Local Description of Decoherence of Quantum Superpositions by Black Holes and Other Bodies

TL;DR

This paper presents a local field-theoretic approach to understanding how black holes and other bodies cause quantum superpositions to decohere, emphasizing the role of low-frequency Hawking radiation and local two-point functions.

Contribution

It introduces a local perspective on decoherence, avoiding reliance on global spacetime structures, and explicitly calculates effects in Schwarzschild spacetime for different vacua.

Findings

Decoherence arises from low-frequency Hawking quanta in Alice's lab.

Differences in decoherence effects depend on the choice of vacuum state.

No decoherence occurs in the spacetime of a static star despite similar vacuum conditions.

Abstract

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 [arXiv:2205.06279, arXiv:2301.00026, arXiv:2311.11461]. 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.