Classical Electromagnetic Fields of Moving Charges as a Vehicle to Probe the Connection between the Elementary Charge and Heisenberg’s Uncertainty Principle

Abstract

The radiation fields generated when a charged particle is incident on or moving away from a perfectly conducting plane are obtained. These fields are known in the literature as transition radiation. The field equations derived thus are used to evaluate the energy, momentum and the action associated with the radiation. The results show that for a charged particle moving with speed ν , the longitudinal momentum associated with the transition radiation is approximately equal to Δ U / c for values of 1- ν/ c smaller than about 10 -3 where Δ U is the total radiated energy dissipated during the interaction and c is the speed of light in free space. The action of the radiation, defined as the product of the total energy dissipated and the duration of the emission, increases as 1- ν/ c decreases and, for an electron, it becomes equal to h /4 π when ν = c - ν m where ν m is the speed pertinent to the lowest possible momentum associated with a particle confined inside the universe and h is the Planck constant. Combining these results with Heisenberg’s uncertainty principle, an expression that predicts the value of the elementary charge is derived.