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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?

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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. –  user7980 Sep 25 '11 at 4:57
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3 Answers 3

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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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? –  Justin L. Nov 4 '10 at 6:40
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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. –  David Z Nov 4 '10 at 6:55
    
@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. –  Paul Manta Nov 28 '11 at 8:16
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@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. –  Jerry Schirmer Apr 18 '12 at 23:05
    
@JerrySchirmer: Sounds like the way photons find out their path have been traced in Young's experiment. –  Xaqron May 25 '13 at 5:48
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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.

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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.

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protected by Qmechanic Mar 17 '13 at 21:43

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