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Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento

Classical interpretation of the uncertainty relations and the old quantum theory

Emilio Santos

Published Jul 1, 1972• 17 citations
Publisher
DOI
10.1007/bf02757152

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PROBABILITY IN THE OLD QUANTUM THEORY Probability was connected to quantum theory right from the start, in 1900, through the derivation of Planck's radiation law. But not much attention has been paid to the concept of probability in quantized radiation, or in the ‘quantum jumps’ from one energy level to another in an atom, and related problems. A whole chapter or book, instead of a section, could be written on the background of quantum theory in statistical mechanics and spectral analysis with this aspect in mind. Probabilistic properties were included in very many of the most important papers dealing with radiation between 1900 and 1925. It became also clear in time that Planck's law could not be derived from classical physics. Einstein admits this around 1908. Later he said, in a work of 1917, that it is a weakness of the theory of photon emission that ‘it leaves to “chance” the time and direction of the elementary processes,’ thereby, according to Pais (1982, p. 412), making explicit ‘that something was amiss with classical causality.’ It remains somewhat open how the origins and shifting interpretations of probability in the old quantum theory affected the acceptance of the probabilistic interpretation of the new quantum mechanics of 1925–1926, and of the indeterminism that found its confirmation in Heisenberg's uncertainty relation in 1927.

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The concept of ‘Non-permissible experiments’ permeated the literature by Merzbacher as an articulation of Heisenberg’s Rules. Ample experiments in Modern Physics deem forbidden, but never the less, they do not violate the uncertainty relations. In contrast, recent ultrasonic time-of-flight experiments in condensed-matter channels, encounter violation of the uncertainty principle. Accordingly these agree with the de Broglie-Bohm interpretation of quantum mechanics, which does not support the uncertainty relations, and elaborated by the quantum theory of motion. This theory is expanded to account for ultrasound-phononic dispersion in condensed-matter channels.

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Examples of the uncertainty principle

C. G. DARWIN

Abstract 1. In the general synthesis of classical dynamics with the quantum theory, the Uncertainty Principle plays a most useful part. It is of course only one aspect of the new mechanics, but it is a very helpful one since by its means it becomes easy to see where the old classical ideas broke down. The state of affairs in the quantum theory is not unlike that of the early days of relativity, when most of those who studied the subject felt the need of supporting the formal theory by seeing how the old ideas failed in specific cases. Here the formal theory is very abstract and is not easy to follow intuitively, and the Uncertainty Principle plays much the same rôle as did the examples of clocks and rods in relativity theory. For this reason it is more appropriate for illustrative examples, than for any extreme generality, and though a number of examples have been already given by Heisenberg and Bohr, it may not be amiss to have some more. There are probably some who will have shared my experience that it is often by no means easy to detect how the uncertainty enters into a given experiment, though once detected the arguments are usually very simple. In a recent conversation Professor Bohr criticised some rather careless remarks that I had made, and the present work was undertaken to clear matters up. It may be shortly described as a study of the Uncertainty Principle in connection with electrometers and magnetometers. It may be of interest to point out that the Uncertainty Principle can be regarded from a rather different aspect. The "resolving power" of optical instruments was discussed very fully by Rayleigh on wave principles, but as long as matter was regarded in the classical manner, a mechanical instrument could be considered as capable of measuring quantities with absolute accuracy. Now that we know that matter also has wave properties, there is need of a theory of the resolving power of mechanical instruments, and this is exactly what the Uncertainty Principle supplies.

Proceedings of the Royal Society of London Series A Containing Papers of a Mathematical and Physical Character•Mar 2, 1931•6 citations
PROBABILITY IN THE OLD QUANTUM THEORY Probability was connected to quantum theory right from the start, in 1900, through the derivation of Planck's radiation law. But not much attention has been paid to the concept of probability in quantized radiation, or in the ‘quantum jumps’ from one energy level to another in an atom, and related problems. A whole chapter or book, instead of a section, could be written on the background of quantum theory in statistical mechanics and spectral analysis with this aspect in mind. Probabilistic properties were included in very many of the most important papers dealing with radiation between 1900 and 1925. It became also clear in time that Planck's law could not be derived from classical physics. Einstein admits this around 1908. Later he said, in a work of 1917, that it is a weakness of the theory of photon emission that ‘it leaves to “chance” the time and direction of the elementary processes,’ thereby, according to Pais (1982, p. 412), making explicit ‘that something was amiss with classical causality.’ It remains somewhat open how the origins and shifting interpretations of probability in the old quantum theory affected the acceptance of the probabilistic interpretation of the new quantum mechanics of 1925–1926, and of the indeterminism that found its confirmation in Heisenberg's uncertainty relation in 1927.
The concept of ‘Non-permissible experiments’ permeated the literature by Merzbacher as an articulation of Heisenberg’s Rules. Ample experiments in Modern Physics deem forbidden, but never the less, they do not violate the uncertainty relations. In contrast, recent ultrasonic time-of-flight experiments in condensed-matter channels, encounter violation of the uncertainty principle. Accordingly these agree with the de Broglie-Bohm interpretation of quantum mechanics, which does not support the uncertainty relations, and elaborated by the quantum theory of motion. This theory is expanded to account for ultrasound-phononic dispersion in condensed-matter channels.
Abstract 1. In the general synthesis of classical dynamics with the quantum theory, the Uncertainty Principle plays a most useful part. It is of course only one aspect of the new mechanics, but it is a very helpful one since by its means it becomes easy to see where the old classical ideas broke down. The state of affairs in the quantum theory is not unlike that of the early days of relativity, when most of those who studied the subject felt the need of supporting the formal theory by seeing how the old ideas failed in specific cases. Here the formal theory is very abstract and is not easy to follow intuitively, and the Uncertainty Principle plays much the same rôle as did the examples of clocks and rods in relativity theory. For this reason it is more appropriate for illustrative examples, than for any extreme generality, and though a number of examples have been already given by Heisenberg and Bohr, it may not be amiss to have some more. There are probably some who will have shared my experience that it is often by no means easy to detect how the uncertainty enters into a given experiment, though once detected the arguments are usually very simple. In a recent conversation Professor Bohr criticised some rather careless remarks that I had made, and the present work was undertaken to clear matters up. It may be shortly described as a study of the Uncertainty Principle in connection with electrometers and magnetometers. It may be of interest to point out that the Uncertainty Principle can be regarded from a rather different aspect. The "resolving power" of optical instruments was discussed very fully by Rayleigh on wave principles, but as long as matter was regarded in the classical manner, a mechanical instrument could be considered as capable of measuring quantities with absolute accuracy. Now that we know that matter also has wave properties, there is need of a theory of the resolving power of mechanical instruments, and this is exactly what the Uncertainty Principle supplies.