20: Sir Roger Penrose - Plotting the Twist of Einstein’s Legacy: Difference between revisions

And so I had a nice, silent drive coming back, and I started to think about these constructions that Ivor Robinson—he was in Dallas at the time, an English fellow who lived in Dallas—and he constructed these solutions of the Maxwell equations, which had this curious twist to them. And I had understood these things, and I realized that they were described by, as you talked about, the Hopf map or the Clifford parallels, these are, you can think of a sphere in four dimensions, three-dimensional sphere in four dimensions, and you have these circles, which fill the whole space, no two intersect, and every two link. Beautiful configuration.  

'''Eric Weinstein:''' And this is, look, I want to tie this into a bigger thread, which I think is fascinating. I am not a devotee of String Theory, nor am I of Loop Quantum Gravity. I think that most of what has been said about Supersymmetry has been overbearing and wrong.  

So we had a first revolution around the mid 1970s with what's called the Wu-Yang dictionary, where a particular geometer, who becomes the most successful hedge fund manager in human history meets arguably the most accomplished theoretical physicist, if it's not Weinberg it might be Yang in terms of what has been proven of his contributions. They have an unbelievable interaction which shows that the Classical Theory underneath Particle Physics is as or more geometric than the theory of Einstein using Steenrod's fiber bundles and Ehresmann's connections, or vector potentials or what have you. Then you have a second revolution, again involving—so that was the first one that Is Singer takes from Stony Brook to Oxford—and you have another one, which is the geometric quantization revolution with your colleague Nick Woodhouse writing the bible there, in which Heisenberg's Uncertainty Relations strangely come out of curvature rather than just being some sort of weird—  

You guys figure out that this weird grab bag that was called Quantum Field Theory, which is this thing above Quantum Mechanics that is needed for if you're going to have particles that change—regimes in which the number of particles changes like something emits a photon, you need Quantum Field Theory, you can't do it in Quantum Mechanics. So that world was a grab bag that made absolutely no effing sense pedagogically to anybody coming from outside of the discipline. And what they taught us, and this is coming from the 1980s on, is that Quantum Field Theory would have been discovered by topologists and geometers, even if the physical world had never used it, because it was actually a naturally occurring augmentation of what's called Bordism Theory, which is an enhancement of what you previously referred to as cohomology.