could be expressed

with something akin to the beauty you see great poetry. This idea seized Dirac so that by the time he got to the end of that second degree, he was prepared to study theoretical physics. Thank you. Val Gibson. What, at that time, when he got to the end of theoretical physics, what was the classical view of physics which had been valid since Newton? What was it, and was it on the strain? So Dirac came to Cambridge in 1921. And at that time at the beginning of the 20th century, the physics was a rather mature science. There was the classical Newtonian mechanics. There was the theory of electricity and magnetism from Maxwell. And then there was this new theory as well called special relativity from Einstein.

And everybody believed that you could calculate anything. But there are a few persistent problems within experimental physics, which didn't go away. Did the classical view, I'm sorry to interrupt, but just to get it, did the classical view in Newton's view? Was that the one not obtained most strongly at that time? Yes, but it was been followed up in the 19th century with this theory of electricity and magnetism by Maxwell, where actually it was the unification of two of the forces, if you like, electricity and magnetism, that Maxwell actually managed to do. So there was a lot of interest in that sort of area of physics.

with Faraday as well discovering electricity and so on, which was crucial at the time. And there was these problems, these persistent problems, first of all, if you looked at just radiation coming from bodies at some ambient temperature, the prediction was that the radiation would just be unbound at low wavelengths or high frequencies. And people didn't understand also the energy of electrons which were coming off metals, and they were heated with light. And also the atom there. Nobody really understood what was happening with the atom. And at that time, all we knew about was the electron

and also that there was an atomic nucleus, which for hydrogen would be the proton. And the problem with that that people were grappling with, people like Boer and Rutherford, was that you've got a negative electron with minus one charge and a positive proton with plus one charge. Why didn't the electron just spiral into the proton and we'd have no atoms and we wouldn't exist?

So this was the biggest problem at the time. And Dirk declared that he fell in love with, and he was very akin to that, very unusual for him, with Einstein's theory of general relativity, which came out in 15, wasn't it, 1915? It was more the special relativity actually that he was grappling with. He was trying to, there's a relationship in special relativity, which relates energy, and momentum, and mass of particles.

And what Dirac was trying to do, he was trying to describe the theory of the very small, which is the atom, but also include the theory of the very fast, which is the special relativity. And he wanted to put those two together. Is it possible that the engineering background he had and the mathematical studies he'd had, and then he went in for physics, because these are you, helped him at a threesome really. Yeah, I think he was very prolific in his steps to where he was going. So in the beginning he was doing lots of calculations, estimates actually,

which were more on the engineering side rather than the pure theory side. And the pure theory came in the 1920s, late 1920s. So if you were to tell listeners that there was a body of classical theory at the time, that he was one of those, the preeminent one, set out to challenge. How would you put that better than I put it, much better than I put it, I hope? Well, I think we really have to understand

the birth of something called quantum mechanics because this was the new theory that we needed. And this is the theory of the big guns in the field, if you like, at the time. It's the Schrodinger's, it's the Heisenbergs, it's the Boers, and it's Dirac. And he wanted to be part of this, to try and explain the atom and the physics of the atom.

So that brings us to you, David Berman, because his first paper, when he was 23, was about quantum mechanics and was, according to the notes from all of you, a sensation. What did he say, and why was it sensational? So I think one has to understand a little bit about this idea of what quantum mechanics is.

So in this classical world, that was a world of certainty. That was a world where, one should, you knew the position and the speed of something you would know everything in its future. And in quantum mechanics, we abandoned that for the idea of probability. And we described instead that we accepted the uncertainty of our knowledge. And instead, the equations that we had would describe the probability of things. When you say we, did Dira think he was part of a group and when exactly is this happening?

He was certainly part of that. He was part of that group, as we've heard of the people like Boar, and then crucially Schrodinger, with which he eventually shared the Nobel Prize, and Heisenberg. And what he did was take that work of Schrodinger and take that work of Heisenberg and put it on a deep mathematical

footing, where he related it to something much deeper, even in classical physics, so that then he could say that, yes, there were these ideas of the wave function of Schrodinger, yes, there was the operator approach of Heisenberg, and these things, and then find

a universal structure, a mathematical reason that was already present in classical physics and then say, this is how quantum mechanics works. Is this possible for you to go more deeply into the word deeper, for those of us who are just longing to know a bit more? So what do you mean by I went deeper into mathematics? Okay, so often in theoretical physics, what we're about is writing down an equation. So often it's deemed to be sufficient. if you write down an equation that an experimentalist can come along and test and measure,

then you might say that's okay. So that was in some sense where Plank had got to and where Schrodinger had got to. What Dirac did is in some sense give a mathematical reason and explanation as to the structure of that equation itself. So it's not sufficient just to say this is the equation that we can test, but what Dirac said is that the reason why that equation is there, is because it reflects a deep mathematical structure in nature. And what Dirac did was unveil that deep mathematical structure

that was behind the equations of Schrodinger and Dirac and others. No, please go on. The idea of mathematics being at the heart of understanding nature was first aired, was it by Galileo? I've understood the universe. It's the language of mathematics. But let's forget about that and get on with what he found there. And words like phenomenal and sensational carving,

so what did it change that paper for this young man? Well, I mean, I think what's crucial to go to is that there were these problems at that enormously exciting time of physics that we had Einstein's theory of special relativity. We had the quantum mechanics of Schrodinger. But then when you've got these two pillars of the beginning of the 20th century

that changed everything, those two pillars were contradictory. You couldn't bring them together. So what Dirac managed to do in the Dirac equation was to say, yes, I can bring together the quantum mechanics of Schrodinger and the relativistic ideas of Einstein. And that's what he managed to do in this amazing paper, which he now gives what's called the Dirac equation.

And then he did something even bigger and more important. that equation allowed him to describe the electron and I think got to remind me you, listeners, that how important the electron is. It's basically nearly all of physics at the time and nearly all of chemistry. And then to have an equation that could describe that particle, which was something of a mystery,

and perhaps I could say a little bit why it was a mystery. I'd like to come back to that because we're going before our horse to market at the moment. I just want to stay on this, equation in a simpler way, but we'll certainly come back to it. Graham, Graham Farmelow, can we just develop the massive praise why people were so excited by this first paper by this young 23,

unknown 23-year-old from Cambridge, the fundamental equations of quantum mechanics? Yes, it was seen as the work of a great mathematician by the excellent school in Gertigan. They'd never heard of it. Dirac, and to see this beautiful mathematical construction that seemed to give a clear correspondence between the classical equations set out in a particular form with a quantum formation was something that was completely astonishing to them. But I think it's not just that paper. The fundamental equations of quantum mechanics was his first great paper, that is true, but very quickly he followed

up with your great marble statues falling from heaven. That wasn't my phrase. No, no, the late Freeman Dyson. It was a very good phrase because until 1933, he was coming out very regularly with papers that were right at the front of the field with a kind of characteristic elegance and mathematical facility. And was this picked up?

Was he netting into the other people you've mentioned? Oh yes, yes, pretty quickly. when he got his PhD his supervisor a great supervisor wanted him to get out of Cambridge just get out and mix a bit and Dirac wanted to go to Gertigan

the heart of quantum mechanics where it was where its principal discoverers were working at leaving him aside but his supervisor Fowler said no go to Boers Institute first and then go to to the

people in Gertigan When he went to Copenhagen, he wrote two really great papers within 12 weeks, right? One of them, in one of them, he demonstrated that the approaches to quantum mechanics that David has expertly summarized, which is Heisenberg's formulation of quantum mechanics, and Schroedger's, which looked very different, that you could actually go between them, one back to the other. He called that paper his darling. Why did he call it that? because he actually set out to show that those different formulations were equivalent

and you could go one to the other. He says if you wanted to do David's deep mathematics. Yeah, yeah. And he actually had to bring in some new mathematics for him in order to do that. A few weeks later, he introduces a subject that is now absolutely fundamental to fundamental physics, which is called field theory. We're familiar with magnetic fields, electric fields. he brought in the first quantum version of that, right?

Now, people like David and his peers, that is all over physics. But it was in his little office working alone in Copenhagen that he started that subject. Well, Van Gibson, so we have this group working, not group, we have these persons in Europe, in America and in Russia, working towards the same aim. Can you just fill them out with, fill my statement out,

with names and the excitement around that time. So I think the thrust was really to try and combine quantum mechanics and special relativity, Einstein's special relativity. And for some reason, I don't know why. Einstein sort of stud back from that. But Dirac really pushed forward. And he was working on other people's basic knowledge and theories, like Schrodinger, like Heisenberg, like Dierke,

like the guy called Klein and Gordon, who were trying to put the equations down. And the thing that DRAC really did was to realize how to write an equation down which solved a big problem they had at the time, which was there's two solutions to the problem, one which had negative energy and one which had positive energy.

The problem being, if you can remind us, some of us slow at the back. So the problem being is in, Einstein's special theory of relativity, it's a bit like Pythagoras theorem, actually. You've got energy and you've got momentum and you've got mass. And they're related like Pythagoras theorem. So E squared, in its simplest form, E squared is equal to p squared plus m squared. And anybody who's sold Pythagoras theorem for a right-angle triangle

will know that if you take a square root, you get two solutions. So it's like taking the square root of 16 and getting plus and minus four. everybody at that time was ignoring the minus solution but Dirac the way that he formulated his equation he could cope with that negative solution that brought into the picture however because he could not get rid of it it brought into the picture the concept of antimatter

and this is one of the big predictions from his theory was the prediction of the existence of antimatter now can you tell us how how you think he arrived at antimatter which he didn't call antimatter at first? No, he didn't. He called it, well, he was working to try and explain the electron,

as we've already heard, and he's also trying to explain the proton, so he could use the same formulaism for the proton. But he got this solution with this negative energy, and he tried to explain it away, right? He tried to explain what it was, and he did it by thinking about all, the energies that could possibly exist in the universe, both positive and negative.

And he said that, okay, I've got all of these negative energy solutions, but they're all filled up. So we live in a universe which is stable. It's okay. It's stable. We still exist. But having done that, he said, well, if you take some energy, say in light like a photon or something, and you shine it on these negative energy solutions, then you can give them some positive energy. And it's like creating an electron with positive energy, but with positive charge. And that's the antimatter equivalent of the electron, an anti-electron, or as we will probably hear soon, something called the positron, which it got renamed to. David, the DRAC equation. Can we carry this on, please? Yep, sure. So we've heard about this idea of taking a square root. Right. And

And so I think I want to come back to this idea of a mathematical structure. Because to understand what Dirac did and how he changed our understanding of an electron, we've got to think a little bit what we mean by a square root. So we're all used this idea of putting little, you know, like tick sign and indicate the square root. But he did that in a much deeper mathematical way because he asked the question, are there two things that you can somehow multiply together and then to get the equations that people had before? and then just take the square root by saying, you know, what is the thing that I've got to multiply together?

And then he did that even a little bit further. And then where previously there was this idea we've heard of an electric field. Now that's got a vector associated. So it's something with a direction, something that points somewhere. And now you've got to ask yourself a question which Dirac asked,

can you take the square root of a vector? Now that's something that's something that's very hard to get your head around But that's good that you realize it's hard to get your head around Because that's the sort of question that Dirac could ask and actually get an answer to And then as a result make progress in physics And so I unashamedly say yes It's good to realize that you can ask this simple question Realize it's difficult that what is the square root of a vector

And then he came up with a number answer, something called a spinner. Why is it so difficult? Well, if I draw a line for you on a piece of paper and then put a little arrow on it, so there you go, that's a vector. It's got a length and a direction. Now, I want you to come up with something so that when you multiply those two things together, you get that line in that point, you're going to be a bit stumped. And so are many mathematicians. But fortunately, Cartan introduced this idea of a spinner some years earlier.

And then Dirac realized that that was the thing he needed to describe the electron. And it had a crucial property which matched up to what the experimentalists had seen. Because of its nature, it had more information in it. And in fact, it gave the electron an intrinsic quantum property, which was previously identified as something called spin. But here's the thing you got to understand. People think when you say the spin of an electron, You imagine a little yellow ball spinning around.

But Dirac immediately realized that was a problem because if an electron is this infinitesimal point of absolute point, it can't spin. How can a point spin? So then he said, right, I need to describe a property of this electron that looks like spin to an experimentalist, but still has the right properties.

so that it will be described in a relativistic way. And that's what the Deroq equation did. It was the square root equation of the equations at round of time, and the actual equation, the actual thing that the electron describes, is like a square root of a vector. And as a result, it had these additional properties that experimentalists could measure, like spin. Right. Graham, Graham Farmelow, can you pick up on that?

You described this in your notes as one of the greatest, discovery in 20th century. Discover is in 20th century physics. You're referring to the Dirac equation specifically are you there? Yes. Yeah, okay. Well, the thing that I think I would stress out of it is that

in that, he wrote two beautiful papers on this, but what came out of that formalism that David just described is it was completely natural that by bringing quantum mechanics and relativity together, spin was inevitable. Right? Before, only a few years before, it was a complete mystery, right?

That you had this double, this duplicity, not duplicity, double-sidedness that experimental was seeing in the spectral lines and lights coming out of atoms. It was a puzzle. Dirac got exactly the right spin and as well the what's called the magnetic moment, the sense that the electron is in some sense a kind of tiny magnet. Those things just came out from that equation, right? And the ability to write down an equation, you can write it on the palm of your hand, where the spin of the electron and its magnetism are accurately predicted from an equation that he dreamt up in his head, right, was, I think, one of the great achievements. And incidentally, that equation is still at the heart of the deepest series we have of fundamental particles today.

Yeah. So I just wanted to add one more thing. So he didn't just describe the electron, but the Dirac equation also described how the electron would interact with light. So that if you think about it, the light that now flows into your eye, you can see it because when it flows in, it will basically stimulate an electron into your optic nerve and so on. And that's described by the Dirac equation.

So it's not just that it describes the electron itself, but how it interacts with light and other electromagnetic physics. and that is so much of the world that we see and how we interact with the world. Let's go back a bit to the antimatter of it. Were these people, well, let's stick with Dierke, was Dierach aware that he was changing the view of the world? The world now needed to be looked at in a very different,

even radically different way, and that would lead as he did to masses and masses of changing, spreading out like a pebble going to a huge point. Was he aware of that, or was he just doing it for the sake of doing it thinking, ah, that works? I get the impression he was rather cautious in his explanations because he tried to, in some respects, explain it away. And for a long while he was considering that maybe the proton was the anti-electron.

And he did all the calculations and realized that couldn't be the case. So it took him some time to actually say there has to be a particle, which is the same as an electron, much less in mass than the proton. It's identical to the electron, but it has this opposite charge. So I think he took a real cautious approach. He was really methodical in his workings and his papers that came out at the time. David, is there any idea why this creativity sprang from? I mean, a Swiss father making him speak French, a good school in Bristol,

and then he made engineering. and then, as you were, like Topsy, you just growed. I think it's very, very hard for me to imagine such genius. That's the word that keeps coming up in all your hands. It is, you know, when I took the opportunity for this programme, looking back at his original papers again and reading his book, and you realise that Dirac had an almost unique time, an almost unique mind, and especially for that time,

he could take the most abstract pieces of mathematics, as we discussed these obscure things called spinners, ideas in topology, but link it all the way through to the experiment and the prediction of antiparticles. And I think at the time that there were certainly pure mathematicians who could do one thing. There were certainly brilliant physicists who could have done something else. But to take that thread from the most abstract question of the square root of vector to the prediction of an antiparticle which predicts a whole mirror-weller, world is just extraordinary.

I have no idea where that comes from. Wasn't he worried that the anti-world antimatter might wipe out the matter? Because there were a loggerheads, let's put it, that ridiculous way. At some point people have done those, have had those questions, and there's a whole interesting program to be had on antimatter and so on. But I think it's, I would say there was something else that was remarked about him. He was very pragmatic mathematically. So, although we have.

had this immense mathematical complexity, he could actually still do something which mathematicians considered not quite right. And there's something called the Dirac delta function, which he introduced, which is a brilliant thing, because it's not a function, even though he called it one. And mathematicians worried about it for years. But then, and I think this is where the engineering side comes in, because in the end, if it worked and did what he wanted it to do, he didn't worry if it didn't have at that period of time the blessing of pure mathematicians. So he had this fantastic mix of having exquisite mathematical knowledge

but a pragmatism of saying if it's not quite there but it works I'll run with it. You want to come in Val. I want to say something about the experiments at the time as well because it went hand in hand with Dirac's formulation of his formula and the

prediction of antimatter that he was there in Cambridge. He was a very shy, reserved person and worked in college quite frequently in St John's College in Cambridge. And at the time there was a very bumpcious New Zealander in charge of the Cavendish Laboratory called Ernest Rutherford. Now Ernest Rutherford didn't tolerate theorists very much, but he tolerated Dirac. And so Dirac would go to the Cowandish every week, have tea and buns

with all of the experimentalists there, and go to the seminars and listen to the latest developments. And it's where he met somebody called Blackett. Patrick Blackett, who was tantamount very much looking for antimatter in his new experiment that he was developing. And so he was very much involved with predicting what he might see or explaining away what he had seen and really trying to understand whether he'd seen antimatter or not. Graham, can we develop? Well, let's move on to a magnetic monopoles. Yeah. Well, we've been talking about this paper that came out in 1931, where he made this brilliant prediction that there must exist these anti-electrons. But this was, I think this was Dirac's hamlet, because it was something that, full of beautiful stuff, that somehow it had so many different parts to it, it didn't have that elegance that you have in the most compact Shakespeare plays, so to speak.

It starts off that paper with a manifesto that we've got to look in future to be inspired by beautiful mathematics as he'd been, right? He then moved on to his antimatter and then the meat of the paper was one of his most extraordinary contributions and best remembered today. He predicted or showed that quantum mechanics with very slight changes can predict the exact. of the magnetic monopole. Now, it sounds fearsome. You go back to school, everybody knows that you can't just have a north magnet, you can't just have a south, but you have magnets come in pairs. He, what he demonstrated was that the equations of basic quantum mechanics, a slight modification, make it very likely that there exist these things called magnetic monopoles. Now, in doing that, he was using very advanced mathematics

that was being done simultaneously on the continent incidentally, right? And this made a deep impression on him and others because it opened up a door into not just the possibility of these new particles, but the relevance of a subject called topology that David mentioned before. This was the first time that this subject. which is all over fundamental physics now, right? But this was the first time that it had been introduced in physics. You mentioned, Val, about him going into Rutherland's Lions Cage there in the Cavendish.

He led a, we might call it eccentric, but that would be diminishing in a way. He'd let a solitary, interest. Can you give us some idea of the life you led? I think that's probably more a question for Graham actually. Go ahead. Well, very briefly, Dyrrack was a one-off, right? Niels Bohr in Copenhagen said he was, Dierak was the strangest man ever to visit his institute.

That's saying something, if you know theoretical physicists, right? When he was there, he apparently had three phrases, yes, no, and I don't know. He was extremely taciturn, and he lived in extremely regular existence, almost like an Immanuel Kant of physics. He would work five days a week. On Saturday, he would be doing technical projects of his.

On Sunday he would go for his walk, and it was the same every single week. So he was seen quite clearly, seen as an oddity. And something picking up, Melvin, that you mentioned earlier on, about the reception. In Germany, we know from the court of Einstein that was there, that they really did regard him as a very unusual. animal, because he was using this unusual mathematics, he had this engineers, sensibility, and the sensibility of a theoretical physics.

And they thought this was decidedly odd. It wasn't the Germanic tradition of theoretical physics. So it is quite fair to say that Dirac was an outsider, right? And in every sense, he was not somebody who could be regarded as a typical theoretician. Would you agree with that about that? I agree, yeah. There's a nice story, actually, in 1974, he went, In 1972, actually, I think.

He went to Florida State University, Tallahassee. So that's where he ended his life. And before he left, in Cambridge, every dawn has a black gown. And he had his own black gown. And he wrote a little note on it saying, Professor Dirac's gown, please ask the master to look after this for me until my return. And he never did return.

But his gown is still there in the Masters Lodge in St. John's College waiting for him. He's full of stories. I mean, like, somebody at the high table asked him where he was going in his holidays. And three days, three courses later, having said nothing, he turned and said, why do you want to know? That's really important. His literal-mindedness, for him, he didn't mean to be rude, right?

He simply would not understand why someone would be interested in that. He didn't have these, the natural way that most people have, of taking a natural interest in other people's comings and goings. David, you stalled at entering into a discussion of Derex Genius. And we all, I mean, you said you, it was, you didn't say it was beyond you, but you said it was something so extraordinary. Did you, do you think that that extraordinary came from his nature as much as from his learning?

Yeah, so it's always hard to know because you can't do the experiment of if I put someone with the same learning of Dirac and then see how they respond. But I think at this level, as I say, this level of genius, there's always something unique. And so I think there was something intrinsic within the man to be able to take what he did and achieve what he managed to do.

Is he connected with his monosyllabic existence in the way of conversation? I mean, yes and no, those two words at a high table, a big conversation with him, right there. I think there's something that is there about the idea of focus, that when you decide that you're going to combine special relativity with quantum mechanics, that's a lot to think about. And I suspect that he had an enormous focus.

And as a result, maybe he just decided he wasn't that interested in small talk. Graham, Graham, Einstein admired him He did. Enormously, didn't he? He praised him above the skies, but it's been suggested that Dirac is more modern than Einstein.

Is that suggestion worth taking seriously? I think it is. I don't want to look at the rankings. I mean, I personally think that Einstein was a complete phenomenon. I don't want to belittle him in any way. But what I think makes Dirac

look so modern today is first of all he was equally happy with special relativity and quantum mechanics whereas Einstein did not regard quantum mechanics as a truly fundamental theory and Dirac had this

very strong faith that if you pursued beautiful mathematics it would take you into areas that would be of interest. Now, it's not fair to say that Einstein had no inkling of this, but Dirac was a much better mathematician than Einstein.

I mean, Einstein had fantastic curiosity and peerless ability, but Dirac was a very able mathematician, and that attitude towards mathematics as something that would take you by the hand and lead you into productive

pastures for research is something that is very modern. Would you agree with that, David? Yeah, absolutely. I mean, now a lot of the ways that we do theoretical physics is following Dirac's approach. You can ask a very abstract mathematical question and then see where that leads into the physical world. So in some sense, Dirac led the way

and we all follow in that approach of asking those mathematical questions. And then intrinsic to this, though, is a belief that behind nature are deep mathematical structures and that finding those mathematical structures will tell us what nature is. Mal, is it possible to ask the question? Is it possible to answer the question

that he changed what he did change our understanding of the world? I think that's true. There's not just this equation he wrote down. If you look at any good internet encyclopedia, you'll find a list as long as your arm of everything that he did, all the conjectors, all the theorems, all the equations, everything. And I've never seen a list like, like that before. And even though we concentrated on his equation and the explanation of what matter

and antimatter do, it still holds today. We still use it. All the fundamental particles that we know about. We now know that the proton is made of quarks. We know there's heavier electrons called muons or tau's. We know about all the force-carrying particles, the quantum field theories and so on, that's all down to Dirac. And it really is the fundamentals of our theory of everything that we know about of the fundamental particles and the forces of nature. Following up that legacy idea, David,

why is it that compared with Einstein, even Schrodinger and Nielspor, you know what I don't want to ask, why is he so unknown? I think this programme perhaps explains a little bit why. in having those abstract ideas of having and brought in ideas of topology, of spinners and all of these things, it's just very hard to explain to the general public what is he's done.

When Einstein came up with relativity, there were trains with rulers and clocks and all of these things which then made that popular science then used to explain the ideas of relativity. And although relativity is hard, in some way it's now permeated through because there's been all these attempts over the years. Dirac's work, although underpinning all of modern physics, is just so hard to explain because of its reliance on mathematics

and mathematical structures. So I think ultimately it's not just he had a bad publicist, it's the fact that what he managed to do is bring in that abstraction of mathematics and that's why it's so hard to make popular. Would you agree with that, Graham? Yes, I do. It's worth saying that his friend and competitor, Werner Heisenberg, described in the 1970s, the anti-matter revolution as the biggest of all big jumps in 20th century physics. Now, that's saying something to compliment Dirac like that.

And we just take it for granted now. We think of the beginning of the universe having equal amounts of matter and antimatter. This was conjured up inside the head of this guy. He didn't have any experimental clues on this. So this cerebral approach to theoretical physics, I think he characterises that better than almost anybody else. Well, thank you very much. That was a run for your money. Thank you very much, Graham Palmerow, Val Gibson, David Berman.

Next week, it's the commoners, the Scottish Presbyterians who captured Charles I, as they aim to complete the Protestant Reformation in Britain. Thank you for listening. And the In Our Time podcast gets some extra time now with a few minutes of bonus material from Melvin and his guests. What did you want to talk about that you didn't talk about? I'm surprised none of us said his equation.

I mean, it's as elegant as Mozart's music. I gamma Dissai equals M-SI. I don't need to explain to you what those mean. It's just so elegant. It needs all of unpacking, but you're, of course, completely right. And it's in the plaque in Westminster Abbey as well. if anybody would like to go to you. It used to be the only one until Hawking came along

and they put his equation on there. Yeah, I mean, I would have loved to actually have explained how he constructed the monopole using topology and that that led to the fact that... Why do you do it now for us? Enough people are listening to you? I'll have a go at topology and something that goes on. We've spoken about topology, so what is it?

It's this thing that's most easiest exemplified with a Mobius strip. So if you just take a cylinder, that's a piece of paper that you bring round and that's fine, you stick it together. A Mobia strip, you take it around,

you put a twist in and then stick it together. Now, at that point, if you just look at any little bit of that strip, you can't tell the difference between a cylinder or a Mobia strip. You need to go all the way around

to realize there's a twist in it. So the idea of topology is it classifies that thing of you can only see it by going all the way around. If you just look in your little local neighborhood, you can't tell the difference. And what Dirac realized

is that a lot of the laws of physics were written in those little local neighborhoods around, and nobody asked the question, can we get something different by how we glue together these things on literally the size of the universe? And that

was how we managed to construct a monopole was by putting twists in the electric potential and it's not located at any point, monopolis, but that twist is like the twist of the Mobius strip. You only see it by going

all the way around. And then you see there's a twist there. If you just look close, you can't see. I'll tell you. One thing I... I don't know if that helps anymore. Bravo. One thing I wish we'd mentioned that

the epiphany that made Dirac a theoretical physicist was the amazing amount of publicity that Einstein I got in 1919 when his theory of gravity had the endorsement of experiment and became a worldwide sensation. Dirac was an engineering student there and it captured his imagination and heart, right? That is when this engineering student says, I'm interested in this. I'm interested in being a theoretical physicist. What does that mean? We should perhaps have said this too. This means there

is an order to the universe and that we can discover that order through mathematical equations. That's what he wanted to do. What are the equations? That was his constant refrain when talking to people about the field. I would like to say some more about what was going on, what's currently going on in the field of research experimentally. So I've just come back from CERN and the other day I was walking around the antimatter factory there. And we can create antimatter in hundreds of anti-hydrogen. And we can the spectrum like we have the spectrum in hydrogen to see if they agree. And we can drop anti-hydrogen to see whether it goes down or whether it goes up.

And all of these measurements are currently being made. And in the Large Hadron Collider as well at CERN, we make matter and antimatter in a controlled way and recreating the beginning of the universe and just trying to understand why we live in a universe made of matter now and not antimatter. So these questions are still there. We're still trying to answer. answer them. So I don't say something about him, his personality, because for a long time, people just thought he was really a very cold fish, had absolutely no interest, apart from mathematics

and physics. This is not true. He just didn't talk about them. When he was in Florida, when he was in retirement, he would go to concerts, he would read, I think he took three years over war and peace. He absolutely loved 2001 a space odyssey. His favorite singer was Cher. He was on her show, that he really got to know Sting and Elton John? I mean, this was not a complete Philistine in the arts. So I think this was an important thing to realise. He was actually a... He was not a one-dimensional man, as he was cruelly described,

but he was three-dimensional, except that what the world saw was the one dimension of this very silent figure that was walking through the corridors of academia. Yeah, I mean, I can add also about his book. He's got this book called Principles of Quantum Mechanics. Yeah, great book. And I remember when I was first given that and read that in Manchester,

and it was touching almost. Now, very clearly, no one can ever learn quantum mechanics from Dirac's books. What you do is you learn quantum mechanics from any number of sources, and then you think you've understood quantum mechanics, and then you read Dirac's book, and then you realize you've not understood quantum mechanics. and Dirac understood quantum mechanics, and then you're amazed. And I think it's amazing to have a book that is still printed and still read by every theoretical physicist from that period.

And it's almost unique in that fact. Nobody goes back to Einstein's works in relativity because you go, you know what, we've got now probably greater geometric insight than Einstein had at the time in the sense of what we've all understood that math better. But in terms of Dirac, there's nothing better than that book. Yeah. I completely agree. But it's really worth stressing that when he wrote that book, it was published like in 1930, quantum mechanics was still a work in progress.

It was stuff happening all over the place. Remember, Dirac, Heisenberg, Schrodinger, Boer, Yorden, all these people here. They were all doing bits of something, and it wasn't clear how it would all fit together. And what this guy does? He writes this. It's almost poetry. You know what I mean? And even his competitors and people that didn't like his style.

this is a magisterial synthesis of that subject. And that's why, as David said, and I might say it also stimulated the next generation of phyllis from Feynman, Julian Schwinger, Sinaitre Tominaga. These people were, that was their Bible. So it was tremendously influential. Yeah. Is it still, when you read it first, you couldn't understand it.

Could you, can you still not understand it when you read it? No, I mean, I would say I could understand it now. But it was, but, I'm going to use the word deep again. It brings out and constructs things in a very deep way. What's beautiful as well is actually how wordy it is. So in the first few chapters, for a theoretical physics book, we like our equations.

And what Dirac did was replace equations with concepts. And you read those first few chapters. And you go, this is all, this is literature. but it's the fact that he's got such a deep understanding of the concepts in quantum mechanics that the old idea of shut up and calculate, which is often what the theoretical says, that's what you're taught as an undergraduate, take the Schrodinger equation, calculate some energy things, and you go, oh, I've understood quantum mechanics now. What Dirac said is, no, you've not.

There's something much deeper behind it, and that's what he's brought out, and it's beautiful. Well, thank you very much, it's pretty. Well, this is part of the programme. I produce this pacing outside to come in and make an offer you can't refuse. But even so, here he is, Simon. You produced that, didn't you? Do you want tea or coffee? No, that's fine.

Tea, please. Tea. Tea, please. Melvin? Tea. Tea. Tea. Tea.

Thank you very much. That was terrific. In our time with Melvin Bragg is produced by Simon Tillotson. Hi everyone. Russell Kane here. I've got just a few seconds to tell you about evil genius. Our hit podcast, two and a half million downloads in 2019, top 10, where we take people from history, Gandhi,

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