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Superluminal Quantum Reference Frames

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Pith's one-line read The paper claims that quantum reference frames can be extended to superluminal Lorentz transformations by a unitary boost controlled by the frame's momentum operator, resolving negative-energy paradoxes while keeping Bell probabilities…

desk verdict Interesting application of QRFs to superluminal boosts undermined by an incorrect SL(2,R) group claim that the unitary representation depends on. read the letter →

arxiv 2506.11787 v2 pith:K7YRDMWT submitted 2025-06-13 quant-ph gr-qc

Amrapali Sen , Matthias Salzger , {L}ukasz Rudnicki This is my paper · ORCID
classification quant-phgr-qc MSC 81P1683A05
keywords quantumreferenceframessuperluminalLorentztransformationstachyonsnegativeenergyBellinequalitiesgrouprelationalmechanicsrelativity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper claims that the formalism of quantum reference frames, in which observers are quantum systems and changes of perspective are unitary maps, can be extended to observers moving faster than light. The authors construct a transformation that conditionally boosts one system by a unitary representation of an extended Lorentz group whose parameter is the momentum operator of the new reference frame. They use it to resolve the apparent paradox that a subluminal particle or photon acquires negative energy after a superluminal boost: the resolution enlarges the single-particle state space so that a negative-energy state is reinterpreted as a positive-energy state with reversed momentum, making 'incoming' and 'outgoing' frame-dependent and possibly superposed. They also show Bell measurement probabilities stay invariant under these extended transformations, though the causal ordering of settings and outcomes need not. A sympathetic reader would care because it offers a quantum-information-grounded way to test claims that superluminal observers force fundamental indeterminism.

What carries the argument

The load-bearing object is the momentum-controlled unitary boost $\hat U_B(L_{\hat p_A}) = \int d\bar p_A \, |p_A\rangle\langle p_A|_A \otimes \hat U_B(L_{p_A})$ with $d\bar p_A = dp_A\bigl(\delta(p_A^2 - m_A^2) + \delta(p_A^2 + m_A^2)\bigr)$, combined with the parity-swap operator $\hat P_{AC}$. The measure puts both subluminal and superluminal momentum shells on equal footing, and the claim that these shells belong to one group, presented in the paper as $\mathrm{SL}(2,\mathbb{R})$ following reference [17], is what licenses $\hat U_B$ as a unitary representation. The mechanism does the work of making a superluminal change of perspective a reversible quantum operation, so that superpositions of velocities and entanglements between the new frame and the remaining systems can be analysed by ordinary linearity.

What would settle it

Check the determinant of the superluminal boost matrices in Table I: they have determinant $-1$, while every element of $\mathrm{SL}(2,\mathbb{R})$ has determinant $+1$, so a direct computation of the group they generate together with the subluminal boosts would show whether the claimed closure holds. If it does not, the unitary $\hat U_B(L_{\hat p_A})$ in Eq. (11) lacks a well-defined group to represent.

Watch

Extended reading notes

Core claim

The central claim is that quantum reference frame transformations can absorb superluminal Lorentz boosts. For three systems $C$, $A$, $B$, the transformation from $C$'s perspective to $A$'s rest frame is $\hat S_{AC} = \hat P_{AC}\hat U_B(L_{\hat p_A})$, where $\hat P_{AC}$ is the parity-swap operator and $\hat U_B(L_{\hat p_A})$ is a unitary representation of the boost labelled by $A$'s 2-momentum operator, integrated over both subluminal and superluminal mass shells. The same operator that normally describes a relativistic QRF boost is therefore reused with a momentum label that can lie on either branch. With this, the paper argues that negative energies produced by superluminal boosts are not a contradiction: each particle state gets a 'dual' copy so that $(E,p)$ can be re-read as $(-E,-p)$, and the labels incoming and outgoing become frame-dependent, even ending up in superposition or entangled with the frame. The authors further claim that Bell-test probabilities computed through these transformations are frame-independent because the transformations are unitary, while the interpretation of the experiment, such as who is spacelike separated from whom and whether a setting lies in the past of an outcome, can change.

Load-bearing premise

The construction depends on the claim that ordinary and superluminal Lorentz boosts together form a single closed group $\mathrm{SL}(2,\mathbb{R})$; if that group claim fails, the unitary representation that defines the quantum reference frame transformation is not justified.

Editorial extensions

If this is right

  • A photon seen as outgoing from one frame can appear, from a frame in superposition of subluminal and superluminal velocities, as a superposition (or entanglement) of incoming and outgoing states.
  • Negative-energy states after superluminal boosts are reabsorbed by doubling the state space, so no physical energy violation remains in the single-particle description.
  • Bell-test outcome probabilities are invariant under the extended transformations, so superluminal frames do not by themselves change the violation; they can, however, change the causal story attached to the Bell experiment.
  • The same reinterpretation resolves apparent negative temperatures: in the Einstein–Planck and Ott approaches, replacing $\gamma$ by $|\gamma|$ after reinterpretation removes the sign problem.
  • The framework gives a quantum-information route to superluminal transformations that does not require a full quantum field theory.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A natural next step, which the paper leaves implicit, is to identify the minimal extended group that contains both the determinant-$+1$ and determinant$-1$ boost branches and still admits a unitary representation, since the paper takes the closure property as given.
  • The observer-dependent 'incoming/outgoing' superposition suggests a potential bridge to the particle-antiparticle reinterpretation familiar from relativistic quantum theory, although the paper does not claim that connection.
  • The real locus of tension may be the notion of free choice: the paper shows settings can end up in the causal past of their outcomes, and whether 'free' remains meaningful in that regime is a question left open.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper proposes an extension of the quantum reference frame (QRF) formalism to include superluminal Lorentz boosts. The central construction is the transformation S_AC = P_AC U_B(L_hat p_A) in Eq. (9), built on a unitary representation U_B of the group claimed in Table I to be SL(2,R). The paper then applies this formalism to resolve negative-energy paradoxes by enlarging the Hilbert space with a dual copy B*, to show that superluminal observers can see superpositions of incoming and outgoing particles, to discuss entropy and temperature transformations, and to argue that Bell probabilities are invariant under such transformations. The paper is explicitly conceptual rather than computational.

Significance. If the construction were sound, the paper would open a new direction by connecting quantum reference frames with superluminal observers and with the recent program of Dragan and Ekert. Its strengths include that it does not fit free parameters, it makes a concrete claim (Bell probabilities remain invariant), and it is transparent about its limitations and open questions. However, the central group-theoretic foundation is incorrect as stated, and the unitary representation underlying the main transformation is not established. The paper therefore does not currently support its main claim, although the broader idea may be salvageable with a different mathematical framework.

major comments (2)
  1. [Section II, Table I, Eq. (11)] The claim that the subluminal and superluminal Lorentz transformations together form SL(2,R) is false as stated. Every superluminal boost matrix in Table I has determinant -1, whereas every element of SL(2,R) has determinant +1. Moreover, the set displayed in Table I is not closed under matrix multiplication: for example, Btilde_phi^- Btilde_{-phi}^+ = -I, and -I is not in the set {B_phi, Btilde_phi^+, Btilde_phi^-}. Consequently, the existence of the unitary representation U_B(L_{p_A}) used in Eq. (11), and hence the QRF transformation S_AC in Eq. (9), is not justified. The measure-invariance calculation in Eqs. (13)-(15) only shows that the two-shell measure is invariant; it does not supply a unitary representation of SL(2,R) or of any group. Since all applications in Sections III A-III D rely on Eq. (9), the central claim of the paper is unsupported by the submitted text.
  2. [Section II, Eq. (11) and Section III A] For a superluminal boost L, one has L^T η L = -η, a property the paper itself uses in Eq. (14). It follows that L maps the mass shell p^2 = m_B^2 to p^2 = -m_B^2. Therefore the operator U_B(L_{p_A}) defined in Eq. (11) sends a subluminal one-particle state of B into a tachyon state that does not lie in the original Hilbert space H_B. The enlargement of the Hilbert space with the dual copy B* is introduced only later, in Section III A, as a resolution to the negative-energy paradox, and it is not part of the definition of the transformation in Eq. (9). As a result, the transformation S_AC is not a well-defined unitary map between the Hilbert spaces introduced in Eq. (4), and the unitarity invoked in the Bell-invariance argument in Section III D is not established.
minor comments (5)
  1. [Table I caption] The caption states that the set B = {B_phi, Btilde_phi^+, Btilde_phi^-} forms a group; the set itself is not closed under matrix multiplication, and the intended statement should be that the set generates a group.
  2. [Eq. (11)] The integration measure dbar p_A includes both delta(p_A^2 - m_A^2) and delta(p_A^2 + m_A^2); for a particle with a fixed mass m_A these are two different mass shells, and the paper should clarify whether the reference frame A is allowed to be in a superposition of subluminal and tachyon states, and how m_A is defined for both branches.
  3. [Section III A, Eq. (26)] The dual-space mapping is described only by the symbol '~', and the authors state that mapping |−p_B> into |p_B> would destroy unitarity, but no explicit unitary map between B and B* is provided; this leaves the claimed resolution incomplete.
  4. [Section III C] The reinterpretation of heat and temperature with |γ| after a superluminal boost is an additional physical assumption that is not derived from the QRF transformation; it is imposed on top of the formalism.
  5. [Appendix and Section III D] There are minor typos: 'refernce' should be 'reference' in the Appendix, and in Eq. (48) 'spins A' should be 'spin of A' and 's A' should be 's_A'.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation: the superluminal QRF transformation is a stipulated extension of prior QRF and tachyon frameworks; the only self-citation is a non-load-bearing forward pointer.

full rationale

The central construction (Eq. (9)) is obtained by inserting the external group claim of Ref. [17] into the standard QRF formula (Eq. (7)); no parameter is fitted and no target prediction is used as an input. The Lorentz-invariant measure argument (Eqs. (13)-(15)) is a direct calculation, independent of whether the determinant issue with Table I is resolved. The negative-energy 'resolution' is explicitly presented as a reinterpretation convention (Eq. (25) and the surrounding text: 'We can take care of negative energies by simply reinterpreting...' and 'there is nothing stopping us...'), not as a derived prediction, so it cannot be circular in the input-output sense. The Bell-invariance claim follows from unitarity: the same unitary is applied to states and observables, and the paper itself notes 'as the QRF transformations we used were arbitrary'; this is a consistency check, not a fitted result. The one self-citation, Ref. [45], is a forward pointer to follow-up work and is not load-bearing. A genuine caveat exists: the claim from Ref. [17] that subluminal and superluminal boosts jointly form SL(2,R) is mathematically questionable because the superluminal matrices in Table I have determinant -1, and this premise supports the unitary representation in Eq. (11). That is a correctness/evidentiary risk about an external input, not a circular reduction of the paper's outputs to its own assumptions.

Assumptions & free parameters 0 free parameters · 5 assumptions · 2 invented entities

The central claim rests on the speculative existence of superluminal observers, on a cited but questionable group structure, on an assumed unitary representation, and on a conventional reinterpretation of negative energies. None of these have independent experimental support, and the group claim is internally inconsistent with the matrices in Table I.

assumptions (5)
  • domain assumption The linearity and relativity principles allow superluminal Lorentz transformations as a legitimate branch.
    Section I A follows [5,6] in keeping the superluminal branch; this is a speculative physical assumption, not an established fact.
  • ad hoc to paper The SbLT and SpLT together form a group isomorphic to SL(2,R).
    Section II invokes [17]'s group claim to build unitary representations. The determinant of the superluminal matrices is -1, so this group claim is mathematically questionable.
  • domain assumption There is a unitary representation U_B(L_{p_A}) of the extended boost group acting on momentum eigenstates of particle B.
    Eqs. (9)-(12) assume such a unitary exists; this is not proven for superluminal boosts.
  • ad hoc to paper Negative-energy states can be reinterpreted as positive-energy states by passing to a dual copy B* of the Hilbert space.
    Section III A adapts the tachyon reinterpretation of [18,19]; it is a convention needed for unitarity, not a consequence of the dynamics.
  • domain assumption An observer can be placed in a quantum superposition of subluminal and superluminal velocities.
    The QRF framework allows superpositions of frame parameters; applying it to superluminal velocities is the paper's central assumption.
invented entities (2)
  • Dual Hilbert space copy B*
    purpose: Holds reinterpreted negative-energy ('outgoing') states so that QRF transformations remain unitary; used in Section III A and B.
    No independent observable; it is a mathematical bookkeeping device borrowed from tachyon literature.
  • Superluminal observer/reference frame
    purpose: A reference frame moving faster than light; central to the whole paper.
    No experimental evidence for superluminal frames; the paper treats them as a conceptual extension motivated by [6].

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Cite this review

Pith. "Pith review of Superluminal Quantum Reference Frames." pith.science (2026). https://pith.science/paper/K7YRDMWT

@misc{pith2026250611787,
  author       = {Pith},
  title        = {Pith review of: Superluminal Quantum Reference Frames},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/K7YRDMWT}},
  note         = {Machine review of arXiv:2506.11787}
}
read the original abstract

While particles cannot travel faster than the speed of light, nor can information, this assumption has over the years been frequently questioned. Most recently, it has been argued [New J. Phys. 22, 033038 (2020)] 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. We also discuss Bell experiments under superluminal quantum reference frame transformations, showing that involved probabilities remain conserved.

Figures

Figures reproduced from arXiv: 2506.11787 by the authors.

Figure 1
Figure 1. FIG. 1. From the perspective of reference frame [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Above, [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Above, [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The space of single particle states is not Lorentz in [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Frame dependent notion of time. Point [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]

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Forward citations

Cited by 1 Pith paper

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  1. Superluminal Transformations and Indeterminism

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Reference graph

Works this paper leans on

51 extracted references · 48 canonical work pages · cited by 1 Pith paper

  1. [17]

    Classical tachyons and possible applica- tions.La Rivista del Nuovo Cimento (1978-1999), 9(6): 1–178, 1986

    Erasmo Recami. Classical tachyons and possible applica- tions.La Rivista del Nuovo Cimento (1978-1999), 9(6): 1–178, 1986

    work page 1978

  2. [1]

    incoming

    Energy accounting The energy-momentum relations derived from the pos- tulates of special relativity can be broadly classified into two categories: class I, the subluminal particles, i.e., the usual physical systems we encounter in nature and class II: massless particles traveling at the speed of light, e.g., photons. Finally, by including superluminal Lor...

    work page

  3. [2]

    positive energy

    Resolution within superluminal QRF For our quantum reference frames in order to account for this issue while retaining unitarity, this implies that the state space of each particle is actually larger than if we considered only subluminal transformations. We can resolve this by adapting the solution proposed in [18, 19]. For each “positive energy” basis st...

    work page

  4. [3]

    9 Note: The absolute value ofγin the definitions we use, increases 11 FIG

    The first approach by Einstein and Planck [7, 35] assumes entropy to be a Lorentz invariant, and thus one finds: dS′ =dS, dQ ′ = dQ γ T ′ = T γ (37) whereγ 9 is the Lorentz factor, and thus objects look cooler to a (subluminally) moving observer. 9 Note: The absolute value ofγin the definitions we use, increases 11 FIG. 6. Frame dependent notion of time. ...

    work page

  5. [4]

    This can also be understood from the dual velocity relations discussed in Table I

    The second approach by Ott [36] treats heat trans- fer as an energy, and thus: dQ′ =γdQ,(39) which, together with the assumption of entropy be- ing a Lorentz invariant, leads to: T ′ =γT(40) as we approach the speed of light both from the subluminal and superluminal regime. This can also be understood from the dual velocity relations discussed in Table I....

    work page

  6. [5]

    The third approach by Lansberg [37] directly as- sumes the temperature to be a Lorentz invariant: T ′ =T. In order to ensure this one has to define the temperature as: 1 T = 1 γ ∂S ∂E V,p (42) which also implies that the internal energy is a Lorentz invariant, so that; 1 T = ∂S ∂U V,p (43) With the temperature being constant, the entropy and energy have s...

    work page

  7. [6]

    superposition of Lorentz boosts

    The fourth and final approach by Cavalleri and Sal- garelli [38] states that it only makes sense to study thermodynamics in the rest reference frame, hence this case is trivial. D. Bell violations in the superluminal regime For relativistic particles, quantum field theory predicts that the total angular momentum is conserved instead of the spin alone. The...

    work page 2021

  8. [7]

    Quantum mechanics and the covariance of physical laws in quantum reference frames.Nature com- munications, 10(1):494, 2019

    Flaminia Giacomini, Esteban Castro-Ruiz, and ˇCaslav Brukner. Quantum mechanics and the covariance of physical laws in quantum reference frames.Nature com- munications, 10(1):494, 2019

    work page 2019

Show all 51 references
  1. [8]

    The group structure of dynamical transforma- tions between quantum reference frames.Quantum, 5: 470, 2021

    Angel Ballesteros, Flaminia Giacomini, and Giulia Gu- bitosi. The group structure of dynamical transforma- tions between quantum reference frames.Quantum, 5: 470, 2021

    2021

  2. [9]

    The sum of entanglement and subsystem coherence is invariant under quantum reference frame transformations.arXiv preprint arXiv:2406.19448, 2024

    Carlo Cepollaro, Ali Akil, Pawe l Cie´ sli´ nski, Anne- Catherine de la Hamette, and ˇCaslav Brukner. The sum of entanglement and subsystem coherence is invariant under quantum reference frame transformations.arXiv preprint arXiv:2406.19448, 2024

    2024

  3. [10]

    Relativistic quantum reference frames: the op- erational meaning of spin.Physical review letters, 123(9): 090404, 2019

    Flaminia Giacomini, Esteban Castro-Ruiz, and ˇCaslav Brukner. Relativistic quantum reference frames: the op- erational meaning of spin.Physical review letters, 123(9): 090404, 2019

    2019

  4. [11]

    Faster-than-light intertial frames and tachyons.Physical Review, 188(5):2287, 1969

    Leonard Parker. Faster-than-light intertial frames and tachyons.Physical Review, 188(5):2287, 1969

    1969

  5. [12]

    Quantum principle of relativity.New Journal of Physics, 22(3):033038, 2020

    Andrzej Dragan and Artur Ekert. Quantum principle of relativity.New Journal of Physics, 22(3):033038, 2020

    2020

  6. [13]

    ¨Uber das relativit¨ atsprinzip und die aus demselben gezogenen folgerungen.Jahrb

    Albert Einstein. ¨Uber das relativit¨ atsprinzip und die aus demselben gezogenen folgerungen.Jahrb. d. Radioak- tivit¨ at u. Elektronik, 4:411–462, 1907

    1907

  7. [14]

    Velocities greater than that of light

    Richard C Tolman. Velocities greater than that of light. The Theory of the Relativity of Motion, page 54, 1917

    1917

  8. [15]

    “meta” relativity.American Journal of Physics, 30 (10):718–723, 1962

    Olexa Bilaniuk, Vijay Deshpande, and EC George Sudar- shan. “meta” relativity.American Journal of Physics, 30 (10):718–723, 1962

    1962

  9. [16]

    Possibility of faster-than-light particles

    Gerald Feinberg. Possibility of faster-than-light particles. Physical Review, 159(5):1089, 1967

    1967

  10. [18]

    “meta” relativity: Against special relativity?arXiv preprint arXiv:1206.0841, 2012

    Jakub Rembielinski and Marta Wlodarczyk. “meta” relativity: Against special relativity?arXiv preprint arXiv:1206.0841, 2012

    2012 arXiv

  11. [19]

    Tachyon generalization for lorentz trans- forms.Methods of Functional Analysis and Topology, 19 (02):127–145, 2013

    Ya I Grushka. Tachyon generalization for lorentz trans- forms.Methods of Functional Analysis and Topology, 19 (02):127–145, 2013

    2013

  12. [20]

    Impossibility of superluminal signaling in minkowski spacetime does not rule out causal loops.Physical Review Letters, 129(11): 110401, 2022

    Venkatesh Vilasini and Roger Colbeck. Impossibility of superluminal signaling in minkowski spacetime does not rule out causal loops.Physical Review Letters, 129(11): 110401, 2022

    2022

  13. [21]

    The rel- ativistic causality versus no-signaling paradigm for multi- 14 party correlations.Nature communications, 10(1):1701, 2019

    Pawe l Horodecki and Ravishankar Ramanathan. The rel- ativistic causality versus no-signaling paradigm for multi- 14 party correlations.Nature communications, 10(1):1701, 2019

    2019

  14. [22]

    Bohmian mechanics

    Detlev D¨ urr, Sheldon Goldstein, Roderich Tumulka, and Nino Zangh ´ ı. Bohmian mechanics. InCompendium of quantum physics, pages 47–55. Springer, 2009

    2009

  15. [23]

    Towards a group structure for superlu- minal velocity boosts.arXiv preprint arXiv:2409.01773, 2024

    Matthew J Lake. Towards a group structure for superlu- minal velocity boosts.arXiv preprint arXiv:2409.01773, 2024

    2024 arXiv

  16. [24]

    Tachyon dynamics—for neutrinos? International Journal of Modern Physics A, 33(10): 1850056, 2018

    Charles Schwartz. Tachyon dynamics—for neutrinos? International Journal of Modern Physics A, 33(10): 1850056, 2018

    2018

  17. [25]

    Covariant quantum field theory of tachyons.Physical Review D, 110(1):015006, 2024

    Jerzy Paczos, Kacper Debski, Szymon Cedrowski, Szy- mon Charzy´ nski, Krzysztof Turzy´ nski, Artur Ekert, and Andrzej Dragan. Covariant quantum field theory of tachyons.Physical Review D, 110(1):015006, 2024

    2024

  18. [26]

    Relativistic bell test within quantum reference frames.Physical Review Letters, 126(23):230403, 2021

    Lucas F Streiter, Flaminia Giacomini, and ˇCaslav Brukner. Relativistic bell test within quantum reference frames.Physical Review Letters, 126(23):230403, 2021

    2021

  19. [27]

    Lorentz transformations in 1+ 1 dimensional spacetime: mainly the superluminal case

    Bogdan S Damski. Lorentz transformations in 1+ 1 dimensional spacetime: mainly the superluminal case. arXiv preprint arXiv:2510.14085, 2025

    2025

  20. [28]

    Relational quantum mechanics.Inter- national Journal of Theoretical Physics, 35:1637–1678, 1996

    Carlo Rovelli. Relational quantum mechanics.Inter- national Journal of Theoretical Physics, 35:1637–1678, 1996

    1996

  21. [29]

    Riverhead Books, 2021

    Carlo Rovelli.Helgoland: Making Sense of the Quantum Revolution. Riverhead Books, 2021

    2021

  22. [30]

    The two-state vector formalism of quantum mechanics: an updated review

    Yakir Aharonov and Lev Vaidman. The two-state vector formalism of quantum mechanics: an updated review. InTime in quantum mechanics, volume 734 ofLecture Notes in Physics, pages 399–447. Springer, 2008

    2008

  23. [31]

    The two-state vector formalism, 2007

    Lev Vaidman. The two-state vector formalism, 2007

    2007

  24. [32]

    Quantum reference frames for general symmetry groups

    Anne-Catherine de la Hamette and Thomas D Galley. Quantum reference frames for general symmetry groups. Quantum, 4:367, 2020

    2020

  25. [33]

    Operational quantum reference frame transformations

    Titouan Carette, Jan Glowacki, and Leon Loveridge. Operational quantum reference frame transformations. Quantum, 9:1680, 2025

    2025

  26. [34]

    Transformation of spin in quantum reference frames

    Marion Mikusch, Luis C Barbado, and ˇCaslav Brukner. Transformation of spin in quantum reference frames. Physical Review Research, 3(4):043138, 2021

    2021

  27. [35]

    Algebraic prop- erties of quantum reference frames: Does time fluctuate? Quantum Reports, 5(1):22–37, 2022

    Martin Bojowald and Artur Tsobanjan. Algebraic prop- erties of quantum reference frames: Does time fluctuate? Quantum Reports, 5(1):22–37, 2022

    2022

  28. [36]

    Symmetry, reference frames, and relational quantities in quantum mechanics.Foundations of Physics, 48:135–198, 2018

    Leon Loveridge, Takayuki Miyadera, and Paul Busch. Symmetry, reference frames, and relational quantities in quantum mechanics.Foundations of Physics, 48:135–198, 2018

    2018

  29. [37]

    Lake and Marek Miller

    Matthew J. Lake and Marek Miller. Quantum reference frames, revisited, 2023

    2023

  30. [38]

    Operational quantum frames: An oper- ational approach to quantum reference frames.arXiv preprint arXiv:2304.07021, 2023

    Jan G lowacki. Operational quantum frames: An oper- ational approach to quantum reference frames.arXiv preprint arXiv:2304.07021, 2023

    2023 arXiv

  31. [39]

    Superluminal coordinate transformations: Four- dimensional case.Physical Review D, 27(8):1740, 1983

    Louis Marchildon, Adel F Antippa, and Allen E Ev- erett. Superluminal coordinate transformations: Four- dimensional case.Physical Review D, 27(8):1740, 1983

    1983

  32. [40]

    What is the temperature of a moving body?Scientific reports, 7(1):17657, 2017

    Cristian Far ´ ıas, Victor A Pinto, and Pablo S Moya. What is the temperature of a moving body?Scientific reports, 7(1):17657, 2017

    2017

  33. [41]

    Zur dynamik bewegter systeme.Annalen der Physik, 331(6):1–34, 1908

    Max Planck. Zur dynamik bewegter systeme.Annalen der Physik, 331(6):1–34, 1908

    1908

  34. [42]

    Lorentz-transformation der w¨ arme und der temperatur.Zeitschrift f¨ ur Physik, 175:70–104, 1963

    Heinrich Ott. Lorentz-transformation der w¨ arme und der temperatur.Zeitschrift f¨ ur Physik, 175:70–104, 1963

    1963

  35. [43]

    Does a moving body appear cool?Na- ture, 212(5062):571–572, 1966

    PT Landsberg. Does a moving body appear cool?Na- ture, 212(5062):571–572, 1966

    1966

  36. [44]

    Revision of the relativistic dynamics with variable rest mass and application to rel- ativistic thermodynamics.Nuovo Cimento A Serie, 62 (3):722–754, 1969

    G Cavalleri and G Salgarelli. Revision of the relativistic dynamics with variable rest mass and application to rel- ativistic thermodynamics.Nuovo Cimento A Serie, 62 (3):722–754, 1969

    1969

  37. [45]

    Anne-Catherine de la Hamette and Thomas D. Galley. Quantum reference frames for general symmetry groups. Quantum, 4:367, November 2020. ISSN 2521-327X. doi: 10.22331/q-2020-11-30-367. URLhttp://dx.doi.org/ 10.22331/q-2020-11-30-367

    2020 doi

  38. [46]

    Reply to the com- ment on ”quantum priniple of relativity”.arXiv preprint arXiv:2206.15247, 2022

    Andrzej Dragan and Artur Ekert. Reply to the com- ment on ”quantum priniple of relativity”.arXiv preprint arXiv:2206.15247, 2022

    2022 arXiv

  39. [47]

    Comment on ‘quantum principle of relativity’.New Journal of Physics, 25(12):128001, 2023

    Ryszard Horodecki. Comment on ‘quantum principle of relativity’.New Journal of Physics, 25(12):128001, 2023

    2023

  40. [48]

    Covariant quantum field theory of tachyons is unphysical.Physical Review D, 110(11): 115042, 2024

    Krzysztof Jod lowski. Covariant quantum field theory of tachyons is unphysical.Physical Review D, 110(11): 115042, 2024

    2024

  41. [49]

    Comment on ‘quantum principle of relativity’.New Journal of Physics, 24(12):128001, 2023

    Flavio Del Santo and Sebastian Horvat. Comment on ‘quantum principle of relativity’.New Journal of Physics, 24(12):128001, 2023

    2023

  42. [50]

    Comment on ‘quan- tum principle of relativity’.New Journal of Physics, 24 (9):098001, 2022

    Andrzej Grudka and Antoni W´ ojcik. Comment on ‘quan- tum principle of relativity’.New Journal of Physics, 24 (9):098001, 2022

    2022

  43. [51]

    x′ t′ # =   1q 1− V 2 c2 −Vq 1− V 2 c2 −V /c2 q 1− V 2 c2 1q 1− V 2 c2  

    Amrapali Sen and Flavio Del Santo. Superluminal transformations and indeterminism.arXiv preprint arXiv:2601.15263, 2026. APPENDIX The subluminal Lorentz transformation is given by: " x′ t′ # =   1q 1− V 2 c2 −Vq 1− V 2 c2 −V /c2 q 1− V 2 c2 1q 1− V 2 c2   " x t # which c...

    2026 arXiv

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.