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This bugs me, and I don't know if I would be able to understand reasoning in answers on this thought experiment. Let say observer is on the earth in this example. Let him use quantum entangled pair of particles for sending information. Let information move from Earth to Proxima Centauri and back in one second... and that one second is the time where it is by Proxima Centauri. It means it will arrive to Proxima ~4 years before light manages to get there and then it will travel back instantaneously so it will be back after 1 second of being not on Earth. Where is time travel? Is it traveling in time only because light is slower? What happens in present time around Proxima Centauri could be observed after 4 years here. In my opinion what we will observe 4 years in future will be information from 4 years in past(from this present) and not from that present (4 years in future when the light will arrive) It would be time travel if in that first jump we travel 4 years into past and with second jump it would be second jump 4 years into past... Therefore the ship or information would appear 8??? years before starting the experiment on Earth.

edit: There was suggested answer to this example but I don't feel it was specific. Or I'm too stupid to understand it :) There was one example of sending signal by normal means and then it was prevented to send it before he sent it and thus breaking causality. Why should and how could anyone send signal in this example and then be prevented to send it by instantaneous signal from Proxima Centauri before he sends it? I mean,time is everywhere the same, there isn't time shift between relatively stationary objects, or is it?

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    $\begingroup$ Possible duplicate of Can FTL-Communication between two points in the same frame of reference break causality? $\endgroup$
    – StephenG - Help Ukraine
    Commented Jul 11, 2018 at 9:30
  • $\begingroup$ "Let information move from Earth to Proxima Centauri and back in one second": that can't happen, so the rest of your question is really moot. $\endgroup$
    – user107153
    Commented Jul 11, 2018 at 10:49
  • $\begingroup$ Thank you tfb- why it couldn't happen? If there is receiver placed it could be received and then sent back, isn't it so? $\endgroup$
    – Peter Švančárek
    Commented Jul 11, 2018 at 11:07
  • $\begingroup$ That's not how quantum entanglement works. $\endgroup$
    – user107153
    Commented Jul 11, 2018 at 11:22
  • $\begingroup$ I thought that it works this way: you change spin or some characteristic of on particle in pair and second one changes it instantaneously. By reading it it is destabilized(quantum de-coherence). I see I'm even more stupid that I thought :) $\endgroup$
    – Peter Švančárek
    Commented Jul 11, 2018 at 11:36

2 Answers 2

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If you allow faster than light travel in one reference frame and you accept special relativity, you have to conclude it's allowed in every frame.

But what's "faster than light" in one reference frame is "backwards in time" in another. By carefully choosing reference frames, it is easy to create a worldline where every individual path is forward in time in some reference frame, but the overall result is arriving where you started before you left.

You don't see this effect in your example because you assumed it would take 1 second round-trip. But if you allow faster than light travel, it could just as easily take negative time.

NB: In reality, quantum entanglement can't be used to send information faster than light. So absent some other form of FTL, it's just a thought experiment.

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  • $\begingroup$ Thank you Chris. I asked because we had an discussion elsewhere(it was about quantum entanglement and hypothetical possibility of using it for FTL comunication), and an few commentators commented that this case is time traveling. When I wrote question as is on top of this, they stopped to explain me how time travels or causality breaking occurs. $\endgroup$
    – Peter Švančárek
    Commented Jul 11, 2018 at 11:13
  • $\begingroup$ I had read some article a few months ago where experimenters managed to create entangled pairs at faster rate than they decayed(or were erased). And yes, I know it reads rubbish from such pairs without electromagnetic information sent for decoding it. $\endgroup$
    – Peter Švančárek
    Commented Jul 11, 2018 at 11:18
  • $\begingroup$ The "reads rubbish" part is the key. It doesn't matter how many entangled pairs you create, you need accompanying classical information to convey a single bit on that channel. $\endgroup$
    – Chris ♦
    Commented Jul 11, 2018 at 11:28
  • $\begingroup$ So... if that is true then how can we say about entangled particles? When we can't even know whether they are entangled without measuring? And measuring that doesn't give that information and leads to destroying the pair? $\endgroup$
    – Peter Švančárek
    Commented Jul 11, 2018 at 11:47
  • $\begingroup$ @PeterŠvančárek That's an involved topic on its own. Suffice to say comments aren't a good place to answer that. Ask another question if you're interested. $\endgroup$
    – Chris ♦
    Commented Jul 11, 2018 at 16:34
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Assume that Earth and Proxima Centauri are in the same rest frame. Then someone in a moving spaceship will measure one of the two legs as ending before it begins. Of course, if you have two consecutive legs, then the final event "back on Earth" will occur after the event "starting from Earth" in all inertial frames.

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  • $\begingroup$ The last sentence is misleading. Allowing for faster-than-light travel, it's trivial to construct two consecutive legs where the final event "back on Earth" is before the event "starting from Earth" in all inertial frames. $\endgroup$
    – Chris ♦
    Commented Jul 22, 2018 at 10:05

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