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arXiv:2311.11461 · Physical review. D/Physical review. D.

Decoherence from horizons: General formulation and rotating black holes

Samuel E. Gralla, Hongji Wei

Published Mar 29, 2024• 22 citations
arXivHTMLPDF

Abstract

Recent work by Danielson, Satishchandran, and Wald (DSW) has shown that black holes—and, in fact, Killing horizons more generally—impart a fundamental rate of decoherence on all nearby quantum superpositions. The effect can be understood from measurement and causality: An observer (Bob) in the black hole should be able to disturb outside quantum superpositions by measuring their superposed gravitational fields, but since his actions cannot (by causality) have this effect, the superpositions must automatically disturb themselves. DSW calculated the rate of decoherence up to an unknown numerical factor for distant observers in Schwarzschild spacetime, Rindler observers in flat spacetime, and static observers in de Sitter spacetime. Working in electromagnetic and Klein-Gordon analogs, we flesh out and generalize their calculation to derive a general formula for the precise decoherence rate for Killing observers near bifurcate Killing horizons. We evaluate the rate in closed form for an observer at an arbitrary location on the symmetry axis of a Kerr black hole. This fixes the numerical factor in the distant-observer Schwarzschild result, while allowing new exploration of near-horizon and/or near-extremal behavior. In the electromagnetic case we find that the decoherence vanishes entirely in the extremal limit, due to the “black hole Meissner effect” screening the Coulomb field from entering the black hole. This supports the causality picture: Since Bob is unable to measure the field of the outside superposition, no decoherence is necessary—and indeed none occurs. Published by the American Physical Society 2024

DOI
10.1103/physrevd.109.065031

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Recent work by Danielson, Satishchandran, and Wald (DSW) has shown that black holes—and, in fact, Killing horizons more generally—impart a fundamental rate of decoherence on all nearby quantum superpositions. The effect can be understood from measurement and causality: An observer (Bob) in the black hole should be able to disturb outside quantum superpositions by measuring their superposed gravitational fields, but since his actions cannot (by causality) have this effect, the superpositions must automatically disturb themselves. DSW calculated the rate of decoherence up to an unknown numerical factor for distant observers in Schwarzschild spacetime, Rindler observers in flat spacetime, and static observers in de Sitter spacetime. Working in electromagnetic and Klein-Gordon analogs, we flesh out and generalize their calculation to derive a general formula for the precise decoherence rate for Killing observers near bifurcate Killing horizons. We evaluate the rate in closed form for an observer at an arbitrary location on the symmetry axis of a Kerr black hole. This fixes the numerical factor in the distant-observer Schwarzschild result, while allowing new exploration of near-horizon and/or near-extremal behavior. In the electromagnetic case we find that the decoherence vanishes entirely in the extremal limit, due to the “black hole Meissner effect” screening the Coulomb field from entering the black hole. This supports the causality picture: Since Bob is unable to measure the field of the outside superposition, no decoherence is necessary—and indeed none occurs. Published by the American Physical Society 2024
Recently, it was shown by Danielson (DSW) that, for the massive or charged body in a quantum spatial separated superposition state, the presence of a black hole can decohere the superposition inevitably toward capturing the radiation of soft photons or gravitons [D. L. Danielson , Black holes decohere quantum superpositions, ; D. L. Danielson , Killing horizons decohere quantum superpositions, ; D. L. Danielson , Local description of decoherence of quantum superpositions by black holes and other bodies, ]. In this work, we study the DSW decoherence effect for the static charged body in the Reissner-Nordström black holes. By calculating the decohering rate for this case, it is shown that the superposition is decohered by the low-frequency photons that propagate through the black hole horizon. For the extremal Reissner-Nordström black hole, the decoherence of quantum superposition is completely suppressed due to the black hole Meissner effect. It is also found that the decoherence effect caused by the Reissner-Nordström black hole is equivalent to that of an ordinary matter system with the same size and charge.
We recently showed that if a massive (or charged) body is put in a quantum spatial superposition, the mere presence of a black hole in its vicinity will eventually decohere the superposition. In this paper we show that, more generally, decoherence of stationary superpositions will occur in any spacetime with a Killing horizon. This occurs because, in effect, the long-range field of the body is registered on the Killing horizon which, we show, necessitates a flux of ``soft horizon gravitons/photons'' through the horizon. The Killing horizon thereby harvests ``which path'' information of quantum superpositions and will decohere any quantum superposition in a finite time. It is particularly instructive to analyze the case of a uniformly accelerating body in a quantum superposition in flat spacetime. As we show, from the Rindler perspective the superposition is decohered by ``soft gravitons/photons'' that propagate through the Rindler horizon with negligible (Rindler) energy. We show that this decoherence effect is distinct from---and larger than---the decoherence resulting from the presence of Unruh radiation. We further show that from the inertial perspective, the decoherence is due to the radiation of high frequency (inertial) gravitons/photons to null infinity. (The notion of gravitons/photons that propagate through the Rindler horizon is the same notion as that of gravitons/photons that propagate to null infinity.) We also analyze the decoherence of a spatial superposition due to the presence of a cosmological horizon in de Sitter spacetime. We provide estimates of the decoherence time for such quantum superpositions in both the Rindler and cosmological cases. Although we explicitly treat the case of spacetime dimension d=4d=4d=4, our analysis applies to any dimension $d\ensuremath{\ge}4$.
Recently Danielson, Satishchandran, and Wald (DSW) have shown that quantum superpositions held outside of Killing horizons will decohere at a steady rate. This occurs because of the inevitable radiation of soft photons (gravitons), which imprint a electromagnetic (gravitational) “which-path” memory onto the horizon. Rather than appealing to this global description, an experimenter ought to also have a local description for the cause of decoherence. One might intuitively guess that this is just the bombardment of Hawking/Unruh radiation on the system, however simple calculations challenge this idea—the same superposition held in a finite temperature inertial laboratory does not decohere at the DSW rate. In this work we provide a local description of the decoherence by mapping the DSW setup onto a worldline-localized model resembling an Unruh-DeWitt particle detector. We present an interpretation in terms of random local forces which do not sufficiently self-average over long times. Using the Rindler horizon as a concrete example we clarify the crucial role of temperature, and show that the Unruh effect is the only quantum mechanical effect underlying these random forces. A general lesson is that for an environment which induces Ohmic friction on the central system (as one gets from the classical Abraham-Lorentz-Dirac force, in an accelerating frame) the fluctuation-dissipation theorem implies that when this environment is at finite temperature it will cause steady decoherence on the central system. Our results agree with DSW and provide the complementary local perspective. Published by the American Physical Society 2024
We investigate the decoherence of a quantum spatial superposition of a static particle in Schwarzschild and Reissner-Nordström black holes. By treating the particle as a localized classical source coupled to a quantum scalar field, we reformulate the decoherence process in the Danielson-Satishchandran-Wald (DSW) gedankenexperiment through coherent state generation and derive the local expression for the decoherence functional in terms of the Wightman function. In the long-time limit, the decoherence rate is shown to be characterized by the low-frequency behavior of the Wightman function. We then employ the asymptotic matching method to calculate the analytical expressions of the Wightman functions in the Boulware, Unruh, and Hartle-Hawking vacua. We show that the decoherence behavior depends on the quantum state of the environmental field. While the Boulware vacuum gives vanishing decoherence for a static superposition, the thermal effects associated with Hawking radiation in the Unruh and Hartle-Hawking vacua can induce nonvanishing decoherence.
It was previously shown that if an experimenter, Alice, puts a massive or charged body in a quantum spatial superposition, then the presence of a black hole (or more generally any Killing horizon) will eventually decohere the superposition. This decoherence was identified as resulting from the radiation of soft photons/gravitons through the horizon, thus suggesting that the global structure of the spacetime is essential for describing the decoherence. In this paper, we show that the decoherence can alternatively be described in terms of the local two-point function of the quantum field within Alice’s lab, without any direct reference to the horizon. From this point of view, the decoherence of Alice’s superposition in the presence of a black hole arises from the extremely low frequency Hawking quanta present in Alice’s lab. We explicitly calculate the decoherence occurring in Schwarzschild spacetime in the Unruh vacuum from the local viewpoint. We then use this viewpoint to elucidate (i) the differences in decoherence effects that would occur in Schwarzschild spacetime in the Boulware and Hartle-Hawking vacua; (ii) the difference in decoherence effects that would occur in Minkowski spacetime filled with a thermal bath as compared with Schwarzschild spacetime; (iii) the lack of decoherence in the spacetime of a static star even though the vacuum state outside the star is similar in many respects to the Boulware vacuum around a black hole; and (iv) the requirements on the degrees of freedom of a material body needed to produce a decoherence effect that mimics that of a black hole.
Recently, Danielson, Satishchandran, and Wald (DSW) have proposed a novel source of decoherence for uniformly accelerated charges and masses in spatial superposition in spacetimes containing a bifurcating Killing horizon. Such an effect can be traced back to the emission and absorption of soft photons and gravitons, which effectively act as "which-path'' information probes. This results in the decoherence of any such superposition in a finite proper time. With this in mind, we study the DSW mechanism using a gapless finite-time detector prepared in a spatial superposition of uniformly accelerated paths in Minkowski spacetime that interacts with a massive scalar field. The calculation is nonperturbative. Such a model will enable us to analyze the decoherence process in a more controlled manner, highlighting the main factors that give rise to this interesting mechanism.