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Based on the classical light-cone approach it's easy to see you can't transmit information faster than $c$ but why does the speed of light (as far as I know) treat information transmission in this way formally?

For instance going the Sci-Fi route, in Orson Scott Card's Ender universe there is a device called an ansible which seems to be described as some sort of coupled state device - pair two devices and as they move apart they remain linked. The details probably don't matter since this is a hypothetical question. With ansibles, you obviously can only move the devices subject to normal physics so if you found a colony 100 light-years away, it takes (at least) 100 years to get the ansible there. But then, you have communication.

Is it possible in reasonably simple (say degree but not post-graduate level) terms to explain why this is fundamentally impossible, why information cannot by any means violate the light-speed limit, rather than that we just can't think of a way to do it?

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    $\begingroup$ what would you use to transmit information? probably the fastest "messenger" you have $\endgroup$
    – Phoenix87
    Jan 6, 2015 at 23:30
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    $\begingroup$ That's saying information can't travel FTL merely as a corollary that you can't find anything to physically send FTL. My understanding is that information is considered a "first class citizen" as it were, making the whole discussion of FTL information travel moot. $\endgroup$
    – Mr. Boy
    Jan 6, 2015 at 23:35
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    $\begingroup$ @Phoenix87 the fictional device he's talking about transmits information faster than light by using some sort of entangled particles that could be manipulated without breaking the entanglement; such that one particle could be "wiggled" and the other would instantly do the same, allowing a faster-than-light telegraph machine of sorts. It doesn't rely on photons. $\endgroup$
    – Asher
    Jan 6, 2015 at 23:43
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    $\begingroup$ FWIW the ansible (that name anyway) was invented by Ursula Le Guin. The name was taken up by others including OSC. $\endgroup$
    – Steve Jessop
    Jan 7, 2015 at 12:47
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    $\begingroup$ @Jim - I forget. $\endgroup$
    – Hot Licks
    Jan 7, 2015 at 19:27

5 Answers 5

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The thing about the speed of light $c$ is that it's not just a number associated with a certain type of particle. While we could talk about the mass of the proton, and there would be no problem assuming non-protons had greater or lesser masses, the value $c$ is an entirely different beast.

$c$ is an intrinsic property of spacetime itself, not of the particles in spacetime. You wouldn't expect there to exist anything (particle, signal, information) that you could insert into spacetime with the property "changes the nature of spacetime for itself."

The above is meant to undermine the "if it's just a property of everything we've found so far, we haven't ruled out finding things without this property" line of thought.

For a more concrete demonstration of what goes wrong when you alter the structure of spacetime as we know it, take a look at the "tachyonic antitelephone". This demonstrates how any abstract communication faster than light leads to causality violations as observed by even not-faster-than-light observers.

There are many variations on the thought experiment; here's one of them (with the math worked out in the linked article): $A$ is moving away from $B$ with speed $v < c$ in $B$'s reference frame. $A$ sends a faster-than-light message to $B$, who responds in kind with a reply. The problem is for sufficiently fast (but not faster than $c$!) speeds $v$, $A$ will receive the reply before sending the message. Faster-than-light anything begets time travel.

Since it gets repeated far, far too often, I'll also counter quantum entanglement arguments here. Quantum entanglement does nothing in the hypothetical "why can't this communicate faster than light?" scenarios other than guarantee that the two particles will "collapse" to the same (or opposite, or orthogonal, or whatever) states when either is observed. The only quantum mechanical aspect of the whole thing is the fact that the eventual collapsed state can't even exist before the measurement (it's not a hidden variable).

But the correlation -- the thing you want to rely on to communicate faster than light -- could be achieved entirely classically. Take a red marble and a blue marble, put them in a bag, and draw one out randomly without looking. Lock your marble in a box, and hand the bag to someone else, who also doesn't peak. Send the person far away. Then, look at your marble. If it's blue, you instantly know the other person has red. But you transmitted nothing. All quantum mechanics does is make it so who has which marble isn't pre-determined.

This shouldn't come as a surprise, because the only notions of space and time in quantum mechanics are the ones from spacetime itself. Quantum mechanics doesn't come equipped with some independent notion of distances. So whatever structure spacetime has applies to quantum things just as much as marbles and people and signals.

Everything said here stays true even in general relativity, by the way. Enabling things to move faster than $c$ still leads to causality violations. Even wrapping things in a "warp bubble" and moving that faster than $c$ leads to causality violations.

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    $\begingroup$ That sounds very compelling. However, maybe it could turn out that the star was not really 100 light-years away because of a wormhole. So choosing another route from here to the star could be a shortcut so that the true distance is only e.g. 10 light-years. However, my comment may be off-topic since using a wormhole is not "faster-than-light". $\endgroup$
    – Jeppe Stig Nielsen
    Jan 7, 2015 at 14:16
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    $\begingroup$ Ah, but what if you've lost your marbles? $\endgroup$
    – Hot Licks
    Jan 7, 2015 at 18:47
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    $\begingroup$ +1, good answer. I only want to add a N.B. that all this causality violation stuff is based on the notion that there is no privileged or universally preferred frame of reference, which we reasonably believe is true. If there were such a frame of reference, causality violation would easily be avoided by restricting the measurement of FTL speeds to only be valid in that preferred frame. $\endgroup$
    – Jim
    Jan 7, 2015 at 19:26
  • $\begingroup$ Just as quantum entanglement is misunderstood to suggest faster-than-light communication (which you addressed), so is the Bertlmann's Socks concept of correlations to explain the non-classical phenomena of quantum entanglement. It is fundamentally more subtle than your blue/red marble analogy, and to leave it at that is to propagate the misunderstanding I'm afraid. $\endgroup$
    – Matt
    Jan 8, 2015 at 3:00
  • $\begingroup$ As a lay person, I find this description of entanglement exciting. It is exciting as it presents the system as knowledge inference, not transfer. I didn't anticipate that and I love it. $\endgroup$
    – Gusdor
    Jan 8, 2015 at 8:59
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Faster than light communication would violate causality. If FTL communication was somehow allowed by nature, then you could kill someone before firing the gun which just doesn't make any sense. You simply cannot have something that is caused by some event happen before the event occurs. Put simply, FTL communication gives rise to paradoxes.

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    $\begingroup$ As for why it violates causality. $\endgroup$
    – Cole Tobin
    Jan 7, 2015 at 6:40
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    $\begingroup$ "You simply cannot have something that is caused by some event happen before the event occurs" - you don't know that! Violating causality does not make something impossible. The very notion of "impossibility" flies in the face of the philosophy of scientific inquiry. Just a thought. $\endgroup$
    – quant
    Jan 7, 2015 at 6:59
  • $\begingroup$ I don't think the gun analogy is helpful here. How would sending pure information FTL let me kill someone before I fire a gun? $\endgroup$
    – Mr. Boy
    Jan 7, 2015 at 8:01
  • $\begingroup$ @quant Understandable and justified. But! The whole of modern physics is build on these principles for a reason. As soon as you consider FTL communication, paradoxes arise between reference frames and we cannot have that. Would you consider energy violation in one frame possible where in a different frame energy is conserved? Can the laws of physics contradict each other between reference frames? Check out the link above by Cole btw it gives a nice example of how causality is violated. $\endgroup$
    – PhotonBoom
    Jan 7, 2015 at 8:19
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    $\begingroup$ @PhotonicBoom I like to view contradictions as merely breaking our understanding of the universe. If the world is flat then going straight ahead and ending up where you started reduces to a paradox, just as if the first law of thermodynamics holds then perpetual motion is impossible. All notions of law and truth lie on a bedrock of prepositions. I think yours is a good answer, I'm merely playing devil's advocate! Can the laws of physics contradict each other? No, by definition. But reality is not at the whim of our physical laws, and when they are found to contradict they must be changed. $\endgroup$
    – quant
    Jan 7, 2015 at 8:23
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One principal that would be violated is causality. Just looking at things from a single frame (such as here on earth), there is no apparent problem. But as soon as you examine things in other frames it gets tricky.

Once you allow for travel faster than $c$ in one frame, it becomes possible to construct a series of messages, each of which travels forward in time in some particular frame, but where the final message arrives at the transmitter before the time when it sends the message.

Here's a site with some good Minkowski diagrams for it. http://www.theculture.org/rich/sharpblue/archives/000089.html

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Information has to be transmitted by something. The laws of Physics state that the maximum speed that anything can move at is the speed of light, which seems to be a fundamental property of the universe. So, if we can find something that can travel faster than light then it would be possible to transmit information faster, but until then we are limited to light speed. [edited to remove dubious suggestion that quantum entanglement might enable faster-than-light information transmission].

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  • $\begingroup$ So if such a hypothetical mechanism existed, this wouldn't violate any laws? I guess that's what I'm asking really - does FTL information transmission violate special relativity or is it just a side-effect of SR that we cannot find a way to do the transmission? $\endgroup$
    – Mr. Boy
    Jan 6, 2015 at 23:39
  • $\begingroup$ In the context of special relativity, as I understand it, FTL travel of anything would violate it. I don't think information would be treated any differently. Therefore, information travelling FTL would violate special relativity. I guess the question is, in the future, can we find something outside the scope of special relativity that would enable FTL information transmission (e.g. quantum effects)? $\endgroup$
    – Time4Tea
    Jan 6, 2015 at 23:51
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    $\begingroup$ @Mr.Boy yes such a mechanism would violate causality. If you can transmit information faster than light in one reference frame, then you can find some other frame where the messages arrives before the transmitter sends. This can't happen when $c$ is the fastest speed for information transfer. $\endgroup$
    – BowlOfRed
    Jan 6, 2015 at 23:52
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    $\begingroup$ @Time4Tea There are not indications that quantum entanglement can convey information, in fact it's been proven that it can't. $\endgroup$
    – Señor O
    Jan 6, 2015 at 23:57
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    $\begingroup$ @MyStream: I think what they're saying is that you can't choose what state each particle collapses to like that (i.e. to create a pattern), so even though the effect of each collapse is intantaneous, no information is being transmitted. $\endgroup$
    – Time4Tea
    Jan 7, 2015 at 18:38
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A good approach to understand is the consideration of the two components of c, permittivity and permeability of vacuum. They are two constants of space, and already by their name we understand that it is a physical property/ a physical limit of space not to transmit any radiation faster than with light speed.

The hypothetical proper time of photons is zero, because from their hypothetical point of view they are not taking part in spacetime, their Minkowski diagram would be reduced to a dimensionless point. In this sense it could be said that information is transmitted immediately - but this is a consideration which does not take into account the spacetime where we are living in as observers. In the same way as there is a fundamental law (the second SR postulate) that light speed cannot be observed faster than c, there is no mean for spacetime observers to get information faster than at light speed.

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