Quantum gravitational decoherence of matter waves

One 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 recently discovered conformal structure of canonical gravity. This leads to a gravitational analogue of the 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 that 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. Physics on the large scale is based on Einstein’s theory of general relativity (GR), which interprets gravity as the curvature of spacetime. Despite its tremendous success as an isolated theory of gravity, GR has proved problematic in integration with physics as a whole, in particular the physics of the very small governed by quantum mechanics. There can be no unification of physics, which does not include them both. Superstring theory [1] and its recent extension to the more general theory of branes is a popular candidate, but the links with experiment are very tenuous. Loop quantum gravity [2, 3] attempts to quantize GR without unification, and has so far received no obvious experimental verification. One hundred years ago, when Planck introduced the constant named after him, he also introduced the Planck scales, which combined this constant with the velocity of light c and Newton’s gravitational constant G to give the fundamental Planck time TPlanck = (~G/c 5)1/2 ≈ 10−43 s, Planck length LPlanck = c TPlanck ≈ 10−35 m and Planck mass MPlanck = ~/(cTPlanck) ≈ 10−8 kg. Experiments on quantum gravity require access to these scales. To access these scales directly using accelerators would require 1019 GeV accelerators, well beyond any conceivable experiments.