Impact of relativity on particle localizability and ground state entanglement

Maria, Papageorgiou,; Pye, Jason

doi:10.1088/1751-8121/ab3593

Cited by 14 publications

(7 citation statements)

References 83 publications

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“…In Here, we shall now also address Kuchař's first criticism (a) on relativistic localization, which is more subtle to resolve. The main reason, as is well-known from the theorems of Perez-Wilde [92] and Malament [93] (see also the discussion in [94,95]), is that there is no relativistically covariant positionoperator-based notion of localization which is compatible with relativistic causality and positivity of energy. This is a key motivation for quantum field theory [90,94]-and here a challenge for specifying what the "right" localization probability for a relativistic particle should be.…”

Section: Relativistic Localization: Addressing Kuchař's Criticismmentioning

confidence: 99%

“…We show that when conditioning on this covariant clock POVM rather than Minkowski time, one obtains a Newton-Wigner type localization probability [90,91]. While a Newton-Wigner type localization is approximate and not fully Lorentz covariant, due to the relativistic localization nogo theorems of Perez-Wilde [92] and Malament [93] (see also [94,95]), it is generally accepted as the best possible localization in relativistic quantum mechanics (In quantum field theory localization is a different matter [90,94]). This demonstrates the advantage of using covariant clock POVMs in relational quantum dynamics [7,44,45,96,97].…”

Section: Introductionmentioning

confidence: 99%

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Equivalence of Approaches to Relational Quantum Dynamics in Relativistic Settings

2021

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We have previously shown that three approaches to relational quantum dynamics—relational Dirac observables, the Page-Wootters formalism and quantum deparametrizations—are equivalent. Here we show that this “trinity” of relational quantum dynamics holds in relativistic settings per frequency superselection sector. Time according to a clock subsystem is defined via a positive operator-valued measure (POVM) that is covariant with respect to the group generated by its (quadratic) Hamiltonian. This differs from the usual choice of a self-adjoint clock observable conjugate to the clock momentum. It also resolves Kuchař's criticism that the Page-Wootters formalism yields incorrect localization probabilities for the relativistic particle when conditioning on a Minkowski time operator. We show that conditioning instead on the covariant clock POVM results in a Newton-Wigner type localization probability commonly used in relativistic quantum mechanics. By establishing the equivalence mentioned above, we also assign a consistent conditional-probability interpretation to relational observables and deparametrizations. Finally, we expand a recent method of changing temporal reference frames, and show how to transform states and observables frequency-sector-wise. We use this method to discuss an indirect clock self-reference effect and explore the state and temporal frame-dependence of the task of comparing and synchronizing different quantum clocks.

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Section: Relativistic Localization: Addressing Kuchař's Criticismmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Equivalence of Approaches to Relational Quantum Dynamics in Relativistic Settings

2021

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“…However, a clear notion of localized particles is required, in our scenario, to ascribe different proper times to the two particles. Defining this notion clearly in quantum field theory has proved a challenge in itself [55][56][57][58][59][60][61][62] due to a range of issues, from relativistic considerations to the measurement problem. Second, the theory is predominantly used to calculate amplitudes for transitions from an initial state defined at t → −∞ to different final states defined at t → +∞.…”

Section: Discussionmentioning

confidence: 99%

The effect of time-dilation on Bell experiments in the retrocausal Brans model

Sen

2020

Proc. R. Soc. A.

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The possibility of using retrocausality to obtain a fundamentally relativistic account of the Bell correlations has gained increasing recognition in recent years. It is not known, however, the extent to which these models can make use of their relativistic properties to account for relativistic effects on entangled systems. We consider here a hypothetical relativistic Bell experiment, where one wing of the experiment is located in a lab on Earth, whereas the other wing is located inside a relativistic rocket, initially grounded adjacent to the lab. The Stern-Gerlach magnets in both the wings are turned on simultaneously as the rocket lifts off into orbit, and turned off when the rocket returns after a certain duration to its original spot. We show that the retrocausal Brans model (Found. Phys, 49(2), 2019) can be easily generalised to analyse this setup, and that it predicts less separation of eigenpackets in the rocket compared to the stationary lab. This causes the particle distribution patterns on the photographic plates to differ between the wings -an experimentally testable prediction of the model. We argue that the description of the experiment and the verification of this prediction using quantum field theory is a challenging task, in contrast to the ease of handling in the retrocausal Brans model. We mention the implications of our hypothetical experiment for hidden variable models in general.

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“…This is an expression of the fact that there are no position operators in relativistic quantum field theory. For a recent detailed investigation of this and related phenomena, see [78]. However, in the nonrelativistic regime, where the rest mass of the UDW detector dominates over the occurring momenta, ω D p,a is approximately constant.…”

Section: Recovering a Prior Model In The First Quantized Nonrelativis...mentioning

confidence: 99%

Second-quantized Unruh-DeWitt detectors and their quantum reference frame transformations

Giacomini,

Kempf

2022

Preprint

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We generalize the Unruh-DeWitt detector model to second quantization. We illustrate this model by applying it to an excited particle in a superposition of relativistic velocities. We calculate, to first order, how its decay depends on whether its superposition of velocities is coherent or incoherent. Further, we generalize the framework of quantum reference frames to allow transformations to the rest frames of second-quantized Unruh DeWitt detectors. As an application, we show how to transform into the rest frame of a decaying particle that, in the laboratory frame, is in a linear superposition of relativistically differing velocities.

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Impact of relativity on particle localizability and ground state entanglement

Cited by 14 publications

References 83 publications

Equivalence of Approaches to Relational Quantum Dynamics in Relativistic Settings

Equivalence of Approaches to Relational Quantum Dynamics in Relativistic Settings

The effect of time-dilation on Bell experiments in the retrocausal Brans model

Second-quantized Unruh-DeWitt detectors and their quantum reference frame transformations

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