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Again, I edited, after reading a related question question asked yesterday (that wasn't closed). It's easier to read now too, but the content hasn't changed, basically.

In mainstream physics, it is assumed that an infinite speed of light is in conflict with the laws of cause and effect. A finite speed (whatever its value) isn't.

Now assume the speed of gravity is infinite (see this article, which is addressed in this question of mine). Of course, one can wonder how it can be that this is the case. So let us assume that a gravitational effect anywhere in this a Universe causes simultaneously an effect on all other masses in the Universe. I.e, cause, and effect are inseparable.

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 gravity, ignoring the fact that it's very difficult to SEND a cause with the aid of gravity, but nevertheless, gravity is capable of doing so (e.g. by two neutron stars accelerating towards each other). The other two forces, the weak and strong ones, are obviously unable to send a cause over great distances.

Does this mean that if all masses in the Universe cause (simultaneous) effects on everything else in the Universe, while actually, the rule that a cause precedes an effect can't be applied anymore in such a Universe? So you also can't speak anymore of cause and effect altogether.

What will be the implications (not to be confused with the consequences) for the motion of all masses present in this Universe (apart from the EM interactions)? Will all these masses still be able to move? I mean that even though these masses (seen apart) can move in continuous trajectories, will, seen in the light (speaking of which...) of their instantaneous connection with all other masses, an infinite speed of gravity make it impossible for all masses to move in sync? Or do they form a holistic ensemble? Will an infinite speed of gravity prevent them to move in sync?

Will an infinite speed of gravity prevent the speed of light (of the EM interaction) to be infinite, whatever it's value?

Does there exist irrefutable and indisputable evidence about the speed of gravity? Like the measurements made after the arrival of the gravitational waves from neutron mergers which formed a black hole in two different places?

Deschele Schilder
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    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? –  Mar 21 '19 at 13:39
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    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. – JMac Mar 21 '19 at 14:52
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    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? – UKMonkey Mar 21 '19 at 15:32
  • Of course you might! – Deschele Schilder Mar 21 '19 at 16:08
  • @ben-crowell It is common knowledge that under Einstein-ian relativity ftl does away with causality. – industry7 Mar 21 '19 at 16:19
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    @industry7 ok, but what is FTL when c = infinity? – Carl Witthoft Mar 21 '19 at 17:53
  • I mentioned one way to avoid the vagueness of "infinite". – JdeBP Mar 21 '19 at 18:56
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    @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. –  Mar 21 '19 at 19:35
  • @carl-wittholf Good question! I don't know :-/

    But, just to expand a little bit more on my previous answer: If you start with Einstein's relativity and start messing with c and/or the possibility of moving as fast or faster than c, well it's just really easy to accidentally break causality.

    Now that's not even what the OP was asking, but my point was just that any half-way decent intro to relativity is going to mention this stuff in passing and so it's completely understandable for someone to end up having the OP's question.

     – industry7 Mar 21 '19 at 20:11
  • @ben-crowell Hence why it is a perfectly reasonable question. – industry7 Mar 21 '19 at 20:11
  • @industry7 - You're talking about ftl. But what makes the difference in GR if the speed of light is higher (though finite) that it actually is? – Deschele Schilder Dec 15 '19 at 12:52
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    @descheleschilder Please don't ping everyone who closed your question. There's an automated question reopening process. – JMac Dec 15 '19 at 13:10
  • After having read the answers and comments, my conclusion is that your question can be simplified quite dramatically: would the assumption of an infinite speed of light lead to contradictions (e.g. for cause and effect) such that, in hindsight, you could have predicted that the speed is finite? Btw. Light is not special. There is a finite maximum speed in the universe and light happens to travel at that speed. – Hartmut Braun Dec 15 '19 at 13:52
  • But the question remains: Why does light travel at that specific speed? – Deschele Schilder Dec 15 '19 at 15:08
  • @descheleschilder The speed of light is connected to a lot of equations and other constants, so it would depend on how you adjust everything else. I would expect it to be possible to change c to a different finite number and adjust everything else such that the universe seems to pretty much work the same as it does now in the general sense. – industry7 Dec 17 '19 at 17:06

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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.

MichaelS
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    "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. – Yakk Mar 21 '19 at 13:42
  • 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. – Deschele Schilder Mar 21 '19 at 14:18
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    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. – industry7 Mar 21 '19 at 16:19
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    @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. – Ryan_L Mar 21 '19 at 18:27
  • 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. – The_Sympathizer Mar 22 '19 at 02:13
  • @Yakk, Cort Ammon has already pointed out that the term "infinite speed" is of dubious use here. There's no evidence anything in our universe is literally infinite. The point is that we can have a universe with sufficiently high precision that it mimics our universe to some definition of "well enough". A quadrillion quadrillion quadrillion frames per second, with sufficiently precise variables, would be indistinguishable from infinity to human science. – MichaelS Mar 22 '19 at 02:19
  • FWIW, "infinite speed" implies an effect occurring an "infinitesimal time" after the cause. In practice, we treat "infinitesimal" as zero, but if we're talking about literally infinite framerates, that's not necessarily helpful. – MichaelS Mar 22 '19 at 02:20
  • @Yakk : You can describe it with mathematics, even if a physical computer cannot simulate it. In fact, the equations used in games are discretizations of mathematical equations that take place in an imaginary (i.e. (probably) unrealizable in existing reality, but we're not talking existing reality now with regard to this question of course!), but still as far as we can tell (it cannot be proven thanks to Goedel) logically consistent "reality" with infinite precision and infinite "frame rates", i.e. differential equations. – The_Sympathizer Mar 22 '19 at 02:24
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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.
Cort Ammon
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  • 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). – Deschele Schilder Mar 21 '19 at 10:53
  • 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. – JdeBP Mar 21 '19 at 11:51
  • "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. – Acccumulation Mar 21 '19 at 15:22
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    @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. – Cort Ammon Mar 21 '19 at 15:29
  • @Acccumulation 0 time with what error margin? I don't disagree that the question asserts that the speed is infinate; and that the universe is non-relativistic - so it's not really a question for here, but more "World building" - but my point is that there is always a margin of error, and while that may include 0; the measured value is unlikely to be exactly 0 with no error. – UKMonkey Mar 21 '19 at 15:30
  • @UKMonkey You bring up a good point. Ask this same question on WorldBuilding and I'll answer the question differently, based on how one may relax the laws of physics on that site. – Cort Ammon Mar 21 '19 at 15:31
  • @CortAmmon You're quibbling about nomenclature. "infinity" is shorthand for "finite number divided by zero". It's clear in this context what it means, and it refers to a well-defined attribute of the universe. – Acccumulation Mar 21 '19 at 15:39
  • @UKMonkey "margin of error" refers to measurement. The OP is positing an actual speed of infinity. – Acccumulation Mar 21 '19 at 15:39
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    @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. – Cort Ammon Mar 21 '19 at 15:43
  • Indeed, the entire beauty of Newton's work was a rigorous handling of these concepts which permit us to create laws of physics which are highly effective at predicting the behavior of the natural world. – Cort Ammon Mar 21 '19 at 15:48
  • I think stating $ c = \infty $ is equivalent to saying that it's not just entangled photons which propogate information instantly. – Carl Witthoft Mar 21 '19 at 17:54
  • "That infinite is not a real number" is, imo, a poor way of talking about maths but one often repeated. "Infinity" can mean a number of different things, and here the relevant notion of "infinity" here is the specific mathematical object $\infty$ in the extended real number system . This is mathematically something that can be made very rigorous and well-defined indeed - you just have to be careful with it and what you are and are not allowed to do. That said, you can avoid referencing explicitly this infinite $c$ just by taking Newtonian mechanics as-is, which makes no mention of it. – The_Sympathizer Mar 22 '19 at 02:27
  • And also, that is equivalent to passing to the limit of relativity theory as $c \rightarrow \infty$, which anyway is what you have to do to extend consistently the theory to when $c$ is allowed to range in the extended reals in the first place since $\infty$ is effectively an accumulation point of $\mathbb{R}$, a fundamentally "limit-like" object, and thus the "natural way of extension" it comes with is limits. – The_Sympathizer Mar 22 '19 at 02:28
  • And there is nothing "wrong" with the extended real numbers - you just have to be clear you're using them, instead of just the default which is to assume $c$ is in $\mathbb{R}$, so that you don't end up inadvertently breaking rules. – The_Sympathizer Mar 22 '19 at 02:30
  • @The_Sympathizer The laws of physics are typically defined on the real number line, not the extended real number line. You also have to be very careful about what assumptions you make about a given number, because $\infty$ is a number on the extended real number line which does not have the same properties as the other numbers. You're right that you can do such an extension, but such an extension is not trivial because every statement where one says "for all values," one has to actually check to see if the statement is still true. – Cort Ammon Mar 22 '19 at 02:32
  • Most of physics is done on fields. The extended number line is not even a semigroup. – Cort Ammon Mar 22 '19 at 02:33
  • @Cort Ammon : Sure you have to be careful. I'm simply saying what the mathematical framework is you need to use to make the OP's post mathematically rigorous, and to point out it is possible to do that. If we're going outside real-world physics anyways, then of course you're gonna have to bend some stuff. Nonetheless, once you take that limit, you can effectively forget about "$c$" and go back to $\mathbb{R}$ as you have Newtonian mechanics. – The_Sympathizer Mar 22 '19 at 02:33
  • @Cort Ammon : What most physics is done on, and what we can do when we venture off into speculative exercises about fictional worlds that build from it, are two different things. (Hence also why someone (you?) mentioned here that WorldBuilding may be a better home for this? :) ) – The_Sympathizer Mar 22 '19 at 02:34
  • Also, just to add, we don't need to promote everything to the extended reals, e.g. the space-time coordinates - simply the parameter $c$ appearing in the Lorentz transformation (actually, we need only promote it to the half extended line $[0, \infty]$, because negative speed makes no sense.). – The_Sympathizer Mar 22 '19 at 02:37
  • @The_Sympathizer Do you think you can get away with just altering $c$ without altering everything? I'm thinking it would be difficult to do kinematics without promoting the equations of motion as well. After all, electromagnitism can cause forces. Perhaps there's a way to cancel them out so that the rest of physics stays extended-real-free. – Cort Ammon Mar 22 '19 at 03:13
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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.

The_Sympathizer
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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.

G. Smith
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    But what if the Universe was non-relativistic and the speed of light infinite in those ancient times? – Deschele Schilder Mar 21 '19 at 06:06
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    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? – Luaan Mar 21 '19 at 11:38
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    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? – Peter - Reinstate Monica Mar 21 '19 at 11:50
  • 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? – Cham Mar 22 '19 at 01:46
  • @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. – G. Smith Mar 22 '19 at 16:09
  • @G.Smith, you are right about the Coulomb potential, it is still present under the non-relativistic limit. – Cham Mar 22 '19 at 16:37