Tolman versus Recami: tachyons

[nomadreid]

In his 1995 article "The Tolman-Regge Antitelephone Paradox: Its Solution by Tachyon Mechanics", at www.ejtp.com/articles/ejtpv6i21p1.pdf, the author Recami seems to present a key fault in the paradox, and hence rules out this objection (albeit not others) to the existence of tachyons. However, I still see lots of more recent references to the antitelephone. Did I miss something wrong in Recami's work, or did everyone else miss this paper?

 

[JesseM]

In his 1995 article "The Tolman-Regge Antitelephone Paradox: Its Solution by Tachyon Mechanics", at www.ejtp.com/articles/ejtpv6i21p1.pdf, the author Recami seems to present a key fault in the paradox, and hence rules out this objection (albeit not others) to the existence of tachyons. However, I still see lots of more recent references to the antitelephone. Did I miss something wrong in Recami's work, or did everyone else miss this paper?

Skimming it, it seems like the paper is just restating the "Feinberg reinterpretation principle" discussed here. But the author doesn't even touch on the issue of information transmission, which is where the real causality problems arise. As it says in the wiki article (I helped to edit this section):

According to the Feinberg reinterpretation principle every tachyon detector will register tachyons in every possible detection mode; from the perspective of a frame where the registration by the "detector" preceded the activation of the "emitter", the "detector" in the past is actually spontaneously emitting tachyons, only some of which will be intercepted by the detector in the future. However, Feinberg's reinterpretation principle, which simply relabels the events so that the earlier event is defined as the "emission" and the later one the "detection", does not in itself solve the causality problems associated with tachyon information transmission.[8] For example, suppose experimenter A could selectively influence the rate at which tachyons from her emitter traveled to the detector of experimenter B, and B could measure changes in the rate tachyons arrived at his detector, so that A could transmit a message to B in binary code. Then in a frame where B's detector went off at an earlier time than A influenced her emitter, merely relabeling B's device as a "spontaneous emitter" and A's as a "detector" wouldn't change the fact that B, by observing the changing rates of tachyons being spontaneously emitted from his device, could gain information about A's interactions with her own device in the future. Only in the case where it was impossible to influence tachyon emissions in such a way as to transmit information would Feinberg's reinterpretation principle fully resolve the issues with causality.

 

[nomadreid]

Thanks, JesseM. One of Recami's arguments in that article (which, sorry, was earlier than 1995; that was the date of the reprint) was that the paradox results from its construction by mixing the two reference frames, that using only one of them eliminates the paradox.

Thank you for the reference to the Wiki article. I followed it up, reading that article's references, the most interesting of which I found
http://www.xs4all.nl/~johanw/PhysFAQ/ParticleAndNuclear/tachyons.html
One of the arguments is curious. Essentially,
tachyon ==> negative m²==> Gordon-Klein has various solutions, one of which is that localized tachyon disturbances are subluminal -- which I am not sure how to envision for a tachyon going superluminally.

Finally, I am a bit confused as to how one can have emission-absorption real time yet a tachyon having imaginary time.

 

[JesseM]

Thanks, JesseM. One of Recami's arguments in that article (which, sorry, was earlier than 1995; that was the date of the reprint) was that the paradox results from its construction by mixing the two reference frames, that using only one of them eliminates the paradox.

But if tachyons obey the principle of relativity (i.e. the equations governing their behavior are Lorentz-invariant), then any experiment with tachyons that is possible to do in one frame must be possible to replicate in another frame. Thus, if there is any single inertial frame where it's possible to use tachyons to transmit information FTL, then according to relativity it must be possible to do this in all inertial frames, and it's easy to show that a necessary consequence of this is that it would be possible to violate causality by passing a message back into one's own past light cone. The only way out of this would be to say that tachyons cannot be used to send any type of FTL messages, as might be implied by the ideas you mention about how tachyon fields would behave in quantum field theory.

Finally, I am a bit confused as to how one can have emission-absorption real time yet a tachyon having imaginary time.

The equations describing the dynamics of a tachyon in some sublight inertial frame could just involve how their position coordinate changes with time coordinate in that frame, there need not be any reference to a tachyon's own "proper time" (and saying that the proper time would be imaginary is just another way of saying that the metric assigns a spacelike worldline a proper distance, not a proper time). Relativity only allows inertial frames to be slower-than-light, so there need not be any notion of what things are like in the tachyon's "own frame" (such a notion has no meaning for photons either).

 

[nomadreid]

Thanks for following up so quickly.

then any experiment with tachyons that is possible to do in one frame must be possible to replicate in another frame.

Fair enough... but shouldn't any experiment then be done in one or the other reference frame, not in both at the same time? That is, it seems that in the paradox as it is formulated, with the tachyons going from A to B to A1, part of the calculation is done in the reference frame of A, and some in the reference frame of B. Isn't that cheating?

there need not be any notion of what things are like in the tachyon's "own frame" (such a notion has no meaning for photons either).

Enlightening (no pun intended)! Thanks.

 

[JesseM]

Fair enough... but shouldn't any experiment then be done in one or the other reference frame, not in both at the same time?

I would say that experiments aren't done "in" any frame, as the same experiment can be analyzed from the perspective of any frame you wish (a frame is just a coordinate system after all), and all frames make the same predictions about local events like the readings on dials of machines. If you had some set of Lorentz-invariant laws governing tachyons, you could indeed analyze the whole tachyonic anti-telephone experiment from the perspective of a single frame, and the predictions you'd get would necessarily agree with the predictions you'd get from first analyzing one tachyon signal in the rest frame of device #1, and then analyzing the second tachyon signal (sent from device #2 after it had already received the first signal) in the rest frame of device #2. This is just a consequence of what it means for the laws of nature to be Lorentz-invariant--if they are, this implies you can analyze the same initial conditions in different frames and use the same equations to make predictions about what will occur given those initial conditions, and you are guaranteed to get the same predictions about subsequent local events like instrument-readings.

 

[nomadreid]

Thanks a lot for the answers. A big help.