I've always heard people saying, "Faster than light information transfer can't happen because it would violate causality! Effects can precede their causes!"

However, I'm trying to think of a situation where this would happen. I'm sure it has something to do with relativity or something like that. I sort of understand that people going faster perceive time slower.

Can someone help illuminate this for me by showing a scenario where causality is clearly violated due to FTL information transfer?

  • $\begingroup$ I don't know how to give you the violation of causeality in this argument. But if you are an alien mathematician on another planet for instance, propagation of truth such as someone proving a theorem is a FTL phenomena in the sense that the alien might not know the theorem exists but the fact that the theorem is true is instantaneous and invariant throughout the whole universe. This was a comment a mathematician friend of mine made to me that probably does not apply here because of the philosophical interpretation of causality. $\endgroup$ – user7980 Sep 25 '11 at 4:57
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    $\begingroup$ @user7980 That's silly, there is no information transfer in that case. It's just two people separated by a vast distance that notice something about reality. The reality never changed, just your models. It's actually quite similar to the main problem people have understanding why entanglement doesn't mean FTL information transfer - nothing changed anywhere, you just read a value and we know that the other side must read the "opposite" value. You both measured reality, and you both read a consistent output, because reality is consistent. $\endgroup$ – Luaan Feb 15 '16 at 9:19
  • $\begingroup$ So if I'm to understand this correctly, it's been almost seven years since the question was asked, and in that time nobody has been able to demonstrate a situation where causality is violated by FTL communication? Why does everyone keep claiming FTL comm. violates causality then if there aren't any scenarios where it can happen? $\endgroup$ – Malvineous Sep 24 '17 at 3:34
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    $\begingroup$ I agree with @Malvineous on this. Whenever the question is asked, the responder is always forced to fall back to equations and graphs because no real example can be provided where FTL communication actually violated causality. Just because an observer can observe events out of order it does not follow that the observer can “call back” the the cause and prevent it before the effect is created. The observation that an event happens in an arbitrary order based on the observers coordinates does not imply that the event actually happened in that order, the observer can calculate the true order. $\endgroup$ – Josh Dec 27 '20 at 16:31

Suppose you and I have a conversation from a long distance away. We're at rest with respect to each other and communicate much faster than light. I say "How are you", and you wait a short time and say, "I'm fine thanks."

From our point of view, you were responding to my question. However, from a reference frame moving from me to you at relativistic speed, your clock is significantly ahead of mine (a relativistic effect). This means that although you thought you received the message shortly after I sent it, in this frame you didn't. You actually received the message at an earlier time (before I sent it), but you thought it was later because your clock is ahead.

From your and my point of view, the order of events is

  1. I say "How are you?"
  2. You hear me say "How are you?"
  3. You pause a short time.
  4. You say, "I'm fine thanks."
  5. I hear you say, "I'm fine thanks."

From the frame moving from me to you, the order of events is

  1. You hear me say "How are you?"
  2. You pause a short time.
  3. You say "I'm fine thanks."
  4. I say, "How are you?"
  5. I hear you say, "I'm fine thanks."

The fact that the order of events changes between reference frames is simply part of relativity, with or without faster-than-light communication. However, it seems strange in this scenario because you are responding to me. Presumably, if I had said, "Where are my car keys?", you would have chosen a different response than "I'm fine thanks." How then is it possible that you responded to my greeting before I uttered it, at least in some frame?

I'm not sure if this "violates causality", but it's unintuitive.

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    $\begingroup$ Just to clarify, is it that, in the spaceship's frame, the spaceship perceives the events out of order? (That is, if there was a light at our houses that beeped each time we got a call or sent one, it sees these beeps out of order). Or is, in that frame, the events actually are out of order? $\endgroup$ – Justin L. Nov 4 '10 at 6:40
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    $\begingroup$ The events actually would be out of order. In other words, the sequence of events Mark described would emerge after you corrected for the time it takes light to travel between you, your conversation partner, and/or the spaceship. $\endgroup$ – David Z Nov 4 '10 at 6:55
  • $\begingroup$ @JustinL. A way you could think about this is perceiving a 2D plane (a paper) from different angles in 3D; if 'all is right', your perception will distort, but you'll never see an impossible shape. The same way with perceiving a 3D body in 4D; depending on how you move in 4D, your perception of the 3D body might change, but you shouldn't ever see something that is impossible. $\endgroup$ – Paul Manta Nov 28 '11 at 8:16
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    $\begingroup$ @JustinL.: the events would actually be out of order. Place the events far enough apart, and your spaceship could blow up the speaker asking "How are you?" before the question was asked but after it was responded to. If I observe a FTL traveller, then I can find a traveller who is moving slower than light relative to me who will say that the FTL traveller is travelling into her past. $\endgroup$ – Jerry Schirmer Apr 18 '12 at 23:05
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    $\begingroup$ This doesn't sound like a violation of causaility but simply an illusion created by the finite speeds of photons. $\endgroup$ – David Oct 8 '15 at 14:56

Basically, this is because simultaneity is not an invariant notion in SR.

You probably know the classical example of two lightnings striking at the same time but different spots with respect to an observer who is at rest. But for an observer moving towards one of the lightnings, the lightning he is moving towards will have struck first. To an observer moving in the opposite direction, it will be the lightning he's moving towards. So each observer arranges the events in a different temporal sequence. This is true for space-like separated events, to use the technical jargon.

This is not problematic because space-like separated events should not be causally related... unless there is FTL communication/travel/whatever... That's when the funny things happen, when Jack responds to the phone call before Judy ever made it.

I've always wondered if the show writers of Star Trek, or any other SF series using FTL com, thought about it. For all the time travel stories these shows have, I can't remember a story that exploited this particular effect.

EDIT: Since some people have a hard time understanding special relativity, I thought it'd be nice to add a simple diagram to illustrate the relativity of the concept of simultaneity:

Spacetime diagram

In this drawing, I represent two lightning strikes happening at a distance 1 (doesn't matter what units you choose, but the drawing is such that 1 unit on the position axis (horizontal) is equal to 1 unit on the time axis (vertical) such that the speed of light is 1 in this picture), on the left and right of an observer sitting at position zero. He perceives both lightning strikes at time 1, when the light from both strikes has traveled to him (blue lines crossing at coordinates (0,1)).

But, another person is traveling at half the speed of light towards the lightning strike on the right (red line). He therefore sees that strike first, and only after that sees the second strike (the green intersections of the red line with both blue lines).

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    $\begingroup$ But a reference frame existing where the events appear out of order doesn't seem to violate causality, it just means that there is a delay between the events happening and that observer seeing them, and the delays are such that the events look like they happened out of order, even though they didn't. So that doesn't seem to violate causality? $\endgroup$ – Malvineous Oct 1 '17 at 8:16
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    $\begingroup$ Re your edit, I am reading it like two events happen simultaneously, but the light from them is delayed, so an observer sees one event happen before the other. But like us observing a supernova in a distant galaxy and calculating that it actually happened millions of years ago, presumably the observer of the two lightning strikes happening one after the other could calculate the distance and work out that both strikes actually occurred at the same time? I still can't see how this could lead to someone receiving a phone call before the caller made it. $\endgroup$ – Malvineous Mar 17 '20 at 4:48
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    $\begingroup$ I agree with what you say, however to me the key is that both travellers only see the events happening out of order. If they calculate the distance and take the speed of light into account, they can work out the real order of events and presumably both will come up with the same answer, that the call was placed before it was answered. $\endgroup$ – Malvineous Mar 17 '20 at 6:28
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    $\begingroup$ It is true that there are many different frames for different observers, but they are all affected by the delay of how long it takes light from the event to reach them. If you were to calculate things for the frames where each event itself took place, wouldn't that give you the true order of events? At any rate while I agree that it is easy enough to make it look to an observer like a phone call is answered before the caller has dialled, it seems to me like the two people having the phone call will always have it in the correct order, even where FTL is involved? $\endgroup$ – Malvineous Mar 17 '20 at 8:12
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    $\begingroup$ Any chance you can construct an example? I have read all the answers here and not one seems to give an example where causality is violated, they all seem to focus on an observer unrelated to the events seeing things happening out of order, which doesn't violate causality. (Maybe post it as a new answer to avoid confusion with what has been discussed here so far?) $\endgroup$ – Malvineous Mar 18 '20 at 7:49

Let's assume you are stationary and are observing a spaceship flying by at a velocity $v$.

  • Case $v \lt c$: If the spaceship flies at relativistic speeds, you will notice their clocks going slower, but everything would happen in the same order as if they were stationary with respect to you. The causal relationships between events is preserved, so is the second law of thermodynamics.

  • Case $v = c$: If the spaceship flies at the speed of light, you will notice their clocks stopped. Nothing is moving, so, in a limit sense, the causal relationships between events is preserved, so is the second law of thermodynamics.

  • Case $v \gt c$: If the spaceship flies faster than light, you will notice their clocks going backwards. All the causal relationships are reversed and the second law of thermodynamics is violated.

  • $\begingroup$ What about the case where the ships travel slowly, but the communication is FTL? Does that reverse any causal relationships? $\endgroup$ – Malvineous Sep 24 '17 at 3:38
  • $\begingroup$ @Malvineous yes, but it's more subtle. Anyone with a FTL communication device would be able to see the future of the spaceship and act on it. Remember that in relativity "synchronicity" is replaced by "on the same light cone". $\endgroup$ – Sklivvz Sep 24 '17 at 8:27
  • $\begingroup$ But how could someone with an FTL communication device see the future of the spaceship? They would be able to communicate with the ship before its light reaches them, but that's just a delay, not truly communicating into the future. $\endgroup$ – Malvineous Oct 1 '17 at 8:19
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    $\begingroup$ @Malvineous that's not "just a delay", that's what the future is according to relativity. There is no absolute frame of reference for time. $\endgroup$ – Sklivvz Oct 1 '17 at 8:49
  • $\begingroup$ I'm not quite sure how to answer that. I know what you're saying, and I get what you mean, but I still think it's an incomplete picture of what's really going on. The only way I can grasp the concept in my mind is by imagining that there is an absolute reference frame for time, which only becomes apparent once you start using FTL communication. Without that, yes, I guess causality violations could be possible, which suggests that one of those things is not possible (either FTL communication or an absolute frame of reference for time) with both required for FTL to exist. $\endgroup$ – Malvineous Oct 1 '17 at 10:35

Oh boy it's my favorite topic, causality violations!

Depending on the definition you give to causality violations and tachyons, it is fairly easy to give a causality violation on a spacetime. Here are some nice examples. Spacetime here is assumed flat (although topology may change), no math included as they are mostly diagrams that speak for themselves (just your basic Minkowski spacetime diagrams), and no coordinate change involved : this is just causality violation in a coordinate-invariant way.

Tachyon trajectories are in red, observers in blue, coordinate axis in black.

Here's a simple example involving two observers : Observer $A$ emits a tachyon (very slanted) in the direction of observer $B$, which emits back a tachyon to observer $A$.

enter image description here

You can check that the observers are all timelike while the tachyons are all spacelike trajectories. Given enough distances between $A$ and $B$, you can send tachyons arbitrarily far back in the past of the emission of $T_1$, and of course send arbitrarily many tachyons to compose whatever message you want.

One may object that the fact that $T_1$ points to the "past" is cheating, but this is entirely a coordinate artefact : a boosted observer $A$ will see $T_1$ as future-pointing, with respect to its own spacelike hypersurface.

Slightly fancier example : take the spacetime to be the Minkowski cylinder $\mathbb{R} \times S^1$, with a single observer.

enter image description here

A single observer can communicates with itself. This is not possible to do in $1+1$ dimensions in Minkowski space (it can be shown somewhat easily by the fact that in $1+1$ dimensions, timelike and spacelike dimensions are interchangeable and there are no closed timelike curves, so there are also no closed (smooth) spacelike curves).

If we allow more dimensions, things become easier. Consider the $2+1$ dimensional example with (non-free) tachyons.

enter image description here

It is possible to have some helicoidal shape in $2+1$ dimension that is entirely spacelike, but goes back in the past of its own lightcone, which is a fairly bad thing.

Once you have those various scenarios, it's not hard to construct one of the classic horrible causality paradox to show the various Cauchy development problems involved.


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