Boy what a fun course! Dr. Carlip is a very funny man.
It has been a very enlightening experience so far. I have a new perspective on nonlocal operators; before I used to be influenced by the Relativist’s motto “Locality, Good! Nonlocality, evil!” But when you think about it with an example, say we want to know the position of Mercury. That’s not too well defined, what one really means is “The time it takes for radiation to hit mercury and return according to a nuclear clock”. It turns out that all the variables of general relativity are nonlocal…which makes it difficult to deal with quantization of the thing because quantization deals with local operators!
I suppose one would also have to take into account the effects of quantum gravity into quantum field theory. I mean, there would be a discrete (possibly finite?) number of points in space time. That would change the number of dimensions of the Hilbert space we would be dealing with! You see, originally quantum field theory had an infinite number of dimensions to represent classical, continuous spacetime! But if gravity is indeed quantized, it would no longer be a continuous spacetime! This would not change anything if it were still infinite however…it would just make it countably many, albeit infinite, dimensions of the Hilbert space.
Perhaps, if I may take up my role as Devil’s advocate, both theories are wrong! General Relativity is “obviously” quantizeable based on the empirical results of semiclassical gravity experiments. But there is something unappealing about quantum theory…chiefly its sole defect that it makes no sense! That’s just a small problem though…
There is hope however that there is a kernel of truth in both theories, perhaps both are approximations to an underlying theory that is heavily observer dependent? Who knows! I’m certainly not going to pretend to!
I’ll continue ranting about how great Carlip’s class is later…I have class to go to now.
