The theory of relativity takes its name from a very simple and appealing idea: that the laws of physics should look the same to moving observers as to stationary ones. “Laws of physics” here includes Maxwell’s equations for electricity and magnetism, which necessarily means that moving observers must see the same speed of light as stationary observers (Einstein included the constancy of the speed of light as a second postulate in his original relativity paper, but it’s redundant– the constancy of the speed of light is a direct consequence of the principle of relativity). This leads directly to all the observed weirdness of relativity– clocks running at different rates for different observers, moving objects shrinking, disagreements about the simultaneity of events, etc.
Of course, the notion of a single universal time also has a certain aesthetic appeal, which is part of why it was the default assumption of physics from the days of Galileo and Newton through to 1905. Having every clock in the universe, moving or not, tick at exactly the same rate would be simple and elegant in a manner similar to that of relativity. It would, however, require some drastic revisions of the laws of physics as we understand them.
The question is, what would need to change, and what would the consequences be?
You would clearly need to change the structure of Maxwell’s equations to accommodate a variable speed of light, but what would that do to, say, atoms and molecules, that are held together by electromagnetic forces? The speed of light shows up in things like the Rydberg constant that gives you the energy of atomic energy levels, so presumably these would get pushed around as the speed of an object changed. Would that mean, for example, that objects moving at too high a speed would literally fall apart as the energy levels determining the bonds between their component atoms shifted into a new configuration?
(I’m imagining a world that’s as similar to ours as possible, but has a variable speed of light, so things like the Michelson-Morley experiment would not give the negative result that they do in our world. I’m not looking for aether drag theories that use some baroque method to match those observations, but a version of reality in which those observations are consistent with a variable speed of light)
I don’t expect that anybody has put all that much thought into this– it would take a good deal of mathematical effort to reformulate E&M in a way that wasn’t consistent with relativity, and why would you do that? (Then again, there’s some amazingly abstract stuff on the arxiv, so who knows?) It’s kind of an interesting topic for idle speculation, though. So consider the comments section an open thread for idle speculation, or the posting of actual relevant information, should any exist.
(This post brought to you by Emmy, who asked “Would having all observers see the same time really be all that bad?” in chapter 3 of the book-in-progress.)