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Zeitschrift für Naturforschung A

Substratum Interpretation of the Sagnac-and the Aharonov-Bohm Effect

Friedwardt Winterberg

Published Dec 1, 1989• 5 citations
Publisher

Abstract

Abstract It is shown that a substratum interpretation reveals a close relationship between the Sagnac- and the Aharonov-Bohm-effect. The characteristic peculiarity of the Aharonov-Bohm-effect, to produce a phase shift of the electron wave function even in the absence of any electromagnetic force fields, can be duplicated by a thought experiment for light waves in the gravitational field of a massive rotating cylinder, which demonstrates that the somewhat similar Sagnac-effect is not caused by centrifugal and Corioli’s forces, as it is sometimes claimed. In the substratum interpretation, both the Sagnac and Aharonov-Bohm effect find their explanation in a rotational motion of the substratum. If the substratum flow is irrotational, having the form of a potential vortex, these effects persist even though there are no force fields present.

DOI
10.1515/zna-1989-1202

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Abstract It is shown that a substratum interpretation reveals a close relationship between the Sagnac- and the Aharonov-Bohm-effect. The characteristic peculiarity of the Aharonov-Bohm-effect, to produce a phase shift of the electron wave function even in the absence of any electromagnetic force fields, can be duplicated by a thought experiment for light waves in the gravitational field of a massive rotating cylinder, which demonstrates that the somewhat similar Sagnac-effect is not caused by centrifugal and Corioli’s forces, as it is sometimes claimed. In the substratum interpretation, both the Sagnac and Aharonov-Bohm effect find their explanation in a rotational motion of the substratum. If the substratum flow is irrotational, having the form of a potential vortex, these effects persist even though there are no force fields present.
This article describes the Aharonov-Bohm (AB) effect of electron waves travelling in free space and its application to the observation of gauge fields (vector potentials). The AB effect is inconceivable in classical physics since an observable effect is produced on electrons passing through field-free spaces. Electrons can be affected only by Lorentz forces due to electromagnetic fields. The situation is different in quantum mechanics, where electrons show wave properties: the concept of force is no longer relevant, so electric field E and magnetic field B, defined as forces acting on a unit charge, take on secondary meanings. “Phase shifts” come into play, and the primary physical entities become neither E nor B but electrostatic potential V and vector potential A. These potentials interact with electron waves and shift their phases.
The magnetic Aharonov-Bohm effect shows that charged particles may be affected by the vector potential in regions without any electric or magnetic fields [1]. The Aharonov-Bohm effect was experimentally confirmed [2-3] and has been found in many situations [4-6]. A common explanation is based on quantum mechanics, which states that the wavefunctions associated with the charges will accumulate a phase shift due to the vector potential. However, consensus about its nature and interpretation has not been achieved [7-14]. We here propose a simple but reasonable interpretation based on the theory for electromagnetic radiation and couplings [15]. The energy associated with a pulse radiator is divided into a Coulomb-velocity energy and a radiative energy, together with a macroscopic Schott energy accounting for the energy exchange between them. All these energies are expressed with terms including the potentials, so are the mutual coupling energies. There exists a force acting on the moving charges even though the fields completely vanish. This force makes the charges pass through the magnetic solenoid in different velocity with different path length, causing a phase shift the same as that obtained with quantum mechanics. The theory is originally aimed for providing an interpretation for electromagnetic radiation and mutual coupling. It is derived directly from the Maxwell theory with no modification but only substitution and reorganization.
The independence of the Aharonov-Bohm phase shift on particle velocity is one of its defining properties. The classical counterpart to this dispersionless behavior is the absence of forces along the direction of motion of the particle. A reevaluation of the experimental demonstration that forces are absent in the AB physical system is given, including previously unpublished data. It is shown that the debate on the presence or absence of forces is not settled, and an experiment searching for dispersionless forces is proposed.
The analogy between general relativity and electromagnetism suggests that there is a gravitational analog of the Aharonov–Bohm effect. There is indeed such an effect. Since gravitation couples to all fields, the effect should exist for photons. There is a close connection with the Sagnac effect. Both the electromagnetic field and the gravitational field are classical fields, so the effect could have been predicted in the interval between the publication of the theory of general relativity in 1915 and the discovery of quantum mechanics in the mid 1920s.
The Aharonov-Bohm (AB) effect is a purely quantum mechanical effect. The original (classified as type-I) AB-phase shift exists in experimental conditions where the electromagnetic fields and forces are zero. It is the absence of forces that makes the AB effect entirely quantum mechanical. Although the AB-phase shift has been demonstrated unambiguously, the absence of forces in type-I AB effects has never been shown. Here, we report the observation of the absence of time delays associated with forces of the magnitude needed to explain the AB-phase shift for a macroscopic system.