Complex-Valued Electromagnetic Fields Suggest that Time is Three Dimensional

The goal of this study is to determine the implications of assuming that electromagnetic (EM) fields have complex-valued components whose imaginary portions are unobservable. Maxwell’s equations (MEs) are extended to accommodate complex fields without violating existing experimental results, and their increased symmetry is demonstrated via a formal EM duality transformation [1,2]. While the imaginary-valued field components are not directly observable, analysis indicates that they should be indirectly detectable experimentally. Predictions that follow from the complex MEs include that time (like space) has an underlying 3D nature, that magnetic monopoles exist while explaining why they have not been detected in past experimental searches, and that the imaginary-valued parts of EM waves propagate through time at the same rate as an inertial observer at rest in space. These predictions indicate a critical need for experimental tests that could falsify/support the existence of complex-valued EM fields.

1. Reggia, J. Physica Scripta, 99, 2024, doi.org/10.1088/1402-4896/ad10dc

2. Reggia, J. Frontiers in Physics, 12, 2024, doi.org/10.3389/fphy.2024.1388397