Expectation values, experimental predictions, events and entropy in quantum gravitationally decohered quantum mechanics

Abstract

We restate Kay's 1998 hypothesis which simultaneously offers an objective definition for the entropy of a closed system, a microscopic foundation for the Second Law, a resolution of the Information Loss (and other) Black-Hole Puzzle(s) and an objective mechanism for decoherence. Presupposing a conventional unitary theory of low-energy quantum gravity, it offers all this by taking the physical density operator of a closed system to be the partial trace of its total density operator (assumed pure) over gravity and by defining its physical entropy to be its `matter-gravity entanglement entropy'. We also recall Kay's 1998 modified non-relativistic (many-body) quantum mechanics based on Kay's hypothesis with a Newtonian approximation to quantum gravity. In this modification, we find formal expectation values for certain `observables' such as momentum-squared and Parity are altered but those for functions of positions are unaltered. However, by arguing that every real measurement can ultimately be taken to be a position measurement, we prove that, in practice, it is impossible to detect any alteration at all and, in particular, we predict no alteration for Roger Penrose's experiment. Nevertheless, Kay's modification contains no Schrödinger Cat-like states, and also allows an `events' interpretation which we tentatively propose and begin to explore. We also obtain a Second-Law type result for a non-relativistic toy-model closed system and argue that similar results will apply for a wide class of model Newtonian and post-Newtonian closed systems although we argue that ordinary actual lab-sized systems can never be treated as closed for the purpose of calculating their entropy. Compared with `collapse models' such as GRW, Kay's Newtonian theory does a similar job while being free from ad hoc assumptions.

62 pages, 5 figures

References in corpus (7)

• Towards quantum superpositions of a mirror
• Hawking Radiation and Black Hole Thermodynamics
• Decoherence of Macroscopic Closed Systems within Newtonian Quantum Gravity
• On the mathematical Structure of Quantum Measurement Theory
• Entropy Defined, Entropy Increase and Decoherence Understood, and Some Black-Hole Puzzles Solved
• Black Holes and Thermodynamics
• The robustness of a many-body decoherence formula of Kay under changes in graininess and shape of the bodies

Cited by in corpus (9)

• Generalised uncertainty relations from superpositions of geometries
• Generally covariant dynamical reduction models and the Hadamard condition
• Entropy and quantum gravity
• Instability of enclosed horizons
• Modern foundations for thermodynamics and the stringy limit of black hole equilibria
• Remarks on matter-gravity entanglement, entropy, information loss and events
• The Black Hole Uncertainty Principle Correspondence
• Quantum electrostatics, Gauss's law, and a product picture for quantum electrodynamics; or, the temporal gauge revised
• A product picture for quantum electrodynamics