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[The mathematician] Roger Penrose has mentioned that you always ask awkward questions. What questions are you asking right now?
I'm working on how to reconcile the apparent loss of information when a black hole evaporates with our understanding of physics that information is never lost. I raised the question 40 years ago and, despite a large number of papers since, no satisfactory resolution of the paradox has been proposed. Indeed, it has been shown that there is a contradiction between information not being lost and the usual assumption that physics is local. It has been suggested that the resolution is that there is a firewall just outside a black hole that would burn up anything falling in, but I don't believe in firewalls. Instead I think space-time is warped.
You also believe that the universe doesn't have a single past but various possible histories. What kind of experimental evidence would be needed to prove this theory?
Feynman's idea of a sum over histories is that a system evolves by every path of history. This can be demonstrated by directing a stream of particles at a sheet with two slits in it. The number of particles arriving at a subsequent screen will form fringes, as if they were light rays. The interpretation is that each particle has two alternative histories, one going through one slit, and the other through the other slit, and they interfere like light rays.
In your book The Grand Design, you write that M-theory is the theory that Einstein was hoping to find, one that predicts and describes the universe, and that physicists were led to it by abstract considerations of logic. However, the theory hasn't been confirmed by observations. If experimental physics weren't limited by current technology and financial budgets, what predictions from your theories would you love to confirm empirically? And if you could devise an experiment without such constraints, what would that experiment be?
I'm beginning to have doubts about M-theory, but there seems no viable alternative. M-theory presumes supersymmetry is a symmetry between matter particles, like the electron, with force-carrying particles, like the photon. Supersymmetry would imply that all the particles we know have superpartners, but none have been found. The experiment I would like performed is to detect Hawking radiation from a black hole, because then I would win the Nobel Prize.
Hawking radiation is very difficult to detect, because the radiation from a black hole with mass a few times that of the sun would have a temperature of only a millionth of a degree above absolute zero. Smaller primordial black holes would have a higher temperature but there don't seem to be any around.
Your longtime friend, physicist Kip Thorne, has described how, as you lost the use of your hands, you developed a powerful set of tools that no one else has, including an unusual ability to manipulate mental images of objects, curves, surfaces, shapes, not merely in three dimensions but in the four dimensions of space and time. Can you describe that mental process? Do you think you managed to solve problems that others couldn't because of that special set of mental tools?
No one can visualise four dimensions. Three dimensions are hard enough. What I do is visualise two-dimensional sections, remembering they are part of a four-dimensional whole. This geometric visualisation I used in proving singularity theorems and my work on black holes, including black-hole radiation. My disability makes it difficult to write down complicated equations so I prefer problems with a geometric interpretation.
You said that there's nothing like the eureka moment of discovering something new. Can you describe your favourite eureka moment?
I was getting into bed shortly after the birth of my daughter, Lucy. My disability made this slow, so I had time to think about black holes. Suddenly I realised that if two black holes collided and merged, the area of the horizon of the final black hole would be greater than the sum of the areas of the original black holes. I was so excited I didn't get my sleep that night.