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? Dirac: 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. Dirac: 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. Dirac: 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 ? Dirac: 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? Dirac: 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. Dirac: 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? Dirac: 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. The 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? Dirac: 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. Dirac: 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? Dirac: 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. Dirac: 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? Dirac: 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? Dirac: I don't know. DP You'd be there if you knew, I guess. Dirac: Yes. PB Will it also depend on developments in mathematical theory? Dirac: That's possible. PB In the 1920s the mathematics had to be partially invented as well, along with the experiments. Dirac: 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. Dirac: 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.