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Why shall Quantum Mechanics accept Relativity?

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lugita15
#19
Mar12-12, 01:35 AM
P: 1,583
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
#20
Mar12-12, 10:25 PM
Sci Advisor
P: 1,924
Quote Quote by lugita15 View Post
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?
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.

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.
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
#21
Mar12-12, 10:53 PM
P: 1,583
Quote Quote by strangerep View Post
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.
OK, what about "fundamentally different" in some sense or another?
strangerep
#22
Mar13-12, 04:07 AM
Sci Advisor
P: 1,924
Quote Quote by lugita15 View Post
OK, what about "fundamentally different" in some sense or another?
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
#23
Mar13-12, 05:54 AM
P: 140
Quote Quote by dpa View Post
Hi all,
Quantum Mechanics has everything wierd and unacceptable to classical theory and its foundations with phenomena like:
Uncertainity/Entanglement/Decoherence/Tunneling and lets say almost all Quantum Mechanical Phenomena are non classical.

My silly question is why do we expect QM to follow relativity? I dont know, but is it solely because we are chasing a fantasy where all forces unite and unification of QM and GR is the only way that is apparent to us?
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
#24
Mar13-12, 09:46 AM
P: 660
Quote Quote by Fredrik View Post
Would you care to elaborate? This doesn't make sense to me. Would you also say that the statements "x=0" and "x≠0" can both be correct, since non-contradiction is an assumption?
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
#25
Mar21-12, 12:21 AM
P: 2
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


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