My belief is that the quest to find a unified physics that describes everything is provably impossible due to Godel's theorem.
How would that happen? Physics is an empirical science, all we have to do is to look at what actually happens and write it down. Even if we fail to find good mathematical expression to describe what we see, we can always just create charts and tables describing what happens. There is nothing that prevents us from fully describing physics.
Unifying physics then just means finding one mathematical model that is able to describe all the aspects we discovered in different limits. I can not see how Gödel's incompleteness theorem would have any bearing on this. We just have to find a set of equations that reproduce our observations given the experimental setup. This does not involve any proofs, it's just the question whether a set of equations accurately describes the universe.
I can really only think of one way in which describing the universe with mathematics must fail and that is if there is no mathematical description of the universe. Otherwise we could always guess a set of equations and then verify that it works in all experiments we ever performed. You can of course never be sure that you did not simply miss one experiment that causes your theory to fail, but that is in the nature of physics. This also seems pretty unlikely, I fail to imagine anything that could escape all attempts of mathematical describing it in principle.
How would that happen? Physics is an empirical science, all we have to do is to look at what actually happens and write it down. Even if we fail to find good mathematical expression to describe what we see, we can always just create charts and tables describing what happens. There is nothing that prevents us from fully describing physics.
Unifying physics then just means finding one mathematical model that is able to describe all the aspects we discovered in different limits. I can not see how Gödel's incompleteness theorem would have any bearing on this. We just have to find a set of equations that reproduce our observations given the experimental setup. This does not involve any proofs, it's just the question whether a set of equations accurately describes the universe.
I can really only think of one way in which describing the universe with mathematics must fail and that is if there is no mathematical description of the universe. Otherwise we could always guess a set of equations and then verify that it works in all experiments we ever performed. You can of course never be sure that you did not simply miss one experiment that causes your theory to fail, but that is in the nature of physics. This also seems pretty unlikely, I fail to imagine anything that could escape all attempts of mathematical describing it in principle.