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I have come to understand, that faster-than-light communication is problematic with special relativity, because it leads to the possibility of sending signals into the past. I also read about the historical "Lorentz ether theory" (LET) which makes the same predictions like STR, but has absolute simultaneity (even though ultimately undetectable).

Is that LET compatible with FTL communication(through yet unexplained means) ? (My qualitative, unprofessional/unmathematical consideration leads me to think: Yes, it is.)

But if it isn’t compatible, then how does it violate LET ? And what’s the minimum difference between STR and some version of LET which tolerates FTL communication? (It’s not necessary that the theory could explain it, it just shouldn’t lead to problems.)

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If by "Lorentz ether theory" you mean something like a philosophical interpretation of special relativity which is in principle impossible to distinguish experimentally from SR (akin to the Bohmian interpretation of quantum mechanics), then this indistinguishability would require that all experimentally testable laws of physics be Lorentz-symmetric, including whatever future laws govern FTL signaling. If that's the case, then there's no way to avoid the conclusion that you can use FTL signaling to build a tachyonic antitelephone which allows information to be transmitted backwards in time (see my answer here for more on this point, but basically the argument is that if you can transmit information FTL in one frame there must be some other frame where the information was received before it was sent, and Lorentz-symmetry of all measurable laws implies that if information can be transmitted back in time in one frame, it must be possible for information to be transmitted back in time in all frames). Of course there is nothing logically impossible about this sort of causality violation (physicists don't rule out a priori the possibility of closed timelike curves which show up in certain spacetimes that are theoretically possible in general relativity, for example), so in this sense even SR is logically compatible with FTL communication, but the point is that there's no way to have it in SR without being forced to accept causality violation as well.

On the other hand, if by "Lorentz ether theory" you just mean a model which is compatible with all currently known Lorentz-symmetric laws, but which allows for the possibility that in future some new phenomena will be discovered to obey laws which are not Lorentz-symmetric, then in such a model it might be possible to have FTL without causality violation. But the discovery of new non-Lorentz-symmetric laws would falsify SR, by definition, since the two postulates of SR require that all laws of physics obey the same equations in the set of inertial frames derived from these postulates (which you can show must be related to one another by the Lorentz transfromation provided the two postulates hold).

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The impossibility of rewriting the past is a principle so general that it doesn't depend on the branch of the physics, electromagnetism, Q. mechanics, whatever you want.

Is that LET compatible with FTL communication . . .?

For building an FTL communication scheme you have to show a phenomenon that while in some frame of reference (at rest with respect with the aether) the laws of physics are respected, while in another frame some laws aren't.

But if it isn’t compatible (with FTL), then how does it violate LET ?

You seem to connect the aether assumption with the FTL, in the sense that no FTL implies no aether. With aether or without, rewriting the past is not allowed in our universe.

And what’s the minimum difference between STR and some version of LET which tolerates FTL communication?

Two answers:

a) Bohm's mechanics seems to require a preferred frame of coordinates (it is not sure). However, until now, no experiment were predicted to imply FTL, because the statistical predictions of Bohm's mechanics are the same as of Standard QM.

b) Which version of LET implies FTL? You have to indicate such a version. So, indicate a scheme of FTL communication in base of the existence of the aether, and then we'll examine the difference w.r.t SR. In particular saying, some people try(ed) schemes of FTL by exploiting the non-locality displayed by quantum entanglements, without any LET. (Each one of these schemes were proved to be wrong, even without using the argument that the past cannot be re-written.) So, if you know a scheme due to LET, we will examine it.

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  • $\begingroup$ Clarification...I didn’t mean to say anything known leads to FTL transmission of information. Rather: If, as unexpected and unlikely as that may be, an experiment shows FTL communication to be possible (through some yet unkown effect) … then how far would we have to back in physical theories ? STR would be invalidated, right ? But how about Lorentz-Poincare Ether theory, could the STR-equivalent version still be used or another only slightly different LET ? (Because LET has absolute simultaneity, it seems to me like: yes.) I don’t mean to advocate “alternative” theories, I’m just curious. $\endgroup$ Mar 10 '15 at 14:42
  • $\begingroup$ @BenjaminPalan I know that the quantum theory might be invalidated if we had a frame of coordinates in which the wave-function isn't correct. For instance, the Hardy thought-experiment might be a candidate for that. For the rest, I didn't see in the literature any experiment based on aether that leads to FTL communication. This is why I suggested you to indicate such a scheme. $\endgroup$
    – Sofia
    Mar 10 '15 at 15:11

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