Why shall Quantum Mechanics accept Relativity?

strangerep

I don't know how to answer that in any useful way.

Suppose we pick a point on a 2D plane -- call the point (x,y). Your question is a bit like asking "under what circumstances are lines which lead to (x,y) straight or curved?"

lugita15

I had assumed that it was rare for a group whose Inonu-Wigner contraction is the Galilei group to have boosts and translation not commuting, and that the Poincare group (and those that contain it) are one of the few (or perhaps the only ones) that satisfy this condition. Am I wrong in that impression? If having them not commute is a fairly common property of groups which reduce to the Galilei group, then Kaiser's result wouldn't be that significant to me.

strangerep

Take any Lie algebra, modify its structure constants a little, and you (probably) have a different Lie algebra (modulo those modifications which are equivalent to a change of basis in the original Lie algebra).

So there are infinitely many.

What matters is which groups are already well-proven experimentally to be of deep importance in physics. Poincare fits that description -- it's already well established from over a century of special relativity.

Another reason why I find Kaiser's result to be thought provoking is that it banishes the old puzzle about why there's no straightforward extension of the position-momentum CCRs
to an analogous time-energy relation.

lugita15

OK, what about "fundamentally different" in some sense or another?

strangerep

The important phrase in my previous post was "well-proven experimentally to be of deep importance in physics.". Even if you found a "fundamentally different" group, you still must show that it is physically important in its own right.

But such open-ended questions are too speculative for my tastes, and are not something that interests me any further.

faen

Even if quantum mechanics is non classical, it is consistent with classical mechanics. We try to figure out how it can be consistent with GR as well.

RUTA

Yes, this is a violation of the principle of non-contradiction. And, yes, it doesn't "make sense" to me either because the principles of logic are just a reflection of what "makes sense." How am I applying it to physics? When we had Maxwell's eqns and Newtonian mechanics, both of which worked in their respective realms, we had a contradiction in that Maxwell's eqns are Lorentz inv while Newtonian mech is Galilean inv. Thus, assuming non-contradiction, we "knew" that at least one of these theories wasn't "correct." And, of course, special relativity came along to show us it was Newtonian mech that was only a v << c approximation to the "correct" theory. Now we have QM and GR, both of which work in their respective realms, but they contradict one another, e.g., spacetime is flat, spacetime is locally Lorentz inv, etc. So, we "assume" that at least one of these theories is "wrong."

andresB

My two cents.

maybe not general relativity, but at least some theory of gravitation, (presumably ,but not necesarily, one that have in its postulate the princile of equivalence) is necesary for the consistance of quatum mechanics.

maybe I am wrong, but the Einstiein clock in the box paradox (and the bohr solution) seems to imply that