Also consider the speed of light is also the speed of causality. If there was no such limit it means it would be possible for effects to precede causes which would lead to a very different kind of universe!
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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.
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”.
Also infinite speed of causality doesn't have to imply infinite speed of light, does it?
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...
No matter how fast an effect propogates, it is always after the cause (with an infinite speed, I guess effects happen instantaneously, but not before).
Of course, this doesn't fit with a universe described by general relativity, where time can be different for different observers. But you wouldn't have a universe described by general relativity without that constraint in the first place.
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.
At least, that's what I surmise. I'm not a physicist.
Edit: in short, not all reference frames can agree on the order of events, and FTL events propogate "backwards" between some reference frames.
> No matter how fast an effect propogates, it is always after the cause (with an infinite speed, I guess effects happen instantaneously, but not before).
If everything happens instantaneously then there is no real cause and effect, and the universe would be over before it really got started.
Imagine a universe like Conway's way of life, where only neighboring cells can be affected in one timestep. Now add to it a rule that all blocks have a color, and the color of all blocks are changed when one block changes color. Now you have a universe with both immediate and non-immediate effects.
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.
The distance between the mirrors is a number of meters. A meter is based on how far light travels in a second. How long it takes light to go between them is based on the speed of light. Speed, distance and time are connected.
If we untether the speed of light and it’s unlimited, then in some sense there is no way to say how long it takes light to bounce between the mirrors - it doesn’t take any time. And there is no way to say how far apart the mirrors are, if light passes between them instantly that implies there must be no gap to cross. If light crosses no distance in no time then it also bounces back covering no distance in no time, ahh does lots of bounces in no time. There goes the concept of a time step and any concept of “non immediate effects”.
If you try and add time as a separate thing, then you have some kind of Conway’s game simulation - but that gives you a way to track where light is (which simulation cell it’s in) and therefore a kind of distance (how far the mirrors are apart in simulation cells) and then you lock down how light moves in “simulation cells travelled per timestep” which brings you back to a fixed speed of light again.
on edit: not everything travels at the speed limit, if the speed limit right now is the speed of light - then why doesn't everything travel at the speed of light?
People say if the speed limit was infinite that everything would happen instantaneously - but they still need to explain why everything should go at the speed limit in this other universe, when not everything goes at the speed limit in ours.
If we imagine something going faster than the speed of causality, we're simply misconcieving the properties of space.
> 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.
Or is this just a metaphysical way of saying that no particle can move faster than the speed of light, assuming that causality is just an abstraction of moving particles around?
That is, if you assume relativity, then for anything which moves faster than speed c, there exists some reference frame where it appears to move backwards in time. (This needs to be slightly qualified because it's kind of like when you're looking in a mirror and you intuitively don't think it does what it actually does -- flip front to back -- but you mentally rotate and then think that it flips left-to-right. So to be clear, if someone on a hyperluminal rocket cracks an egg into a pan, there exists someone else whose best understanding of this situation is a rocket that is traveling "backwards" engine-first, onboard of which an egg is flying up from the pan into an eggshell. But you would mentally reorient to say that the rocket is traveling "forwards" and that "forwards" direction is backwards in time.)
Now, this doesn't directly violate causality by itself, it depends on whether you can move faster than light according to an arbitrary observer. So if Carol goes faster than light according to Alice and then turns and goes faster than light according to Bob, and Bob is moving relative to Alice, only then can Carol potentially meet up with her "past self" according to Alice & Bob. The idea is that the first time she moves, Alice says she's moving very fast, but forward in time, and Bob says she's moving backward in time. Then the second time she moves, Bob says she's moving very fast, but forward in time, and Alice says she's moving backward in time. You combine these two to find that both agree that she has objectively moved backward in time.
The way this manifests in the mathematics is that in relativity, after something happens, light kind of "announces" that it happened to the rest of the world, via an expanding bubble of photons traveling away from the event at speed c. This expanding bubble is formally known as a "light cone". There is another light cone as well: before the event happens you can understand a contracting bubble of photons traveling towards the event. And basically these partition the world into five regions: The contracting bubble is the "objective past" of the event, that bubble itself is the "null past" of the event, the spacetime between the bubbles is the "general present" of the event, the expanding bubble is the "null future" of the event, and the points inside of the bubble are the "objective future" of the event. Moving faster than light, is moving from the objective future of an event, into its general present. This is "general" because different reference frames regard these points as either before or after the event in time. You need a second trajectory to then go from the general present of the event, to its objective past.
https://en.wikipedia.org/wiki/One-way_speed_of_light
A lot of scientists have thought about this. Step one is checking their work.
The limit of causality is the light speed limit in vacuum, not "whatever happens to be the max speed of light in some medium".
Light (as in visible light) is also irrelevant to this, it's just an example of something moving at that speed.
I see nothing there that would invalidate my synchrotron argument, though.
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.
a hypothetical universe is mostly worth discussing seriously if there's a physics that is coherent, not just a mathematical landscape. At least it isn't that interesting in the discussion of universes, but might be in discussing mathematical ideas, but those do not necessarily mean there's a universe represented by it.
Replace periscope with “wormhole” and you get a more traditional experiment. The question of can we use this to violate casualty is non-sensical, because we can’t violate casualty (even with faster than light travel). In the traditional experiment, if I see the light turn on, the cause has already happened; sending a message “back in time” won’t change that.
However, this is only because all frames of reference stay the same. If you could actually travel back in time, who knows what would happen. That’s largely why this whole conversation makes no sense. You can’t violate casualty with FTL, only with time machines and FTL isn’t a Time Machine.
If light is slower in other mediums, that has no effect on how quickly causation can happen.
It's just that light (if there is nothing in its way, so in a vacuum) will travel at the max speed of causality.
Causality violation can happen in general relativity when something moves faster than the max speed of causality (which is the same speed as light in a vacuum).
Light actually has nothing to do with it; it just happens to travel at the max speed allowed by the universe when there's nothing that impedes it's motion (i.e. in a vacuum).
So the acronym should really be "FTLIAV"!
See also [https://en.m.wikipedia.org/wiki/Electromagnetic_four-potenti...]
Notably, light is a form of electromagnetism, so this shouldn’t be as surprising as it is. c is an explicit part of many formulas, interestingly. And electromagnetism was the first thing tackled in special relativity.
I can't think of anything purely in the physical plane, though there's this:
https://en.m.wikipedia.org/wiki/Retrocausality
But if one includes metaphysics, one example (there are others) is an individual's anticipation of another individual doing something in the future could cause them to act in the present.
This is quite the stretch on its own, but if you include this (which exists, as much as people don't like to admit it depending on the context):
https://en.m.wikipedia.org/wiki/Consensus_reality
...it is possible, in that it comes down to the question of is it true that the effect proceeded the cause, and if enough people believe something is true, it is true. And if you disagree, observe human behavior for a while and see for yourself - people will tell you it is true with absolute sincerity, and they often will act in the physical plane based upon that "truth". Wars are started over "not true" "truths", perhaps even all of them.
And if that's not enough, another route is perhaps people really can see the future. People with absolute sincerity tell me they can constantly. Perhaps they are hallucinating (they swear to me they are not), but perhaps they are not, maybe it is yet another thing that science has yet to discover, or cannot discover due to non-determinism, non-falsifiability, consensus reality (a theory cannot be(!) true unless there is consensus agreement that it is true), etc.
Please don't shoot the messenger.
If light happens to move slower than c under some conditions, that is irrelevant. It isn't the speed of light we care about, it is c.
Essentially, when we say FTL, it means "faster than c", not "faster than light".
Edit: wrong one https://youtu.be/yP1kKN3ghOU?si=hsBj0RpzOb3JZWdS the one above is the "why."
Before I looked at stack exchange, I thought of another, much simpler experiment. Generate plane wave radio waves of a frequency such that the nominal wavelength would be meters or tens of meters. (By "nominal wavelength", I mean the wavelength l=c/f, the wavelength as if the speed of light were the same both directions.) Run those plane waves into a reflector a couple of nominal wavelengths away. Measure the RF energy at various points along the path to the reflector. Does it look like a standing wave of the expected wavelength, or not?
I actually saw that idea on the discussion I found on stack exchange. The only reply I saw was "well, the relationship between wavelength and frequency might not hold if the speed of light is asymmetrical", which seemed very weak to me. What, we have waves propagating with velocity v, but wavelength l =/= v/f? How can you do that without destroying the continuity of the wave? How much of physics is that going to destroy? And, how many "well, maybe..." items are you willing to stack up to make it impossible to detect your first "well, maybe"?
I didn't leave a question on stack exchange. The discussion was nine years old.
In quantum entanglement, two particles can be entangled in such a way that measuring one particle instantly determines the state of the other, even if they are light-years apart. This "instantaneous" connection seems faster than light, but it cannot be used to transmit usable information in a meaningful way.
The phenomenon does not violate relativity because no classical information can travel between the particles faster than light. Entanglement is a correlation, not a means of communication and hence NOT a means of causation.