Effect of Earth's Rotation on the Quantum Mechanical Phase of the Neutron

Abstract

Using a neutron interferometer of the type first developed by Bonse and Hart for x rays, we have observed the effect of Earth's rotation on the phase of the neutron wave function. This experiment is the quantum mechanical analog of the optical interferometry observations of Michelson, Gale, and Pearson.In 1925 Michelson, Gale, and Pearson 1 carried out a remarkable experiment designed to detect the effect of Earth's rotation on the speed of light. Using an interferometer in the form of a rectangle of the size 2010 ftx 1113 ft they were able to detect a retardation of light due to Earth's rotation corresponding to about i of a fringe, in agreement with the theory of relativity. An experiment demonstrating that angular rotation could be detected by optical interf erometry was carried out earlier by Sagnac. 2 In view of the differences in the coordinate transformation properties of light waves and matter waves, it is not obvious that an analogous quantum mechanical effect should exist for neutrons. We find that it does.A schematic diagram of our experiment is shown in Fig. 1. We use a perfect-silicon-crystal interferometer of the type first developed for x rays by Bonse and Hart. 3 The first demonstration that such a device could be used for neutrons was achieved by Rauch, Treimer, and Bonse. 4 In this experiment a nominally monoenergetic neutron beam of wavelength X = 1.262 A is reflected vertically by a beryllium crystal. This beam passes through a collimator and subsequently through a 7-mm-diam cadmium aperture onto the interferometer. The beam incident on the interferometer is coherently split in the first Si-crystal slab at point A by Bragg reflection from the (220) lattice planes. The two resulting beams are coherently split again in the second Si slab near points B and C. Two of these beams are directed toward point D in the third Si slab, where they overlap and interfere. The outgoing interfering beams are detected in two 3 He proportional detectors, labeled C x and C 2 in Fig. 1. If the beam traversing the path ACD is shifted in phase by an angle /3 relative to the beam traversing the path ABD, it can be shown 5 that the expected intensities observed at detectors C x and C 2 areand I 2 =y -a COS/3.The constants a and y depend on the incident flux. The perfect contrast predicted by these equations is never exactly realized in practice. In this experiment we have observed a phase shift /3 of the neutron wave function, which we will call j3 Sa gnac> resulting from the rotation of Earth. According to the theory developed below, this phase shift phase shifter collimator^] beam from L^ monochromator-V/ff/f ™] Be crystal FIG. 1. Schematic diagram of the apparatus.The drawing is not to scale. The collimator is approximately 1 m in length and the interferometer is approximately 8 cm long from point A to point D. The angle 6 of the phase-shifting slab is zero when it is parallel to the three interferometer slabs.

Quantum Systems in Weak Gravitational Fields

“…(38) is the energy-momentum effect observed by Bonse and Wroblewski [4]. The term − ω · L was predicted by Page [36] and observed by Werner and collaborators [3]. The term − ω · σ 2 was found by Mashhoon.…”

Spacetime Metric from Local and Linear Electrodynamics: A New Axiomatic Scheme

“…• The Werner, Staudenmann, and Colella experiment [62] in 1979 on the phase shift of neutron waves induced by the rotation of the Earth (Sagnactype effect), • the Bonse & Wroblewski experiment [5] in 1984 on neutron interferometry in a noninertial frame (verifying, together with the COW experiment, the equivalence principle for neutron waves),…”

“…6 In technical terms this means, see the solutions (61), (62), that β = 0 and γ = 0. Then we have the degenerate solution…”

Spin in Special and General Relativity

“…The Sagnac effect for matter waves was first directly measured by Werner et al [8] via neutron interferometry. Subsequently, it has been measured for electrons [9] and atoms [10].…”

“…The next term, ω.L, represents a coupling of rotations with orbital angular momentum and appears in the work of Page [37] and Werner et al [8]. The final term, ω.S, is the spin-rotation coupling whose existence was first mooted by Mashhoon [21]; see also [38].…”