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Journal of Physics Conference Series

Signature of self-gravitation in vibrating mirror interferometry

Tamás Geszti

Published May 1, 2007• 0 citations
Publisher

Abstract

If - according to the Newton-Schrodinger scheme - gravitation is a classical field and its source is the mean mass density, that provides a force of attraction between the Schrodinger cat partners of the vibrating mirror in the proposed Marshall et al.experiment. That force is observable in principle as a shift of the visibility revival frequency, with respect to the c.o.m. vibration frequency to be observed mechanically. The effect is of observable size if short-range gravity is much stronger than long-range gravity.

DOI
10.1088/1742-6596/67/1/012061

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If - according to the Newton-Schrodinger scheme - gravitation is a classical field and its source is the mean mass density, that provides a force of attraction between the Schrodinger cat partners of the vibrating mirror in the proposed Marshall et al.experiment. That force is observable in principle as a shift of the visibility revival frequency, with respect to the c.o.m. vibration frequency to be observed mechanically. The effect is of observable size if short-range gravity is much stronger than long-range gravity.
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.
We show that a single spatially superposed 'source' mass acting on a 'probe' matter wavepacket can reveal the quantum nature of the gravitational field. For this we use a specific state preparation and measurement of the superposed source mass, including a postselection, which altogether results in a repulsive gravitational force on the probe particle. A classical gravitational field can never lead to repulsion, as the effect requires quantum interference of two distinct states of gravity. The eventual observation of such an effect would be a violation of Einstein's theory of general relativity, where gravity is always attractive. We also present a calculation in the Heisenberg picture under the formalism of weak values that illustrates how repulsion is achieved. Finally, we estimate the range of parameters (masses and the spatio-temporal extent of interference) for which the experiment is feasible.
Abstract We probe the dynamics of a modified form of the Schrödinger–Newton (SN) system of gravity coupled to single particle quantum mechanics. At the masses of interest here, the ones associated with the onset of ‘collapse’ (where the gravitational attraction is competitive with the quantum mechanical dissipation), we show that the Schrödinger ground state energies match the Dirac ones with an error of . At the Planck mass scale, we predict the critical mass at which a potential collapse could occur for the self-coupled gravitational case, Planck mass, and show that gravitational attraction opposes Gaussian spreading at around this value, which is a factor of two higher than the one predicted (and verified) for the SN system. Unlike the SN dynamics, we do not find that the self-coupled case tends to decay towards its ground state; there is no collapse in this case.
We propose a feasible laboratory interferometry experiment with matter waves in a gravitational potential caused by a pair of artificial field-generating masses. It will demonstrate that the presence of these masses (and, for moving atoms, time dilation) induces a phase shift, even if it does not cause any classical force. The phase shift is identical to that produced by the gravitational redshift (or time dilation) of clocks ticking at the atom's Compton frequency. In analogy to the Aharonov-Bohm effect in electromagnetism, the quantum mechanical phase is a function of the gravitational potential and not the classical forces.
We propose a feasible laboratory interferometry experiment with matter waves in a gravitational potential caused by a pair of artificial field-generating masses. It will demonstrate that the presence of these masses (and, for moving atoms, time dilation) induces a phase shift, even if it does not cause any classical force. The phase shift is identical to that produced by the gravitational redshift (or time dilation) of clocks ticking at the atom’s Compton frequency. In analogy to the AharonovBohm effect in electromagnetism, the quantum mechanical phase is a function of the gravitational potential and not the classical forces.