The physical significance of the electromagnetic potentials and the meaning of gauge



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A brief history of electromagnetic theory is presented in which the introduction of the potentials and the first concepts of gauge are discussed. Gauge transformations and the various gauge conditions are then presented. Predictions of the effects of potentials on electrons (i.e., the Aharanov-Bohm effect) and the subsequent experimental affirmation of these effects to within an accuracy of 4%, are reported. As a result, the potentials were said to possess a physical significance--a claim that was to be widely assailed in the literature. A large percentage of these criticisms are reported and many of them are discussed. On the most part they represent a tremendous diversity of opinion which tends to obscure the real issues. The physical significance of gauge is discussed in which one of the possibilities is that gauge is related to charge conservation. Several other possibilities are also.reported. Finally, certain aspects of gauge are discussed in a five-dimensional field theory formulation in which a geometrical interpretation of gauge is given, and various five-dimensional gauge conditions are reported. This theory is presented as a possible basis for attacking the many problems associated with the significance of the potentials and the meaning of gauge.