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arXiv:hep-th/9411193

Information Loss in Black Holes and/or Conscious Beings?

Don Nelson Page

Published Nov 25, 1994• 13 citations
arXivHTMLPDF

Abstract

In 1976 Stephen Hawking proposed that information may be lost from our universe as a pure quantum state collapses gravitationally into a black hole, which then evaporates completely into a mixed state of thermal radiation. Although this proposal is controversial, it is tempting to consider analogous processes that might occur in certain theories of consciousness. For example, one might postulate that independent degrees of freedom be ascribed to the mental world to help explain the feeling of a correlation between one's desires and one's choice of actions. If so, one might ask whether information in the physical world can be lost to such postulated degrees of freedom in the mental world. Or, one might hypothesize that the mental world can affect the physical world by modifying the quantum action for the physical world in a coordinate-invariant way (analogous to the alpha parameters in wormhole theory).

DOI
10.48550/arxiv.hep-th/9411193

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In 1976 Stephen Hawking proposed that information may be lost from our universe as a pure quantum state collapses gravitationally into a black hole, which then evaporates completely into a mixed state of thermal radiation. Although this proposal is controversial, it is tempting to consider analogous processes that might occur in certain theories of consciousness. For example, one might postulate that independent degrees of freedom be ascribed to the mental world to help explain the feeling of a correlation between one's desires and one's choice of actions. If so, one might ask whether information in the physical world can be lost to such postulated degrees of freedom in the mental world. Or, one might hypothesize that the mental world can affect the physical world by modifying the quantum action for the physical world in a coordinate-invariant way (analogous to the alpha parameters in wormhole theory).
Stephen Hawking has argued that universes containing evaporating black holes can evolve from pure initial states to mixed final ones. Such evolution is non-unitary and so contravenes fundamental quantum principles on which Hawking's analysis was based. It disables the retrodiction of the universe's initial state from its final one, and portends the time-asymmetry of quantum gravity. Small wonder that Hawking's paradox has met with considerable resistance. Here we use a simple result for C*-algebras to offer an argument for pure-to-mixed state evolution in black hole evaporation, and review responses to the Hawking paradox with respect to how effectively they rebut this argument.
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.
Suppose a black hole forms from a pure quantum state ∣ψ⟩\ketψ∣ψ⟩. The black hole information loss paradox arises from semiclassical arguments suggesting that, even in a closed system, the process of black hole formation and evaporation evolves a pure state into a mixed state. Resolution to the paradox typically demands violation of quantum mechanics or relativity in domains where they should hold. Instead, I propose that in a complete theory of quantum gravity, any region U\mathcal{U}U that could collapse into a black hole should already be described by a mixed state, thus bypassing the paradox entirely. To that end, I present a model in which the universe is in a quantum error-corrected state, such that any local black hole appears mixed and encodes no information locally.
Abstract In 1974 Steven Hawking showed that black holes emit thermal radiation, which eventually causes them to evaporate. The problem of the fate of information in this process is known as the “black hole information paradox”. Two main types of resolution postulate either a fundamental loss of information in Nature — hence the breakdown of quantum mechanics — or some sort of new physics, e.g. quantum gravity, which guarantee the global preservation of unitarity. Here we explore the second possibility with the help of recent developments in continuous-variable quantum information. Concretely, we employ the solution to the Gaussian quantum marginal problem to show that the thermality of all individual Hawking modes is consistent with a global pure state of the radiation. Surprisingly, we find out that the mods of radiation of an astrophysical black hole are thermal until the very last burst. In contrast, the single-mode thermality of Hawking radiation originating from microscopic black holes, expected to evaporate through several quanta, is not excluded, though there are constraints on modes' frequencies. Our result paves the way towards a systematic study of multi-mode correlations in Hawking radiation.
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 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.