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The problems are more difficult now and there is not the same hope of making rapid progress which there was in those days. Excitement is usually combined with the hope of making rapid progress, when any second rate student can do really first-rate work. But the easier fundamental problems have by now all been worked out. Those that are left are very difficult to work on, and one doesn't seem able to get the right basic ideas for handling them.
It is quite possible that they will require wholly new ideas. In fact it's pretty certain they will; otherwise they would already have been thought up.
PB But they will still be related to the existing development of theory in some sense at least.
Yes. The present theory must be an approximation to any improved theory which we get in the future.
DP Some people we've spoken to seem to think it's a matter for new experiments, particularly in elementary particle physics.
If the theorists are not good enough to solve it on their own, that's what one has to do. It needs an Einstein, or someone like that. Einstein didn't depend on new experiments to get his ideas.
DP Do you feel that the progress in particle physics is fruitful?
It's not really fundamental; it's collecting a mass of information and one doesn't know really how to get the basic ideas from it. Just like in the early 1920s one had a mass of spectroscopic information and it needed Heisenberg to find the real basis of a new theory from that wealth of material.
DP Do you think a unification necessarily will have to include relativity ?
I should think so, ultimately. Perhaps not gravitation in the first place; gravitation is rather separate from ordinary atomic physics and it plays very little role.
DP It seems to be an insurmountable problem to most people: the quantization of relativity. It is something you have worked on.
One can deal with it up to a certain point, but one cannot complete the theory in a satisfactory way.
DP Could you summarize your thinking on the large numbers hypothesis?
The large numbers hypothesis concerns certain dimensionless numbers. An example of a dimensionless number provided by nature is the ratio of the mass of the proton to the mass of the electron. There is another dimensionless number which connects Planck's constant and the electronic charge. This number is about 137, quite independent of the units. When a dimensionless number like that turns up, a physicist thinks there must be some reason for it. Why should it be, well, 137, and not 256 or something quite different. At present one cannot set up a satisfactory reason for it, but still people believe that with future developments a reason will be found.
Now, there is another dimensionless number which is of importance. If you have an electron and a proton, the electric force between them is inversely proportional to the square of the distance; the gravitational force is also inversely proportional to the square of the distance; the ratio of those two forces does not depend on the distance. The ratio gives you a dimensionless number. That number is extremely large, about ten to the power thirty-nine. Of course it doesn't depend on what units you're using. It's a number provided by nature and we should expect that a theory will some day provide a reason for it.
How could you possibly expect to get an explanation for such a large number? Well, you might connect it with another large number - the age of the universe. The universe has an age, because one observes that the spiral nebulae, the most distant objects in the sky, are all receding from us with a velocity proportional to their distance, and that means that at a certain time in the past, they were all extremely close to one another. The universe started quite small or perhaps even as a mathematical point, and there was a big explosion, and these objects were shot out. The ones that were shot out fastest are the ones that have gone the farthest from us. That explains the relationship (Hubble's relationship) that the velocity of recession is proportional to the distance, and from the connection between the velocity of recession and the distance we get the age when the universe started off.
It's called the big bang hypothesis. There is a definite age when the big bang occurred. The most recent observations give it to be about eighteen billion years ago.
Now, you might use some atomic unit of time instead of years, years is quite artificial, depending on our solar system. Take an atomic unit of time, express the age of the universe in this atomic unit, and you again get a number of about ten to the thirty-nine, roughly the same as the previous number.
Now, you might say, this is a remarkable coincidence. But it is rather hard to believe that. One feels that there must be some connection between these very large numbers, a connection which we cannot explain at present but which we shall be able to explain in the future when we have a better knowledge both of atomic theory and of cosmology.
Let us assume that these two numbers are connected. Now one of these numbers is not a constant. The age of the universe, of course, gets bigger and bigger as the universe gets older. So the other one must be increasing also in the same proportion. That means that the electric force compared with the gravitational force is not a constant, but is increasing proportionally to the age of the universe.
The most convenient way of describing this is to use atomic units, which make the electric force constant; then, referred to these atomic units, the gravitational force will be decreasing. The gravitational constant, usually denoted by G, when expressed in atomic units, is thus not a constant any more, but is decreasing inversely proportional to the age of the universe.
One would like to check this result by observation, but the effect is very small. However, one can hope that with observations that will be made within the next few years, it will be possible to check whether G is really varying or not. If it is varying, then we have the problem of fitting this varying G with our previous ideas of relativity. The ordinary Einstein theory demands that G shall be a constant. We thus have to modify it in some way. We don't want to abandon it altogether because it is so successful.
I have proposed a way of modifying it which refers to two standards of length, one standard of length which is used in the Einstein equations, and another which is determined by observations with atomic apparatus. I should say that the idea of two standards of length and of G varying with time is not original. This sort of idea was first proposed by E.A. Milne about forty years ago. But he used different arguments from mine. His equations are in some respects similar to mine; in other respects there are differences. So this theory of mine is essentially a different theory from Milne's, although based on some ideas which were first introduced by Milne. One should give Milne the credit for having the insight of thinking that perhaps the gravitational constant is not really constant at all. Nobody else had questioned that previously.
DP This theory has an important consequence for the creation of matter.
Yes, the amount of particles - elementary particles, protons, and neutrons - in the universe is about ten to the seventy-eight, the square of the age of the universe. It seems again one should say that this is not a coincidence. There is some reason behind it, and therefore the number of particles in the universe will be increasing proportionally to the square of the age of the universe. Thus new matter must be continually created.
There was previously a theory of continuous creation of matter called the steady state cosmology, but this theory of mine is different because the steady state cosmology demands that G shall be a constant. Everything then has to be steady, and in particular G has to keep a steady value. Now, I want to have G varying, and I also want to have continuous creation. It's possible to combine those two ideas and I've worked out some equations on possible models of the universe incorporating them.
PB One of the consequences of your theory is that it rules out an expanding-contracting universe.
That is so, yes, because in the theory there will be a maximum size. This maximum size, expressed in atomic units, would give a large number which does not vary with the time. Now, I want all large numbers to be connected with the age of the universe so that they will all increase as the universe gets older. If you have a theory giving you a large number, of the order of ten to the thirty-nine, which is constant, you must rule out that theory.
PB This implies a constantly expanding universe.
Yes. It must go on expanding forever. It can't just turn around and contract, like many people believe.
PB So that avoids the singularity at the end, so to speak.
Yes, that is avoided; there is just a singularity at the beginning.
PB There seems to be, or at least it 's possible that one may observe such a thing as, a black hole, which is a theoretical consequence of general relativity. That is also a singularity, is it not?
It depends on what mathematical variables you use. It would be a very local singularity anyway, not a cosmological one.
PB But it seems staggering to the imagination that the mass of the star is concentrating into a smaller and smaller volume. I know there are repulsive forces that can stop it at various stages, but finally, I understand, with a star that is perhaps five or ten times the mass of our sun, it need not stop.
That is what it seems, according to current theories.
PB It is difficult to imagine such an object, but I suppose that is not a necessary condition for doing physics.
If you can find equations for it, that's all the physicist really wants. It is quite likely that the laws will get modified under these extreme conditions; we'll have to try to find out what the correct laws are.
PB But they need not contradict physical theory, wouldn't they simply be modifications ?
They would be modifications, modifications holding under extreme conditions.
DP Would you comment on the divergences and infinities which occur in quantum field theory? Many think that they can be removed by renormalization. Is this your feeling?
It's just a stop-gap procedure. There must be some fundamental change in our ideas, probably a change just as fundamental as the passage from Bohr's orbit theory to quantum mechanics. When you get a number turning out to be infinite which ought to be finite, you should admit that there is something wrong with your equations, and not hope that you can get a good theory just by doctoring up that number.
DP Some people have suggested that by introducing curved space you can get rid of these infinities, Abdus Salam for example.
I know that he is working on that idea, but I feel that with a good theory these infinities would never arise in the first place.
DP The papers you produced have been universally considered beautiful. Were you guided by notions of beauty?
Very much so. One can't just make random guesses. It's a question of finding things that fit together very well. You're solving a problem, it might be a crossword puzzle, and things don't fit, and you conclude you've made some mistakes. Suddenly you think of corrections and everything fits. You feel great satisfaction. T he beauty of the equations provided by nature is much stronger than that. It gives one a strong emotional reaction.
DP Do you get this reaction from certain branches of modern physics today?
Not the renormalization theory, no!
PB I have a question about the interpretation of equations. There are certain equations and certain theories where interpretations have been open to a great deal of discussion. It is not quite clear what's really meant in non-mathematical terms; I'm thinking of the principle of complementarity.
Yes, there is an uncertainty in the interpretation. But I don't feel it is too profitable to discuss the uncertainty because the basic equations themselves are uncertain, as I was trying to explain to you previously. If you don't have very great confidence in the basic equations, then there's not really much point in spending a lot of time on the interpretation of the equations, as you believe they will be superseded after a while in any case.
PB I was thinking of the uncertainty relations themselves. Do you believe that these will be superseded?
It's possible. You'd probably have to pay a price for it and give up some other cherished idea.
PB The problem of observation and measurement seems to be important.
Yes, but you're discussing these problems on the basis of our present theories, which are just, I believe, a transient phase of physics and will be superseded after maybe a few decades - or, well, one just doesn't know when they will be superseded. It is rather as though one tried to build up a new philosophy on Bohr's orbit theory. You might have gone a long way with it, but all that argument would have been completely valueless when Bohr's orbit theory was superseded.
DP If you were giving advice to young physicists today, which area would you suggest they look into?
I think perhaps they ought to avoid fundamental physics because all the worthwhile problems there have already been very thoroughly explored.
DP I mean in the sense of which area you think the breakthrough will come in?
I don't know.
DP You'd be there if you knew, I guess.
Yes.
PB Will it also depend on developments in mathematical theory?
That's possible.
PB In the 1920s the mathematics had to be partially invented as well, along with the experiments.
The basic mathematical ideas were known previously to the mathematicians. They knew about Hilbert space; they knew about spinors. They had never thought that these things would ever have any physical application.
PB So it's quite possible that some branches of mathematics already known contain useful approaches.
Yes. However, an enormous volume of mathematics exists, and to look for which part is going to be useful in the future is pretty hopeless.
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