How exactly would this chronology protection for my FTL drive look like?

The problem with FTL is that, due to the tachyonic antitelephone, it allows causality violation: I send you a superluminal message (you are moving away from me at relativistic speed), you reply with a superluminal message that reaches me before I send the first one.

It is crucial to see that this causality violation happens because of the return message.

Now, suppose the very act of sending a FTL message creates a bubble around the sender that may not be entered by FTL signals. Wikipedia on antitelephone gives the delay $T$ between my message and my receipt of the reply as $T = (\frac{1}{a}+\frac{1-av}{a-v})L$. ($a$ is message speed and $v$ is our relative velocity in units of $c$; $L$ is distance). Even if $v$ approaches one (relative velocity approaches $c$), $T$ will be some finite (likely negative) amount. $T$ remains finite even for $a$ approaching infinity. From this I conclude that we don't need to prevent return messages for eternity, just for some finite amount of time.

In other words, there's no need to have FTL travel/communication only into one direction, we can loop back if we wait long enough.

What would be the smallest such bubble and why? What shape would it have, how would it evolve over time?

The simplest assumption would be a sphere surrounding the first sender, shrinking with $c$. However, I see no reason why the bubble should expand in all directions equally, it ought to be flatter on the backside.

As we see, $v$, the relative velocity of both participants in the message exchange, goes into $T$; so assume $v=1$ or close to it so that size and shape of our bubble depends solely on features of the FTL device - namely speed of signal $a$ and distance travelled $L$, not on nearby random objects. Also assume the FTL signal travels point to point without affecting anything inbetween.

Different values for $a$ for the return message need not be considered.

I've looked at this and this question and I don't see my specific idea addressed - the closest is a4android's answer, but they only go into unidirectional superluminal travel and I think we need not go that far, as outlined above.

posted almost 7 years ago

mart‭

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