What Theories Explore the Deeper Meaning Behind the Constancy of c?

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I understand that the constancy of c is a postulate, back in the day guided by the Michelson experiment and Maxwell's equations. I was wondering, are there any (speculative) theories out there that have this fact as an outcome of something deeper/more basic?
 
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You can arrange things somehow that the speed of light turns out to be constant. Read "Special Relativity in general frames" by Eric Gourgoulhon.
 
You can show that there is an invariant speed from the principle of relativity alone (here). If you let that invariant speed be infinite you get Newton; if you let it be finite you get Einstein. The speed of light has not been mentioned yet.

You can then observe that photons are massless and that they must therefore travel at that invariant speed. Otherwise you get infinite accelerations for any applied force.

In that sense, the constancy of the speed of light is already a consequence of something else. Einstein used it to derive relativity, but it isn't actually necessary.
 
Thank you! That is a fascinating paper, and at a level I can understand too it seems.
 
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