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Decoherence-induced violations of Einstein equivalence principle

Abel Camacho, Investigaciones Nucleares

Published Jan 1, 2001• 0 citations
OpenAlex

Abstract

In this essay it will be shown that Decoherence Model and Einstein Equivalence Principle are conceptually incompatible. In other words, assuming only the validity of the Weak Equivalence Principle the present work concludes that we face two possibilities: (i) if Decoherence Model provides a correct description of nature at quantum level, then there are systems which violate Local Position Invariance, or, (ii) if all the postulates behind Einstein Equivalence Principle are valid, even on quantum realm, then Decoherence Model breaks down in curved spacetimes. Finally, the present results are confronted against Schiff's conjecture.

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DECOHERENCE-INDUCED VIOLATIONS OF EINSTEIN EQUIVALENCE PRINCIPLE

A. CAMACHO

In this essay it will be shown that Decoherence Model and Einstein Equivalence Principle are conceptually incompatible. In other words, assuming only the validity of the Weak Equivalence Principle the present work concludes that we face two possibilities: (i) if Decoherence Model provides a correct description of nature at quantum level, then there are systems which violate Local Position Invariance, or, (ii) if all the postulates behind Einstein Equivalence Principle are valid, even on quantum realm, then Decoherence Model breaks down in curved spacetimes. Finally, the present results are confronted against Schiff's conjecture.

arXiv:gr-qc/0107028•International Journal of Modern Physics D•Dec 1, 2001•1 citation

Quantum superposition of spacetimes obeys Einstein's equivalence principle

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We challenge the view that there is a basic conflict between the fundamental principles of Quantum Theory and General Relativity and, in particular, the fact that a superposition of massive bodies would lead to a violation of the Equivalence Principle. It has been argued that this violation implies that such a superposition must inevitably spontaneously collapse (like in the Diósi–Penrose model). We identify the origin of such an assertion in the impossibility of finding a local and classical reference frame in which Einstein's Equivalence Principle would hold. In contrast, we argue that the formulation of the Equivalence Principle can be generalized so that it holds for reference frames that are associated with quantum systems in a superposition of spacetimes. The core of this new formulation is the introduction of a quantum diffeomorphism to such Quantum Reference Frames. This procedure reconciles the principle of linear superposition in Quantum Theory with the principle of general covariance and the Equivalence Principle of General Relativity. Hence, it is not necessary to invoke a gravity-induced spontaneous state reduction when a massive body is prepared in a spatial superposition.

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Universal Decoherence under Gravity: A Perspective through the Equivalence Principle

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Pikovski et al. [Nat. Phys. 11, 668 (2015)] show that a composite particle prepared in a pure initial quantum state and propagated in a uniform gravitational field undergoes a decoherence process at a rate determined by the gravitational acceleration. By assuming Einstein's equivalence principle to be valid, we analyze a physical realization of the (1+1)D thought experiment of Pikovski et al. to demonstrate that the dephasing between the different internal states arises not from gravity but rather from differences in their rest mass, and the mass dependence of the de Broglie wave's dispersion relation. We provide an alternative view to the situation considered by Pikovski et al., where we propose that gravity plays a kinematic role by providing a relative velocity to the detector frame with respect to the particle; visibility can be easily recovered by giving the screen an appropriate uniform velocity. We then apply this insight to their thought experiment in (1+1)D to draw a direct correspondence, and obtain the same mathematical result for dephasing. We finally propose that dephasing due to gravity may in fact take place for certain modifications to the gravitational potential where the equivalence principle is violated.

arXiv:1603.01984•Physical Review Letters•Aug 24, 2016•37 citations
In this essay it will be shown that Decoherence Model and Einstein Equivalence Principle are conceptually incompatible. In other words, assuming only the validity of the Weak Equivalence Principle the present work concludes that we face two possibilities: (i) if Decoherence Model provides a correct description of nature at quantum level, then there are systems which violate Local Position Invariance, or, (ii) if all the postulates behind Einstein Equivalence Principle are valid, even on quantum realm, then Decoherence Model breaks down in curved spacetimes. Finally, the present results are confronted against Schiff's conjecture.
In this essay it will be shown that Decoherence Model and Einstein Equivalence Principle are conceptually incompatible. In other words, assuming only the validity of the Weak Equivalence Principle the present work concludes that we face two possibilities: (i) if Decoherence Model provides a correct description of nature at quantum level, then there are systems which violate Local Position Invariance, or, (ii) if all the postulates behind Einstein Equivalence Principle are valid, even on quantum realm, then Decoherence Model breaks down in curved spacetimes. Finally, the present results are confronted against Schiff's conjecture.
We challenge the view that there is a basic conflict between the fundamental principles of Quantum Theory and General Relativity and, in particular, the fact that a superposition of massive bodies would lead to a violation of the Equivalence Principle. It has been argued that this violation implies that such a superposition must inevitably spontaneously collapse (like in the Diósi–Penrose model). We identify the origin of such an assertion in the impossibility of finding a local and classical reference frame in which Einstein's Equivalence Principle would hold. In contrast, we argue that the formulation of the Equivalence Principle can be generalized so that it holds for reference frames that are associated with quantum systems in a superposition of spacetimes. The core of this new formulation is the introduction of a quantum diffeomorphism to such Quantum Reference Frames. This procedure reconciles the principle of linear superposition in Quantum Theory with the principle of general covariance and the Equivalence Principle of General Relativity. Hence, it is not necessary to invoke a gravity-induced spontaneous state reduction when a massive body is prepared in a spatial superposition.
The agreement between the predictions of general relativity and observations of the energy loss due to gravitational waves emitted by binary pulsars is just as impressive as the agreement between prediction of quantum electrodynamics and the measured value of Lamb shift in atoms. However, general relativity has not yet yielded to a successful quantised theory. There is a widespread belief that the two thories are incompatible at some deep level. The question is: where? Here, I show that the conceptual foundations of the theory of general relativity and quantum mechanics are so rich that they suggest concrete modifications into each other in the interface region. Specifically, I consider quantum states that have no classical counterpart and show that such states must carry an inherent violation of the principle of equivalence. On the other hand, I show that when gravitational effects are incorporated into the quantum measurement process one must induce a gravitationally induced modification to the de Broglie's wave-particle duality. The reported changes into the foundations of the two theories are far from in-principle modifications. These are endowed with serious implications for the understanding of the early universe and, in certain instances, can be explored in terrestrial laboratories.
Whether the principles of general relativity extend to a quantum regime remains one of the open questions in modern physics. In classical general relativity, Einstein's equivalence principle underpins the interpretation of gravity as spacetime geometry. However, it is not known whether the principle remains valid when the source of gravity could be quantum. Here we show that gravity-induced entanglement (GIE) of quantum clocks provides a framework to characterize local position invariance (LPI) in such a regime, which constitutes one of the subprinciples of the equivalence principle. By adapting the existing formulation of quantum LPI to the context of GIE, we analyze two schemes that address complementary aspects of LPI and differ only in the choice of the initial clock state: one in which entanglement will be generated if and only if there is a genuinely quantum violation of LPI, and the other where classical-like LPI violation manifests in the frequency of entanglement oscillation. Our results suggest that GIE of quantum clocks offers an approach to investigating fundamental principles of general relativity in the quantum regime, shedding new light on the interplay between quantum mechanics and the theory of gravity.
The relation between Einstein equivalence principle and a continuous quantum measurement is analyzed in the context of the recently proposed flavor-oscillation clocks, an idea pioneered by Ahluwalia and Burgard (Gen. Rel. Grav.29, 681(E) (1997)). We will calculate the measurement outputs if a flavor-oscillation clock, which is immersed in a gravitational field, is subject to a continuous quantum measurement. Afterwards, resorting to the weak equivalence principle, we obtain the corresponding quantities in a freely falling reference frame. Finally, comparing this last result with the measurement outputs that would appear in a Minkowskian space–time it will be found that they do not coincide, in other words, we have a violation of Einstein equivalence principle. This violation appears in two different forms, namely: (i) the oscillation frequency in a freely falling reference frame does not match with the case predicted by general relativity, a feature previously obtained by Ahluwalia; (ii) the probability distribution of the measurement outputs, obtained by an observer in a freely falling reference frame, does not coincide with the results that would appear in the case of a Minkowskian space–time. Concerning this last difference, the probability distribution differs in two directions. Firstly, the maximum, as function of the energy of the system (that emerges if we calculate first the probability distribution in the original curved manifold and then, resorting to the weak equivalence principle, we find the corresponding expression in a freely falling reference frame) is shifted with respect to the case in which the system is in a Minkowskian space–time. Secondly, the magnitude of this maximum is not equal to the respective quantity predicted by general relativity. In other words, we obtain two new theoretical results that predict a violation of Einstein equivalence principle, and that could be measured.
Pikovski et al. [Nat. Phys. 11, 668 (2015)] show that a composite particle prepared in a pure initial quantum state and propagated in a uniform gravitational field undergoes a decoherence process at a rate determined by the gravitational acceleration. By assuming Einstein's equivalence principle to be valid, we analyze a physical realization of the (1+1)D thought experiment of Pikovski et al. to demonstrate that the dephasing between the different internal states arises not from gravity but rather from differences in their rest mass, and the mass dependence of the de Broglie wave's dispersion relation. We provide an alternative view to the situation considered by Pikovski et al., where we propose that gravity plays a kinematic role by providing a relative velocity to the detector frame with respect to the particle; visibility can be easily recovered by giving the screen an appropriate uniform velocity. We then apply this insight to their thought experiment in (1+1)D to draw a direct correspondence, and obtain the same mathematical result for dephasing. We finally propose that dephasing due to gravity may in fact take place for certain modifications to the gravitational potential where the equivalence principle is violated.