Tachyonic antitelephone

The tachyonic antitelephone is a hypothetical device in theoretical physics that can be used to send signals into one's own past. Such a device was first contemplated by R. C. Tolman in 1917 [R. C. Tolman, "The theory of the Relativity of Motion", (Berkeley 1917), p. 54] in a demonstration of how faster-than-light signals can lead to a paradox of causality (a.k.a. "Tolman's paradox"). The problem of detecting faster-than-light particles (a.k.a. tachyons) via causal contradictions is considered in Ref. [G. A. Benford, D. L. Book, and W. A. Newcomb, [http://link.aps.org/abstract/PRD/v2/p263 "The Tachyonic Antitelephone"] , "Physical Review" D 2, 263-5 (1970)]

ending signals into one's own past

Suppose we have a device that is capable of transmitting and receiving tachyons at a speed of a c with a>1. Consider sending such a tachyon to a spacecraft that moves away from us in the negative x-direction with speed v. Let's choose the origin of the coordinates to coincide with the reception of the tachyon by the spacecraft. If the spacecraft sends a tachyon back to us then, in the rest frame of the spacecraft, the coordinates of the tachyon are given by:

:(t,x) = (t,act)

To find out when the particle is received by us, let's perform a Lorentz transformation to the frame S' moving in the positive x-direction with velocity v, with respect to the spacecraft. In this frame we are at rest at position x'=L where L is the distance the tachyon we send to the spacecraft traversed in our rest frame. The coordinates of the tachyon are given by:

:(t',x')=left(gammaleft(1-frac{av}{c} ight)t,gammaleft(ac-v ight)t ight)

The tachyon is received by us when x'=L. This means that t=frac{L}{gamma(ac-v)} and thus:

:t'=frac{c-av}{ac-v}frac{L}{c}

Since the tachyon we send to the spacecraft took a time of frac{L}{ac} to reach it, the tachyon we receive back from the spacecraft will reach us a time:

:T=frac{L}{ac} + t'=left [frac{1}{a}+frac{c-av}{ac-v} ight] frac{L}{c}

later than we send it. However, if v>frac{2ac}{1+a^{2 then T<0 and we'll receive the tachyon back from the spacecraft before we have sent our tachyon to the spacecraft.

References


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