Maximizing the symmetry of Maxwell’s equations

Abstract

Maxwell’s equations can be successfully extended to electromagnetic fields having three complex-valued components rather than their usual three real-valued components. Here the implications of interpreting the imaginary-valued components as extending into time rather than space are explored. The complex-valued Maxwell equations remain consistent with the original Maxwell equations and the experimental results that they predict. Further, the extended equations predict novel phenomena such as the existence of electromagnetic waves that propagate not only through regular space but also through a separate temporal space (time) that is implied by the three imaginary components of the fields. In a vacuum, part of these imaginary valued waves propagates through time at the same rate as an observer stationary in space. While the imaginary valued field components are not directly observable, analysis indicates that they should be indirectly detectable experimentally based on secondary effects that occur under special circumstances. Experimental investigation attempting to falsify or support the existence of complex valued electromagnetic fields extending into time is merited due to the substantial theoretical and practical implications involved.