“If it’s not on the web, then it does not exist!”
Yesterday I went to the library for the first time in a long time. I had forgotten how interesting it can be to browse the shelves. I picked up a copy of Roger Penrose’s thesis “An Analysis of the Structure of Space-Time” (1969?) which has, so far, been a totally fascinating read. I have vague recollections of the importance of spinors in general relativity from the class I took from Kip Thorne, but at the time it hadn’t really occured that this could be more than a nice mathematical trick. Penrose really drives home how the employment of spinors, rather than tensors, for describing general relativity might be a more appropriate representation of space-time.
Also, in his introduction Penrose describes what is my favorite path towards reconciling quantum theory and general relativity:
The second attitude would be that quantum mechanics and general relativity cannot, or at least should not, be forced together into each other’s framework…that what is required is something more in the line of a “grand synthesis,” i.e. a new theory in which general relativity and quantum theory would emerge as different limiting cases, each applicable to its appropriate domain of phenomena, and in which, hopefully, semi-philosophical quantum mechanical questions as the meaning of an “observation” might be resolved. In fact, this…point of view is the one to which I would, myself more readily incline. But it is, for the present, possibly something of the lazy man’s way out, since it provides the relativist with an excuse for not tackling directly the substantial problems of quantization!
In physics, history has shown us many examples of theories whose validity in certain regimes breaks down when the theory is moved into a new regime. Sometimes the answer to resolving this is revolutionary (Why doesn’t an electron in orbit around an atom radiate away all it’s energy? The Bohr atom and then quantum theory!) and sometimes it is not as revolutionary (How do we explain the weak force? Fermi’s theory seems fairly good but it is not renormalizable. Do we need to talk about nonrenormalizable theories? No Glashow-Weinberg-Salam theory is renormalizable! We just had the wrong theory!) What astonishes me about the theoretical physics community is just how much is invested in the nonrevolutionary point of view: that it should be possible to “quantize gravity” (either string theory or loop quantum gravity.) There are only a few crazies (t’Hooft and Penrose, for example) who seem to be persuing Penrose’s “second attitude.” Part of the reason for this is dictated by the success of the traditional program: we’ve bagged electrondynamics, the weak force, and the strong force. Since in all of these cases we successfully quantized a classical theories, it seems reasonable to suggest that the “final” classical theory, gravity, should also fall to the quantization gods. But historical success does not the future guarantee! And so I will joyously spend too much of my time dreaming up ways to derive quantum theory and general relativity in the respective domains!