So, it has been a while since I last wrote on my blog, and I honestly don't know where I was going with the last entry, so I am going to go with something different. I was sitting there thinking about a question that has puzzled me, and pretty much every other physicist on the planet. Why is it that we understand gravity so poorly? Essentially, all we know about it is its low energy approximation. It has the same basic mathematical structure of electroweak and strong nuclear theory and yet for some reason we can't truly understand it. There are of course two fundamental possibilities 1. that gravity is a unique force which is non quantum and unrelated to the others 2. we have missed a subtle aspect of the nature of gravity or the mathematical formulation of its theory.
When you consider QFT, it is almost trivial after the fact to quantize E&M, and strong and weak theories are inherently quantum. In the published version of his lecture notes, Feynman laid forth and early attempt at quantization of general relativity by guessing at a gauge and showing that it had the right mathematical and physical attributes of a quantum theory of gravity... namely that it produced a massless spin 2 particle. That theory of course was plagued by divergences which made it intractable. Now, that could mean something in and of itself since the only way that we can cope with the divergences in our other theories is by renormalization. This could be telling us that we are going about things in the wrong way and that a nonperturbative framework is the only alternative. Be that as it may, a more fundamental problem is the interpretation of GR. In the classic interpretation, we think of gravitation as a continuous distortion (for lack of a better word) of the fabric of space-time. This is clearly not consistent with our particle exchange understanding of electro weak and strong theories. In addition, there is also the philosophical argument that one can't have a Universe that is only part quantum. At any rate, if we assume that there exists some gauge for gravitation G(x), then we can write out our field theoretic equation G(X) + A(x) + B(x) + G(x)... of course ignoring the interaction terms and indices for nonspatial DoF. That kind of equation of course begs out for unification in that it ought to represent modes of a higher order function F(x) whose low energy approximation (i.e. series) gives us the three forces that we know and love so well.
It makes one think that maybe we might not be so off with renormalization since only those gauges which are renormalizeable to all order of magnitude are physically achievable... sort of like a rationality clause on nature. Modern theory has of course gotten away from the gauge view of the forces and opted for a different approach. What if we had a theory which produced particles of exactly the right helicity and mass, then we could correlate those particles with the massive and massless particles that we know and love so well. There is of course the presupposition (correct as far as we can tell) that a particle of mass m, spin s etc will behave the way it would in QFT. Superstring theory is an interesting example in that it gave us all the right particles, but unfortunately in it's original formulation in the 80s (the full history of string theory is something we can get into another time) had the same problem of divergences that the gauge theories had in addition to the fact that it allowed for more than has been observed in the universe.
It seems that SR and GR are simultaneously a blessing and a curse since they have allowed for the understanding of electroweak and strong forces while confusing the picture for gravitation. Maybe we can get into some of the technical details of the quantization of gravity over Christmas break... that would be a nice exercise in understanding exactly what our problem is. Alright, time to go...