Tachyonic antitelephone

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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[1] 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.[2]

[edit] Sending signals into one's own past

Suppose we have a device that is capable of transmitting and receiving tachyons at a speed of ac 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(\gamma\left(1-\frac{av}{c}\right)t,\gamma\left(ac-v\right)t\right)

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}\right]\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.

[edit] References

  1. ^ R. C. Tolman, The theory of the Relativity of Motion, (Berkeley 1917), p. 54
  2. ^ G. A. Benford, D. L. Book, and W. A. Newcomb, The Tachyonic Antitelephone, Physical Review D 2, 263-5 (1970)