Effects of uniform acceleration on quantum states and vacuum entanglement in relativistic quantum information

Krzysztof Lorek

REVIEW 3 major objections 5 minor 94 references

Effects of uniform acceleration on quantum states and vacuum entanglement in relativistic quantum information

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read This thesis argues that a uniformly accelerating particle-decay clock ticks at a rate deviating from the special-relativistic prediction, and that accelerated observers see more vacuum entanglement as their acceleration grows and their…

desk verdict A solid doctoral thesis that repackages peer-reviewed RQI results with a few genuinely new extensions; the ideal-clock claim is the one place where the conclusion visibly outruns the calculation. read the letter →

arxiv 1908.06002 v1 pith:V2HXSRQ7 submitted 2019-08-16 quant-ph

Krzysztof Lorek This is my paper · ORCID

classification quant-ph PACS 03.65.Ud03.67.-a04.62.+v

keywords relativisticquantuminformationUnruheffectclocksGaussianchannelvacuumentanglementharvestinglogarithmicnegativity

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

The thesis argues three things. First, a quantum clock that measures time by the decay of an unstable particle ticks, when uniformly accelerated, at a rate that differs from the special-relativistic prediction, because the Unruh thermal bath surrounding the accelerated clock alters the decay. Second, in a Gaussian-channel description, two uniformly accelerated observers perceive more bipartite entanglement in the Minkowski vacuum as their accelerations increase and as the size and central frequency of their localized modes decrease, and for separated observers the entanglement can suddenly die. Third, three particle detectors in a cavity can harvest genuine tripartite entanglement from the vacuum, more easily than bipartite entanglement, and periodic boundary conditions harvest both kinds more efficiently than Dirichlet ones.

What carries the argument

The load-bearing object is the Gaussian quantum channel defined by (7.20)-(7.21), in which the output covariance matrix is $\sigma^{(d)} = M \sigma^{(f)} M^T + N$. Here $M$ encodes the inevitable mismatch between inertial and accelerated localized modes through Bogolyubov overlaps, and $N$ is the noise matrix obtained by tracing the modes outside the two observers' wavepackets; both are built from the decomposition of the Minkowski vacuum as a product of two-mode squeezed states in Rindler wedges. Modified Rindler coordinates with an independent wedge separation $D$ disentangle the observers' accelerations from their distance. In the cavity part, the same covariance-matrix formalism is run non-perturbatively, with the Unruh-DeWitt interaction written as a quadratic phase-space Hamiltonian, and genuine tripartite entanglement is detected through unitary localization followed by logarithmic negativity across each bipartition.

What would settle it

For the clock claim, measure muon decay rates in storage rings at accelerations where the Unruh temperature approaches the muon rest energy and compare with the special-relativistic prediction; exact agreement would falsify the deviation, while a deviation matching the computed rate would support it. For the boundary-condition claim, a cavity-QED experiment harvesting two- and three-detector entanglement should show earlier and stronger entanglement with periodic walls than with Dirichlet walls.

Watch

Extended reading notes

Core claim

On the paper's own terms, the proper-time rule of special relativity is not the whole story for real clocks. A decay-based clock in uniform acceleration sees a thermal Unruh bath; the bath changes the decay probability and hence the ticking rate, so the discrepancy between stationary and accelerated clocks deviates from the special-relativistic prediction. For fields, the thesis constructs a Gaussian quantum channel that maps any two-mode Gaussian state of inertial localized modes to the state seen by two accelerated observers, and applies it to the vacuum. The observed logarithmic negativity grows with the observers' proper accelerations and falls with mode size and central frequency; for counter-accelerating observers separated by a distance it exhibits oscillations and sudden death, while for co-accelerating observers in the weak-noise regime entanglement is absent. Finally, three harmonic-oscillator detectors coupled briefly to a cavity field become entangled without causal contact; the tripartite entanglement appears earlier and in a wider parameter region than bipartite entanglement, and a periodic cavity outperforms a Dirichlet cavity. If these results hold, the ideal clock is a fiction rather than a physical limit, and the spatial structure of vacuum entanglement is richer and more extractable than previously mapped.

Load-bearing premise

The broad clock conclusion assumes that a single toy model — one uniformly accelerated trajectory, one coupling, first-order perturbation theory in 1+1 dimensions — tells us what any realistic clock would do; if that model is not representative, the ideal-clock-impossibility claim does not follow.

Editorial extensions

If this is right

If the clock result is right, no physical device can serve as an ideal clock at high accelerations, and operational time along arbitrary accelerated trajectories is not identical to proper time.
Gaussian states of two localized field modes, including squeezed and thermal states, become less faithful under acceleration because the mode mismatch $M$ and noise $N$ degrade them; fidelity falls with acceleration.
Accelerated observers can extract more vacuum entanglement by using smaller, lower-frequency modes, and separated counter-accelerating observers lose entanglement abruptly at finite separations.
Genuine tripartite entanglement can be harvested without causal contact, and it is easier to harvest than bipartite entanglement in the same setting.
Periodic boundary conditions are more efficient for harvesting both bipartite and tripartite vacuum entanglement than Dirichlet boundary conditions.

Reading between the lines

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

A concrete next step the thesis does not perform: computing the skew-angle interpolation between antiparallel and parallel observers in 3+1 dimensions would locate the transition where vacuum entanglement switches on.
If the clock deviation were generic, precision clocks at very high accelerations would need trajectory-dependent corrections, making proper time a derived quantity rather than a directly measurable one.
The periodic-boundary advantage suggests that the topology of the cavity, not merely its size, controls how much vacuum entanglement can be harvested; ring or effectively-periodic experiments would be the direct test.
The fermionic negativity is computed only as a lower bound, so the roughly one-order-of-magnitude gap to bosons may be partly an artifact of the bound.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Read this as a compilation thesis rather than a fresh preprint. Most of Parts II–IV are the published PRD/PRA/CQG papers, and the genuinely new material is the D≠0 modified-Rindler channel in 1+1, its 3+1 extension (without D≠0 numerics), and the detailed harvesting maps in Part IV. The thesis does those extensions carefully. The channel derivations are spelled out at a level that lets a determined reader redo them, the a-independence argument is a legitimate change of variables rather than numerology, and the figures match the qualitative claims: more vacuum entanglement at higher acceleration, smaller modes, smaller central frequency, and easier tripartite harvesting under periodic boundary conditions. No code or data files accompany the numerics, but the main qualitative claims also exist in peer-reviewed form, so that omission is a practicality issue, not a correctness charge.

The weak spot is Part II. The calculated deviation for one specific clock—a massless 1+1 cavity mode coupled to a massive external scalar at first order—is internally consistent, and the low-acceleration limit correctly recovers Eq. (6.9). But Sec. 6.5 then reaches the sweeping conclusion that no ideal clock exists and proper time loses operational meaning. The thesis itself admits: “We have not proven that the effect occurs for every accelerated trajectory and for every interaction Hamiltonian.” That is not a minor footnote; it is the load-bearing gap between a toy calculation and the conceptual claim. A referee should ask the authors to either present the Sec. 6.5 statements as a conjecture with the model limitations up front, or add an argument that the relevant features are generic. A second, softer gap: the D≠0 mode decomposition is introduced with an unspecified Φ_III(D), and completeness of the modified Rindler basis is asserted but not proved. Since the channel only uses overlaps in regions I/II, this may be harmless, but an explicit statement is needed.

Who gets value: relativists and quantum-information people tracking vacuum entanglement harvesting, and PhD students looking for a readable tour of the Dragan group’s Gaussian-channel toolkit. It deserves a serious referee, not a desk reject. If I were refereeing, I would return CONDITIONAL, with the clock conclusion and mode-completeness caveats as the revision triggers.

Referee Report

3 major / 5 minor

Summary. This doctoral thesis studies the influence of uniform acceleration on quantum states and quantum vacuum entanglement. Part II analyzes a quantum clock based on the decay of an unstable particle, comparing a stationary and a uniformly accelerating clock, and claims a deviation from the special-relativistic prediction for the difference of their ticking rates, attributed to the Unruh effect. Part III constructs a Gaussian quantum channel that maps two localized inertial modes of a quantum field to two uniformly accelerated localized modes, developed for real scalar fields in 1+1 and 3+1 dimensions and for a Dirac spinor field in 1+1 dimensions, and applies it to the Minkowski vacuum to investigate bipartite vacuum entanglement as a function of observer accelerations, mode size, central frequency, and separation. Part IV studies the extraction of bipartite and tripartite entanglement by three harmonic-oscillator detectors in a cavity, comparing periodic and Dirichlet boundary conditions. The main reported findings are: more perceived vacuum entanglement for stronger accelerations and for smaller mode sizes and central frequencies; sudden death of entanglement for antiparallel accelerated observers at finite separation; absence of vacuum entanglement for observers accelerating in the same direction; and easier extraction of tripartite than bipartite entanglement, with periodic boundary conditions more efficient than Dirichlet.

Significance. If the results hold, the thesis provides a systematic framework for analyzing how uniformly accelerated observers perceive Gaussian states, including a detailed derivation of the channel matrices, a proof of the a-independence of the channel, and new predictions about the structure of vacuum entanglement. The thesis also challenges the universality of the clock postulate at high accelerations. Strengths include thorough analytic derivations, explicit specification of the observer modes, numerical evaluation of the derived integrals without parameter fitting, and non-perturbative Gaussian calculations for entanglement harvesting. The results are largely based on published peer-reviewed papers, which adds credibility. However, the broad claim that ideal clocks are fundamentally impossible and the results for nonzero wedge displacement depend on unproven assumptions, as detailed in the major comments.

major comments (3)

[Sec. 6.5, Eq. (6.17), Abstract] The universal conclusion that 'no clock would correctly measure the proper time along arbitrary high-acceleration trajectories' (Sec. 6.5) and the abstract's implication that the clock postulate fails generically are not supported by the presented calculation. The derivation is restricted to a 1+1-dimensional massless cavity mode linearly coupled to a massive external scalar field, computed in first-order perturbation theory along a uniformly accelerated trajectory, and the thesis itself concedes that 'We have not proven that the effect occurs for every accelerated trajectory and for every interaction Hamiltonian.' The concrete deviation in Eq. (6.17) is a legitimate model prediction, but the extrapolation to a general impossibility of ideal clocks is not. Please reframe the abstract and Sec. 6.5 as demonstrating a model-dependent breakdown of the clock postulate, and present the universal claim as a conjecture or as a conclusion supported by supplementary evidence (e.g., the muon calculation [40]), not as an established result.
[Sec. 7.2, Eq. (7.2); Sec. 7.4.2, Eq. (7.54)] The D≠0 channel is derived using the modified Rindler decomposition (7.2), which for D>0 contains an unspecified operator Φ_III(D) and for D<0 is explicitly overcomplete. The thesis asserts that the form of Φ_III(D) is irrelevant, but it never proves that the extra or overlapping degrees of freedom decouple from the observer modes, nor that the canonical commutation relations assumed for the shifted Rindler modes remain valid when the basis is overcomplete. Since the D≠0 results (sudden death and oscillations, Figs. 7.7–7.8) are central new findings, this is a load-bearing technical gap. Please provide a completeness/decoupling argument, for example by showing that the localized wavepackets ψΛ have vanishing overlap with the Φ_III modes and that the overcompleteness for D<0 does not affect the traced-out channel, or restrict the D≠0 claims to a case in which the basis is complete and well-defined.
[Sec. 9.4, Eq. (9.23), Figs. 9.2–9.3] The fermionic logarithmic negativity is only a lower bound Ẽ_N, as the text correctly notes, but it is subsequently relabelled as the logarithmic negativity and used for quantitative statements, including the claim that fermionic vacuum entanglement is 'lower than for bosons by approximately one order of magnitude.' The lower bound is not proven to be close to the true value, so these quantitative comparisons are unsupported. Please present the fermionic results explicitly as bounds on the negativity, remove or clearly qualify the quantitative comparison with bosons, and state which qualitative trends are robust under the lower-bound approximation.

minor comments (5)

[Sec. 6.4, Eq. (6.18)] The recovery of the ideal-clock limit (6.18) relies on an averaging over the acceleration; please state explicitly that this averaging is an additional smoothing assumption beyond the model, since the unaveraged result in the small-acceleration limit contains superimposed rapid oscillations.
[Sec. 4.2 (title)] Typo: 'Rindler cooridnates' should be 'Rindler coordinates.'
[Sec. 7.6] The 'extra cut-off at zero frequency' used to enforce the no-negative-frequency condition (7.16) is not specified; please provide its precise definition or a reference, so that the procedure is reproducible.
[Sec. 8.5] The 3+1 numerical results are presented only for D=0, although the framework for D≠0 is derived; please state explicitly in the abstract and conclusions that the sudden-death and oscillation phenomena are established only in the 1+1-dimensional scalar-field case.
[Sec. 10.5.1] The statement that tripartite entanglement is 'easier to extract' than bipartite entanglement should be qualified: the comparison is between EN(s|s) and EN(s|ss), and EN(s|ss) ≥ EN(s|s) follows from partial tracing, so the nontrivial content is the existence of regions where the tripartite sector is entangled without pairwise entanglement; consider highlighting this distinction explicitly.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the derivations are reproduced in the thesis and the quantitative results are direct evaluations of derived integrals, not fits or self-referential definitions.

full rationale

The thesis is self-contained with respect to its central derivations. Part II computes the decay probabilities for stationary and uniformly accelerated clocks from a stated Hamiltonian and first-order perturbation theory (Eqs. (6.8), (6.9), (6.16), (6.17)); the comparison is a direct evaluation, and the low-acceleration limit explicitly recovers the stationary formula, so no fitted parameter is renamed as a prediction. Part III derives the Gaussian channel from Bogolyubov coefficients and mode overlaps (Secs. 7.3-7.5); the a-independence is a change of integration variables, not a fit, and the mode choices in Sec. 7.6 are openly stated modelling assumptions rather than parameters tuned to produce the entanglement maps. The tripartite estimator in Sec. 10.4 is admittedly not a proper entanglement measure, and the inequality E_N(s|s) <= E_N(s|ss) is a partial-trace monotonicity; however, the paper's claims about broader regions and earlier emergence rest on the numerical maps that exhibit strict inclusion, so the claim is not merely the inequality itself. The thesis cites the author's own publications ([1]-[5]), but the relevant chapters reproduce the derivations instead of importing them as black boxes, so the self-citations are not load-bearing. The only notable weakness is explicit: Sec. 6.5 admits the ideal-clock conclusion is not proven for every trajectory or interaction Hamiltonian; that is an extrapolation or scope concern, not a circular reduction. Similarly, the unproven completeness of the D != 0 modified-Rindler mode set is a technical assumption, not a circularity. Overall, no step in the claimed derivation chain reduces by construction to its own inputs.

Assumptions & free parameters 5 free parameters · 7 assumptions · 0 invented entities

No new physical entities are postulated. The modified Rindler chart and Phi_III(D) are mathematical constructions, not entities with independent evidence.

free parameters (5)

Mode width L = L = 2 (also 0.1; L perpendicular = 2 in 3+1)
Chosen for numerical plots in Secs. 7.7 and 8.5; qualitative trends are scanned over L, not fitted to data.
Central frequency Omega_0 = Omega_0 approximately 5 (also 5.5)
Chosen for numerical plots; the frequency dependence is scanned, not fitted.
Field mass m = m = 0.1
Chosen for numerical plots in Part III; no data fitting.
Detector coupling lambda = lambda = 0.01
Fixed in Part IV calculations (Sec. 10.5); results are evaluated at this coupling.
UV cutoff n_c = n_c = 50
Number of cavity modes kept; convergence is tested numerically (Sec. 10.5) but no analytic error bound is given.

assumptions (7)

ad hoc to paper The observer wavepackets have no overlap with negative-frequency modes of their rest frames, enforced by an extra zero-frequency cutoff (Sec. 7.6).
Needed to justify Eqs. (7.17)-(7.18) and the purely positive-frequency form of the channel; the cutoff modifies the spatial profile.
ad hoc to paper For D not equal to zero, the modified Rindler expansion (7.2) with the unspecified Phi_III(D) term can be used; the extra or overlapping degrees of freedom do not affect the channel.
Underlies all D not equal to zero numerical results in Sec. 7.7; the explicit form of Phi_III(D) is never given and completeness or overcompleteness is not proven.
domain assumption Accelerated observer modes are exactly localized within their Rindler wedge and orthogonal to the other wedge modes (Sec. 7.2).
Gives the block-diagonal M matrix; real wavepackets have tails, so this is an idealization.
domain assumption A particle-decay clock can be modeled by a single boson in a rigid cavity coupled to a massive external scalar field through the interaction lambda integral Phi_cav Phi_ext, treated in first-order perturbation theory (Sec. 6.2).
Basis for Part II; the thesis states it is a proof of principle and not a quantitative model for any physical particle.
ad hoc to paper The fermionic logarithmic negativity is adequately approximated by the lower bound in Eq. (9.23).
The upper bound is unknown; quantitative fermion results and the boson-fermion comparison rely on assuming the true value is close to the lower bound (Sec. 9.4).
domain assumption Truncating the cavity field to n_c = 50 modes is sufficient for the detector entanglement maps (Sec. 10.5).
Only numerical convergence is tested; no analytic error bound is provided.
domain assumption The geometric mean of bipartite negativities in Eq. (10.18) indicates the presence of genuine tripartite entanglement.
Acknowledged not to be a proper measure; used to conclude that tripartite entanglement is easier to extract (Sec. 10.4).

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Pith. "Pith review of Effects of uniform acceleration on quantum states and vacuum entanglement in relativistic quantum information." pith.science (2026). https://pith.science/paper/V2HXSRQ7

@misc{pith2026190806002,
  author       = {Pith},
  title        = {Pith review of: Effects of uniform acceleration on quantum states and vacuum entanglement in relativistic quantum information},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/V2HXSRQ7}},
  note         = {Machine review of arXiv:1908.06002}
}

read the original abstract

In this thesis we focus on the influence of uniform acceleration on quantum states and their properties, as well as on quantum entanglement contained in the vacuum. First, we analyze a quantum clock measuring time in terms of the decay of an unstable particle. We compare the rate of ticking of a stationary clock to the one of a uniformly accelerating clock. We discover that there exists a deviation from what the discrepancy between those rates is predicted to be by special relativity. In a further part of this thesis we focus on the family of two-mode Gaussian states of two localized modes of a given quantum field. A general framework is developed for investigating the properties of such states, when observed by two uniformly accelerated observers, having access to another pair of localized modes. In particular, we focus on the vacuum state and examine the amount of quantum entanglement perceived by the observers. The framework is developed for three cases: the quantum scalar field in 1+1 and 3+1 dimensions and the Dirac spinor field in 1+1 dimensions. We find that in general more entanglement is seen when the accelerations of the observers increase and when the size of the modes of the observers and their central frequencies decrease. Furthermore, we extend our attention also to tripartite entanglement and investigate its extraction from the quantum vacuum by three particle detectors in a cavity, interacting with a quantum field for a finite time. Detailed maps of amounts of tripartite and bipartite entanglement extracted by the detectors, are produced and compared between two types of boundary conditions. It is found vacuum entanglement is most easily extracted in the case of periodic boundary conditions and it is easier to extract tripartite than bipartite entanglement.

Figures

Figures reproduced from arXiv: 1908.06002 by the authors.

**Figure 3.1.** Four regions of the Rindler coordinate chart, drawn in the xt plane of the Minkowski coordinates. The solid curves are the uniformly accelerated observers’ trajectories (3.9) and the dashed lines are the future and the past event horizon. and II. Furthermore, while information can get inside the region F from any other wedge, once it is inside, it cannot get back outside. Information from region P in turn, can acce… view at source ↗

**Figure 7.1.** The modified Rindler coordinate system with D > 0. servers, having access to modes ψI and ψII respectively. Let us begin with introducing the coordinate system which they are described in. At the time of the observation t = 0, the modes φI and ψI are taken to be localized within the region I of the Rindler coordinates, and φII and ψII are localized within region II. In this section we however generalize slightly wha… view at source ↗

**Figure 7.2.** The modified Rindler coordinate system with D < 0. where + refers to the coordinates covering region I, and − refers to the coordinates covering region II, and D may be positive or negative. We are not interested in this work in coordinates covering region III for D > 0. When the Rindler coordinates are modified, the mode decomposition (4.23) is also altered. For any D let us write: Φ =ˆ Z∞ 0 dΩ wIΩ ˆbIΩ + w ? IΩ … view at source ↗

Figures from the paper (18 more)

**Figure 7.3.** Figure 7.3: The modified Rindler coordinate system with D > 0, whereby the proper accelerations of the observers are in the same direction. The corresponding modified Rindler coordinate transformation, takes the following form: t = χ sinh aη, x = χ cosh aη ± D 2 , (7.3) where + …

**Figure 7.4.** Figure 7.4: Comparison between the spatial profiles of modes φΛ and ψΛ for the following choice of parameters: AΛ = 0.15, L = 2, Ω0 ≈ 5, m = 0.1. region, i.e., Λ ∈ {I,II}. The exact form of the exponential envelope appearing in the definition (7.69) is chosen for later computati…

**Figure 7.5.** Figure 7.5: Logarithmic negativity of the Minkowski vacuum for two counteraccelerated modes, as a function of their proper accelerations for D = 0. We have chosen L = 2, m = 0.1 and Ω0 ≈ 5. These results are not very surprising and find confirmation in the literature on entangl…

**Figure 7.6.** Figure 7.6: Logarithmic negativity of the Minkowski vacuum for two counteraccelerated modes characterized by the same proper acceleration AΛ = 0.1 as a function of L and Ω0. We have chosen D = 0 and m = 0.1. a finite distance D. The results plotted in [PITH_FULL_IMAGE:figures/…

**Figure 7.7.** Figure 7.7: Logarithmic negativity of the Minkowski vacuum for two counteraccelerated modes, for fixed and equal proper accelerations AI = AII = 0.1 as a function of the distance D. We have chosen L = 2, m = 0.1, and Ω0 ≈ 5. In the upper plot we focus on the neighborhood of D =…

**Figure 7.8.** Figure 7.8: Logarithmic negativity of the Minkowski vacuum for two counteraccelerated modes, as a function of proper acceleration AI = AII ≡ AΛ for D = 20 − 2 AΛ such that the separation between modes is fixed and equal to 20. We have chosen L = 2, m = 0.1, and Ω0 ≈ 5. In the u…

**Figure 8.1.** Figure 8.1: Comparison between the spatial profiles of modes φΛ and ψΛ for the following choice of parameters: AΛ = 0.1, L|| = L⊥ = 2, Ω0 ≈ 5, m = 0.1, κ⊥ = 2, along the x axis at y = z = 1. Moreover, in order to make the negative frequency contributions negligible we let Ω0 1 L…

**Figure 8.2.** Figure 8.2: Logarithmic negativity of the Minkowski vacuum for two counteraccelerated modes, as a function of their proper accelerations for D = 0. We have chosen L|| = L⊥ = 2, m = 0.1, Ω0 ≈ 5.5 and κ⊥ = 2. dinate system, and perform the integration over the polar angle analyti…

**Figure 8.3.** Figure 8.3: Logarithmic negativity of the Minkowski vacuum for two counteraccelerated modes, as a function of L|| and Ω0 for D = 0. We have chosen AI = AII = 0.1, L⊥ = 2, m = 0.1, and κ⊥ = 2. been chosen to be equal for both wavepackets. Again, as in the previous chapter, most …

**Figure 8.4.** Figure 8.4: Logarithmic negativity of the Minkowski vacuum for two counteraccelerated modes, as a function of L⊥ and κ⊥ for D = 0. We have chosen AI = AII = 0.1, L|| = 2, m = 0.1, Ω0 ≈ 5.5. 96 [PITH_FULL_IMAGE:figures/full_fig_p096_8_4.png]

**Figure 8.5.** Figure 8.5: Schematic depiction of the skew-accelerating observers’ setup. The modes φI and ψI are rotated around the origin, in the xz plane, by an angle Θ. section provides an outlook at investigating it in more detail. 8.6 Skew-accelerating observers Let us now discuss an out…

**Figure 9.1.** Figure 9.1: Comparison between the real parts of the spatial profiles of modes φ + Λ and ψ + Λ for the following choice of parameters: AΛ = 0.1, L = 2, Ω0 ≈ 5, m = 0.1. with the constant of normalization Nψ. The spatial profiles of the real parts of these modes are compared in …

**Figure 9.2.** Figure 9.2: Logarithmic negativity E˜N of the Minkowski vacuum for two counteraccelerated modes, as a function of their proper accelerations. We have chosen m = 0.1, L = 2 and Ω0 ≈ 5. logarithmic negativity exactly. However, it was shown that a lower bound can be obtained [84, …

**Figure 9.3.** Figure 9.3: Logarithmic negativity E˜N of the Minkowski vacuum for two counteraccelerated modes characterized by the same proper acceleration AΛ = 0.1 as a function of L and Ω0. We have chosen m = 0.1. 106 [PITH_FULL_IMAGE:figures/full_fig_p106_9_3.png]

**Figure 10.1.** Figure 10.1: Entanglements EN (s|s), E˜N (sss) in the system subject to periodic boundary conditions, as a function of T and Ωd at L = 10 and λ = 0.01; On the right: regions of existence of EN (s|s) and E˜N (sss) plotted together. d d d EN (s|s) E˜N (sss) [PITH_FULL_IMAGE:figur…

**Figure 10.2.** Figure 10.2: Entanglements EN (s|s), E˜N (sss) in the system subject to periodic boundary conditions, as a function of L and Ωd at T = 0.4r and λ = 0.01; On the right: regions of existence of EN (s|s) and E˜N (sss) plotted together. 119 [PITH_FULL_IMAGE:figures/full_fig_p119_10…

**Figure 10.3.** Figure 10.3: Entanglements EN (m|s), EN (s|s) and EN (m|ss) in the system subject to Dirichlet boundary conditions, as a function of T and Ωd at L = 10 and λ = 0.01; Bottom right: regions of existence of EN (m|s) and EN (m|ss) plotted together. 121 [PITH_FULL_IMAGE:figures/full…

**Figure 10.4.** Figure 10.4: A comparison, between the cases of periodic and Dirichlet boundary conditions, of the regions in which bipartite entanglement is harvested between neighboring detectors. Here L = 10 and λ = 0.01. which is more broadly available, persists in the spacelike regime down…

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Reference graph

Works this paper leans on

94 extracted references · 43 canonical work pages

[40]

Can a charged decaying particle serve as an ideal clock in the presence of the magnetic field?

author author R. Pierini , author K. Turzynski , \ and\ author A. Dragan ,\ https://arxiv.org/abs/1708.00327 journal journal arXiv:1708.00327 [quant-ph] \ ( year 2017 ) NoStop

work page Pith review arXiv 2017
[1]

Lorek , author D

author author K. Lorek , author D. Pecak , author E. G. \ Brown , \ and\ author A. Dragan ,\ 10.1103/PhysRevA.90.032316 journal journal Phys. Rev. A \ volume 90 ,\ pages 032316 ( year 2014 ) NoStop

work page doi:10.1103/physreva.90.032316 2014
[2]

Lorek , author J

author author K. Lorek , author J. Louko , \ and\ author A. Dragan ,\ http://stacks.iop.org/0264-9381/32/i=17/a=175003 journal journal Class. Quantum Grav. \ volume 32 ,\ pages 175003 ( year 2015 ) NoStop

2015
[3]

Ahmadi , author K

author author M. Ahmadi , author K. Lorek , author A. Ch e e ci n \' n ska , author A. R. H. \ Smith , author R. B. \ Mann , \ and\ author A. Dragan ,\ 10.1103/PhysRevD.93.124031 journal journal Phys. Rev. D \ volume 93 ,\ pages 124031 ( year 2016 ) NoStop

work page doi:10.1103/physrevd.93.124031
[4]

Richter , author K

author author B. Richter , author K. Lorek , author A. Dragan , \ and\ author Y. Omar ,\ 10.1103/PhysRevD.95.076004 journal journal Phys. Rev. D \ volume 95 ,\ pages 076004 ( year 2017 ) NoStop

work page doi:10.1103/physrevd.95.076004 2017
[5]

Lorek , author P

author author K. Lorek , author P. Grochowski , author M. Ahmadi , \ and\ author A. Dragan ,\ @noop \ ( year in preparation ) NoStop
[6]

Planck ,\ 10.1002/andp.19013090310 journal journal Annalen Phys

author author M. Planck ,\ 10.1002/andp.19013090310 journal journal Annalen Phys. \ volume 309 ,\ pages 553 ( year 1901 ) NoStop

doi:10.1002/andp.19013090310 1901
[7]

Einstein ,\ 10.1002/andp.19053220607 journal journal Annalen Phys

author author A. Einstein ,\ 10.1002/andp.19053220607 journal journal Annalen Phys. \ volume 322 ,\ pages 132 ( year 1905 a ) NoStop

doi:10.1002/andp.19053220607 1905

Show all 94 references

[8]

Dirac ,\ @noop title The Principles of Quantum Mechanics ,\ International series of monographs on physics\ ( publisher Clarendon Press ,\ year 1981 ) NoStop

author author P. Dirac ,\ @noop title The Principles of Quantum Mechanics ,\ International series of monographs on physics\ ( publisher Clarendon Press ,\ year 1981 ) NoStop

1981
[9]

Shankar ,\ @noop title Principles of quantum mechanics \ ( publisher Plenum ,\ address New York, NY ,\ year 1980 ) NoStop

author author R. Shankar ,\ @noop title Principles of quantum mechanics \ ( publisher Plenum ,\ address New York, NY ,\ year 1980 ) NoStop

1980
[10]

Einstein ,\ 10.1002/andp.19053221004 journal journal Annalen Phys

author author A. Einstein ,\ 10.1002/andp.19053221004 journal journal Annalen Phys. \ volume 322 ,\ pages 891 ( year 1905 b ) NoStop

1905 doi
[11]

Einstein ,\ 10.1002/andp.19163540702 journal journal Annalen Phys

author author A. Einstein ,\ 10.1002/andp.19163540702 journal journal Annalen Phys. \ volume 354 ,\ pages 769 ( year 1916 ) NoStop

1916 doi
[12]

Klein ,\ 10.1007/BF01397481 journal journal Z

author author O. Klein ,\ 10.1007/BF01397481 journal journal Z. Phys. \ volume 37 ,\ pages 895 ( year 1926 ) NoStop

1926 doi
[13]

Gordon ,\ 10.1007/BF01390840 journal journal Z

author author W. Gordon ,\ 10.1007/BF01390840 journal journal Z. Phys. \ volume 40 ,\ pages 117 ( year 1926 ) NoStop

1926 doi
[14]

author author P. A. M. \ Dirac ,\ 10.1098/rspa.1928.0023 journal journal Proc. Royal Soc. A \ volume 117 ,\ pages 610 ( year 1928 ) NoStop

1928
[15]

author author P. A. M. \ Dirac ,\ 10.1098/rspa.1930.0013 journal journal Proc. Royal Soc. A \ volume 126 ,\ pages 360 ( year 1930 ) NoStop

1930
[16]

author author M. E. \ Peskin \ and\ author D. V. \ Schroeder ,\ @noop title An Introduction to Quantum Field Theory \ ( publisher Addison-Wesley ,\ address Reading, USA ,\ year 1995 ) NoStop

1995
[17]

author author S. L. \ Glashow ,\ http://dx.doi.org/10.1016/0029-5582(61)90469-2 journal journal Nucl. Phys. \ volume 22 ,\ pages 579 ( year 1961 ) NoStop

1961 doi
[18]

Weinberg ,\ 10.1103/PhysRevLett.19.1264 journal journal Phys

author author S. Weinberg ,\ 10.1103/PhysRevLett.19.1264 journal journal Phys. Rev. Lett. \ volume 19 ,\ pages 1264 ( year 1967 ) NoStop

1967 doi
[19]

Salam ,\ booktitle booktitle 8th Nobel Symposium Lerum, Sweden, May 19-25, 1968 ,\ @noop journal journal Conf

author author A. Salam ,\ booktitle booktitle 8th Nobel Symposium Lerum, Sweden, May 19-25, 1968 ,\ @noop journal journal Conf. Proc. \ volume C680519 ,\ pages 367 ( year 1968 ) NoStop

1968
[20]

Englert \ and\ author R

author author F. Englert \ and\ author R. Brout ,\ 10.1103/PhysRevLett.13.321 journal journal Phys. Rev. Lett. \ volume 13 ,\ pages 321 ( year 1964 ) NoStop

1964 doi
[21]

author author P. W. \ Higgs ,\ 10.1103/PhysRevLett.13.508 journal journal Phys. Rev. Lett. \ volume 13 ,\ pages 508 ( year 1964 ) NoStop

1964 doi
[22]

author author G. S. \ Guralnik , author C. R. \ Hagen , \ and\ author T. W. B. \ Kibble ,\ 10.1103/PhysRevLett.13.585 journal journal Phys. Rev. Lett. \ volume 13 ,\ pages 585 ( year 1964 ) NoStop

1964 doi
[23]

author author N. D. \ Birrell \ and\ author P. C. W. \ Davies ,\ in\ @noop booktitle Quantum Fields in Curved Space ,\ series and number Cambridge Monographs on Mathematical Physics \ ( publisher Cambridge University Press ,\ year 1982 ) NoStop

1982
[24]

author author S. W. \ Hawking ,\ 10.1007/BF02345020 journal journal Commun. Math. Phys. \ volume 43 ,\ pages 199 ( year 1975 ) NoStop

1975 doi
[25]

author author W. G. \ Unruh ,\ 10.1103/PhysRevD.14.870 journal journal Phys. Rev. D \ volume 14 ,\ pages 870 ( year 1976 ) NoStop

1976 doi
[26]

author author S. A. \ Fulling \ and\ author P. C. W. \ Davies ,\ 10.1098/rspa.1976.0045 journal journal Proc. Royal Soc. A \ volume 348 ,\ pages 393 ( year 1976 ) NoStop

1976
[27]

Alber , author T

author author G. Alber , author T. Beth , author M. Horodecki , author P. Horodecki , author R. Horodecki , author M. R \"o tteler , author H. Weinfurter , author R. Werner , \ and\ author A. Zeilinger ,\ @noop title Quantum Information: An Introduction to Basic Theoretical Co...

2003
[28]

author author M. A. \ Nielsen \ and\ author I. L. \ Chuang ,\ @noop title Quantum Computation and Quantum Information: 10th Anniversary Edition \ ( publisher Cambridge University Press ,\ address New York, NY, USA ,\ year 2011 ) NoStop

2011
[29]

Martín-Martínez \ and\ author N

author author E. Martín-Martínez \ and\ author N. C. \ Menicucci ,\ http://stacks.iop.org/0264-9381/29/i=22/a=224003 journal journal Class. Quantum Grav. \ volume 29 ,\ pages 224003 ( year 2012 ) NoStop

2012
[30]

Reznik ,\ @noop journal journal Found

author author B. Reznik ,\ @noop journal journal Found. Phys. \ volume 33 ,\ pages 167 ( year 2003 ) NoStop

2003
[31]

Reznik , author A

author author B. Reznik , author A. Retzker , \ and\ author J. Silman ,\ 10.1103/PhysRevA.71.042104 journal journal Phys. Rev. A \ volume 71 ,\ pages 042104 ( year 2005 ) NoStop

2005 doi
[32]

Ch e e ci n \' n ska , author K

author author A. Ch e e ci n \' n ska , author K. Lorek , \ and\ author A. Dragan ,\ 10.1103/PhysRevA.95.013817 journal journal Phys. Rev. A \ volume 95 ,\ pages 013817 ( year 2017 ) NoStop

2017 doi
[33]

Ahmadi , author D

author author M. Ahmadi , author D. E. \ Bruschi , author C. Sabín , author G. Adesso , \ and\ author I. Fuentes ,\ 10.1038/srep04996 journal journal Sci. Rep. \ volume 4 ,\ pages 4996 ( year 2014 ) NoStop

2014 doi
[34]

author author D. E. \ Bruschi , author A. Dragan , author A. R. \ Lee , author I. Fuentes , \ and\ author J. Louko ,\ 10.1103/PhysRevLett.111.090504 journal journal Phys. Rev. Lett. \ volume 111 ,\ pages 090504 ( year 2013 ) NoStop

2013 doi
[35]

author author V. V. \ Nesvizhevsky , author H. G. \ Borner , author A. K. \ Petukhov , author H. Abele , author S. Baeszler , author F. J. \ Ruesz , author T. Stoferle , author A. Westphal , author A. M. \ Gagarski , author G. A. \ Petrov , \ and\ author A. V. \ Strelkov ,\ 10...

doi
[36]

author author C. M. \ Wilson , author G. Johansson , author A. Pourkabirian , author M. Simoen , author J. R. \ Johansson , author T. Duty , author F. Nori , \ and\ author P. Delsing ,\ 10.1038/nature10561 journal journal Nature \ volume 479 ,\ pages 376 ( year 2011 ) NoStop

doi
[37]

Steinhauer ,\ http://dx.doi.org/10.1038/nphys3104 journal journal Nature \ volume 10 ,\ pages 864 ( year 2014 ) NoStop

author author J. Steinhauer ,\ http://dx.doi.org/10.1038/nphys3104 journal journal Nature \ volume 10 ,\ pages 864 ( year 2014 ) NoStop

2014 doi
[38]

Steinhauer ,\ http://dx.doi.org/10.1038/nphys3863 journal journal Nature \ volume 12 ,\ pages 959 ( year 2016 ) NoStop

author author J. Steinhauer ,\ http://dx.doi.org/10.1038/nphys3863 journal journal Nature \ volume 12 ,\ pages 959 ( year 2016 ) NoStop

2016 doi
[39]

Lindkvist , author C

author author J. Lindkvist , author C. Sab\' n , author I. Fuentes , author A. Dragan , author I.-M. \ Svensson , author P. Delsing , \ and\ author G. Johansson ,\ 10.1103/PhysRevA.90.052113 journal journal Phys. Rev. A \ volume 90 ,\ pages 052113 ( year 2014 ) NoStop

doi
[41]

Dragan , author J

author author A. Dragan , author J. Doukas , \ and\ author E. Mart\' n-Mart\' nez ,\ 10.1103/PhysRevA.87.052326 journal journal Phys. Rev. A \ volume 87 ,\ pages 052326 ( year 2013 ) NoStop

2013 doi
[42]

author author R. F. \ Werner ,\ 10.1103/PhysRevA.40.4277 journal journal Phys. Rev. A \ volume 40 ,\ pages 4277 ( year 1989 ) NoStop

1989 doi
[43]

Peres ,\ 10.1103/PhysRevLett.77.1413 journal journal Phys

author author A. Peres ,\ 10.1103/PhysRevLett.77.1413 journal journal Phys. Rev. Lett. \ volume 77 ,\ pages 1413 ( year 1996 ) NoStop

1996 doi
[44]

Horodecki , author P

author author M. Horodecki , author P. Horodecki , \ and\ author R. Horodecki ,\ http://dx.doi.org/10.1016/S0375-9601(96)00706-2 journal journal Phys. Lett. A \ volume 223 ,\ pages 1 ( year 1996 ) NoStop

1996 doi
[45]

Horodecki , author P

author author R. Horodecki , author P. Horodecki , author M. Horodecki , \ and\ author K. Horodecki ,\ 10.1103/RevModPhys.81.865 journal journal Rev. Mod. Phys. \ volume 81 ,\ pages 865 ( year 2009 ) NoStop

2009 doi
[46]

Horodecki , author P

author author M. Horodecki , author P. Horodecki , \ and\ author R. Horodecki ,\ 10.1103/PhysRevLett.80.5239 journal journal Phys. Rev. Lett. \ volume 80 ,\ pages 5239 ( year 1998 ) NoStop

1998 doi
[47]

author author D. M. \ Greenberger , author M. A. \ Horne , \ and\ author A. Zeilinger ,\ @noop title ``Going Beyond Bell's Theorem'' in ``Bell's Theorem, Quantum Theory, and Conceptions of the Universe'' ,\ edited by\ editor M. Kafatos NoStop
[48]

D\"ur , author G

author author W. D\"ur , author G. Vidal , \ and\ author J. I. \ Cirac ,\ 10.1103/PhysRevA.62.062314 journal journal Phys. Rev. A \ volume 62 ,\ pages 062314 ( year 2000 ) NoStop

doi
[49]

Vidal \ and\ author R

author author G. Vidal \ and\ author R. F. \ Werner ,\ 10.1103/PhysRevA.65.032314 journal journal Phys. Rev. A \ volume 65 ,\ pages 032314 ( year 2002 ) NoStop

2002 doi
[50]

author author M. B. \ Plenio ,\ 10.1103/PhysRevLett.95.090503 journal journal Phys. Rev. Lett. \ volume 95 ,\ pages 090503 ( year 2005 ) NoStop

2005 doi
[51]

author author B. L. \ Schumaker ,\ 10.1016/0370-1573(86)90179-1 journal journal Phys. Rep. \ volume 135 ,\ pages 317 ( year 1986 ) NoStop

1986 doi
[52]

author author N. C. \ Menicucci , author S. T. \ Flammia , \ and\ author P. van Loock ,\ 10.1103/PhysRevA.83.042335 journal journal Phys. Rev. A \ volume 83 ,\ pages 042335 ( year 2011 ) NoStop

2011 doi
[53]

author author E. G. \ Brown , author E. Mart\' n-Mart\' nez , author N. C. \ Menicucci , \ and\ author R. B. \ Mann ,\ 10.1103/PhysRevD.87.084062 journal journal Phys. Rev. D \ volume 87 ,\ pages 084062 ( year 2013 ) NoStop

2013 doi
[54]

author author A. S. \ Holevo \ and\ author R. F. \ Werner ,\ 10.1103/PhysRevA.63.032312 journal journal Phys. Rev. A \ volume 63 ,\ pages 032312 ( year 2001 ) NoStop

2001 doi
[55]

Adesso , author A

author author G. Adesso , author A. Serafini , \ and\ author F. Illuminati ,\ 10.1103/PhysRevA.70.022318 journal journal Phys. Rev. A \ volume 70 ,\ pages 022318 ( year 2004 a ) NoStop

2004 doi
[56]

author author J. B. \ Hartle ,\ @noop title Gravity: An Introduction to Einstein’s General Relativity \ ( publisher Addison Wesley ,\ year 2003 ) NoStop

2003
[57]

Rindler ,\ 10.1119/1.1972547 journal journal Am

author author W. Rindler ,\ 10.1119/1.1972547 journal journal Am. J. Phys. \ volume 34 ,\ pages 1174 ( year 1966 ) NoStop

1966 doi
[58]

Rindler ,\ @noop title Relativity: Special, General, and Cosmological ,\ Relativity: Special, General, and Cosmological\ ( publisher Oxford University Press ,\ year 2001 ) NoStop

author author W. Rindler ,\ @noop title Relativity: Special, General, and Cosmological ,\ Relativity: Special, General, and Cosmological\ ( publisher Oxford University Press ,\ year 2001 ) NoStop

2001
[59]

Takagi ,\ 10.1143/PTP.88.1 journal journal Prog

author author S. Takagi ,\ 10.1143/PTP.88.1 journal journal Prog. Theor. Phys. Suppl. \ volume 88 ,\ pages 1 ( year 1986 ) NoStop

1986 doi
[60]

author author L. C. B. \ Crispino , author A. Higuchi , \ and\ author G. E. A. \ Matsas ,\ 10.1103/RevModPhys.80.787 journal journal Rev. Mod. Phys. \ volume 80 ,\ pages 787 ( year 2008 ) NoStop

2008 doi
[61]

DLMF ,\ http://dlmf.nist.gov/ title NIST Digital Library of Mathematical Functions , \ howpublished http://dlmf.nist.gov/, Release 1.0.9 of 2014-08-29 NoStop

2014
[62]

Passian , author H

author author A. Passian , author H. Simpson , author S. Kouchekian , \ and\ author S. Yakubovich ,\ http://dx.doi.org/10.1016/j.jmaa.2009.06.067 journal journal J. Math. Anal. Appl. \ volume 360 ,\ pages 380 ( year 2009 ) NoStop

2009 doi
[63]

Dragan , author I

author author A. Dragan , author I. Fuentes , \ and\ author J. Louko ,\ 10.1103/PhysRevD.83.085020 journal journal Phys. Rev. D \ volume 83 ,\ pages 085020 ( year 2011 ) NoStop

2011 doi
[64]

author author T. M. \ Dunster ,\ 10.1137/0521055 journal journal SIAM J. Math. Anal. \ volume 21 ,\ pages 995 ( year 1990 ) NoStop

1990 doi
[65]

author author R. C. \ Tolman ,\ 10.1103/PhysRev.35.904 journal journal Phys. Rev. \ volume 35 ,\ pages 904 ( year 1930 ) NoStop

1930 doi
[66]

Tolman \ and\ author P

author author R. Tolman \ and\ author P. Ehrenfest ,\ 10.1103/PhysRev.36.1791 journal journal Phys. Rev. \ volume 36 ,\ pages 1791 ( year 1930 ) NoStop

1930 doi
[67]

Retzker , author J

author author A. Retzker , author J. I. \ Cirac , author M. B. \ Plenio , \ and\ author B. Reznik ,\ 10.1103/PhysRevLett.101.110402 journal journal Phys. Rev. Lett. \ volume 101 ,\ pages 110402 ( year 2008 ) NoStop

2008 doi
[68]

Radd \ and\ author D

author author N. Radd \ and\ author D. Singleton ,\ https://doi.org/10.1140/epjd/e2012-30387-6 journal journal Eur. Phys. J. D \ volume 66 ,\ pages 258 ( year 2012 ) NoStop

2012 doi
[69]

Cozzella , author A

author author G. Cozzella , author A. G. S. \ Landulfo , author G. E. A. \ Matsas , \ and\ author D. A. T. \ Vanzella ,\ 10.1103/PhysRevLett.118.161102 journal journal Phys. Rev. Lett. \ volume 118 ,\ pages 161102 ( year 2017 ) NoStop

doi
[70]

Gerry \ and\ author P

author author C. Gerry \ and\ author P. Knight ,\ @noop title Introductory Quantum Optics \ ( publisher Cambridge University Press ,\ year 2005 )\ pp.\ pages 176--178 NoStop

2005
[71]

M\"uller ,\ 10.1103/PhysRevD.56.953 journal journal Phys

author author R. M\"uller ,\ 10.1103/PhysRevD.56.953 journal journal Phys. Rev. D \ volume 56 ,\ pages 953 ( year 1997 ) NoStop

1997 doi
[72]

Bailey , author K

author author J. Bailey , author K. Borer , author F. Combley , author H. Drumm , author F. Krienen , author F. Lange , author E. Picasso , author W. von Ruden , author F. J. M. \ Farley , author J. H. \ Field , author W. Flegel , \ and\ author P. M. \ Hattersley ,\ 10.1038/26...

doi
[73]

Bailey , author K

author author J. Bailey , author K. Borer , author F. Combley , author H. Drumm , author C. Eck , author F. Farley , author J. Field , author W. Flegel , author P. Hattersley , author F. Krienen , author F. Lange , author G. Lebée , author E. McMillan , author G. Petrucci , au...

doi
[74]

author author S. R. \ Mainwaring \ and\ author G. E. \ Stedman ,\ 10.1103/PhysRevA.47.3611 journal journal Phys. Rev. A \ volume 47 ,\ pages 3611 ( year 1993 ) NoStop

1993 doi
[75]

ansch , author G. Huber , author S. Karpuk , author A. Krieger , author T. K\

author author B. Botermann , author D. Bing , author C. Geppert , author G. Gwinner , author T. W. \ H\"ansch , author G. Huber , author S. Karpuk , author A. Krieger , author T. K\"uhl , author W. N\"ortersh\"auser , author C. Novotny , author S. Reinhardt , author R. S\'anch...

doi
[76]

author author B. L. \ Hu , author S.-Y. \ Lin , \ and\ author J. Louko ,\ http://stacks.iop.org/0264-9381/29/i=22/a=224005 journal journal Class. Quantum Grav. \ volume 29 ,\ pages 224005 ( year 2012 ) NoStop

2012
[77]

author author B. S. \ DeWitt ,\ http://adsabs.harvard.edu/abs/2010grae.book.....H title General Relativity: an Einstein Centenary Survey ,\ edited by\ editor S. Hawking \ and\ editor W. Israel \ ( publisher Cambridge University Press ,\ year 1979 ) NoStop

1979
[78]

Dragan , author J

author author A. Dragan , author J. Doukas , author E. Martín-Martínez , \ and\ author D. E. \ Bruschi ,\ http://stacks.iop.org/0264-9381/30/i=23/a=235006 journal journal Class. Quantum Grav. \ volume 30 ,\ pages 235006 ( year 2013 ) NoStop

2013
[79]

D e bski \ and\ author A

author author K. D e bski \ and\ author A. Dragan ,\ @noop \ ( year in preparation ) NoStop
[80]

Salton , author R

author author G. Salton , author R. B. \ Mann , \ and\ author N. C. \ Menicucci ,\ http://stacks.iop.org/1367-2630/17/i=3/a=035001 journal journal New J. Phys. \ volume 17 ,\ pages 035001 ( year 2015 ) NoStop

2015
[81]

Doukas , author E

author author J. Doukas , author E. G. \ Brown , author A. Dragan , \ and\ author R. B. \ Mann ,\ 10.1103/PhysRevA.87.012306 journal journal Phys. Rev. A \ volume 87 ,\ pages 012306 ( year 2013 ) NoStop

2013 doi
[82]

author author P. M. \ Alsing , author I. Fuentes-Schuller , author R. B. \ Mann , \ and\ author T. E. \ Tessier ,\ 10.1103/PhysRevA.74.032326 journal journal Phys. Rev. A \ volume 74 ,\ pages 032326 ( year 2006 ) NoStop

2006 doi
[83]

Friis , author A

author author N. Friis , author A. R. \ Lee , \ and\ author J. Louko ,\ 10.1103/PhysRevD.88.064028 journal journal Phys. Rev. D \ volume 88 ,\ pages 064028 ( year 2013 ) NoStop

2013 doi
[84]

Eisler \ and\ author Z

author author V. Eisler \ and\ author Z. Zimborás ,\ http://stacks.iop.org/1367-2630/17/i=5/a=053048 journal journal New J. Phys. \ volume 17 ,\ pages 053048 ( year 2015 ) NoStop

2015
[85]

Eisert , author V

author author J. Eisert , author V. Eisler , \ and\ author Z. Zimborás ,\ https://arxiv.org/abs/1611.08007 journal journal arXiv:1611.08007 [quant-ph] \ ( year 2016 ) NoStop

2016 arXiv
[86]

Rajchel \ and\ author A

author author G. Rajchel \ and\ author A. Dragan ,\ @noop \ ( year in preparation ) NoStop
[87]

author author P. T. \ Grochowski , author G. Rajchel , author F. Kia ka , \ and\ author A. Dragan ,\ 10.1103/PhysRevD.95.105005 journal journal Phys. Rev. D \ volume 95 ,\ pages 105005 ( year 2017 ) NoStop

2017 doi
[88]

Dragan \ and\ author I

author author A. Dragan \ and\ author I. Fuentes ,\ https://arxiv.org/abs/1105.1192 journal journal arXiv:1105.1192 [quant-ph] \ ( year 2011 ) NoStop

2011 arXiv
[89]

Mart\' n-Mart\' nez , author E

author author E. Mart\' n-Mart\' nez , author E. G. \ Brown , author W. Donnelly , \ and\ author A. Kempf ,\ 10.1103/PhysRevA.88.052310 journal journal Phys. Rev. A \ volume 88 ,\ pages 052310 ( year 2013 ) NoStop

2013 doi
[90]

Adesso , author A

author author G. Adesso , author A. Serafini , \ and\ author F. Illuminati ,\ 10.1103/PhysRevLett.93.220504 journal journal Phys. Rev. Lett. \ volume 93 ,\ pages 220504 ( year 2004 b ) NoStop

2004 doi
[91]

Serafini , author G

author author A. Serafini , author G. Adesso , \ and\ author F. Illuminati ,\ 10.1103/PhysRevA.71.032349 journal journal Phys. Rev. A \ volume 71 ,\ pages 032349 ( year 2005 ) NoStop

2005 doi
[92]

Adesso \ and\ author F

author author G. Adesso \ and\ author F. Illuminati ,\ http://stacks.iop.org/1751-8121/40/i=28/a=S01 journal journal J. Phys. A \ volume 40 ,\ pages 7821 ( year 2007 ) NoStop

2007
[93]

author author D. E. \ Bruschi , author T. C. \ Ralph , author I. Fuentes , author T. Jennewein , \ and\ author M. Razavi ,\ 10.1103/PhysRevD.90.045041 journal journal Phys. Rev. D \ volume 90 ,\ pages 045041 ( year 2014 ) NoStop

2014 doi
[94]

Castelvecchi ,\ https://doi.org/10.1038/nature.2017.22142 journal journal Nature, 10.1038/nature.2017.22142 \ ( year 2017 ) NoStop

author author D. Castelvecchi ,\ https://doi.org/10.1038/nature.2017.22142 journal journal Nature, 10.1038/nature.2017.22142 \ ( year 2017 ) NoStop

2017

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [40]

Can a charged decaying particle serve as an ideal clock in the presence of the magnetic field?

author author R. Pierini , author K. Turzynski , \ and\ author A. Dragan ,\ https://arxiv.org/abs/1708.00327 journal journal arXiv:1708.00327 [quant-ph] \ ( year 2017 ) NoStop

work page Pith review arXiv 2017

[2] [1]

Lorek , author D

author author K. Lorek , author D. Pecak , author E. G. \ Brown , \ and\ author A. Dragan ,\ 10.1103/PhysRevA.90.032316 journal journal Phys. Rev. A \ volume 90 ,\ pages 032316 ( year 2014 ) NoStop

work page doi:10.1103/physreva.90.032316 2014

[3] [2]

Lorek , author J

author author K. Lorek , author J. Louko , \ and\ author A. Dragan ,\ http://stacks.iop.org/0264-9381/32/i=17/a=175003 journal journal Class. Quantum Grav. \ volume 32 ,\ pages 175003 ( year 2015 ) NoStop

2015

[4] [3]

Ahmadi , author K

author author M. Ahmadi , author K. Lorek , author A. Ch e e ci n \' n ska , author A. R. H. \ Smith , author R. B. \ Mann , \ and\ author A. Dragan ,\ 10.1103/PhysRevD.93.124031 journal journal Phys. Rev. D \ volume 93 ,\ pages 124031 ( year 2016 ) NoStop

work page doi:10.1103/physrevd.93.124031

[5] [4]

Richter , author K

author author B. Richter , author K. Lorek , author A. Dragan , \ and\ author Y. Omar ,\ 10.1103/PhysRevD.95.076004 journal journal Phys. Rev. D \ volume 95 ,\ pages 076004 ( year 2017 ) NoStop

work page doi:10.1103/physrevd.95.076004 2017

[6] [5]

Lorek , author P

author author K. Lorek , author P. Grochowski , author M. Ahmadi , \ and\ author A. Dragan ,\ @noop \ ( year in preparation ) NoStop

[7] [6]

Planck ,\ 10.1002/andp.19013090310 journal journal Annalen Phys

author author M. Planck ,\ 10.1002/andp.19013090310 journal journal Annalen Phys. \ volume 309 ,\ pages 553 ( year 1901 ) NoStop

doi:10.1002/andp.19013090310 1901

[8] [7]

Einstein ,\ 10.1002/andp.19053220607 journal journal Annalen Phys

author author A. Einstein ,\ 10.1002/andp.19053220607 journal journal Annalen Phys. \ volume 322 ,\ pages 132 ( year 1905 a ) NoStop

doi:10.1002/andp.19053220607 1905