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arXiv:1702.06670

Comment on "Quantum mechanics for non-inertial observers"

Igor Pikovski, Magdalena Zych, Fabio Costa, Časlav Brukner

Published Feb 22, 2017• 2 citations
arXivHTMLPDF

Abstract

In a recent paper (arXiv:1701.04298 [quant-ph]) Toroš, Großardt and Bassi claim that the potential necessary to support a composite particle in a gravitational field must necessarily cancel the relativistic coupling between internal and external degrees of freedom. As such a coupling is responsible for the gravitational redshift measured in numerous experiments, the above statement is clearly incorrect. We identify the simple mistake in the paper responsible for the incorrect claim.

DOI
10.48550/arxiv.1702.06670

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Reply to Comment on "Quantum mechanics for non-inertial observers"

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Our recent paper (arXiv:1701.04298 [quant-ph]) discussed the occurrence of a coupling of centre of mass and internal degrees of freedom for complex quantum systems in non-inertial frames. There, we pointed out that an external force supporting the system against gravity plays a crucial role for the coupling between center of mass position to the internal degrees of freedom. In a comment (arXiv:1702.06670 [quant-ph]) to our paper, Pikovski et al. question our conclusion and present the argument that the lack of the coupling term would be in contradiction with the observation of gravitational time dilation using atomic clocks. Here, we elaborate on our results in reply to their criticism and clarify why our arguments remain valid.

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The fact that gravitational environments cannot be shielded (since gravity is universal) makes them of great theoretical interest to decoherence mechanisms and to the quantum-to-classical transition. While past results seemed to indicate that graviton-induced decoherence of spatial superpositions happens only for macroscopic systems, recently it was shown that this mechanism can be enhanced through the system's own dynamical internal structure. In this work, we extend this analysis by including the interaction with a classical Newtonian potential. We show that, although the graviton bath alone dominates the mechanism for short times compared to a timescale established by the size of the quantum spatial superposition, the interaction between the gravitons and the internal degrees of freedom of the system renders decoherence inevitable in the long-time limit, even for microscopic masses. We also show that this mechanism is slightly slowed down by the interplay with the classical Newtonian potential, which, for systems without dynamical internal degrees of freedom, can even lead to recoherence-like behaviour, at least in principle.

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In a recent paper (arXiv:1701.04298 [quant-ph]) Toroš, Großardt and Bassi claim that the potential necessary to support a composite particle in a gravitational field must necessarily cancel the relativistic coupling between internal and external degrees of freedom. As such a coupling is responsible for the gravitational redshift measured in numerous experiments, the above statement is clearly incorrect. We identify the simple mistake in the paper responsible for the incorrect claim.
Our recent paper (arXiv:1701.04298 [quant-ph]) discussed the occurrence of a coupling of centre of mass and internal degrees of freedom for complex quantum systems in non-inertial frames. There, we pointed out that an external force supporting the system against gravity plays a crucial role for the coupling between center of mass position to the internal degrees of freedom. In a comment (arXiv:1702.06670 [quant-ph]) to our paper, Pikovski et al. question our conclusion and present the argument that the lack of the coupling term would be in contradiction with the observation of gravitational time dilation using atomic clocks. Here, we elaborate on our results in reply to their criticism and clarify why our arguments remain valid.
The fact that gravitational environments cannot be shielded (since gravity is universal) makes them of great theoretical interest to decoherence mechanisms and to the quantum-to-classical transition. While past results seemed to indicate that graviton-induced decoherence of spatial superpositions happens only for macroscopic systems, recently it was shown that this mechanism can be enhanced through the system's own dynamical internal structure. In this work, we extend this analysis by including the interaction with a classical Newtonian potential. We show that, although the graviton bath alone dominates the mechanism for short times compared to a timescale established by the size of the quantum spatial superposition, the interaction between the gravitons and the internal degrees of freedom of the system renders decoherence inevitable in the long-time limit, even for microscopic masses. We also show that this mechanism is slightly slowed down by the interplay with the classical Newtonian potential, which, for systems without dynamical internal degrees of freedom, can even lead to recoherence-like behaviour, at least in principle.
A recent analysis by Pikovski et al. [Nat. Phys. 11, 668 (2015)] has triggered interest in the question of how to include relativistic corrections in the quantum dynamics governing many-particle systems in a gravitational field. Here we show how the center-of-mass motion of a quantum system subject to gravity can be derived more rigorously, addressing the ambiguous definition of relativistic center-of-mass coordinates. We further demonstrate that, contrary to the prediction by Pikovski et al., external forces play a crucial role in the relativistic coupling of internal and external degrees of freedom, resulting in a complete cancellation of the alleged coupling in Earth-bound laboratories for systems supported against gravity by an external force. We conclude that the proposed decoherence effect is an effect of relative acceleration between quantum system and measurement device, rather than a universal effect in gravitational fields.
A recent debate has ensued over the claim by Pikovski et al. [Nat. Phys. 11, 668 (2015)] that systems with internal degrees of freedom undergo a universal, gravity-induced, type of decoherence that explains their quantum-to-classical transition. This decoherence is supposed to arise from the different gravitational redshifts experienced by such systems when placed in a superposition of two wave packets at different heights in a gravitational field. Here we investigate some aspects of the discussion with the aid of simple examples. In particular, we first resolve an apparent conflict between the reported results and the equivalence principle by noting that the static and free-fall descriptions focus on states associated with different hypersurfaces. Next, we emphasize that predictions regarding the observability of interference become relevant only in the context of concrete experimental settings. As a result, we caution against hasty claims of universal validity. Finally, we dispute the claim that, at least in the scenarios discussed by Pikovski et al., gravitation is responsible for the reported results, and we question the alleged ability of decoherence to explain the quantum-to-classical transition. In consequence, we argue against the extraordinary assertion by Pikovski et al. that gravity can account for the emergence of classicality.
Abstract In our paper, ‘Matter waves and clocks do not observe uniform gravitational fields’ (Asenbaum et al 2024 Phys. Scr. 99 046103), we analyze how measurements with matter waves and clocks depend on non-gravitational forces and on a UGF. The comment on our paper rests primarily on a misreading of the paper’s central physical setup. We do not consider the simplification that the redshift apparatus is fixed. Rather, our description remains general and keeps the non-gravitational forces independent of the UGF, which covers all configurations: the redshift setup being fixed, in free fall, or arbitrary upward or downward acceleration. This allows us to establish that the redshift measurement follows the non-gravitational forces rather than the UGF.
Building on the relativistic Hamiltonian of Sonnleitner and Barnett arXiv:1806.00234 and its post-Newtonian extensions by Schwartz and Giuilini arXiv:1908.06929, we investigate composite atomic systems in dynamical gravitational backgrounds. Using a local inertial frame and a perturbed Minkowski metric, we derive curvature-dependent corrections to both center-of-mass and internal Hamiltonians for atoms interacting with weak gravitational waves. The resulting Hamiltonian contains distinct curvature couplings modifying the internal potential and affecting the center-of-mass dynamics. These contributions imply that internal-energy variations do not always reduce to mass renormalization and can induce genuine forces due to changes in momentum. The initial research was motivated by anomalous friction-like forces emerging in quantum optics, and clarified that the anomalous forces are mere relativistic corrections from mass-energy equivalence. Our results suggest that, with increasingly sensitive detectors, additional forces from gravitational wave interactions may become visible in future experiments.