Breaching the light barrier without paradoxes

Abstract

In this paper, we propose the regularization principle that resolves the temporal paradoxes associated with faster-than-light particles or tachyons at the macroscopic scale. The principle involves using the properties of the $\zeta$-function to regularize the unphysical momenta of tachyons that moves backwards in-time as an infinite sum of physical tachyon momenta that travel forwards in-time. Since, the tachyon moves forward in-time in all interial frames, this ensures that the tachyon processes are paradox-free without invoking the Reinterpretation Principle (RIP). Apart from resolving these paradoxes associated with faster-than-light particles, its other notable consequences especially pertaining to the censorship of naked singularities and faster-than-light communication are also discussed.

18 pages, 4 figures, TMPh-RAS accepted version, To appear in August 2026 issue

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• On the stability of naked singularities
• Cosmological structure formation with negative mass
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• On negative mass
• Lectures on Faster-than-Light Travel and Time Travel
• Interacting tachyon with varying mass dark matter