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Hund: Yesterday, you gave us a short account of a very important development in theoretical physics that started with Einstein's special relativity, the symmetry of space and time and then lead to a very large development which ended with the other symmetry, the symmetry with the particle and antiparticle. That was your main subject and the keyword was symmetry. Dirac: Yes, that is so. I wanted to emphasize that Einstein was the first to realize the importance of symmetry. Lorentz had worked out the mathematics of the transformations, the transformations are called Lorentz transformations but Lorentz did not realize the symmetry which

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was implied by these transformations.

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He thought that there was one frame of reference which was the good frame, the physical frame and that other frames of reference were just mathematical fictions. Hund: I remember the words he introduced local time as a concept, but he said local time is different from the real time. There he emphasized that there is one absolute system, the Aether. Dirac: And there he was quite wrong. Hund: Yes. Dirac: And it took him a long time, I believe until 1909, before he accepted the Einstein view. Hund: Yes, he gave a lecture in Göttingen in 1909 or 1910 and he said that perhaps

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we must give up the concept of equal time, of the absolute equal time, but he - I say it in German: 'Ich würde es ungern aufgeben.' Dirac: Yes, Einstein started off with a different point of view and he showed how he was an independent thinker.

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Hund: With the word symmetry in this connection you mean symmetry between time and space?

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Dirac: Correct, yes.

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Hund: What symmetry was in the centre and has changed in time, at first it was symmetry of space and time, then came other symmetries, symmetries between electron and anti-electron, positive and negative charge.

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Dirac: And then more recently other symmetries have appeared in physics, a symmetry between proton and neutron. Hund: Yes. Dirac: And this is only an approximate symmetry what physicists call a broken symmetry. Hund: Yes, but I would ask you something on the former symmetry: in your work, that symmetry space, time showed it's important if you

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constructed your - what we call Dirac equation of the electron. In the days before physicists preferred the so-called Schrödinger-Klein-Gordon-equation and this equation has the time in a second derivative. Dirac: Yes. Hund: And that was not acceptable for you, before you had constructed what we call transformation theory. There you needed the concept of probability and the first derivative.

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Dirac: That is correct, yes. And that forced me into a different kind of equation, and this different equation brings in a spin of the electron. It was very unexpected to me to see the spin appearing in this way.

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Hund: And spin, that means, moment of momentum and magnetic moment, both together. Dirac: They both come together.

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I thought one would first get a satisfactory theory of a particle without spin and then one would precede to a more complicated theory of the particle with spin. But it turned out differently. The simplest kind of particle does have a spin.

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Hund: Yes, you mean perhaps Pauli-Weisskopf with the scalar theory. Physicists saw that they can incorporate any spin into a consequent theory but it is more complicated. I agree with this, the simplest particle that could exist was the fermion with the spin one half, the electron. Dirac: That is so, yes. It was a great revelation when this appeared. Then with the solution of these difficulties one was able to concentrate on the one remaining difficulty how one should deal with negative energy states. It took quite a while, perhaps a year, to understand that and to bring in

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the concept of a vacuum in which all the

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negative energy states were occupied. Hund: Is it possible to express it in the following manner: in this theory of the electron, let me say the Dirac theory, you can treat pairs of particles, positrons, electrons in the form

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of a one-particle theory. That if you have scalar spin or scalar particles, the Pauli-Weisskopf theory you can treat pairs of a many-body theory. Dirac: Yes, that is so, yes.

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Dirac: Now, should we speak a little about general relativity? Hund: Yes. Dirac: General relativity was considered by Einstein as his most important discovery. He was working entirely alone on the new mathematical ideas and it was a big triumph for him to be able to get his ideas straightened out and to introduce a new theory of gravitation, bringing in a very powerful kind of symmetry.

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This symmetry is of importance in physics only where gravitational fields occur.

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While the symmetry previously, a symmetry of special relativity, is of importance in all physics.

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So that this further symmetry introduced by general relativity, although it is such a wonderful mathematical theory, does not have the big effect on physics.

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I might say that my recent work has been very much concerned with Einstein's general relativity and I believe that the times and the distances which are to be used in Einstein's general relativity are not the same as the times and distances which would be provided by atomic clocks. There are good theoretical reasons for believing that that is so and for believing that

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gravitational forces are getting weaker compared to electric forces.

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As the world gets older there is some observational evidence for that. Observations of the moon which have been made accurately for centuries with respect to the time provided by the Einstein theory and which have been made since 1955 with atomic clocks. There is some evidence of a difference between the two times.

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The evidence is not as complete as one would like to have, people are still working on the subject, in particular with the Viking lander which was put onto Mars in 1976 one is able to send radar waves to Mars and get back the reflected waves. Then one can measure in atomic time how long it takes these waves to go

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to Mars and to come back.

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The results that one gets are unfortunately very complicated because there are many disturbances. There are disturbances caused even by meteors. There are many more meteors passing close to Mars than there are passing close by the Earth. These disturbances all have to be taken into account. Well, people are still working on this subject and I hope that they get a definite answer pretty soon about the question of whether there are these

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two times, the Einstein time and the atomic time with a difference between them.

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Hund: What is a natural clock then? Today physicists use to say the vibration of a molecule or an atom is a natural clock and the extension of an undisturbed crystal is a natural length. What would be the natural time and natural length then? Dirac: Those are the atomic times and the atomic lengths and that is the best way to define these quantities.

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But it may be that quantities defined in this way are not the ones to be used in the Einstein theory for astronomical observations.

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Hund: Should we say, Einstein's theory then must be changed or completed or can it remain with another interpretation?

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Dirac: Well the equations remain but they are to be applied differently. Hund: Yes, but in Einstein's equations the gravitational constant is assumed to be constant Dirac: Yes. Hund: and in these modern developments it is not.

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Dirac: Whether the gravitational constant is a constant or not will depend on what units you use because Hund: it's a matter of interpretation. Dirac: Yes, yes. There is no suggestion that Einstein is wrong but it's just on how his equations are to be used. Einstein's theory has turned out to be a wonderful theory, so successful in all its applications. But there is this question of the interpretation which is not yet settled.

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Hund: But now then it can happen that Einstein's general relativistic theory becomes more important, nearly so

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general as the special.

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Dirac: It is not so important for Hund: Of course, it had only to do with cosmology and gravitation. Dirac: Yes. Hund: But perhaps, gravitation one day will be connected with the other forces, weak forces, strong forces, electromagnetic forces. Dirac: That is possible but that lies far ahead. Hund: Yes, it does, the factor 10 to the minus 14 is very, very little. Dirac: Yes.

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Hund: I think you were the first who lead the attention to these extreme constants, 10 to the minus 14, ten to the minus 18. Dirac: Yes, yes.

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Hund: But we have no exact, no certain results, the question is open. Dirac: There is some evidence from the observations of the moon, but one would like to have some confirmation coming from the radar observations from Mars.

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Hund: Yes, but can we say that quantum mechanics also had a great, great consequence? The whole theory of matter, the whole theory of the properties of matter, chemistry and so on is a consequence of quantum mechanics.

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In the atom the motion of the electron is slower than that of light Dirac: Yes. Hund: and chief features of quantum mechanics are not relativistic.

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Dirac: That I would agree and I think that the correct connection between quantum theory and relativity has not yet been discovered.

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Hund: Can I ask you something of the modern development? Now we hope that perhaps in a short time we get a unified theory of the particles. Now we make differences between strong interaction, electromagnetic interaction, weak interaction, gravitation, these four. What are your hopes?

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Dirac: I think that the present methods which theoretical physicists are using are not the correct methods. They use what they call a renormalisation technique which involves handling infinite quantities. This is not really mathematically a logical process.

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I would say that it is just a set of working rules rather than a correct mathematical theory and I don't like this whole development at all. I think that some other important discoveries will have to be made before these questions are put into order.

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In particular there is the problem of explaining the fine-structure constant, the number 137 which plays an important role in physics. The question is why should it be 137 instead of some other number? That has not been explained at all and I feel that it is necessary to get an explanation of that before one will make an important advance in understanding atomic theory.

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Hund: The fine-structure constant is one of them, also the relation between weak and strong interaction. For strong interaction perhaps you can say the constant is nearly 1. The mass, the proportion of the masses, electron mass, proton, neutron mass, I think that's the other problem. These two problems will be connected, I think. Dirac: Probably yes, there is

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quite a different problem of the ratio of the mass of the proton to the mass of the electron and the question is whether the ratio of these masses remains constant or whether it develops slowly with time.

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People are now looking into this problem.