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Killing horizons decohere quantum superpositions
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 , our analysis applies to any dimension
Killing Horizons Decohere Quantum Superpositions
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 , our
analysis applies to any dimension .Comment: 16 pages, 1 figure. Accepted for publication in Phys. Rev. D. v2:
Added clarifying remarks and a figure, and pointed out that the effect arises
for any d>=4; corrected equation (3.18
Gravitationally Mediated Entanglement: Newtonian Field vs. Gravitons
We argue that if the Newtonian gravitational field of a body can mediate
entanglement with another body, then it should also be possible for the body
producing the Newtonian field to entangle directly with on-shell gravitons. Our
arguments are made by revisiting a gedankenexperiment previously analyzed by
Belenchia et al., which showed that a quantum superposition of a massive body
requires both quantized gravitational radiation and local vacuum fluctuations
of the spacetime metric in order to avoid contradictions with complementarity
and causality. We provide a precise and rigorous description of the
entanglement and decoherence effects occurring in this gedankenexperiment,
thereby significantly improving upon the back-of-the-envelope estimates given
in the analysis of Belenchia et al. and also showing that their conclusions are
valid in much more general circumstances. As a by-product of our analysis, we
show that under the protocols of the gedankenexperiment, there is no clear
distinction between entanglement mediated by the Newtonian gravitational field
of a body and entanglement mediated by on-shell gravitons emitted by the body.
This suggests that Newtonian entanglement implies the existence of graviton
entanglement and supports the view that the experimental discovery of Newtonian
entanglement may be viewed as implying the existence of the graviton.Comment: 11 pages, 3 figure