Electric and magnetic charge in Einstein's unified field theory

Abstract

Some new approximate solutions to the field equations of Einstein's unified field theory are constructed, and the physical significance of the theory is examined. According to the conventional physical interpretation of the theory, the singularities of the new solutions should represent magnetically charged point masses. It is found that in order to satisfy the field equations, such solutions must contain not only the usual pointlike singularities, but also "string" singularities similar to those in Dirac's theory of magnetic poles. It is possible, nevertheless, to derive equations of motion for the pointlike charges at the ends of the "strings," which turn out to be very similar to the Lorentz-Dirac equation. The paths of the "strings" are not arbitrary, but must also satisfy certain constraint conditions. On the basis of the equations of motion obtained, it is suggested that it may be possible to make an alternative physical interpretation of Einstein's theory, in which the point singularities of the new solutions are electric charges, rather than magnetic charges. The conventional interpretation of the theory is based on equations of motion found by Johnson, for some different approximate solutions to the field equations. If either interpretation is accepted, then the equations of motion in each case imply modifications of Maxwell's equations for macroscopic electromagnetic fields. The modifications are similar, but not identical, in the two cases. Some observational tests of the modified electromagnetic fields predicted by the theory are discussed, with emphasis on contrasting the two possible interpretations of electric charge. In each case, the field which deviates from the usual Maxwell theory involves a length parameter, an integration constant whose magnitude is not fixed by the theory, at this stage. It is shown that terrestrial tests of Maxwell's equations imply that this length must be greater than about 15 Earth radii, regardless of which interpretation one supposes to be true. It is then observed that the theory does imply an upper bound on the length parameter. Although this theoretical upper limit is not precise, a limit only a few orders of magnitude larger than the current experimental lower limit is suggested. This means that Einstein's theory deviates significantly from Maxwell's theory over astronomical distances. Some astrophysical situations where effects of the theory could be seen in static magnetic dipole fields are mentioned. These offer the possibility of testing whether Einstein's theory is correct, and of determining which type of singularity represents a point electric charge.