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:2406.14225 · Physical review. D/Physical review. D.

Covariant quantum field theory of tachyons is unphysical

Krzysztof Jodłowski

Published Dec 30, 2024• 6 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevd.110.115042

Related papers

Is There Superluminal Causation in Relativistic Quantum Field Theory?

Miklós Rédei

Springer eBooks•Jan 1, 1996•5 citations

Is a covariant virtual tachyon viable?

Krzysztof Jodłowski

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.

hep-phCross-listedarXiv:2602.20474•Feb 25, 2026

The $$(1+3)$$-dimensional ‘quantum principle of relativity’ is Einstein’s principle of relativity

Matthew J. Lake

Abstract We show that the $$(1+3)$$ ( 1 + 3 ) -dimensional ‘superboost’ operators, proposed in Dragan and Ekert’s most recent work on superluminal reference frames (Dragan et al. in Class Quantum Gravity 40(2): 025013, 2023), are simply the canonical Lorentz boosts, expressed in nonstandard notation. Their $$(1+3)$$ ( 1 + 3 ) -dimensional ‘superflip’, which is claimed to interchange time and space dimensions for a superluminal observer, travelling with infinite speed, is equivalent to applying the identity operator together with an arbitrary relabeling. Physically, it corresponds to staying put within the canonical rest frame, then renaming space as ‘time’ and time as ‘space’. We conclude that their extension of the ‘quantum principle of relativity’, proposed in earlier work on $$(1+1)$$ ( 1 + 1 ) -dimensional spacetimes (Dragan and Ekert in New J Phys 22(3): 033038, 2020), to ordinary Minkowski space, is simply Einstein’s principle of relativity, proposed in 1905.

arXiv:2410.07017•The European Physical Journal C•Jan 27, 2025•1 citation

Theory of Relativity or Quantum Mechanics

Valentin Malinov

Why scientists stating that the Theory of Relativity and Quantum Mechanics they are not compatible, and one of them probably is wrong?

•Dec 1, 2020•0 citations

Scattering amplitude from quantum computing with reduction formula

Tianyin Li, Wai Kin Lai, Enke Wang +1 more

Utilizing the Lehmann-Symanzik-Zimmermann reduction formula, we present a new general framework for computing scattering amplitudes in quantum field theory with quantum computers in a fully nonperturbative way. In this framework, one only has to construct one-particle states of zero momentum, and no wave packets of incoming particles are needed. The framework is able to incorporate scatterings of bound states, and is ideal for scatterings involving a small number of particles. We expect this framework to have particular advantages when applied to exclusive hadron scatterings. As a proof of concept, by simulations on classical hardware, we demonstrate that in the one-flavor Gross-Neveu model, the fermion propagator, the connected fermion four-point function, and the propagator of a fermion-antifermion bound state obtained from our proposed quantum algorithm have the desired pole structure crucial to the implementation of the Lehmann-Symanzik-Zimmermann reduction formula.

arXiv:2301.04179•Physical review. D/Physical review. D.•Feb 22, 2024•13 citations

Causal Trade-Offs in Superluminal Extensions of Relativity. A no-go theorem

Amrapali Sen, Matthias Salzger, V. Vilasini

Extensions of relativity that include superluminal reference frames have recently been proposed by Dragan and Ekert as a way to reconcile relativistic symmetry with quantum uncertainty. In this work, we develop a causal modelling framework to formally study this proposal and prove a no-go theorem demonstrating that a theory permitting superluminal reference frames can avoid superluminal signalling only if it severely constrains which spacetime regions are accessible to operational protocols, if the choice of reference frame has observable consequences or if free variables do not exist or their existence depends on the reference frame. Crucially, our result goes beyond the familiar intuition that superluminal transformations may lead to superluminal signalling; our no-go result shows that Dragan and Ekert's proposal of introducing objective uncertainty does not, by itself, eliminate this conflict. In fact, because superluminal signalling might instead be avoided by relaxing other fundamental assumptions in the presence of superluminal reference frames, the proposed objective uncertainty may not be necessary at all. Our results clarify the limitations of uncertainty-based resolutions and the causal trade-offs faced by superluminal extensions of relativity.

quant-pharXiv:2610.00494•Oct 2, 2026•0 citations
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.
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.
The (1+3)(1+3)(1+3)-dimensional ‘quantum principle of relativity’ is Einstein’s principle of relativity
Abstract We show that the (1+3)(1+3)(1+3) ( 1 + 3 ) -dimensional ‘superboost’ operators, proposed in Dragan and Ekert’s most recent work on superluminal reference frames (Dragan et al. in Class Quantum Gravity 40(2): 025013, 2023), are simply the canonical Lorentz boosts, expressed in nonstandard notation. Their (1+3)(1+3)(1+3) ( 1 + 3 ) -dimensional ‘superflip’, which is claimed to interchange time and space dimensions for a superluminal observer, travelling with infinite speed, is equivalent to applying the identity operator together with an arbitrary relabeling. Physically, it corresponds to staying put within the canonical rest frame, then renaming space as ‘time’ and time as ‘space’. We conclude that their extension of the ‘quantum principle of relativity’, proposed in earlier work on (1+1)(1+1)(1+1) ( 1 + 1 ) -dimensional spacetimes (Dragan and Ekert in New J Phys 22(3): 033038, 2020), to ordinary Minkowski space, is simply Einstein’s principle of relativity, proposed in 1905.
Utilizing the Lehmann-Symanzik-Zimmermann reduction formula, we present a new general framework for computing scattering amplitudes in quantum field theory with quantum computers in a fully nonperturbative way. In this framework, one only has to construct one-particle states of zero momentum, and no wave packets of incoming particles are needed. The framework is able to incorporate scatterings of bound states, and is ideal for scatterings involving a small number of particles. We expect this framework to have particular advantages when applied to exclusive hadron scatterings. As a proof of concept, by simulations on classical hardware, we demonstrate that in the one-flavor Gross-Neveu model, the fermion propagator, the connected fermion four-point function, and the propagator of a fermion-antifermion bound state obtained from our proposed quantum algorithm have the desired pole structure crucial to the implementation of the Lehmann-Symanzik-Zimmermann reduction formula.
Extensions of relativity that include superluminal reference frames have recently been proposed by Dragan and Ekert as a way to reconcile relativistic symmetry with quantum uncertainty. In this work, we develop a causal modelling framework to formally study this proposal and prove a no-go theorem demonstrating that a theory permitting superluminal reference frames can avoid superluminal signalling only if it severely constrains which spacetime regions are accessible to operational protocols, if the choice of reference frame has observable consequences or if free variables do not exist or their existence depends on the reference frame. Crucially, our result goes beyond the familiar intuition that superluminal transformations may lead to superluminal signalling; our no-go result shows that Dragan and Ekert's proposal of introducing objective uncertainty does not, by itself, eliminate this conflict. In fact, because superluminal signalling might instead be avoided by relaxing other fundamental assumptions in the presence of superluminal reference frames, the proposed objective uncertainty may not be necessary at all. Our results clarify the limitations of uncertainty-based resolutions and the causal trade-offs faced by superluminal extensions of relativity.