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Is it possible to have an alternative theory which is consistent with experiments supporting GR, but which doesn't mandate a speed limit on causality?

In other words, I understand there is experimental evidence for gravitational/relativistic time dilation, spacetime curvature, etc. but is there any inherent reason why these effects cannot be explained without the max speed requirement?

QM clearly shows that "communication" can happen instantaneously but, supposedly, causality cannot break the speed limit.

I also know the speed of light is derived from other principles, but is there anything that says that speed has to be a max limit of any kind?

I want to emphasize that the QM "communication" doesn't imply causation or information exchange, merely the establishment of the entangled attribute. Bell's inequality tells us that the attributes were not predetermined and were only established upon measuring one of the particles.

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is there anything that says that speed has to be a max limit of any kind?

Yes, the so-called chronometric distance definition; whereby the (mutually equal) value of distance between two participants, $A$ and $B$, at rest to each other is evaluated as

$$\ell[~A, B~] = \ell[~B, A~] := \frac{c_0}{2} ~ \tau A[~\text{signal}, \circledR B \circledR \text{signal}~] = \frac{c_0}{2} ~ \tau B[~\text{signal}, \circledR A \circledR \text{signal}~],$$

where the mutual ping durations between $A$ and $B$ are determined with respect to signal fronts; specificly such that

  • $B$'s reception indication of $A$'s signal, $B_{\circledR A \text{signal}}$, denotes the first indication of $B$ having noticed $A$'s signal indication, $A_{\text{signal}}$,

  • $A$'s reception indication of $B$'s ping echo, $A_{\circledR B \circledR A \text{signal}}$, denotes the first indication of $A$ having noticed that $B$ had first noticed $A$'s signal indication, $A_{\text{signal}}$, and likewise in turn

  • $A$'s reception indication of $B$'s signal, $A_{\circledR B \text{signal}}$, denotes the first indication of $A$ having noticed $B$'s signal indication, $B_{\text{signal}}$, and

  • $B$'s reception indication of $A$'s ping echo, $B_{\circledR A \circledR B \text{signal}}$, denotes the first indication of $B$ having noticed that $A$ had first noticed $B$'s signal indication, $B_{\text{signal}}$.

(Consistently, the determination of whether $A$ and $B$ had been and had remained at rest with respect to each other at all, as well as the determination of duration ratios, are also based on considerations of signal fronts; to ensure, as presumed above, that $A$'s and $B$'s mutual ping durations are indeed equal if they are found having been and remained at rest to each other.)

Together with the usual definition of "(average) speed (of something, with respect to suitable ends)" as ratio between

  • the distance between two suitable "ends" (at rest to each other, such as $A$ and $B$) and

  • the duration of either end having been occupied by the specific "something" being exchanged between the two ends

it follows that the (non-zero) symbol $c_0$ which appeared in the distance definition is identified as signal front speed.

As a consequence, the signal front speed $c_0$ constitutes a maximum:
any signals having been exchanged, as far as a speed value can be attributed at all, had at most the speed of the corresponding signal front.

And in turn: any speed value in excess of the signal front speed $c_0$ can only be attributed to phenomena which don't involve the exchange of signals (directly, at that speed).

(This general conclusion applies to many specific cases, of course; such as involving signalling "by electro-magnetic waves", "by neutrinos", "by re-arrangement of matter", "by spin", etc.)

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    $\begingroup$ @Benito Ciaro: "your argument says nothing about a maximum." -- I wrote already: "the signal front speed $c_0$ constitutes a maximum: any signals having been exchanged, as far as a speed value can be attributed at all, had at most the speed of the corresponding signal front." I can add: the symbol $c_0$ is not "infinity" either, because a finite ping duration should define a finite distance value; and zero ping duration should define zero distance. "only talks about the speed of communication between participants." -- Sure. What else? [continued] $\endgroup$ – user12262 Nov 26 '15 at 21:35
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    $\begingroup$ Benito Ciaro: "if $c_0$ were speed of sound or the speed of carrier pigeons." -- $c_0$ is signal front speed (cmp. the link given in the answer). In the hypothetical case that a carrier pigeon has landed on your shoulder and that only on this occasion you're learning for the very first time that it had taken off from "somewhere else" at all, then the speed of this carrier pigeon (wrt. yourself and the suitable "starting pad") is correctly evaluated as $c_0$. (More typically you can see a pigeon already as it approached you, thus learning that it had started before it lands on you.) $\endgroup$ – user12262 Nov 26 '15 at 21:35
  • $\begingroup$ @Benito Ciaro: "signaling mechanism [...] Why stop there, just because we don't yet [...]?" -- We're considering thought experiments where each participant is supposed to be able to judge whether some signal had been observed (first) regardless of whatever "mechanism"; as a prerequisit for even being able to define various "mechanisms" and (possibly) attributing the signal front to one particular such "signaling mechanism". The remaining difficult practical questions: How sensitive is some actual detector to some definite "sig. mechanism"?, and: What's its actual index of refraction? $\endgroup$ – user12262 Nov 26 '15 at 23:13

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