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Suppose the Universe was non-relativistic so time and space would be independent of each other. In other words, both of them separately would be absolute and independent of an observer's motion (unlike the absolute spacetime in relativity).

Above that, let's suppose the speed of light is infinite. Would the kind of cause and effect that we experience in our real Universe be the same in this imaginary Universe?

In our Universe, it takes time for a cause to propagate and have an effect at a distance from the cause. I assume the cause is transferred by e.m. radiation and ignore the other three forces. In case of the weak force the cause will propagate with a finite speed, but because I believe the weak force is not a fundamental force, but a residue force of a more fundamental force, namely the hyper color force transmitted by hyper gluons as is explained by Haim Harari in his Rishon Model (just as the strong force was once thought to be transmitted by massive pions which turned out to be wrong; the force transmitted by the pions was a residue force of the fundamental color force transmitted by massless gluons, but that aside).

So I think all causes in the sketched imaginary Universe are transmitted with infinite speed. Does this mean that everything in the Universe causes (simultaneous) effects on everything in the Universe? Of course, you can wonder how it can be that an effect anywhere in this Universe occurs simultaneously with a cause anywhere else [which seems to imply that they are the same, while in fact, they are inseparable in the absolute time that walks at the same pace everywhere in this Universe (?)] but particles move in continuous trajectories, which according to me means that all processes follow the rule that the cause occurs prior to the effect.

But I think there is a problem here. The question remains what will happen if all particles cause a simultaneous effect on all other particles and this effect simultaneously backfires on all particles. What will happen, if anything happens at all?

My stock answer to this is to point to video games. We have zero trouble modeling crude "universes" in which light and gravity travel instantaneously, but yet objects move at normal speeds using standard Newtonian mechanics. Taking the limit as framerates go to infinity doesn't change anything.¹

A more important issue would be addressing issues like Olber's Paradox. With infinite light speeds, all the light in the universe goes everywhere, instantly. The result would be an instantaneous leveling of all heat levels everywhere due to black-body radiation.

Since all energy levels would be constant, no thermodynamic processes would function, and entropy would instantly go to 100%. Heat death at the moment of creation. No causes. No effects.²

Of course, nobody knew about blackbody radiation back then either, so it's logical to conceive of a universe where light doesn't directly transfer energy, and space dust absorbs most of the light in the universe, fixing Olber's Paradox.

But then you have to head down the rabbit hole to figure out how light allows us to see things in the first place. Then figure out how to get chemistry to work like it does in real life without light transferring energy. And how the Sun keeps the Earth warm. Etc.

At the end of the day, if you ask "is it possible?", it probably is, but the universe in question might ultimately have little in common with ours.

_{¹I don't think there's any reason to presume this statement is wrong in and of itself, but I'm also not the most expert mathmetician in the world. As mentioned in a comment, the only thing necessary here is to show that any arbitrarily high, finite framerate can be achieved, which would be functionally equivalent to "infinite" framerate from a human perspective, provided "arbitrarily high" is high enough. A quadrillion quadrillion quadrillion frames per second puts each frame under Planck time, for example.}

_{²From the comments, there's some debate about whether this is 100% true. One comment suggests energy would fail to transfer at all, locking everything at its original energy. Entropy wouldn't increase, but you'd still effectively stop thermodynamics from functioning. The main point here is that setting the speed of light to "infinity" requires a lot of modifications to current theory to make things appear to work the same way.}

Cause and effect would still exist because not everything propagates at the speed of light. My fist punching you could still be the cause for you feeling pain.

However, this infinite-speed-of-light approach would open the door for a few interesting effects

• Causality may be non-local. We may be forced to recognize a pair of events separated by a photon's motion as a single event for purposes of defining causality. This comes from the reality that information can indeed propagate sufficiently instantaneously as to be treated as instant.


• The exact definition of "speed of light is infinite" would come under intense scrutiny. We can't actually say a speed is infinite because infinity is not a real number. It is, instead, typically used as a shorthand for a limit which says something more along the lines of "the speed of light is boundless." Tiny quivvers in your wording can change things dramatically.


• Uncaused causes could be more frequent. If two systems exchange photons, they could easily form a chain reaction which starts to look more and more like uncaused causes. Whether they are actually uncaused causes would depend on your precise wording, as mentioned earlier.

"Cause and effect" would still work, except that in some cases, an effect could be coincident with its cause. You would never have an effect before a cause, though - because in Newtonian (Galilean) spacetime, what constitutes "the present" is an absolute.

An example of an effect coincident with cause would be Newtonian gravity - if you had two distant masses, and you grabbed one and shook it, the other would start shaking at the same time thanks to the infinite rate of transmission of force, and information, implied by $c = infty$.

However, the real problem with this universe is that it would, sadly, be lifeless. The very same instant cause-and-effect above would imply that, without any additional changes to our laws of physics, there would be no force fields - especially electromagnetic - that would propagate disturbances at a finite speed. That means there would be no electromagnetic radiation, and thus no way for objects to lose heat or accumulated energy to the vacuum of space. Objects would continually be heated up through collisions and otherwise until they came apart. Indeed, one could question whether any would even form at all since charged particles like protons and electrons would be unable to shed energy to form stable atoms.

Relativity is, at least with the setup of the other laws, necessary for life. To abrogate this, you'd need to more drastically rewrite the script.

Yes. Everyone observed cause and effect for thousands of years before Einstein came up with Relativity and before anyone knew that the speed of light was finite.

For example, I hit a golf ball and it sails into the air. It sails into the air because I hit it. This has nothing to do with Relativity.