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Physica B+C

Neutron interference induced by gravity: New results and interpretations

S. Werner, Helmut Kaiser, M. Arif, R. Clothier

Published Jul 1, 1988• 63 citations
Publisher
DOI
10.1016/0378-4363(88)90141-6

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The phase shift of matter wave due to the Earth's rotation and gravity has been demonstrated in the neutron-interferometry experiments where the Bragg reflection of the neutron wave from crystals is used to form a closed path. In the literature, the rotation-induced phase shift is ascribed to an extra energy term associated with angular momentum in the Hamiltonian. In this investigation, based on a classical treatment of the collision of neutrons with the lattice planes, the modifications in the particle velocity due to the Earth's rotation as well as those due to gravity are calculated. Then, in conjunction with the relation between the particle velocity and the propagation vector of matter wave, it is shown that the corresponding phase shifts in matter wave are in accord with the interference experiments. Thereby, based on the velocity modification due to collision, a reinterpretation of the effects of the Earth's rotation and gravity on the neutron-wave interference is presented. Meanwhile, a null effect of the Earth's orbital motion is predicted.
Gravity is the weakest of all four known forces in the universe. Quantum states of an elementary particle due to such a weak field is certainly very shallow and would therefore be an experimental challenge to detect. Recently an experimental attempt was made by V. V. Nesvizhevsky et al., Nature 415, 297 (2002), to measure the quantum states of a neutron, which shows that ground state and few excited states are \sim 10^{-12}eV. We show that the energy of the ground state of a neutron confined above Earth's surface should be \sim 10^{-37}eV. The experimentally observed energy levels are 10^{25} times deeper than the actual energy levels it should be and thus certainly not due to gravitational effect of Earth. Therefore the correct interpretation for the painstaking experimental results of Ref. \cite{nes1} is due to the confinement potential of a one dimensional box of length L \sim 50μm, generated from the experimental setup as commented before \cite{hansoon}. Our results thus creates a new challenge to the experimentalist to resolve the shallow energy levels of the neutron in Earth's gravitational field in future.