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Take this non-FTL scenario, involving a phone call and the postal service.

I send a postcard to my friend in Paris, asking whether they would like to visit me. Since it will take some time to arrive, I decide to telephone instead and ask the same question. I mention there is a postcard on the way, and my friend says yes, they would like to visit me.

After we finish speaking, my friend realises we didn't agree on a date for the visit, so my friend sends me a postcard to ask which date suits me best. After realising that it will take some time to arrive, I get a telephone call from my friend asking the same question. We agree on a date for the visit and hang up.

Some time later a postal worker in Paris is very confused, as they first see a postcard thanking the recipient for the invitation to visit, and then a few days later they see a second postcard inviting the same person to visit. Somehow they have received the reply before the invitation. They decide to telephone both my friend and I as our phone numbers are listed on the postcard, but we explain to the postal worker that we used the telephone to convey the information some time ago, and the postcards are arriving out of order due to the speed of the postal service.

Shortly afterwards, my friend receives my letter, and a day later I receive my friend's letter.

None of this violates causality, despite the postal worker seeing the events out of order, by getting the response before seeing the invitation.

Now if my friend was located in a distant star system, the postcard and postal service was replaced by a message sent at the speed of light, and the telephone was replaced by an instant FTL communication device, what exactly would change?

Apparently FTL communication allows things like the reply to arrive before the message was sent, but I cannot see how this would happen any more than telephoning before a postcard arrives results in time travel.

Even if my friend was travelling close to the speed of light (relative to me), experiencing a slower ticking clock, I cannot see how this would result in causality violation. Sure, when I call my friend on the FTL-phone they'd hear my voice sound like a chipmunk because I am experiencing time faster than they are, but I can't see how any of this could result in anything going backwards in time.

Sorry to ask yet another of these questions but all the other answers I can find seem to involve a certain element of hand waving that avoids the key points of the issue. In the hopes of avoiding this question being flagged as a duplicate, here are similar questions and my reasons why they don't answer this question:

I would really appreciate a detailed example showing exactly how FTL could produce a paradox and more specifically, why the paradox cannot be avoided. Thanks in advance for any help you might be able to provide to help me wrap my head around this!

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  • $\begingroup$ Essentially a duplicate of physics.stackexchange.com/q/113690/50583, which also asks if FTL travel necessarily violates causality. $\endgroup$
    – ACuriousMind ♦
    Commented Sep 16, 2017 at 13:25
  • $\begingroup$ What's wrong with physics.stackexchange.com/a/199/109928 ? I do not see any hand-waving there, it shows rather simply how FTL communication makes the order of events dependent on the reference frame. $\endgroup$
    – Stéphane Rollandin
    Commented Sep 16, 2017 at 15:23
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    $\begingroup$ Your story, with the phone calls, etc, does not violate causality. That doesn't mean it's impossible to tell a story that violates causality. Forget the second postcard; forget the phone calls -- what if there's one post card, which arrives at the post office before it was sent? Are you willing to call that a causality violation? $\endgroup$
    – WillO
    Commented Sep 16, 2017 at 15:26
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    $\begingroup$ Possible duplicate of What are some scenarios where FTL information transfer would violate causality? $\endgroup$
    – ProfRob
    Commented Sep 16, 2017 at 17:00
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    $\begingroup$ @Malvineous Different observers disagreeing on the order of events is a causality violation when one of the events causes the other. Mark Eichenlaub's answer is correct. $\endgroup$
    – ProfRob
    Commented Sep 24, 2017 at 8:10

1 Answer 1

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For an explicit causality violation (with all times and distances calculated in my frame):

At $E=(t=0,x=0)$, just as you are passing me at speed $v$, I release a light beam.

You say that $H=(t=v,x=1)$ is simultaneous with $E$.

The light beam arrives at $F=(t=1,x=1)$.

If $v>1$, you say that $F$ occurred before $H$. We've already agreed that you say $H$ is simultaneous with $E$. Therefore if $v>1$, you say that $F$ occurred before $E$. In other words, if $v>1$, then in your frame the light beam arrived before it was sent.

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  • $\begingroup$ What is E? What are t, x, H, and F? $\endgroup$
    – Malvineous
    Commented Sep 24, 2017 at 3:25
  • $\begingroup$ $E$ is the event $(t=0,x=0)$. $H$ is the event $(t=v,x=1)$. $F$ is the event $(t=1,x=1)$. $t$ and $x$ are time and space coordinates in a given frame. $\endgroup$
    – WillO
    Commented Sep 24, 2017 at 3:56
  • $\begingroup$ I'm a bit confused where you say I am passing you at speed $v$, but then you say $t=v$, I'm not sure how a speed can represent an elapsed time? I see that $E$ is me passing you, and $F$ is the light beam arriving, but I'm not sure what event $H$ refers to, that would occur at the same instant as $E$. Sorry for being so dense. $\endgroup$
    – Malvineous
    Commented Oct 1, 2017 at 8:34
  • $\begingroup$ $v$ is a number. We use numbers to represent both speeds and times. $\endgroup$
    – WillO
    Commented Oct 1, 2017 at 13:36

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