Example:
When one studies the spin statistics theorem, one of the phrases that's been repeated a lot was that "the spin statistics theorem was derived from relativistic physics… there's no way to prove it in non-relativistic physics."
However, if it could not be derived from non-relativistic physics, why does one assume that it is true for the non-relativistic case as well?
Part of me tried to argue that, with a switch of reference frame, non-relativistic physics becomes relativistic.
However, another case – from particle physics – is that electro-weak only works in a certain energy interval. And the fact that classical mechanics works just fine with first order configuration space! It doesn't seem to be a requirement that a result of relativistic physics must hold for non-relativistic physics.
Must conclusions from relativistic physics hold for non-relativistic physics?
Best Answer
Physics is not just a branch of math: it is a method for modeling phenomena in the real world. If a fact is proven experimentally, but a theory fails to account for it, it is a problem with the theory, rather than with the reality.
E.g., spin arises naturally in relativistic theory, but there is no reason why it should exist in non-relativistic quantum mechanics. Yet, we do include the Zeeman term in the Schrödinger equation, since otherwise we wouldn't be able to describe the spin-related phenomena. Same is true for symmmetrizing/antisymmetrizing the wave functions.