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Capt. Robert M. Collins. Soviet research on the A-vector potential and scalar waves.
The Soviets have a number of theoretical research programs dealing with the A-vector potential and scalar waves. The A-vector potential is defined as the potential of the magnetic field. The theoretical ideas for the vector potential were first developed by James C. Maxwell, a 19th century theoretical physicist...
At one time it was believed that A had no real physical significance, but over the years this viewpoint had been altered, although some theoretical physicists still believe there is no significance to the A-vector. There are some physicists while believing that A is not real believe that the Aharonov-Bohm effect is real. The argument in this case is whether the A-vector is termed to be gauge invariant. Many other Soviet and US physicists, however, believe that the only way to explain the Aharonov-Bohm effect is to designate the A-vector potential as a real field. This might entail a new interpretation of electromagnetic theory; only time will tell if this is the case...
Special scalar fields (waves) (not electromagnetic) are thought to permeate the entire universe but their only utility is theoretical at this time. Electromagnetic fields can be represented by vector and scalar potentials, but the scalar field itself does not impart energy momentum under present physical conditions. The 19th century physicists Faraday, Ampere and Volta perceived that electromagnetism originates from scalar and vector potentials. More recently, a number of Soviet researchers have done extensive theoretical work with scalar fields and the early universe. Scalar fields are considered to have a real physical significance in the early universe when coupled to a gravitational field to produce effective gravitational force which was repulsive, which gave rise to an inflationary universe. However, the scalar field in this case is a Higgs field or special scalar field which has properties unlike that of the electromagnetic or gravitational fields...
Observations
• The Soviets have a basic research program dedicated to understanding the A-vector potential which could have possible technology applications.
• The Soviets are at par with the West in their theoretical and experimental research efforts for the A-vector potential and theoretical efforts with scalar waves fields.
• Although there is no indication of any military interest in the areas of the A-vector potentials and scalar waves, most of the institutes mentioned are some way connected with military projects.
• Advancements in this work may produce the basis for whole new concepts in communications, weapons and propulsion systems. Such applications will likely be interest to the military and most likely be cloaked in secrecy...
UNCLASSIFIED
E. J. Konopinski. 1977. What the electromagnetic vector potential describes. Physics Department, Indiana University.
However, only E, B are usually regarded as “real” physical fields. It remains quite customary to make statements that at least the vector potential A has no physical meaning – to regard its introduction as no more than a mathematical convenience, useful as a step in solving the Maxwell equations for E, B. The author has contradicted such statements to several generations of students, on the basis of some quite elementary findings, and has lately been urged to make these known to a wider, and perhaps more critical, audience.
A reason for hesitation has been doubt that questions about “reality” have any meaning in physics; it seems enough that a concept be useful, as is A in electromagnetism. That point is well expressed by Feynman, who goes on to stress the unavoidable role of A in quantum theory. The best-known explicit of such role is provided by the Bohm-Aharonov effect, which seems to have led to agreement that the vector potential acquires physical meaning only though its quantum effects. The effort here will be to show that A has always had a more explicit physical meaning, and direct measurability, already in “classical” situations.
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The direct detectability of the potentials ɸ and A, comparable to that of E and B, makes possible to regard descriptions of electromagnetic fields by potentials quite as “fundamental” as descriptions by E and B. Indeed, the potentials might be considered the more “basic” with (1) providing definitions of E and B as “derived” concepts. Potentials represent field energies and field momenta, per unit charge, as those participate in the universal conservation of energy and momentum, whereas force and work rate per unit charge, can be regarded as merely convenient terms for the transfers rates.
Giuseppe Giuliani. 2010. Vector potential, electromagnetic induction and “physical meaning”. Dipartimento di Fisica “Volta”, Universita degli Studi di Pavia, Italy.
A forgotten experiment by Andre Blondel (1914) proves, as held on the basis of theoretical arguments in a previous paper, that the time variation of the magnetic flux is not the cause of the induced emf: the physical agent is instead the vector potential though the term –ƏA/Ət (when the induced circuit is at rest)...
The history of the role of vector potential – and, more generally, of potentials – in electromagnetism is an intricate one. A reader willing to go through the vast literature might consider the compendious paper by Roche as starting point, the paper by Jackson and Okun as a second step and the book by Darrigol for an overall picture of nineteenth century electrodynamics.
The main thread may described as follows: does the vector potential have “physical meaning” or is it just a mathematical device that could, in the end be dismissed? As the historical development shows, the issue has physical and epistemological relevance. Therefore, it cannot be neglected in teaching electromagnetism to physics students at university (undergraduate/graduate) level. In particular, teachers should be well aware of the subtitles underlying the interplay between fields and potentials. It is well known that Maxwell made ample use of a “physically meaningful” vector potential in the description of electromagnetic phenomena. However, at the end of the nineteenth century, owing to the challenges by Heaviside and Hertz, the vector potential was reduced to a “magnitude which serves as calculation only”...
Thereafter, according to [1], the vector potential has been usually treated in textbooks according to Heaviside’s and Hertz’s approach until the appearance of Feynman Lectures with his discussion about what must be considered as a “real field”. According to Feynman, a “real field” is “a mathematical function we are using for avoiding the idea of action at a distance” [7, page 15.7]. This definition appears as an unwitting quotation of Hertz’s comment reported above: however, Feynman does not reach Hertz’s conclusion that the vector potential can be dismissed. In fact, Feynman writes that “We have introduced A because it does have an important physical significance . . . In any region where B = 0 even if A is not zero, such as outside a solenoid, there is no discernible effect of A. Therefore, for a long time it was believed that A was not a “real” field. It turns out, however, that there are phenomena involving quantum mechanics [Aharonov - Bohm effect] which show that the field A is in fact a “real” field in the sense we have defined it [7, page 15.8].” Clearly, according to Feynman, the vector potential acquires “physical meaning” only from quantum phenomena.
[1] Roche JJ. A critical study of the vector potential in: Roche JJ, ed. 1990 Physicists look back (Bristol: Adam Hilger) p. 144
[2] Jackson DJ and Okun LB. 2001. Historical roots of gauge invariance Rev. Mod. Phys.73, 663
[3] Darrigol O. 2003 Electrodynamics from Ampere to Einstein (Oxford: Oxford University Press)
[7] Feynman R, Leighton R and Sands M. 1964. The Feynman Lectures on Physics (Reading, Ma.: Addison Wesley) vol 2


