I've been wondering about this for a while, and it could make for an interesting discussion (or a stupid one if the answer is obvious, but it isn't to me). My question is, is there good reason to think that Physics is unique? Now, obviously this question is impossible to answer because we do not even have a complete discription of nature yet - i.e. both the Standard Model and GR are known to be incomplete. However, assuming some complete description of nature does exist, which has absolute predictive power for any possible observation or measurement we choose to make (within certain limits on computability of course), then is it reasonable to expect that that description will be a unique one? It seems to me that it may be possible for there to be many theories which will agree to within any possible experimental precision, but which make fundamentally different assumptions about the basic aspects of nature, and which are different in their mathematical structure. If we could program a bunch of computers with the brilliance of Newton, and gave them each a vast array of experiemental data, would they each produce their own version of Physics? I'm inclined to think so, but it could be that it is necessary that there if there exists a complete mathematical desciption of nature, then it is a unique one. Perhaps this is closely related to the question of the "reality" of mathematics, which may border to close to Philosophy, if this thread doesn't already.
What do you mean by this? And I guess that due to uncertainty principle of QM, we can never predict everything. I found a good description of scientific determinism in Stephen Hawking's books. There are different possibilities : We may arrive at a theory after which we cannot progress further or we can get more and more accurate theories but not an exact one. Also see Godel's incompleteness theorem. http://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems
I won't pretend I can understand Godel's theorm by skimming a wiki article, but I'm not asking if Physics is homomorphic with Mathematics and thus subject to every mathematical theorem. I'm posing the question that if there exists a complete mathematical description of nature, if it will be a unique one. Godel's theorem doesn't really apply the real world as I understand it. If you can phrase a question in such a way that it is ameanable to calculation and experimentation then there is no doubt about it's correctness - if the experiment and calculation agree, then that is proof. If you want to pose some mathematical question which can not be determined by experiment, then I don't really see how it's relevant to Physics. Now, the fact that you can ask many questions which may be impossible to verify experimentally seems to imply that Physics will never be unique, but I don't think you can conlude that from that possibility alone.
Even I don't understand the theorem completely but I understand what it wants to convey. Well, I don't think the theory will be a unique one. In the case of M-theory which tries to unify GR and QM, it seems that we can try out different approaches and arrive at different theories which point at this one theory. Source: "The Universe In a Nutshell" by Stephen Hawking. No, if they agree with each other, they provide more support to the theory but you never know if one day some observation might not agree with predictions and that one observation is enough to prove the theory wrong(or less accurate).
We have a number of different interpretations of quantum mechanics, which propose different stories about the way the universe "really works", but which are all constructed to make the same predictions about things that we can actually observe (even in principle). That is, they all reduce to the standard QM that one finds in textbooks. Would you consider these to be a single description or multiple descriptions?