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Physical Review Letters

Electromagnetic acceleration of neutrons

Russell C. Casella, Samuel A. Werner

Published Sep 14, 1992• 17 citations
Publisher

Abstract

We note that the neutron spin must be treated as an intrinsically quantum variable when determining electromagnetically induced phase shifts in neutron interferometry by computing the otherwise-classical action over the classical orbit. We show that a putative acceleration of the neutron (\ensuremath{\gamma}/mc)E\ifmmode\times\else\texttimes\fi{}(\ensuremath{\mu}\ifmmode\times\else\texttimes\fi{}B) recently suggested by Anandan, is essentially unobservable in such measurements over segments of the orbit where the electric and magnetic fields are constant (or vary slowly), within standard electroweak theory.

DOI
10.1103/physrevlett.69.1625

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We note that the neutron spin must be treated as an intrinsically quantum variable when determining electromagnetically induced phase shifts in neutron interferometry by computing the otherwise-classical action over the classical orbit. We show that a putative acceleration of the neutron (\ensuremath{\gamma}/mc)E\ifmmode\times\else\texttimes\fi{}(\ensuremath{\mu}\ifmmode\times\else\texttimes\fi{}B) recently suggested by Anandan, is essentially unobservable in such measurements over segments of the orbit where the electric and magnetic fields are constant (or vary slowly), within standard electroweak theory.
Electromagnetic optical phenomena are generally understood via Maxwell’s equations for the electric and magnetic vector fields. Neutron optical phenomena are based upon de Broglie matter waves and the Schrödinger wave equation which involves a scalar wave function. Nevertheless, a description of interference effects requires the solution of a Helmholtz scalar wave equation in both cases. Gravitational, inertial, and motional effects lead to rather large phase shifts in neutron interferometry. This chapter describes how the quantum phase shift is calculated, usually by evaluating the action as an integral over the Lagrangian. A connection to relativity theory is given when the Compton frequency depending on the mass of the neutron is taken as a physical quantity. It concludes with a list of the approximately 40 neutron interferometry experiments carried out in various laboratories worldwide, which form the subject of this book.
The question as to whether neutron acceleration can occur in uniform electromagnetic fields is examined. Although such an effect has been predicted using the canonical equations of motion, some doubt has been raised recently as to whether it is in principle observable for a spin-1/2 particle. To resolve this issue a gedanken experiment is proposed and analyzed using wave-packet construction for the neutron beam. By allowing an arbitrary orientation for the neutron spin as well as for the electric and magnetic fields, a nonvanishing acceleration of the center of the neutron wave packet is found that confirms the predictions of the canonical formalism.
Einstein's theory of general relativity and quantum theory form the two major pillars of modern physics. However, certain inertial properties of a particle's intrinsic spin are inconspicuous while the inertial properties of mass are well known. Here, by performing a neutron interferometric experiment, we observe phase shifts arising as a consequence of the spin's coupling with the angular velocity of a rotating magnetic field. This coupling is a purely quantum mechanical extension of the Sagnac effect. The resulting phase shifts linearly depend on the frequency of the rotation of the magnetic field. Our results agree with the predictions derived from the Pauli-Schrodinger equation.
Neutron interferometry has been performed on an accelerated interferometer under conditions where gravitational effects on the interfering beams very nearly compensate each other. The observed neutron phase shift is found to be in excellent agreement with that calculated from Schr\"odinger's equation transformed to the accelerated frame where it is found essential to include the spherical wave aspect. The present experiment thus verifies the validity of the classical transformation laws for noninertial frames also in the quantum limit.
Abstract Einstein’s theory of general relativity and quantum theory form the two major pillars of modern physics. However, certain inertial properties of a particle’s intrinsic spin are inconspicuous while the inertial properties of mass are well known. Here, by performing a neutron interferometric experiment, we observe phase shifts arising as a consequence of the spin’s coupling with the angular velocity of a rotating magnetic field. This coupling is a purely quantum mechanical extension of the Sagnac effect. The resulting phase shifts linearly depend on the frequency of the rotation of the magnetic field. Our results agree with the predictions derived from the Pauli–Schrödinger equation.