Communication theory and physics

The electromagnetic signals used in communication are subject to the general laws of radiation. One obtains a complete representation of a signal by dividing the time-frequency plane into cells of unit area and associating with every cell a "ladder" of distinguishable steps in signal intensity. The steps are determined by Einstein's law of energy fluctuation, involving both waves and photons. This representation, however, gives only one datum per cell, viz. the energy, while in the classical description one has two data; an amplitude and a phase. It is shown in the second part of the paper that both descriptions are practically equivalent in the long-wave region, or for strong signals, as they contain approximately the same number of independent, distinguishable data, but the classical description is always a little less complete than the quantum description. In the best possible experimental analysis the number of distinguishable steps in the measurement of amplitude and phase is only the fourth root of the number of photons. Thus it takes a hundred million photons per cell in order to define amplitude and phase to one percent each.