Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2602.20474

Is a covariant virtual tachyon viable?

Krzysztof Jodłowski

hep-phgr-qchep-thquant-phSubmitted Feb 24, 2026• Announced Feb 25, 2026• Revised Oct 15, 2026 (v3)
v1 · Feb 24, 2026v2 · Sep 7, 2026v3 · Oct 15, 2026
arXivHTMLPDF

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 [1]. Recently, Dragan and Ekert have significantly developed similar ideas even further, which lead to formulation of ``quantum principle of relativity'' that intimately links the two theories [2]. 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 show that the supports of the real part of the tachyon Feynman propagator, which is also the principal-value propagator (PVP), and the Wheeler propagator intersect only on the light cone. We show that PVP cannot be time-ordered two-point function of a local Hermitian field, excluding the direct extension of the canonical formalism to free fakeon tachyon. Finally, with an imposed tachyonic PVP, interactions with electrons generate composition-dependent accelerations that violate the weak equivalence principle, and we provide a quantitative bound on this scenario. Our analysis identifies obstacles to formulating covariant quantum field theory of interacting virtual tachyon.

Journal reference
Phys. Rev. D 113, 065016 (2026)
DOI
10.1103/spbd-sd3s
Comments
8 pages, 3 figures

Related papers

Covariant quantum field theory of tachyons is unphysical

Krzysztof Jodłowski

Tachyons have fascinated generations of physicists due to their peculiar behavior, but they did not solve any real physical problem. This may have changed with the recent works of Dragan et al. [J. Paczos et al., Covariant quantum field theory of tachyons, Phys. Rev. D 110, 015006 (2024); A. Dragan and A. Ekert, Quantum principle of relativity, New J. Phys. 22, 033038 (2020); A. Dragan and A. EkertNew J. Phys.25, 088002(A) (2023); A. Dragan, K. D\ifmmode \mbox{\k{e}}\else \k{e}\fi{}bski, S. Charzy\ifmmode \acute{n}\else \'{n}\fi{}ski, K. Turzy\ifmmode \acute{n}\else \'{n}\fi{}ski, and A. Ekert, Relativity of superluminal observers in $1+3$ spacetime, Classical Quantum Gravity 40, 025013 (2023); J. Paczos, S. Cedrowski, K. Turzy\ifmmode \acute{n}\else \'{n}\fi{}ski, and A. Dragan, Higgs field as a source of tachyons, arXiv:2407.06640], who have shown that superluminal observers may be related to the foundations of quantum mechanics (QM) because they require introducing nondeterminism and wavelike behavior at the fundamental level. Unfortunately, we show that the tachyon quantum field theory proposed as a part of this program is not quantum since the tachyon field commutes at all points and the canonical commutations relations of a quantum scalar field are not satisfied. We also discuss other authors' theories, e.g., we show that the Dhar-Sudarshan's formula for the Feynman propagator violates unitarity, and we apply the Lehmann--Symanzik--Zimmermann (LSZ) formalism to tachyons for the first time, where we find that one cannot prove the LSZ asymptotic condition just by replacing plane waves with wave packets.

arXiv:2406.14225•Physical review. D/Physical review. D.•Dec 30, 2024•6 citations

Superluminal quantum reference frames

Amrapali Sen, Matthias Salzger, Łukasz Rudnicki

Abstract Particles cannot travel faster than the speed of light, nor can information. Nonetheless, this assumption has been frequently questioned over the years. This includes radical proposals like tachyons that can be observed in particle accelerators to more subtle ideas like studying superluminal causation to find classical explanations for quantum correlations. Most recently, it has been argued (Dragan and Ekert 2020 New J. Phys. 22 033038) that in a world with superluminal observers local determinism is impossible, linking the two pillars of physics-quantum theory and relativity-suggesting that the latter serves as the foundation for the former. Motivated by this approach, in this work, we extend the framework of quantum reference frames to incorporate superluminal Lorentz transformations. We apply this conceptual result to examine an apparent paradox where particles acquire negative energies after undergoing a superluminal Lorentz boost and propose a resolution within our framework. A consequence of this resolution is that different observers no longer agree whether a particle is incoming or outgoing or in a superposition of the two. We further find a similar apparent paradox for the entropy and/or temperature under superluminal Lorentz boosts and resolve it in an analogous fashion. Finally, we discuss Bell experiments under superluminal quantum reference frame transformations, showing that the involved probabilities still remain conserved. By applying the toolbox of quantum reference frames, we start charting an unexplored territory of superpositions between sub-and-superluminal quantum observers which gives rise to new conceptual questions.

New Journal of Physics•Apr 1, 2026•0 citations

From Kinematics to Interference: Operational Requirements for the Quantum Principle of Relativity

Mikołaj Sienicki, Krzysztof Sienicki

The quantum principle of relativity (QPR) puts forward an ambitious idea: extend special relativity with a formally superluminal branch of Lorentz-type maps, and treat the resulting consistency constraints as hints about why quantum theory has the structure it does [1]. The discussion that followed has emphasized a basic point: writing down coordinate maps is not the same thing as providing a physical theory. In particular, quantum superposition is not operationally defined by drawing multiple paths on paper: it is defined by what happens when alternatives recombine in an interference loop [2, 3]. In parallel, careful 1+1 analyses have clarified how sign conventions and time-orientation choices enter the superluminal formulas [4]. Finally, tachyonic QFT proposals suggest a possible mathematical bridge via an enlarged (twin) Hilbert space [5], although this proposal remains contested (e.g., on commutator covariance and microcausality grounds) [6]. The aim of this short note is organizational. We keep three layers separate: (K) kinematics (which maps exist and what they preserve), (O) operational content (what an experiment must actually reproduce, especially closed-loop interference), and (D/B) dynamics and bridges (how amplitudes and probabilities are generated, and how subluminal and superluminal sectors might be linked). The goal is not relativity derives quantum theory, but a clear checklist of what must be added for that ambition to become a well-posed programme.

quant-pharXiv:2512.05164•Dec 5, 2025•0 citations

Relativistic collapse model with tachyonic features

Philip Pearle

A finite relativistic model for free particles, which describes the collapse of the state vector, is presented. The interaction of particles with a classical fluctuating field $w(x)$ causes collapse, as in the (so far) physically satisfactory nonrelativistic continuous spontaneous localization (CSL) model. In previous relativistic models, where $w(x)$ has a white-noise spectrum, collapse is accompanied by spontaneous creation of particles with all energies out of the vacuum [amounting to infinite energy/(sec-volume)]. In this paper we explore one way of eliminating such vacuum excitation. We present a formalism which allows an arbitrary spectrum for $w(x).$ We point out, in lowest order of perturbation theory, that it is timelike components of this spectrum which are responsible for vacuum excitation but (appropriate, it seems, to a fundamentally nonlocal phenomenon) it is spacelike components which are responsible for collapse. We restrict the spectrum of $w(x)$ to that of a tachyon of mass $\ensuremath{\mu}=\ensuremath{\Elzxh}/ac\ensuremath{\approx}1 \mathrm{eV},$ where $a\ensuremath{\approx}{10}^{\ensuremath{-}5} \mathrm{cm}\mathrm{}$ is the Ghirardi-Rimini-Weber (GRW) collapse model scale parameter used in CSL. However, in higher orders than the first, there is still vacuum excitation due to the energy-momentum supplied by particle propagators. We opt to explore a simple means of eliminating this vacuum excitation: by removing the time-ordering operation from the state vector evolution so that particle propagators are on the mass shell. The result is a finite theory: there is no vacuum excitation (and no need for renormalization) as each vertex describes a finite physical process, the spontaneous emission or absorption of a real tachyon by a particle (pair creation or annihilation is not permitted by energy-momentum conservation). This process may be thought of as analogous to the GRW ``hitting'' description of collapse. The cost of no time ordering is that at each vertex a mass M particle's wave function can spread by as much as $\ensuremath{\approx}cT(\ensuremath{\mu}/M)$ in time T. This has the result that, beginning at perturbation order $2M/\ensuremath{\mu},$ there is a nonvanishing probability for the particle to be found outside its light cone: for electrons and nucleons, the probability of this spacelike transport is negligibly small. Apart from this effect, the density matrix of particles in one region evolves independently of particles in another spacelike separated region. We thus obtain a finite, reasonably sensible, relativistic collapse model for free particles.

arXiv:quant-ph/9902046•Physical Review A•Jan 1, 1999•90 citations

LOCAL CAUSALITY AND THE FOUNDATIONS OF QUANTUM MECHANICS

Robert S. Goldstein

Quantum mechanics implies the existence of correlations which cannot be described by any local theory. These nonlocal correlations possibly suggest the existence of particles traveling faster than light (tachyons). But the potential paradoxes associated with their existence imply that, even i f these tachyons do exist, it should not be possible to control them in a manner necessary for human superluminal (faster than light) communication. Indeed, the unitary nature of the time development operator precludes the possibility of using non-local correlations to communicate superluminally within the quantum formalism. A simplified model which preserves unitary time development i s shown to be useful in studying 'thought experiments' which appear init ially to allow for superluminal communication. The consistency of quantum mechanics is questioned when measurements of retarded fields are considered. I f certain idealized measurements are possible in principle, then the quantum formalism appears inconsistent. I f the measurements are not possible in principle, then 'state reduct ion' (non-unitary time evolution of the state operator) in a pragmatic sense can be said to have occurred. The suggestion that tachyons be used to explain the non-local correlations i s abandoned in favor of another model whose philosophy is supported by the tenets of relativity theory. Such a model may imply the existence of a more general quantum theory where a quantum system itself can be taken as a (generalized) frame of reference.

•Jan 1, 1987•0 citations

A Causal Alternative to Feynman's Propagator

Jurjen F. Koksma, W. Westra

The Feynman propagator used in the conventional in-out formalism in quantum field theory is not a causal propagator as wave packets are propagated virtually instantaneously outside the causal region of the initial state. We formulate a causal in-out formalism in quantum field theory by making use of the Wheeler propagator, the time ordered commutator propagator, which is manifestly causal. Only free scalar field theories and their first quantization are considered. We identify the real Klein Gordon field itself as the wave function of a neutral spinless relativistic particle. Furthermore, we derive a probability density for our relativistic wave packet using the inner product between states that live on a suitably defined Hilbert space of real quantum fields. We show that the time evolution of our probability density is governed by the Wheeler propagator, such that it behaves causally too.

arXiv:1012.3473•Dec 15, 2010•6 citations
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 [1]. Recently, Dragan and Ekert have significantly developed similar ideas even further, which lead to formulation of ``quantum principle of relativity'' that intimately links the two theories [2]. However, field theory descriptions of an on-shell tachyon, described by scalar field φφφ 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 show that the supports of the real part of the tachyon Feynman propagator, which is also the principal-value propagator (PVP), and the Wheeler propagator intersect only on the light cone. We show that PVP cannot be time-ordered two-point function of a local Hermitian field, excluding the direct extension of the canonical formalism to free fakeon tachyon. Finally, with an imposed tachyonic PVP, interactions with electrons generate composition-dependent accelerations that violate the weak equivalence principle, and we provide a quantitative bound on this scenario. Our analysis identifies obstacles to formulating covariant quantum field theory of interacting virtual tachyon.
Tachyons have fascinated generations of physicists due to their peculiar behavior, but they did not solve any real physical problem. This may have changed with the recent works of Dragan et al. [J. Paczos et al., Covariant quantum field theory of tachyons, Phys. Rev. D 110, 015006 (2024); A. Dragan and A. Ekert, Quantum principle of relativity, New J. Phys. 22, 033038 (2020); A. Dragan and A. EkertNew J. Phys.25, 088002(A) (2023); A. Dragan, K. D\ifmmode \mbox{\k{e}}\else \k{e}\fi{}bski, S. Charzy\ifmmode \acute{n}\else \'{n}\fi{}ski, K. Turzy\ifmmode \acute{n}\else \'{n}\fi{}ski, and A. Ekert, Relativity of superluminal observers in 1+31+31+3 spacetime, Classical Quantum Gravity 40, 025013 (2023); J. Paczos, S. Cedrowski, K. Turzy\ifmmode \acute{n}\else \'{n}\fi{}ski, and A. Dragan, Higgs field as a source of tachyons, arXiv:2407.06640], who have shown that superluminal observers may be related to the foundations of quantum mechanics (QM) because they require introducing nondeterminism and wavelike behavior at the fundamental level. Unfortunately, we show that the tachyon quantum field theory proposed as a part of this program is not quantum since the tachyon field commutes at all points and the canonical commutations relations of a quantum scalar field are not satisfied. We also discuss other authors' theories, e.g., we show that the Dhar-Sudarshan's formula for the Feynman propagator violates unitarity, and we apply the Lehmann--Symanzik--Zimmermann (LSZ) formalism to tachyons for the first time, where we find that one cannot prove the LSZ asymptotic condition just by replacing plane waves with wave packets.
Abstract Particles cannot travel faster than the speed of light, nor can information. Nonetheless, this assumption has been frequently questioned over the years. This includes radical proposals like tachyons that can be observed in particle accelerators to more subtle ideas like studying superluminal causation to find classical explanations for quantum correlations. Most recently, it has been argued (Dragan and Ekert 2020 New J. Phys. 22 033038) that in a world with superluminal observers local determinism is impossible, linking the two pillars of physics-quantum theory and relativity-suggesting that the latter serves as the foundation for the former. Motivated by this approach, in this work, we extend the framework of quantum reference frames to incorporate superluminal Lorentz transformations. We apply this conceptual result to examine an apparent paradox where particles acquire negative energies after undergoing a superluminal Lorentz boost and propose a resolution within our framework. A consequence of this resolution is that different observers no longer agree whether a particle is incoming or outgoing or in a superposition of the two. We further find a similar apparent paradox for the entropy and/or temperature under superluminal Lorentz boosts and resolve it in an analogous fashion. Finally, we discuss Bell experiments under superluminal quantum reference frame transformations, showing that the involved probabilities still remain conserved. By applying the toolbox of quantum reference frames, we start charting an unexplored territory of superpositions between sub-and-superluminal quantum observers which gives rise to new conceptual questions.
The quantum principle of relativity (QPR) puts forward an ambitious idea: extend special relativity with a formally superluminal branch of Lorentz-type maps, and treat the resulting consistency constraints as hints about why quantum theory has the structure it does [1]. The discussion that followed has emphasized a basic point: writing down coordinate maps is not the same thing as providing a physical theory. In particular, quantum superposition is not operationally defined by drawing multiple paths on paper: it is defined by what happens when alternatives recombine in an interference loop [2, 3]. In parallel, careful 1+1 analyses have clarified how sign conventions and time-orientation choices enter the superluminal formulas [4]. Finally, tachyonic QFT proposals suggest a possible mathematical bridge via an enlarged (twin) Hilbert space [5], although this proposal remains contested (e.g., on commutator covariance and microcausality grounds) [6]. The aim of this short note is organizational. We keep three layers separate: (K) kinematics (which maps exist and what they preserve), (O) operational content (what an experiment must actually reproduce, especially closed-loop interference), and (D/B) dynamics and bridges (how amplitudes and probabilities are generated, and how subluminal and superluminal sectors might be linked). The goal is not relativity derives quantum theory, but a clear checklist of what must be added for that ambition to become a well-posed programme.
A finite relativistic model for free particles, which describes the collapse of the state vector, is presented. The interaction of particles with a classical fluctuating field w(x)w(x)w(x) causes collapse, as in the (so far) physically satisfactory nonrelativistic continuous spontaneous localization (CSL) model. In previous relativistic models, where w(x)w(x)w(x) has a white-noise spectrum, collapse is accompanied by spontaneous creation of particles with all energies out of the vacuum [amounting to infinite energy/(sec-volume)]. In this paper we explore one way of eliminating such vacuum excitation. We present a formalism which allows an arbitrary spectrum for w(x).w(x).w(x). We point out, in lowest order of perturbation theory, that it is timelike components of this spectrum which are responsible for vacuum excitation but (appropriate, it seems, to a fundamentally nonlocal phenomenon) it is spacelike components which are responsible for collapse. We restrict the spectrum of w(x)w(x)w(x) to that of a tachyon of mass $\ensuremath{\mu}=\ensuremath{\Elzxh}/ac\ensuremath{\approx}1 \mathrm{eV},$ where $a\ensuremath{\approx}{10}^{\ensuremath{-}5} \mathrm{cm}\mathrm{}$ is the Ghirardi-Rimini-Weber (GRW) collapse model scale parameter used in CSL. However, in higher orders than the first, there is still vacuum excitation due to the energy-momentum supplied by particle propagators. We opt to explore a simple means of eliminating this vacuum excitation: by removing the time-ordering operation from the state vector evolution so that particle propagators are on the mass shell. The result is a finite theory: there is no vacuum excitation (and no need for renormalization) as each vertex describes a finite physical process, the spontaneous emission or absorption of a real tachyon by a particle (pair creation or annihilation is not permitted by energy-momentum conservation). This process may be thought of as analogous to the GRW ``hitting'' description of collapse. The cost of no time ordering is that at each vertex a mass M particle's wave function can spread by as much as $\ensuremath{\approx}cT(\ensuremath{\mu}/M)$ in time T. This has the result that, beginning at perturbation order $2M/\ensuremath{\mu},$ there is a nonvanishing probability for the particle to be found outside its light cone: for electrons and nucleons, the probability of this spacelike transport is negligibly small. Apart from this effect, the density matrix of particles in one region evolves independently of particles in another spacelike separated region. We thus obtain a finite, reasonably sensible, relativistic collapse model for free particles.
Quantum mechanics implies the existence of correlations which cannot be described by any local theory. These nonlocal correlations possibly suggest the existence of particles traveling faster than light (tachyons). But the potential paradoxes associated with their existence imply that, even i f these tachyons do exist, it should not be possible to control them in a manner necessary for human superluminal (faster than light) communication. Indeed, the unitary nature of the time development operator precludes the possibility of using non-local correlations to communicate superluminally within the quantum formalism. A simplified model which preserves unitary time development i s shown to be useful in studying 'thought experiments' which appear init ially to allow for superluminal communication. The consistency of quantum mechanics is questioned when measurements of retarded fields are considered. I f certain idealized measurements are possible in principle, then the quantum formalism appears inconsistent. I f the measurements are not possible in principle, then 'state reduct ion' (non-unitary time evolution of the state operator) in a pragmatic sense can be said to have occurred. The suggestion that tachyons be used to explain the non-local correlations i s abandoned in favor of another model whose philosophy is supported by the tenets of relativity theory. Such a model may imply the existence of a more general quantum theory where a quantum system itself can be taken as a (generalized) frame of reference.
The Feynman propagator used in the conventional in-out formalism in quantum field theory is not a causal propagator as wave packets are propagated virtually instantaneously outside the causal region of the initial state. We formulate a causal in-out formalism in quantum field theory by making use of the Wheeler propagator, the time ordered commutator propagator, which is manifestly causal. Only free scalar field theories and their first quantization are considered. We identify the real Klein Gordon field itself as the wave function of a neutral spinless relativistic particle. Furthermore, we derive a probability density for our relativistic wave packet using the inner product between states that live on a suitably defined Hilbert space of real quantum fields. We show that the time evolution of our probability density is governed by the Wheeler propagator, such that it behaves causally too.