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Is there a way to "build" special relativity by using causality as one of the axioms? Or is it just a consequence of a fact that the speed of light is same in all reference frames?

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    $\begingroup$ Well, what exactly do you mean by causality? $\endgroup$ – David Z Jul 28 '15 at 16:37
  • $\begingroup$ Speed of light same in all frames of reference is postulate to special relativity. There is no assertion of fact. $\endgroup$ – paparazzo Jul 28 '15 at 18:28
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Not quite. Galilean relativity, which has absolute time, is definitely causal; you can't have future events influence past ones because all observers agree on all times.

However, it is interesting how much relativity you can get with incomplete axioms. There's a derivation on page 38 here that shows you can get the Lorentz transformations, but with a general $v$ in place of $c$, using just the postulate that inertial frames are equivalent. Then adding in the 'speed of light is same' axiom sets $v = c$. Like your causality thing, this doesn't rule out Galilean relativity because that's just the limit $v \rightarrow \infty$.

Given that, I'm not sure if just a "causality" axiom is enough to get equally far. Maybe you could argue that causality really is the same thing as "all inertial frames are equivalent", but I'm not sure about that.

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Based on this post:

Is causality a formalised concept in physics

and the content within, the issue of causality seems to me to be a philosophical as much as a physical question. So I would guess there is no clearcut answer to your question.

Have a read, see what you think, and see will you end up as confused as everybody else seems to be regarding the issue.

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