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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?

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closed as unclear what you're asking by Ben Crowell, JMac, GiorgioP, ZeroTheHero, ahemmetter Mar 22 at 9:04

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    $\begingroup$ Would cause and effect still exist in this Universe? This seems like a non sequitur. Could you edit the question to explain why you think there is any logical connection between this and the preceding material? $\endgroup$ – Ben Crowell Mar 21 at 13:39
  • $\begingroup$ Can we even really apply our physics to "infinite speed light"? I thought even classical approaches to optics still considered that light moved with a non-infinite speed; they just didn't relate that to the speed of light being the limit of velocity, and assumed light speed was limited by its medium. $\endgroup$ – JMac Mar 21 at 14:52
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    $\begingroup$ Given that you're starting off with discarding the laws of physics - and then making assertions the result (eg speed of light infinate) - might I suggest that the world builder forum be a better place to ask? $\endgroup$ – UKMonkey Mar 21 at 15:32
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    $\begingroup$ @industry7 ok, but what is FTL when c = infinity? $\endgroup$ – Carl Witthoft Mar 21 at 17:53
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    $\begingroup$ @industry7: It is common knowledge that under Einstein-ian relativity ftl does away with causality. But that argument doesn't hold in Galilean relativity, so there is no issue. $\endgroup$ – Ben Crowell Mar 21 at 19:35
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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.

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    $\begingroup$ "Taking the limit as framerates go to infinity doesn't change anything." - citation needed. If there is anything higher maths has taught me is that assuming things do/don't break in limits to infinity is a mug's game without proof. As framerates go to infinity, you either need to have precision to go infinity (which has weird effects) or you need to chunk things (which makes the framerate not actually be infinity). Things "changing the next frame" at unbounded distances are not infinite speed. Things changing their own frame is infinite speed. $\endgroup$ – Yakk Mar 21 at 13:42
  • $\begingroup$ Olber's Paradox doesn't hold. The light coming from distant stars that reaches us instantaneously is to faint to contribute to an instantaneous leveling of all heat levels of all massive bodies. But to be sure you have to make a calculation. $\endgroup$ – descheleschilder Mar 21 at 14:18
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    $\begingroup$ I don't think that infinite speed of light would change the rate at which heat energy is released as photons. Obviously it changes the rate at which those emitted photons get absorbed on the other end (when accounting for the static delay). But the process would, I think, still require the same amount of time on the production side. $\endgroup$ – industry7 Mar 21 at 16:19
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    $\begingroup$ @descheleschilder That's only true if the universe is not infinite. We don't know if the universe is infinite in size in real life because we can't see past the cosmological event horizon. But if the speed of light is infinite, and the universe is infinite in size, every point in the night sky will be a star. $\endgroup$ – Ryan_L Mar 21 at 18:27
  • $\begingroup$ Actually, there would be no radiation at all. At $c = \infty$, Planck's law becomes zero everywhere. This seems to suggest it would be actually impossible for an object to cool off in a vacuum. That doesn't seem good. This makes sense because the only way the electromagnetic field can transmit energy from point to point is if there is a finite transmission speed so that waves - which carry energy - can exist. $\endgroup$ – The_Sympathizer Mar 22 at 2:13
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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.
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  • $\begingroup$ I agree, of course, that the elementary particles (with a mass) don't travel with the speed of light (which is infinite in this hypothetical Universe). But I think it is more appropriate in this case to say that the whole Universe is part of a chain of cause and effect. If you punch me on the nose it's not your fist that is the cause for the effect that my nose starts to hurt but rather the whole collection of elementary particles in the Universe (I refer to the non-locality you mention). $\endgroup$ – descheleschilder Mar 21 at 10:53
  • $\begingroup$ Perhaps instead of "the speed of light is infinite" one could consider one or both of the classical vacuum permittivity or permeability to be zero, and the consequences thereof. $\endgroup$ – JdeBP Mar 21 at 11:51
  • $\begingroup$ "We can't actually say a speed is infinite because infinity is not a real number." Speed is distance divided by time. If there is finite distance and zero time, then speed is infinite. $\endgroup$ – Acccumulation Mar 21 at 15:22
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    $\begingroup$ @Acccumulation That is not actually true. A finite real number divided by zero is undefined, not infinity. For rigorous handling of division by infintessimally small numbers, we may rely on limits, but those have their own set of rules. $\endgroup$ – Cort Ammon Mar 21 at 15:29
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    $\begingroup$ @Acccumulation The difference is a very important detail. It isn't that big of a deal when working with nice finite numbers like in the real world, but in a question like this, the difference between $\frac{1}{0}=\infty$ and $\lim_{x\to 0}{\frac{1}{x}}=\infty$ is on the scale of the difference between causality and not, so for this question pedantic attention to that detail does indeed matter. $\endgroup$ – Cort Ammon Mar 21 at 15:43
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"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.

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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.

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    $\begingroup$ But what if the Universe was non-relativistic and the speed of light infinite in those ancient times? $\endgroup$ – descheleschilder Mar 21 at 6:06
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    $\begingroup$ You're asserting exactly the thing that the OP is skeptical about. If the universe was non-relativistic and the speed of light was infinite, would it still be possible to hit a golf ball and have it sail into the air? We're not talking about the knowledge of relativity, but rather the (imagined) reality. Relativity explains why causes always precede their consequences; if relativity is wrong and speed of light infinite, do we still have that guarantee or not? $\endgroup$ – Luaan Mar 21 at 11:38
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    $\begingroup$ That "everyone observed cause and effect [...] before Einstein came up with Relativity" does not mean that the universe was non-relativistic before Einstein, does it? So the statement is completely irrelevant, isn't it? $\endgroup$ – Peter A. Schneider Mar 21 at 11:50
  • $\begingroup$ If $c \rightarrow \infty$, how could there be any particle/field interaction? If there's no interaction at all, how could we punch someone on the face or hit a golf ball? $\endgroup$ – Cham Mar 22 at 1:46
  • $\begingroup$ @Cham The interactions involved in punching someone in the face, or hitting a golf ball, are adequately explained by the instantaneous Coulomb interaction in the Schrodinger equation. There is no $c$ in this equation because in nonrelativistic quantum mechanics it is taken to be infinite. $\endgroup$ – G. Smith Mar 22 at 16:09

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