Decoherence of macroscopic closed systems within Newtonian quantum gravity

TY - JOUR

T1 - Decoherence of macroscopic closed systems within Newtonian quantum gravity

AU - Kay, Bernard S.

PY - 1998/12

Y1 - 1998/12

N2 - A theory recently proposed by the author aims to explain decoherence and the thermodynamical behaviour of closed systems within a conservative, unitary framework for quantum gravity by assuming that the operators tied to the gravitational degrees of freedom are unobservable and equating physical entropy with matter - gravity entanglement entropy. Here we obtain preliminary results on the extent of decoherence this theory predicts. We treat first a static state which, if one were to ignore quantum gravitational effects, would be a quantum superposition of two spatially displaced states of a single classically well describable ball of uniform mass density in empty space. Estimating the quantum gravitational effects on this system within a simple Newtonian approximation, we obtain formulae which predict, for example, that as long as the mass of the ball is considerably larger than the Planck mass, such a would-be-coherent static superposition will actually be decohered whenever the separation of the centres of mass of the two ball-states exceeds a small fraction (which decreases as the mass of the ball increases) of the ball radius. We then obtain a formula for the quantum-gravitational correction to the would-be-pure density matrix of a non-relativistic many-body Schrödinger wavefunction and argue that this formula predicts decoherence between configurations which differ (at least) in the `relocation' of a cluster of particles of Planck mass. We estimate the entropy of some simple model closed systems, finding a tendency for it to increase with `matter-clumping' suggestive of a link with existing phenomenological discussions of cosmological entropy increase.

AB - A theory recently proposed by the author aims to explain decoherence and the thermodynamical behaviour of closed systems within a conservative, unitary framework for quantum gravity by assuming that the operators tied to the gravitational degrees of freedom are unobservable and equating physical entropy with matter - gravity entanglement entropy. Here we obtain preliminary results on the extent of decoherence this theory predicts. We treat first a static state which, if one were to ignore quantum gravitational effects, would be a quantum superposition of two spatially displaced states of a single classically well describable ball of uniform mass density in empty space. Estimating the quantum gravitational effects on this system within a simple Newtonian approximation, we obtain formulae which predict, for example, that as long as the mass of the ball is considerably larger than the Planck mass, such a would-be-coherent static superposition will actually be decohered whenever the separation of the centres of mass of the two ball-states exceeds a small fraction (which decreases as the mass of the ball increases) of the ball radius. We then obtain a formula for the quantum-gravitational correction to the would-be-pure density matrix of a non-relativistic many-body Schrödinger wavefunction and argue that this formula predicts decoherence between configurations which differ (at least) in the `relocation' of a cluster of particles of Planck mass. We estimate the entropy of some simple model closed systems, finding a tendency for it to increase with `matter-clumping' suggestive of a link with existing phenomenological discussions of cosmological entropy increase.

KW - REDUCTION

U2 - 10.1088/0264-9381/15/12/003

DO - 10.1088/0264-9381/15/12/003

M3 - Article

SN - 1361-6382

VL - 15

SP - L89-L98

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

IS - 12

ER -