In case anyone was wondering about the state of string theory today, this review by Sean Carroll of Lee Smolin's new book, The Trouble with Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next, and the subsequent debate in the comment thread (in which Lee Smolin participates) gives a good picture. I gave myself permission to skip over the bits that read like this: "The correlation function W(x,y) ~ |x-y|^-2h. is clearly not diffeomorphism invariant." and instead attempt to grasp the bits that read like this: "[A fundamental theory] cannot-by definition-have a more fundamental underpinning. So it must stand up on its own. This means we must be able to formulate it cleanly and precisely and the important properties it enjoys should be theorems. It doesn’t mean physicists should all work at a rigorous level, but that rigorous framework must be there to refer to.
This is not an unrealizable ideal. Classical Newtonian mechanics satisfies it. So does classical statistical mechanics, ordinary non-relativisitic quantum mechanics and general relativity. In each of these cases there is a body of rigorous results and a community of mathematical physicists who work on them.
Is this too much to hope for theories of quantum gravity. No!"
I found out what "diffeomorphism invariance" means by accident while I trying to find diagrams of "background independence." link Closely related to background independence is another basic ingredient of general relativity, known by the imposing name diffeomorphism invariance. It concerns the coordinates physicists use to describe space and time. The principle of diffeomorphism invariance implies that, unlike in theories prior to general relativity, there are no additional structures in physics that allow us to distinguish preferred coordinate systems. As far as the laws of physics are concerned, no coordinate system is better than another, and one is free to choose.
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In case anyone was wondering about the state of string theory today, this review by Sean Carroll of Lee Smolin's new book, The Trouble with Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next, and the subsequent debate in the comment thread (in which Lee Smolin participates) gives a good picture. I gave myself permission to skip over the bits that read like this: and instead attempt to grasp the bits that read like this:
- sally mckay 10-11-2006 12:54 am
I found out what "diffeomorphism invariance" means by accident while I trying to find diagrams of "background independence." link
- sally mckay 10-13-2006 8:52 pm