What are some scenarios where FTL information transfer would violate causality?

Question

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?

Answer 1

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.

Answer 2

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.

Answer 3

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.