Classical Underpinnings of Gravitationally Induced Quantum Interference

We show that the gravitational modification of the phase of a neutron beam (the COW experiment) has a classical origin, being due to the time delay which classical particles experience in traversing a background gravitational field. Similarly, we show that classical light waves also undergo a phase shift in traversing a gravitational field. We show that the COW experiment respects the equivalence principle even in the presence of quantum mechanics. In a landmark series of experiments [1], [2] Colella, Overhauser and Werner (COW) and their subsequent collaborators (see e.g. Refs. [3], [4] for overviews) detected the modification of the phase of a neutron beam as it traverses the earth’s gravitational field, to thus realize the first experiment which involved both quantum mechanics and gravity. A typical generic experimental set up is shown in the schematic Fig. (1) in which a neutron beam from a reactor is split by Bragg or Laue scattering at point A into a horizontal beam AB and a vertical beam AC (we take the Bragg angle to be 45◦ for simplicity and illustrative convenience in the following), with the subsequent scatterings at B and C then producing beams which Bragg scatter again at D, after which they are then detected. If the neutrons arrive at A with velocity v0 (typically of order 2× 10 5 cm sec) and ABCD is a square of side H , then the phase difference φCOW = φACD − φABD is given by −mgH /h̄v0 to lowest order in the acceleration g due to gravity [1], and is actually observable despite the weakness of gravity, since even though ∫ p̄·dr̄ only differs by the very small amountm(vCD−vAB)H = −mgH /v0 between the CD and AB paths, nonetheless this quantity is not small compared to Planck’s constant, to thus give an observable fringe shift even for H as small as a few centimeters. The detected COW phase is extremely intriguing for two reasons. First, it shows that it is possible to distinguish between different paths which have common end points, with the explicit global ordering in which the horizontal and vertical sections are traversed leading to observable consequences. And second, it yields an answer which explicitly depends on the mass of the neutron even while the classical neutron trajectories (viz. the ones explicitly followed by the centers of the wave packets of the quantum mechanical neutron beam) of course do not. The COW result thus invites consideration of whether the detected ordering UCONN 96-08, October 1996