[Dylan16807]

There's a lot of ways to implement that and most of them aren't a problem.

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.

[setopt]

“Instant” (i.e. infinite speed of light) also permits causality. That’s the historical Galilean model.

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”.

[Dylan16807]

Couldn't you have the laws of physics change based on your speed but without changing based on location, direction, or over time?

Also infinite speed of causality doesn't have to imply infinite speed of light, does it?

[setopt]

> Couldn't you have the laws of physics change based on your speed but without changing based on location, direction, or over time?

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.

[Dylan16807]

> The principle of reality is first stated in general terms, leading to the idea of equivalent frames of reference connected through "inertial" transformations obeying a group law. [...] Only the Lorentz transformations and their degenerate Galilean limit obey these constraints.

> 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.

[dcow]

Could you even measure or experience variable speed causality? Or, it doesn’t matter what made up constant you assign the speed of causality. You’re just bits on a page and you only perceive anything as the clock cycles.

[ben_w]

I've heard it claimed that we can only measure the round-trip speed of light, not the one-way speed of light, because the maths says that reality would look identical if it was 0.5c in the x+ direction and ∞ in the x- direction.

I find this hard to stomach, but I'm going to trust it also applies to e.g. magnetism being Lorenz transformed electric fields, because relativity violates "common sense" all over the place and reality doesn't care about my stomach.

https://www.youtube.com/watch?app=desktop&v=pTn6Ewhb27k&them...

[AnimalMuppet]

I also have heard that, multiple times. I don't buy it. I think there are at least two experiments that could show the difference.

First, you could time the travel of light from one place to another. To do that, you need synchronized clocks. The easy way to do that is to start with clocks synchronized at a central point, then very slowly move them from the central point to the endpoints. Why very slowly? Because you have to worry about time dilation with the clocks. For small v, the difference in the rate of time is approximately v^2/2c^2 (to first order). The amount of time you have to maintain it is t = d/v. The corresponding difference in clock time still approaches zero as v approaches zero, so in principle, the clocks can be arbitrarily close to each other in time if you just move them slowly enough.

But what if c has different values in opposite directions? Well, then time dilates different amounts for the clocks going in opposite directions, but the amount of time dilation for each clock still approaches zero if the velocity is low enough.

Second: If you have a cyclotron or synchrotron, with charged particles moving in a circle in a magnetic field, and those charged particles are moving a significant fraction of the speed of light, if the speed of light is not uniform, their motion should deviate from a circle. Why? Because the force on them due to the magnetic field should be the same, but the acceleration should be different depending on what fraction of the speed of light they're moving. (Due to increased mass, if you think of it that way. If you don't, well, the equation doesn't change.)

I think that some experiments would fail to show a non-uniform speed of light, but I think experiments could be devised that would show it.

[Dylan16807]

Unfortunately, if the one-way speed of light is anisotropic, the correct time dilation factor becomes 1/(γ(1−κv/c)), with the anisotropy parameter κ between -1 and +1.[17] This introduces a new linear term, meaning time dilation can no longer be ignored at small velocities, and slow clock-transport will fail to detect this anisotropy. Thus it is equivalent to Einstein synchronization.

https://en.wikipedia.org/wiki/One-way_speed_of_light

A lot of scientists have thought about this. Step one is checking their work.

[AnimalMuppet]

Ah, I see.

I see nothing there that would invalidate my synchrotron argument, though.

[Dylan16807]

If you apply the more detailed equation I bet it says the mass doesn't change, so there is no change around the circle to measure.

I'm sure someone has thought of an experiment that simple. If you can't find anything close enough you can ask on one of the stack exchanges.