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Physical Review

Remarks on the Possibility of Quantum Electrodynamics without Potentials

Yakir Aharonov, David Böhm

Published Mar 15, 1962• 56 citations
Publisher

Abstract

In this article, we reply to a suggestion of DeWitt for formulating a nonlocal quantum electrodynamics without potentials, showing that his proposal is not a real elimination of potentials, but only a substitution with the aid of which the essential role of potentials is somewhat obscured. Thus, we are not led to change our conclusion that potentials are significant in the formulation of quantum electrodynamics. We do, however, discuss some of the conditions that would have to be satisfied by an essentially nonlocal electrodynamics, and show that such a theory, if it could be developed, would very probably bring about profound modifications in the forms of the laws of quantum mechanics.

DOI
10.1103/physrev.125.2192

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In this article, we reply to a suggestion of DeWitt for formulating a nonlocal quantum electrodynamics without potentials, showing that his proposal is not a real elimination of potentials, but only a substitution with the aid of which the essential role of potentials is somewhat obscured. Thus, we are not led to change our conclusion that potentials are significant in the formulation of quantum electrodynamics. We do, however, discuss some of the conditions that would have to be satisfied by an essentially nonlocal electrodynamics, and show that such a theory, if it could be developed, would very probably bring about profound modifications in the forms of the laws of quantum mechanics.
In this article, we discuss in further detail the significance of potentials in the quantum theory, and in so doing, we answer a number of arguments that have been raised against the conclusions of our first paper on the same subject. We then proceed to extend our treatment to include the sources of potentials quantum-mechanically, and we show that when this is done, the same results are obtained as those of our first paper, in which the potential was taken to be a specified function of space and time. In this way, we not only answer certain additional criticisms that have been made of the original treatment, but we also bring out more clearly the importance of the potential in the expression of the local character of the interaction of charged particles and the electromagnetic field.
In this paper, we discuss some interesting properties of the electromagnetic potentials in the quantum domain. We shall show that, contrary to the conclusions of classical mechanics, there exist effects of potentials on charged particles, even in the region where all the fields (and therefore the forces on the particles) vanish. We shall then discuss possible experiments to test these conclusions; and, finally, we shall suggest further possible developments in the interpretation of the potentials.
The Feynman path integral plays a crucial role in quantum mechanics, offering significant insights into the interaction between classical action and propagators, and linking quantum electrodynamics (QED) with Feynman diagrams. However, the formulations of path integrals in classical quantum mechanics and QED are neither unified nor interconnected, suggesting the potential existence of an important bridging theory that could be key to solving existing puzzles in quantum mechanics. In this work, we delve into the theoretical consistency, completeness, and integration with established path integral theories, revealing this concealed path integral form. This newly uncovered form not only connects various path integral approaches but also demonstrates its potential in explaining quantum phenomena like the origin of spin and quantum nonlocal correlations. It transcends conventional quantum mechanics, proposing a more profound and fundamental physical principle.
Quantum electrodynamics under conditions of distinguishability of interacting matter entities, and of controlled actions and back-actions between them, is considered. Such ``mesoscopic quantum electrodynamics'' is shown to share its dynamical structure with the classical stochastic electrodynamics. In formal terms, we demonstrate that all general relations of the mesoscopic quantum electrodynamics may be recast in a form lacking Planck's constant. Mesoscopic quantum electrodynamics is therefore subject to ``doing quantum electrodynamics while thinking classically,'' allowing one to substitute essentially classical considerations for quantum ones without any loss in generality. Implications of these results for the quantum measurement theory are discussed.
Is it possible to offer a "no drama" quantum theory? Something as simple (in principle) as classical electrodynamics - a theory described by a system of partial differential equations in 3+1 dimensions, but reproducing unitary evolution of a quantum field theory in the configuration space? The following results suggest an affirmative answer: 1. The scalar field can be algebraically eliminated from scalar electrodynamics; the resulting equations describe independent evolution of the electromagnetic field. 2. After introduction of a complex 4-potential (producing the same electromagnetic field as the standard real 4-potential), the spinor field can be algebraically eliminated from spinor electrodynamics; the resulting equations describe independent evolution of the electromagnetic field. 3. The resulting theories for the electromagnetic field can be embedded into quantum field theories. Another fundamental result: in a general case, the Dirac equation is equivalent to a 4th order partial differential equations for just one component, which can be made real by a gauge transform. Issues related to the Bell theorem are discussed.
I argue that the metaphysical import of the Aharonov-Bohm effect has been overstated: correctly understood, it does not require either rejection of gauge invariance or any novel form of nonlocality. The conclusion that it does require one or the other follows from a failure to keep track, in the analysis, of the complex scalar field to which the magnetic vector potential is coupled. Once this is recognised, the way is clear to a local account of the ontology of electrodynamics (or at least, to an account no more nonlocal than quantum theory in general requires); I sketch a possible such account.