The Deep Physics Hidden within the Field Expressions of the Radiation Fields of Lightning Return Strokes

Based on the electromagnetic fields generated by a current pulse propagating from one point in space to another, a scenario that is frequently used to simulate return strokes in lightning flashes, it is shown that there is a deep physical connection between the electromagnetic energy dissipated by the system, the time over which this energy is dissipated and the charge associated with the current. For a given current pulse, the product of the energy dissipated and the time over which this energy is dissipated, defined as action in this paper, depends on the length of the channel, or the path, through which the current pulse is propagating. As the length of the channel varies, the action plotted against the length of the channel exhibits a maximum value. The location of the maximum value depends on the ratio of the length of the channel to the characteristic length of the current pulse. The latter is defined as the product of the duration of the current pulse and the speed of propagation of the current pulse. The magnitude of this maximum depends on the charge associated with the current pulse. The results show that when the charge associated with the current pulse approaches the electronic charge, the value of this maximum reaches a value close to h/8π where h is the Plank constant. From this result, one can deduce that the time-energy uncertainty principle is the reason for the fact that the smallest charge that can be detected from the electromagnetic radiation is equal to the electronic charge. Since any system that generates electromagnetic radiation can be represented by a current pulse propagating from one point in space to another, the result is deemed valid for electromagnetic radiation fields in general.