Anti-phone

An anti-phone (also called a tachyon anti-phone ) is a hypothetical device that could be used to send signals back to one's past . It is based on a thought experiment by Albert Einstein (1907), according to which signals traveling at faster than light speed move backwards through time according to the special theory of relativity . In a conversation with Arnold Sommerfeld, Einstein (1910) described this as a means of “telegraphing into the past”. A similar thought experiment was made by Richard Chace Tolman(1917), which is why it is also known as Tolman's Paradox . One hypothetical device that could do this was later referred to by Gregory Benford as the "Tachyon anti-phone". When Tachyon is hypothetical, faster than light particles, which unusual properties such. B. be awarded an imaginary mass.

Such “telegraphing into the past” by means of faster than light communication would, however, lead to causality violations , which is why Einstein, Tolman and the vast majority of physicists considered it to be practically impossible. The related Tachyon theories are also controversial.

Disposable example

This was illustrated in 1911 by Paul Ehrenfest using a Minkowski diagram . Two signals are sent in the system B ₁ at an almost infinitely high speed in the opposite directions OP and ON , event O taking place before event N. In another inertial system B ₂ , however, N takes place before O.

Based on Einstein's thought experiment, Tolman considered the following situation: Let a segment L with the endpoints A and B be given. A signal is now sent at A at the point in time with speed in direction B and arrives there at the point in time . For the flight time of the signal results ${\displaystyle t_{0}}$ ${\displaystyle w}$ ${\displaystyle t_{1}}$

${\displaystyle \Delta t=t_{1}-t_{0}={\frac {L}{w}}}$.

So here the cause (event at A) takes place before the consequence (event at B). In an inertial system that moves with the speed relative to it, however, the Lorentz transformation results in the time of flight of the signal up to the arrival at B ${\displaystyle v}$

${\displaystyle {\begin{aligned}\Delta t'&=t'_{1}-t'_{0}={\frac {t_{1}-vB/c^{2}}{\sqrt {1-v^{2}/c^{2}}}}-{\frac {t_{0}-vA/c^{2}}{\sqrt {1-v^{2}/c^{2}}}}\\&={\frac {1-wv/c^{2}}{\sqrt {1-v^{2}/c^{2}}}}\Delta t.\end{aligned}}}$

It can be seen that in the case one reaches a negative by a suitable choice of v . In other words, the effect at B occurs in this system before the cause at A. Einstein and Tolman pointed out that this result contains no logical contradiction, but it contradicts the entirety of experience, so that the impossibility of faster than light speeds is sufficient in their opinion is proven. ${\displaystyle w>c}$ ${\displaystyle \Delta t'}$

Two way example

The relationships become more complicated if the following example is discussed: Let there be an inertial system S 'in which observer A rests, and an inertial system S in which B rests. B moves in the negative x-direction from the point of view of A. It is also assumed that A and B have devices of the same type with which faster- than-light signals can be sent in their respective inertial systems .

At the point in time, A sends a signal that is traveling faster than light (measured in S ') to B, which is there at the point in time ${\displaystyle t_{0}'=0}$ ${\displaystyle -w'}$

${\displaystyle t_{1}'={\frac {L'}{w'}}}$

arrives. Here is the distance that the signal traverses until it has reached B, which flies away in the negative x-direction. At B, your own transmitter is activated immediately afterwards and a signal that propagates at faster than light speed (measured in S) is sent to A. It must be taken into account that the length of the path is contracted and that A runs away from the signal in a positive direction. That gives an arrival time of ${\displaystyle L'}$ ${\displaystyle w}$

${\displaystyle t_{2}={\tfrac {L'{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}{w-v}}}$.

In S ', however, (see formula for in the one-way example) ${\displaystyle \Delta t'}$

${\displaystyle t_{2}'={\frac {1-{\frac {wv}{c^{2}}}}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}t_{2}={\frac {1-{\frac {wv}{c^{2}}}}{w-v}}L'}$.

In total, this gives the total time until you return to A. ${\displaystyle T'}$

${\displaystyle T'=t_{1}'+t_{2}'=\left({\frac {1}{w'}}+{\frac {1-{\frac {wv}{c^{2}}}}{w-v}}\right)L'}$.

Here, too, the result is that with a suitable choice of a negative results, that is, A receives the answer back before the original signal ( ) was even sent. Benford et al. a. wrote about such situations: ${\displaystyle w>c}$ ${\displaystyle v}$ ${\displaystyle T'}$ ${\displaystyle t_{0}'=0}$

“The paradoxes of communicating backwards through time are well known. Assume that A and B make the following agreement: A will send a message at three o'clock if and only if it does not receive a message at one o'clock . Immediately after A's message reaches B at three o'clock, B sends a message that reaches A at one o'clock. The message exchange takes place exactly when it does not take place. That is a real paradox, a causal contradiction. "

From this they concluded that faster-than-light particles such as tachyons should not transmit signals.

See also

• Grandfather paradox

Individual evidence

1. ↑ ^{a b} Einstein, Albert: About the inertia of energy required by the principle of relativity . In: Annals of Physics . 328, No. 7, 1907, pp. 371-384. bibcode : 1907AnP ... 328..371E . doi : 10.1002 / andp.19073280713 .
2. ↑ Ignatowsky, Wv: Some general remarks on the principle of relativity . In: Physikalische Zeitschrift . 11, 1910, p. 975.
3. ^ AI Miller: Albert Einstein's special theory of relativity. Emergence (1905) and early interpretation (1905-1911) . Addison-Wesley, Reading 1981, ISBN 0-201-04679-2 .
4. ^ ^{A b} R. C. Tolman: Velocities greater than that of light . In: The Theory of the Relativity of Motion . University of California Press , 1917, p. 54, OCLC 13129939 .
5. ^ ^{A b c} Gregory Benford , DL Book , WA Newcomb : The Tachyonic Antitelephone . In: Physical Review D . 2, 1970, pp. 263-265. bibcode : 1970PhRvD ... 2..263B . doi : 10.1103 / PhysRevD.2.263 .
6. ↑ The physicist and science fiction author Gregory Benford also used this concept of a tachyon anti-telephone in his novel Timescape (1980; Ger. Zeitschaft (1984), ISBN 3-453-52191-9 ).
7. ↑ John Baez: Do tachyons exist? Accessed August 22, 2018 (English). 
8. ↑ P. Ehrenfest: To Mr. v. Ignatowsky's treatment of Born's definition of rigidity II . In: Physikalische Zeitschrift . 12, 1911, pp. 412-413.
9. ↑ For example: Roman Sexl, Herbert K. Schmid: Raum-Zeit-Relativität . Vieweg, Braunschweig 1979, ISBN 3-528-17236-3 .
10. ^ The paradoxes of backward-in-time communication are well known. Suppose A and B enter into the following agreement: A will send a message at three o'clock if and only if he does not receive one at one o'clock. B sends a message to reach A at one o'clock immediately on receiving one from A at three o'clock. Then the exchange of messages will take place if and only if it does not take place. This is a genuine paradox, a causal contradiction.