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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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  • I had thought about the question too. I haven't found any more satisfactory answer than: special relativity itself only forbids two-way anti-telephones. – Plop Mar 15 '24 at 16:41
  • @Plop I just asked a question about the Two-way telephone here: https://physics.stackexchange.com/questions/806395/two-way-tachyonic-anti-telephone/806399#806399 I think I was able to demonstrate that there is no paradox. – Dr. user44690 Mar 15 '24 at 16:47
  • Arent all one way telephones from future to past necessarily two way telephones by the propagation of the causal cone outward from the past point? – Craig Mar 15 '24 at 21:24
  • @Craig Yeah I realize that now. – Dr. user44690 Mar 16 '24 at 06:15

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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.

Marco Ocram
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  • What you are talking about is the two-way tachyonic telephone involving two people. That I understand is paradoxical. But in this single person tachyonic telephone I don't quite see the paradox. All I see is that from the observer who is not in the spaceship observing the occupants of the spaceship sending messages to their past-selves. Here the consequence of the paradox is not that extreme. I hope you understand what I mean. This is like seeing a paradox in length contraction. – Dr. user44690 Mar 15 '24 at 08:09
  • Yes, but suppose the message is the trigger to explode a bomb. The person then explodes their past self- doesn't that seem problematic too? – Marco Ocram Mar 15 '24 at 08:17
  • Didn't G. Benford deal with that issue? – Michael Harvey Mar 15 '24 at 15:18
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    @MichaelHarvey I think maybe James Blish proposed it first in his story "Beep" which was later expanded into the the novel "The Quincunx of Time". – Wastrel Mar 15 '24 at 16:15
  • @Wastrel - yes, and IMHO Blish is the better writer (Benford could not have written 'Black Easter', and doesn't really 'do' people). – Michael Harvey Mar 15 '24 at 16:22
  • @Marco Ocram: Sure, but there is no paradox if the telephone connects two space-like separated points: in this case, the explosion "in the past" doesn't have the time to reach the person making the phone-call "in the future" to prevent him from doing so. – Plop Mar 15 '24 at 17:00
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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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  • I understand that a tachyonic anti-telephone between two individuals is problematic but I don't see why that is a problem when it is just one person telephoning his past and that is from the point of view of an observer at rest, who is not in the same frame as the person who is using the tachyonic telephone to begin with. – Dr. user44690 Mar 15 '24 at 08:15
  • @Dr.user44690 - Basically, physics is in trouble if anybody can get their future information regardless of frames - the PSPACE computation thing or breaking thermodynamics is not a small issue. – Anders Sandberg Mar 15 '24 at 11:25
  • The thermodynamic concern, absolutely, but I don't really see the physical issue with solving PSPACE-hard problems? I mean, we still haven't been able to prove that hypercomputation is physically impossible, and that would be even more powerful than a computer that solves PSPACE-hard problems in polynomial time. – Idran Mar 15 '24 at 20:46
  • Ah, correction, that would itself qualify as hypercomputation, hypercomputation wouldn't be generally more powerful than it. Still though, since hypercomputation in general hasn't been physically ruled out, I'd still say that's not really a good example of something that shouldn't be allowed by physics. Something as simple as a physical constant that has an incomputable but still real-numbered value would also allow for hypercomputation. – Idran Mar 15 '24 at 20:59
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    @Idran - Note that the PSPACE computer can solve any problem where you can check the correctness of the solution just as quickly. Is there a counterexample of the Riemann hypothesis or the Goldbach conjecture? Done. Find a workable blueprint for any device with describable properties? Done. Global economic optimization? Done. And so on. Sure, not hypercomputation and maybe not impossible, but it would be radical. So radical that many think this is unlikely. – Anders Sandberg Mar 18 '24 at 13:27
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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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