Superluminal Messaging and Causality Paradox: Myth or Reality?

[AdrianMay]

If I could route a signal from here-and-now to an event in my past light cone, then clearly I could make an irresolvable causal paradox by having the arriving signal disable the button that sends it, so I'll choose to believe that I can't send messages back in time TO HERE.

Now I've heard it said that superluminal messaging would boil down to the same thing, but I don't see how.

I can see how it could look to another observer like a message traveling back in time, but not to BACK HERE, and I think that a message arriving in the past OVER THERE is harmless to causality. To get it from over there back to here, still appearing to go back in time, that observer would have to turn around, so it's kinda like the twins paradox.

One thing that all observers agree on is the light cones of a given event, so if a traveling message looks spacelike to somebody then it looks spacelike to everybody, and whether it's in the top half or the bottom half of the spacelike zone is immaterial to causality, isn't it?

So was I misinformed about superluminal messaging leading to some kind of causality paradox?

 

[phinds]

This has been discussed here on PF many times. Have you tried a forum search? HINT: a good place to start is with the links at the bottom of this thread.

 

[Nugatory]

So was I misinformed about superluminal messaging leading to some kind of causality paradox?

Google for "tachyonic antitelephone"

 

[Jonathan Scott]

The short answer:

If there were a preferred frame in which messages were sent instantly, then that would violate relativity but not causality. Science fiction usually calls this concept "subspace" or "hyperspace".

However, if it were possible to send messages a finite amount faster than the speed of light in every frame of reference (giving the same physics in every frame of reference and conforming to the principle of relativity) then in certain frames of reference (for an emitter moving fast in a direction towards the observer) the message would be traveling backwards in time. It would therefore be possible to send a message to that emitter and receive a reply before it was sent, violating causality.

 

[AdrianMay]

I suppose the two-way tachyonic antitelephone on wikipedia was what I was looking for. Thanks!

 

[Demystifier]

See also
https://arxiv.org/abs/gr-qc/0403121

 

[pixel]

If there were a preferred frame in which messages were sent instantly, then that would violate relativity but not causality.

Could you elaborate on this?

 

[Jonathan Scott]

The existence of a preferred frame would by definition be in conflict with the principle of relativity (which requires the laws of physics to take the same form regardless of frame). However, if messages propagated faster than light relative to a specific preferred frame, up to infinite speed (purely spacelike separation) there would still be no way for a message to arrive before it was sent. Applying standard Lorentz transformations to view the message propagation (as a spacelike interval) from another frame, the message might appear to travel backwards in time in certain directions, but the fastest that a message could travel in the opposite direction would be at the same rate forwards in time, so overall no reply could arrive before the message was sent.

 

[vanhees71]

If there where no "relativistic speed limit" but all other symmetries (including the special relativity principle) stay the same as in SRT you'd be back to Newtonian physics, and of course Newtonian physics is in perfect accordance with the principle of causality, without which physics wouldn't make sense (at least not in the form as we know it).

 

[pixel]

If there were a preferred frame in which messages were sent instantly, then that would violate relativity but not causality.

I'm still not following your use of the word "preferred." If in one frame the message was instantaneous, then the event of its transmission and the event of its receipt would be simultaneous. There are many examples of two events being simultaneous in one frame and not in others. Are you saying that the message would have to be instantaneous in all frames if it is in one?

 

[Mister T]

If in one frame the message was instantaneous, then the event of its transmission and the event of its receipt would be simultaneous. There are many examples of two events being simultaneous in one frame and not in others.

Those examples involve simultaneous events that are causally disconnected. The sending of a message and the receipt of that same message are causally connected events.

 

[Ibix]

I'm still not following your use of the word "preferred." If in one frame the message was instantaneous, then the event of its transmission and the event of its receipt would be simultaneous. There are many examples of two events being simultaneous in one frame and not in others. Are you saying that the message would have to be instantaneous in all frames if it is in one?

The exact opposite. Message passing is instantaneous in the one frame, but in any other frame messages arrive in the future when sent in one direction and in the past when sent in the other.

Are you familiar with Minkowski diagrams? The anti-telephone let's people send messages along lines parallel to their personal x-axis. Since the x-axes of different frames cross, this can be used to send messages that cross in transit - both are received before the other was sent. Jonathan's scheme simply picks one frame and says everybody sends messages parallel to this frame's x-axis. Since messages cannot cross there can be no causal paradoxes.