Novel Features of Classical Electrodynamics and Their Connection to the Elementary Charge, Energy Density of Vacuum and Heisenberg’s Uncertainty Principle—Review and Consolidation

Abstract

The paper provides a review and conciliation of the results pertinent to the energy and action associated with electromagnetic radiation obtained using classical electrodynamics and published in several journal papers. The results presented in those papers are based on three systems that generate electromagnetic radiation, namely, frequency domain antennas, time domain antennas and decelerating (or accelerating) charged elementary particles. In the case of radiation generated by a frequency domain antenna, the energy dissipated as radiation within half a period, U , satisfies the order of magnitude inequality U ≥ hv → q ≥ e where q is the magnitude of the oscillating charge in the antenna, e is the elementary charge, v is the frequency and h is the Planck constant. In the case of transient radiation fields generated by time domain antennas or the radiation emitted by decelerating (or accelerating) charged elementary particles, the energy dissipated by the system as radiation satisfies the order of magnitude inequality U τ r ≥ h / 4 π → q ≥ e where U is the energy dissipated as radiation by the system τ r , is the duration of the energy emission and q is either the charge in the current pulse in the case of the time domain antenna or the charge of the elementary particle giving rise to the radiation. These results are derived while adhering strictly to the principles of classical electrodynamics alone. These results were interpreted in different papers in different ways using different assumptions. In this paper, we provide a unified interpretation of the results, and combining these results with two simple quantum mechanical concepts, expression for the elementary charge as a function of other natural constants and the energy density of vacuum is derived. The expressions predict the elementary charge to an accuracy higher than about 1%.