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The London Edinburgh and Dublin Philosophical Magazine and Journal of Science

CIII. Communication theory and physics

Деннис Габор

Published Jan 1, 1950• 61 citations
Publisher

Abstract

Summary 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.

DOI
10.1080/14786445008561157

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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.

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Summary 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.
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.
Hitherto communication theory was based on two alternative methods of signal analysis. One is the description of the signal as a function of time; the other is Fourier analysis. Both are idealizations, as the first method operates with sharply defined instants of time, the second with infinite wave-trains of rigorously defined frequencies. But our everyday experiences—especially our auditory sensations—insist on a description in terms of both time and frequency. In the present paper this point of view is developed in quantitative language. Signals are represented in two dimensions, with time and frequency as co-ordinates. Such two-dimensional representations can be called “information diagrams,” as areas in them are proportional to the number of independent data which they can convey. This is a consequence of the fact that the frequency of a signal which is not of infinite duration can be defined only with a certain inaccuracy, which is inversely proportional to the duration, and vice versa. This “uncertainty relation” suggests a new method of description, intermediate between the two extremes of time analysis and spectral analysis. There are certain “elementary signals” which occupy the smallest possible area in the information diagram. They are harmonic oscillations modulated by a “probability pulse.” Each elementary signal can be considered as conveying exactly one datum, or one “quantum of information.” Any signal can be expanded in terms of these by a process which includes time analysis and Fourier analysis as extreme cases.These new methods of analysis, which involve some of the mathematical apparatus of quantum theory, are illustrated by application to some problems of transmission theory, such as direct generation of single sidebands, signals transmitted in minimum time through limited frequency channels, frequency modulation and time-division multiplex telephony.
This chapter discusses electromagnetic waves and photons. It begins by reviewing some basic ideas on the properties of waves, introducing the wave properties of radiation. There are several reasons for starting with a discussion of electromagnetic radiation. Historically, it was in this area that the quantum theory first developed. The applications of the light-quantum hypothesis, as it was first called, also provide key pieces of evidence for the quantization of energy in atoms and molecules. The chapter then looks at the evidence for the wave nature of light and of X-rays, before putting these two forms of radiation into the context of electromagnetic radiation in general. It also considers Albert Einstein's analysis of the photoelectric effect. Finally, the chapter assesses the statistical nature of photons.
Abstract The question of fluctuations in electromagnetic radiation played an important part during the first period of the development of quantum theory. After having introduced (Einstein 1905) the conception of light quanta or photons in order to explain the observed phenomena of the photoelectric effect, Einstein (1909) considered the consequences of this idea for other properties of the radiation. Planck’s formula for the energy density of radiation implies, by arguments of general thermodynamics and statistics, the following expression for the mean square fluctuation of the energy contained in a volume v in terms of the mean energy Ēv.
On the critical evaluation basis of the signals theory it is shown that it is necessary to develop its physical aspect, based on the quantum ideas. Within the framework of the quantum approach, where the energy of radiation changes over time in jump, the existence of frequency-temporal duality of photons is shown and the absence of operator connection between the time and frequency characteristics of the optical signal. The instantaneous power of the optical signal is described by a sequence of delta functions, similar to the sampled signal in the communication theory. Methods of communication theory and properties of photon spin allowed to make the transition to the classical approximation of the optical signal.
The necessity of development of the physical signal theory (ST) as component of laser theory is justified, and its principles are stated. These principles include quantum description of signals in the form of electromagnetic (EM) field and their classical representation. The submitted researches are based on Planck hypothesis about discrete levels of energy of EM radiation, Einstein hypothesis about light quantum and Bohr rule of frequencies only, and in so doing Heisenberg indeterminateness principle is taken into account.