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arXiv:gr-qc/9801024 · Physical Review Letters

Spacetime Foam as a Quantum Thermal Bath

Luis J. Garay

Published Mar 23, 1998• 139 citations
arXivHTMLPDF

Abstract

An effective model for the spacetime foam is constructed in terms of nonlocal interactions in a classical background. In the weak-coupling approximation, the evolution of the low-energy density matrix is determined by a master equation that predicts loss of quantum coherence. Moreover, spacetime foam can be described by a quantum thermal field that, apart from inducing loss of coherence, gives rise to effects such as gravitational Lamb and Stark shifts as well as quantum damping in the evolution of the low-energy observables.

DOI
10.1103/physrevlett.80.2508

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An effective model for the spacetime foam is constructed in terms of nonlocal interactions in a classical background. In the weak-coupling approximation, the evolution of the low-energy density matrix is determined by a master equation that predicts loss of quantum coherence. Moreover, spacetime foam can be described by a quantum thermal field that, apart from inducing loss of coherence, gives rise to effects such as gravitational Lamb and Stark shifts as well as quantum damping in the evolution of the low-energy observables.
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We study in some detail the master equation, and its solution in a simplified case modelling flavor oscillations of a two-level system, stemming from the Liouville-string approach to quantum space-time foam. In this framework we discuss the appearance of diffusion terms and decoherence due to the interaction of low-energy string matter with space-time defects, such as D-particles in the specific model of ``D-particle foam,'' as well as dark-energy contributions. We pay particular attention to contrasting the decoherent role of a cosmological constant in inducing exponential quantum damping in the evolution of low-energy observables, such as the probability of flavor oscillations, with the situation where the dark-energy relaxes to zero for asymptotically large times, in which case such a damping is absent. Our findings may be of interest to (astrophysical) tests of quantum space-time foam models in the not-so-distant future.
We provide a mechanism by which, from a background-independent model with no quantum mechanics, quantum theory arises in the same limit in which spatial properties appear. Starting with an arbitrary abstract graph as the microscopic model of spacetime, our ansatz is that the microscopic dynamics can be chosen so that (i) the model has a low-energy limit which reproduces the nonrelativistic classical dynamics of a system of NNN particles in flat spacetime, (ii) there is a minimum length, and (iii) some of the particles are in a thermal bath or otherwise evolve stochastically. We then construct simple functions of the degrees of freedom of the theory and show that their probability distributions evolve according to the Schr\"odinger equation. The nonlocal hidden variables required to satisfy the conditions of Bell's theorem are the links in the fundamental graph that connect nodes adjacent in the graph but distant in the approximate metric of the low-energy limit. In the presence of these links, distant stochastic fluctuations are transferred into universal quantum fluctuations.
We investigate the effect of quantum metric fluctuations on qubits that are gravitationally coupled to a background spacetime. In our first example, we study the propagation of a qubit in flat spacetime whose metric is subject to flat quantum fluctuations with a Gaussian spectrum. We find that these fluctuations cause two changes in the state of the qubit: they lead to a phase drift, as well as the expected exponential suppression (decoherence) of the off-diagonal terms in the density matrix. Although in principle observable, the current state of technology prohibits the experimental demonstration of the phase drift. Second, we calculate the decoherence of a qubit in a circular orbit around a Schwarzschild black hole. The no-hair theorems suggest a quantum state for the metric in which the black hole's mass fluctuates with a thermal spectrum at the Hawking temperature. Again, we find that the orbiting qubit undergoes decoherence and a phase drift that both depend on the temperature of the black hole. Third, we study the interaction of coherent and squeezed gravitational waves with a qubit in uniform motion. Finally, we investigate the decoherence of an accelerating qubit in Minkowski spacetime due to the Unruh effect. In this case decoherence is not due to fluctuations in the metric, but instead is caused by coupling (which we model with a standard Hamiltonian) between the qubit and the thermal cloud of Unruh particles bathing it. When the accelerating qubit is entangled with a stationary partner, the decoherence should induce a corresponding loss in teleportation fidelity.
We discuss two classes of semimicroscopic theoretical models of stochastic spacetime foam in quantum gravity and the associated effects on entangled states of neutral mesons, signalling an intrinsic breakdown of CPTCPTCPT invariance. One class of models deals with a specific model of foam, initially constructed in the context of noncritical (Liouville) string theory, but viewed here in the more general context of effective quantum-gravity models. The relevant Hamiltonian perturbation, describing the interaction of the meson with the foam medium, consists of off-diagonal stochastic metric fluctuations, connecting distinct mass eigenstates (or the appropriate generalization thereof in the case of KKK-mesons), and it is proportional to the relevant momentum transfer (along the direction of motion of the meson pair). There are two kinds of CPTCPTCPT-violating effects in this case, which can be experimentally disentangled: one (termed ``$\ensuremath{\omega}$-effect'') is associated with the failure of the indistinguishability between the neutral meson and its antiparticle, and affects certain symmetry properties of the initial state of the two-meson system; the second effect is generated by the time evolution of the system in the medium of the spacetime foam, and can result in time-dependent contributions of the $\ensuremath{\omega}$-effect type in the time profile of the two-meson state. Estimates of both effects are given, which show that, at least in certain models, such effects are not far from the sensitivity of experimental facilities available currently or in the near future. The other class of quantum-gravity models involves a medium of gravitational fluctuations which behaves like a ``thermal bath''. In this model both of the above-mentioned intrinsic CPTCPTCPT violation effects are not valid.