Charles H-T Wang et al 2006 Class. Quantum Grav. 23 L59 doi:10.1088/0264-9381/23/18/L01
Charles H-T Wang1,2, Robert Bingham2,3 and J Tito Mendonça2,4
Show affiliationsOne of the biggest unsolved problems in physics is the unification of quantum mechanics and general relativity. The lack of experimental guidance has made the issue extremely evasive, though various attempts have been made to relate the loss of matter wave coherence to quantum spacetime fluctuations. We present a new approach to the gravitational decoherence near the Planck scale, made possible by the recently discovered conformal structure of canonical gravity. This leads to a gravitational analogue of Brownian motion whose correlation length is given by the Planck length up to a scaling factor. With input from recent matter wave experiments, we show the minimum value of this factor to be well within the expected range for quantum gravity theories. This suggests that the sensitivities of advanced matter wave interferometers may be approaching the fundamental level due to quantum spacetime fluctuations, and that investigating Planck scale physics using matter wave interferometry may become a reality in the near future.
04.20.Gz Spacetime topology, causal structure, spinor structure
04.25.Nx Post-Newtonian approximation; perturbation theory; related approximations
03.65.Yz Decoherence; open systems; quantum statistical methods
83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
Issue 18 (21 September 2006)
Received 13 June 2006, in final form 19 July 2006
Published 18 August 2006
Charles H-T Wang et al 2006 Class. Quantum Grav. 23 L59
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