Abstract. This paper considers the possibility of developing a theory of tachyons in which mutual transitions between tachyons and bradyons (tardions) are mathematically permissible, excluding the passage of a singularity. This question is based on the previously established relative symmetry of the tardion world with the bradyon world, i.e., when an observer in the tachyon world perceives their world as a bradyon world, and perceives our opposite bradyon world as a world of superluminal particles, which follows from the replacement of the spatial coordinate by the time coordinate in the tachyon world. Two approaches related to the modification of the Lorentz factor (γ) are considered: the first is a modification based on the theory of discrete motion; The second is a modification based on the “mirror” reflection of the γ coefficient by introducing finite limiting values of physical quantities determined by the γ factor, for example, finite maximum possible masses that decrease infinitely as the velocity decreases to infinitely small values, or increase to infinitely large values of the object’s extension (particle wavelength) from the minimum possible finite value. The question is raised about the applicability of the “mirror” γ coefficient to axions and axion-like capuscles—hypothetical slow particles with extremely small masses (25–30 orders of magnitude smaller than the mass of an electron) and wavelengths on the order of the size of galaxies. The existence of long-wavelength axions commensurate with the size of the universe is assumed. The theory of polaritons—hybrids of short-wavelength axions and photons — is considered.
A.O. Mayboroda
Leading Researcher, ICER
International Center for Everett Studies (ICER)
January 30, 2026
Keywords: tachyon, bradyon, tardion, three-dimensional time, coordinate inversion, singularity, Lorentz factor, discrete motion theory, axions, polaritons.