The Time Domain Transition Radiation as a Vehicle to Probe the Connection between the Elementary Charge, Heisenberg’s Uncertainty Principle and the Size of the Universe

Starting with the well-established field equations that describe the radiation fields of lightning return strokes, 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 transition radiation. The results show that for a charged particle moving with speed v , the longitudinal momentum associated with the transition radiation is approximately equal to / E c for values of 1 / v c − smaller than about 10-3 where E is the total radiated energy and c is the speed of light in free space. The action of the transition radiation, defined as the product of the energy dissipated and the duration of the emission, increases as 1 / v c − decreases and, for an electron, it becomes equal to / 4 h π when m v c v = − where m v 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.