Is the Principle of Relativity Valid for Faster-than-Light Propagation?

[Saw]

I don't know how anyone could claim that Poincaré was on the verge of coming up with SR on his own. He knew something was amiss but he didn't know what direction to go in.

Probably. It is clear that Lorentz and Poincaré were more timid and Einstein bolder. More specifically, reading for example the accounts of the history of SR in mathpages and wikipedia one gets the impression that:

- The former, especially Lorentz, were refrained by the physical explanation they had in mind. They were focused on the aether and EM phenomena and thus their conclusions were less far-reaching. In this line, the consideration of local time as not true or "real" time.

- Einstein loses those constraints and he generalizes. Thus he claims that local time is simply time, "real" time for all purposes.

I fear, however, lest the virtue might become the defect.

What do we understand by "real" time? Time is a human invented concept. If the invention process is good, it is based on an empirical basis and has an empirical purpose. Time is what you empirically measure with an instrument and your goal is predicting what may empirically happen to a real-life agent and thus solve problems. Between the two things, instrument and real-life agent, there must exist an analogy, so that the former "mirrors" the latter. And that depends precisely on the physical mechanism that is behind each process! Hence you cannot absolutely generalize. You cannot affirm that your measurement is valid for all purposes, it will be valid only for capturing processes ruled by the same physical mechanism.

Thus Einstein's insight is that the speed of light is not only the speed of light but also the speed of causality no matter the physical mechanism, i.e. the force responsible for the relevant interaction, since all of them are essentially equivalent, at least in this respect. To put it in modern terminology, all force-mediating particles travel at c. His merit is hence this generalization.

However, as you point out, it is essential to this theory that nothing can surpass the speed c, though not by chance, not by some whimsical decree but due to some (unknown but for sure existing) physical reason.

What if, however, FTL appears on the scene? Then the generalization is not valid any more, because that FTL travels must be animated by a different force.

[…] the Lorentz transformation does have a "c" and as soon as "v" reaches "c" the transformation falls apart. .

I am just trying to specify in what sense it falls apart. Take a real situation, like the duel defined in post #79.

We have ST diagrams of a certain story drawn with the measurements of two frames, red and blue. Those measurements are related by the LTs. Now we imagine that a FTL signal, even an instantaneous one, joins events P and Q. Is the ST diagram, is the LT with which it has been built still valid? Yes, of course. The LT is still telling us the truth it is meant to provide: if blue clock reads blue t at event Q, then red clock will read red t as provided by the LT. The clocks mechanisms are not based on a FTL mechanism, so blue can perfectly predict red and vice versa. What the LT cannot tell us is whether the signal in question, departing from P at blue time t will arrive at Q, where blue time is also t.

And that is where the aether model turns out to be helpful, as an intellectual tool. No matter if the aether exists or not (I do not care) this model helps me speak out the solution. If the instantaneous signal does so, that is because the blue frame is the aether frame. Hence when the signal returns (also instantaneously) it should hit the aggressor at event P itself (not at R, traveling back in time, as a defective reading of the diagram would suggest).

[Of course, an instantaneous signal (infinite velocity) is an absurd idea. Imagine the signal is just almost instantaneous.]

 

[harrylin]

Maybe you mean this one, given by Poincaré at the St-Louis exhibition in 1904:

". . . the principle of relativity, according to which the laws of physical phenomena should be the same, whether for an observer fixed, or for an observer carried along in a uniform movement of translation, so that we have not or could not have any means of discerning whether or not we are carried along in such a motion."

Edit: whole text here

Yes indeed, that's one of the citations that I referred to - thanks!
The PoR that special relativity refers to (according to Poincare, Lorentz, Einstein etc.) concerns descriptions of physical phenomena - laws that are expressed with equations - and not claims about unmeasurable reality. If there is still an issue with that topic then I'll start a thread on it.

 

[harrylin]

[..] Thus Einstein's insight is that the speed of light is not only the speed of light but also the speed of causality no matter the physical mechanism, i.e. the force responsible for the relevant interaction, since all of them are essentially equivalent, at least in this respect. To put it in modern terminology, all force-mediating particles travel at c. His merit is hence this generalization.

In fact Poincare explained in 1904, based on Lorentz' paper, that his "new mechanics, [..] would be, above all, characterized by this fact, that no velocity could surpass that of light". [PS: I now see that ghwellsjr already mentioned that fact.]

However, as you point out, it is essential to this theory that nothing can surpass the speed c, though not by chance, not by some whimsical decree but due to some (unknown but for sure existing) physical reason.

In the footnote Poincare explained the physical reason for matter as follows:
"Because bodies would oppose an increasing inertia to the causes which would tend to accelerate their motion; and this inertia would become infinite when one approached the velocity of light."

What if, however, FTL appears on the scene? Then the generalization is not valid any more, because that FTL travels must be animated by a different force. [..]

Yes, Poincare also speculated on that and stressed that then "we should observe discrepancies which would render evident the common translation of the two stations" - in other words, that would allow to break the PoR. Thus if one assumes the PoR, measurable FTL cannot be possible. However, we know from QM theory that FTL propagation can be imagined that cannot directly be measured but only inferred. In such a case FTL can be conceived while the PoR (that is, the PoR of Poincare and Einstein) is still not broken.