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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 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.
ose we have a device that is capable of transmitting and receiving tachyons at a speed of with .
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Encyclopedia
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 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.
Sending signals into one's own past
Suppose we have a device that is capable of transmitting and receiving tachyons at a speed of with . Consider sending such a tachyon to a spacecraft that moves away from us in the negative x-direction with speed . 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:
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 where is the distance the tachyon we send to the spacecraft traversed in our rest frame. The coordinates of the tachyon are given by:
The tachyon is received by us when . This means that and thus:
Since the tachyon we send to the spacecraft took a time of to reach it, the tachyon we receive back from the spacecraft will reach us a time:
later than we send it. However, if then and we'll receive the tachyon back from the spacecraft before we have sent our tachyon to the spacecraft.
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