Also consider the speed of light is also the speed of causality. If there was no such limit it means it would be possible for effects to precede causes which would lead to a very different kind of universe!
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For example: If there isn't a speed of light, how fast does light go? If it's variable but not instant, then depending on the details causality violations could still be very rare or impossible. If it's instant, then how do we define instant for different observers? I feel like relativity-style calculations don't really work. If "instant" is agreed upon by all observers then we won't have causality issues.
That is in fact the only other way to make a causal universe that satisfies a few common sense assumptions (“the laws of physics are the same in every location”, “the laws of physics are the same in every direction”, “the laws of physics are the same over time”).
“One more derivation of the Lorentz transformation” by Lévy-Leblond is a very accessible derivation of this if you’re interested in reading more. It was suggested that perhaps relativity should be taught this way in high school, instead of the historical approach of “c appears to be constant in experiments, so how do we work around that with math”.
Also infinite speed of causality doesn't have to imply infinite speed of light, does it?
No you can’t, that’s basically what e.g. the Levy-Leblonde reference proves :).
I encourage giving a read if you’re interested! The proof is just a few pages long, and doesn’t require more advanced mathematics than the average intro to special relativity.
If you’re willing to give up either causality itself, or the invariances of physical laws we discussed above, then of course many other alternatives open up.
> Also infinite speed of causality doesn't have to imply infinite speed of light, does it?
That is correct!
Without experimental data, we can just prove that there must be a “speed of causality” that is constant for every observer in a universe with the properties we discussed above.
That there exist “photons” in this universe that manage to travel at this speed is an experimental result. The exact value of that upper “speed limit” is also an experimental result.
> I will take as a starting point the statement of the principle of relativity in a very general form: there exists an infinite continuous class of reference frames in space-time which are physically equivalent. [...] no physical effects can distinguish between them.
Sounds like this entire paper is built on a foundation of assuming the laws of physics don't change based on speed. Am I misreading?
In that case, the paper proves that the Lorenz transforms are the only way to have both relativity and those rules, but they don't show that those rules by themselves imply relativity.