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When you have length contraction in special relativity

$$L' = L/\gamma$$ the interpretation is that $L'$ is the length of an object with rest-length $L$ moving with respect to an observer at rest. Now, similarly in a tachyonic antitelephone we have $$\Delta t' = \gamma (1- a v)\Delta t$$ where $a$ is the speed of the signal in a spaceship moving with a speed $v$ with respect to an observer at rest. Now, $\Delta t'$ is the time interval for the signal to traverse a distance measured by the observer at rest and the anti-telephonic capabilities are something that is observed by the observer at rest. But for an observer in the moving spaceship he is not going to see anything extraordinary. So I fail to see the contradiction with the concept of tachyonic antitelephone. What does it matter if we at rest observe a moving observer is calling his past self if in the moving frame for that observer everything is just ordinary. Can someone explain this paradox to me?

Dr. user44690
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3 Answers3

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The problem is that it leads to events happening before their causes. The example that is often quoted considers two people who communicate with information that travels faster than light, with the result that the second person's reply arrives before the first person's question was sent.

Professor Sushing
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To extend Marco Ocram's answer: while getting a reply before a question is asked may seem innocent, it allows all sorts of strange actions that look like they should not be allowed by physics. Beside predicting the stock market or future states of chaotic systems, you can use the anti-telephone to solve PSPACE-hard computing problems. Maxwell's demon could use the anti-telephone to extract work from a gas in equilibrium without running into memory problems.

Maybe we live in such a universe. But it doesn't seem likely.

Anders Sandberg
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The one way tachyonic antitelephone violates the principle of relativity, which says that the laws of physics should be the same for all observers in relative motion. If you assume that "causes must come before effects" is a law of physics, then a one way FTL trip or message will be problematic, because in some frames of reference the end of the trip has an earlier time than the beginning of the trip (so the "effect" occurs earlier in time than the "cause").

This isn't technically a paradox though, so it's only a mild objection. But this kind of thing can easily be used to create an actual paradox if a second party is involved (or if the original spaceship is equipped with slower than light engines as well as faster than light ones, so that it can change reference frames and fly back into its own past).

Eric Smith
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