About the nonlocality of QM and faster-than-light/backward-in-time machines The fact the quantum mechanics is nonlocal is known already for a long time, since the Bell works (1966 and later) and the Aspect's group experiments confirming the Bell-type CHSH inequality (1980  and later).
More exactly, it was proved that there are results, obtained in experiments with entangles particles, that cannot be explained by local distribution of variables. To put it simply, it seems that during the measurement carried by Bob it is known what measured Alice (or if she measured), and vice-versa.
(Note: After the experiments testing the Bell-type inequalities, in the years 1990 and after that, there came proofs so-called contextual: mainly, Hardy's paradox and the GHZ experiment. They proved the non-locality without hidden variable distributions, per single experiments. But these experiments seem to do more, they even cast doubt on the possibility to explain entanglement results with non-local, deterministic hidden variables.)
But, this result cannot be exploited for performing FTL (faster-than-light) communication.
What is the most general proof for this statement? Has it something to do with (does it rely on) the QM?
One proposal: a machine able to transmit FTL messages, appears, from the point of view of some frames of coordinates, as a machine that transmits messages backward-in-time.
Well, at least in our part of the universe, we cannot change the past. I consider this as the most basic argument because it doesn't rely on QM, or thermodynamics, or other field of the physics.
Are there other suggestions for a general proof? Could it be that we can't prove the no FTL communication without arguments relying on QM?
 A: Quantum mechanics has not been shown to be non-local. Rather, hidden variable theories that make the same predictions as quantum mechanics are non-local. Quantum systems can be described in terms of observables that evolve locally. Those observables are represented by Hermitian operators, not by hidden variables, i.e. - single numbers. In entanglement of the sort seen in Aspect type experiments, two systems have observables that contain locally inaccessible information: information that can only be revealed by comparing the values of the observables of one system with those of another:
http://arxiv.org/abs/quant-ph/9906007
http://arxiv.org/abs/1109.6223.
Quantum mechanics does not provide any means for FTL communication because quantum systems evolve entirely locally.
In general relativity, some models contain closed timelike curves, paths through spacetime that return you to the point in space and time where you started. These spacetimes do not allow FTL communication. Such spacetimes have not ruled out by theoretical considerations in general relativity:
http://arxiv.org/abs/gr-qc/0701024.
There are some spacetimes that apparently allow FTL travel (and so allow FTL communication):
http://arxiv.org/abs/gr-qc/0009013.
However, these spacetimes include exotic forms of matter that seem to be heavily restricted by quantum field theory, so it is not clear whether they could be realised:
http://arxiv.org/abs/gr-qc/0209036.
Neither closed timelike curves nor FTL spacetimes have been observed, but that doesn't mean they can't be built. Some future law of physics may rule them out and so explain why none have been observed, or not.
