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arXiv:hep-th/0407032

Black Holes, Information Loss, and Hidden Variables

Antony Valentini

Published Jul 6, 2004• 19 citations
arXivHTMLPDF

Abstract

We consider black-hole evaporation from a hidden-variables perspective. It is suggested that Hawking information loss, associated with the transition from a pure to a mixed quantum state, is compensated for by the creation of deviations from Born-rule probabilities outside the event horizon. The resulting states have non-standard or 'nonequilibrium' distributions of hidden variables, with a specific observable signature - a breakdown of the sinusoidal modulation of quantum probabilities for two-state systems. Outgoing Hawking radiation is predicted to contain statistical anomalies outside the domain of the quantum formalism. Further, it is argued that even for a macroscopic black hole, if one half of an entangled EPR-pair should fall behind the event horizon, the other half will develop similar statistical anomalies. We propose a simple rule, whereby the relative entropy of the nonequilibrum (hidden-variable) distribution generated outside the horizon balances the increase in von Neumann entropy associated with the pure-to-mixed transition. It is argued that there are relationships between hidden-variable and von Neumann entropies even in non-gravitational physics. We consider the possibility of observing anomalous polarisation probabilities, in the radiation from primordial black holes, and in the atomic cascade emission of entangled photon pairs from black-hole accretion discs.

DOI
10.48550/arxiv.hep-th/0407032

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We consider black-hole evaporation from a hidden-variables perspective. It is suggested that Hawking information loss, associated with the transition from a pure to a mixed quantum state, is compensated for by the creation of deviations from Born-rule probabilities outside the event horizon. The resulting states have non-standard or 'nonequilibrium' distributions of hidden variables, with a specific observable signature - a breakdown of the sinusoidal modulation of quantum probabilities for two-state systems. Outgoing Hawking radiation is predicted to contain statistical anomalies outside the domain of the quantum formalism. Further, it is argued that even for a macroscopic black hole, if one half of an entangled EPR-pair should fall behind the event horizon, the other half will develop similar statistical anomalies. We propose a simple rule, whereby the relative entropy of the nonequilibrum (hidden-variable) distribution generated outside the horizon balances the increase in von Neumann entropy associated with the pure-to-mixed transition. It is argued that there are relationships between hidden-variable and von Neumann entropies even in non-gravitational physics. We consider the possibility of observing anomalous polarisation probabilities, in the radiation from primordial black holes, and in the atomic cascade emission of entangled photon pairs from black-hole accretion discs.
Hawking's black hole evaporation process suggests that we may need to choose between quantum unitarity and other basic physical principles such as no-signalling, entanglement monogamy, and the equivalence principle. We here provide a quantum model for Hawking pair black hole evaporation within which these principles are all respected. The model does not involve exotic new physics, but rather uses quantum theory and general relativity. The black hole and radiation are in a joint superposition of different energy states at any stage of the evaporation process. In the particular branch where the black hole mass is 0, the radiation state is pure and one-to-one with the initial state forming the black hole. Thus there is no information loss upon full evaporation. The original Hawking's pair entanglement between infalling and outgoing particles gets transferred to outgoing particles via entanglement swapping, without violation of no-signalling or the entanglement's monogamy. The final state after the full black hole evaporation is pure, without loss of information, violation of monogamy, or the equivalence principle.
We show that quantum nonequilibrium (or deviations from the Born rule) can propagate nonlocally across space. Such phenomena are allowed in the de Broglie–Bohm pilot-wave formulation of quantum mechanics. We show that an entangled state can act as a channel whereby quantum nonequilibrium can be transferred nonlocally from one region to another without any classical interaction. This suggests a novel mechanism whereby information can escape from behind the classical event horizon of an evaporating black hole.
We quantify the nature of the information loss in a Schwarzschild black hole as a function of its mass. We consider a scalar field in a two-mode squeezed state in the far past, and study the degradation of entanglement and classical correlations from the perspective of observers outside the black hole due to the Hawking radiation. Due to monogamy constraints on the distribution of entanglement, we show that the lost bipartite entanglement is recovered as multipartite entanglement among modes inside and outside the horizon. In the black hole evaporation limit, all bipartite entanglement between modes outside the black hole vanishes while the genuine multipartite entanglement grows infinitely.
Hawking's black hole evaporation process suggests that we may need to choose between quantum unitarity and other basic physical principles such as no-signaling, entanglement monogamy, and the equivalence principle. We here show that the Hawking's quantum model for the black hole evaporation is consistent with the above fundamental principles. Our analysis does not involve exotic new physics, but rather uses standard quantum theory, general relativity, and the Einstein–Hilbert action including matter. We explicitly show that the whole state consisting of matter and radiation (in a joint superposition of different energy states) is pure at any stage of the evaporation process, including the particular case of 0 mass. Moreover, after full evaporation the state for radiation at infinity is pure and in one-to-one correspondence with the initial state forming the black hole. Thus there is no information loss upon full evaporation according to the quantum information theory. The original entanglement of the black hole matter (if any) gets transferred to the outgoing particles via a process similar to entanglement swapping, without violation of causality (as proved explicitly). On the other hand, if the initial state is a tensor product state, the entanglement of Hawking particles, present in the intermediate phase, is broken when the black hole evaporates completely. Therefore, the final state (entangled or tensor product depending on the nature of initial state) after the full black hole evaporation is pure without loss of information.
Quantum mechanics is a highly successful fundamental theory which has passed every experimental test to date. Yet standard quantum mechanics fails to provide an adequate description of measurement processes, which has long been rationalized with operationalist and positivist philosophical arguments but is nevertheless a serious shortfall in a fundamental theory. In this dissertation we introduce quantum mechanics with a discussion of the measurement problem. We then review the de Broglie-Bohm pilot-wave formulation, a nonlocal hidden-variables theory where the state of a quantum system is described by a configuration (independent of measurements) in addition to the wave function, and we apply it to fundamental problems concerning black holes and the early universe.\nIn de Broglie-Bohm theory, general initial conditions allow for deviations from the statistical predictions of standard quantum mechanics. We review how the Born rule can be understood as the result of an equilibration process for systems with sufficient mixing before proceeding to study the implications of quantum nonequilibrium in various physical contexts.\nIn this work we show that small perturbations to a system are themselves insufficient to drive relaxation to quantum equilibrium even over very long timescales. This has implications for the potential survival of nonequilibrium in relic particles, and renders it unlikely that field perturbations can be driven to equilibrium by small corrections to the Bunch-Davies vacuum during inflation, allowing for the possible detection of imprints of nonequilibrium in the cosmic microwave background. Using a simple model we also demonstrate how quantum nonequilibrium can propagate nonlocally through entanglement, providing a mechanism for information flow from black holes. This opens up a possible path to the resolution of the black hole information paradox by allowing for information to be released in hidden variable degrees of freedom during black hole evaporation. Finally, we consider whether features in the angular power spectrum of temperature anisotropies in the cosmic microwave background radiation could arise from quantum nonequilibrium initial conditions. Preliminary results indicate that this approach can provide a natural explanation for the power deficit anomaly at large angular scales, as well as oscillatory features in the same regime.
The thermodynamic entropy of an isolated system is given by its von Neumann entropy. Over the last few years, there has been an intense activity to understand the thermodynamic entropy from the principles of quantum mechanics. More specifically, is there a relation between the (von Neumann) entropy of entanglement between a system and some (separate) environment and the thermodynamic entropy? It is difficult to obtain the relation for many body systems, hence, most of the work in the literature has focused on small number systems. In this work, we consider black holes—which are simple yet macroscopic systems—and show that a direct connection could not be made between the entropy of entanglement and the Hawking temperature. In this work, within the adiabatic approximation, we explicitly show that the Hawking temperature is indeed given by the rate of change of the entropy of entanglement across a black hole’s horizon with regard to the system energy. This is yet other numerical evidence leading to understanding the key features of black-hole thermodynamics from the viewpoint of quantum information theory.