A tachyonic antitelephone is a hypothetical device in theoretical physics that could be used to send signals into one's own past. Albert Einstein in 1907 presented a thought experiment of how faster-than-light signals can lead to a paradox of causality, which was described by Einstein and Arnold Sommerfeld in 1910 as a means "to telegraph into the past". The same thought experiment was described by Richard Chace Tolman in 1917; thus, it is also known as Tolman's paradox. A device capable of "telegraphing into the past" was later also called a "tachyonic antitelephone" by Gregory Benford, David Book, and William Newcomb. According to the current understanding of physics, no such faster-than-light transfer of information is possible.
One-way example
Tolman used the following variation of Einstein's thought experiment: Imagine a distance with endpoints A {\displaystyle A} and B {\displaystyle B} . Let a signal be sent from A propagating with velocity a {\displaystyle a} towards B. All of this is measured in an inertial frame where the endpoints are at rest. The arrival at B is given by:
Δ t = t 1 − t 0 = B − A a . {\displaystyle \Delta t=t_{1}-t_{0}={\frac {B-A}{a}}.}
Here, the event at A is the cause of the event at B. However, in the inertial frame moving with relative velocity v, the time of arrival at B is given according to the Lorentz transformation (c is the speed of light):
Δ t ′ = t 1 ′ − t 0 ′ = t 1 − v B / c 2 1 − v 2 / c 2 − t 0 − v A / c 2 1 − v 2 / c 2 = 1 − a v / c 2 1 − v 2 / c 2 Δ t . {\displaystyle {\begin{aligned}\Delta t'&=t'_{1}-t'_{0}={\frac {t_{1}-vB/c^{2}}{\sqrt {1-v^{2}/c^{2}}}}-{\frac {t_{0}-vA/c^{2}}{\sqrt {1-v^{2}/c^{2}}}}\\&={\frac {1-av/c^{2}}{\sqrt {1-v^{2}/c^{2}}}}\Delta t.\end{aligned}}}
It can be easily shown that if a > c, then certain values of v can make Δt' negative. In other words, the effect arises before the cause in this frame. Einstein (and similarly Tolman) concluded that this result contains in their view no logical contradiction; he said, however, it contradicts the totality of our experience so that the impossibility of a > c seems to be sufficiently proven.
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