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arXiv:1612.00288

A testable prediction from entropic gravity

Mehmet Süzen

Published Nov 27, 2016• 0 citations
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Abstract

I have shown conceptually that quantum state has a direct relationship to gravitational constant due to entropic force posed by Verlinde's argument and part of the Newton-Schrödinger equation (N-S) in the context of gravity induced collapse of the wavefunction via Diósi-Penrose proposal. This direct relationship can be used to measure gravitational constant using state-of-the-art mater-wave interferometry to test the entropic gravity argument.

DOI
10.48550/arxiv.1612.00288

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I have shown conceptually that quantum state has a direct relationship to gravitational constant due to entropic force posed by Verlinde's argument and part of the Newton-Schrödinger equation (N-S) in the context of gravity induced collapse of the wavefunction via Diósi-Penrose proposal. This direct relationship can be used to measure gravitational constant using state-of-the-art mater-wave interferometry to test the entropic gravity argument.
No experimental evidence exists, to date, whether or not the gravitational field must be quantised. Theoretical arguments in favour of quantisation are inconclusive. The most straightforward alternative to quantum gravity, a coupling between classical gravity and quantum matter according to the semi-classical Einstein equations, yields a nonlinear modification of the Schrödinger equation. Here, effects of this so-called Schrödinger-Newton equation are discussed, which allow for technologically feasible experimental tests.
The Diosi-Penrose model of quantum-classical boundary postulates gravity-related spontaneous wave function collapse of massive degrees of freedom. The decoherence effects of the collapses are in principle detectable if not masked by the overwhelming environmental decoherence. But the DP (or any other, like GRW, CSL) spontaneous collapses are not detectable themselves, they are merely the redundant formalism of spontaneous decoherence. To let DP collapses become testable physics, recently we extended the DP model and proposed that DP collapses are responsible for the emergence of the Newton gravitational force between massive objects. We identified the collapse rate, possibly of the order of 1/ms, with the rate of emergence of the Newton force. A simple heuristic emergence (delay) time was added to the Newton law of gravity. This non-relativistic delay is in peaceful coexistence with Einstein’s relativistic theory of gravitation, at least no experimental evidence has so far surfaced against it. We derive new predictions of such a ‘lazy’ Newton law that will enable decisive laboratory tests with available technologies. The simple equation of ’lazy’ Newton law deserves theoretical and experimental studies in itself, independently of the underlying quantum foundational considerations.
The Diosi-Penrose model of quantum-classical boundary postulates gravity-related spontaneous wave function collapse of massive degrees of freedom. The decoherence effects of the collapses are in principle detectable if not masked by the overwhelming environmental decoherence. But the DP (or any other, like GRW, CSL) spontaneous collapses are not detectable themselves, they are merely the redundant formalism of spontaneous decoherence. To let DP collapses become testable physics, recently we extended the DP model and proposed that DP collapses are responsible for the emergence of the Newton gravitational force between massive objects. We identified the collapse rate, possibly of the order of 1/ms, with the rate of emergence of the Newton force. A simple heuristic emergence (delay) time was added to the Newton law of gravity. This non-relativistic delay is in peaceful coexistence with Einstein's relativistic theory of gravitation, at least no experimental evidence has so far surfaced against it. We derive new predictions of such a 'lazy' Newton law that will enable decisive laboratory tests with available technologies. The simple equation of 'lazy' Newton law deserves theoretical and experimental studies in itself, independently of the underlying quantum foundational considerations.
Erik Verlinde's theory of entropic gravity [E. Verlinde, J. High Energy Phys. 04 (2011) 029], postulating that gravity is not a fundamental force but rather emerges thermodynamically, has garnered much attention as a possible resolution to the quantum gravity problem. Some have ruled this theory out on grounds that entropic forces are by nature noisy and entropic gravity would therefore display far more decoherence than is observed in ultracold neutron experiments. We address this criticism by modeling linear gravity acting on small objects as an open quantum system. In the strong coupling limit, when the model's unitless free parameter $\ensuremath{\sigma}$ goes to infinity, the entropic master equation recovers conservative gravity. We show that the proposed master equation is fully compatible with the qqqBounce experiment for ultracold neutrons as long as $\ensuremath{\sigma}\ensuremath{\gtrsim}250$ at 9090%90 confidence. Furthermore, the entropic master equation predicts energy increase and decoherence on long time scales and for large masses, phenomena that tabletop experiments could test. In addition, comparing entropic gravity's energy increase to that of the Di\'osi-Penrose model for gravity-induced decoherence indicates that the two theories are incompatible. These findings support the theory of entropic gravity, motivating future experimental and theoretical research.