Signaling to Relativistic Observers: An Einstein-Shannon-Riemann Encounter

05/07/2020

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by   Mladen Kovačević, et al.

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A thought experiment is described involving a series of events triggered by a transmitter and observed by a receiver experiencing a relativistic time dilation. This is seen as a communication problem in which the events' timings are selected by the transmitter, and the receiver is required to recover them perfectly regardless of the relative speed of the two frames of reference. It is shown that the largest proportion of the space of all allowed signals consisting of k events, that can possess the property of any two signals being distinguishable, equals ζ(k)^-1, where ζ is the Riemann zeta function.