General Dynamics. Principle of Relativity. [NOOK Book]

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"A System of Physical Chemistry", Volume 3 (1919) by William Cudmore McCullagh Lewis and James Rice explains:

...it is doubtful if the principle of equipartition based on such an interpretation of the word "average" is really proved at all by dynamical principles. The point is fully treated by Jeans in his Dynamical Theory of Gases. It would appear that the "average" really referred to is an average extended over all conceivable conditions or "complexions " of a system (excepting a negligible number) and not merely over such conditions or "complexions" through which the system passes on any particular "path ". The extension to "time" average cannot be made unless by the introduction of Maxwell's assumption of "continuity of path," viz. that the system will in process of time pass through all conceivable "complexions ". This assumption is of doubtful validity, and is known to be unsound in certain of the problems treated in general dynamics, e.g. the periodic orbits of astronomy (a type of vibratory motion).

To proceed, Planck, denying the applicability of equipartition to radiation theory, works out from special considerations (to be dealt with presently) that in the vibratory motion obtaining in wave-trains, each degree of freedom corresponding to a frequency v should possess on the average not kT ergs of kinetic and potential energy...

It is only natural that, in adopting a more or less revolutionary attitude to a principle hitherto enjoying the confidence of the scientific world, Planck and his followers should have modified somewhat the original presentation of their ideas to meet the various criticisms urged by those who seek to retain the traditional standpoint. It is well known that Planck himself has receded somewhat from the position adopted in his earlier papers on the subject. This position is fully expounded in the first (1906) edition of his book, Theorie der Warmestrahlung (Leipzig, Barth); the later form of his theory is contained in Deutsch. Phys. Gesell. Ver., 13, 3, '138, 1911, or in the second (1913) edition of the above book. Einstein's speculations and applications are to be found in various papers in the Annalen der Physik from 1905 onwards.

It is impossible to reproduce the whole of Planck's line of argument here, but the following brief account will bring out the essentially novel principle introduced by him, and serve also to show to some extent why and how he receded from the earlier to the later position.

He remarks that any radiating mecrfanism of frequency v, placed in a temperature enclosure, will acquire an average energy depending on the energy-density of the radiation of that frequency in the enclosure. The radiating mechanism of which he avails himself is an electric doubtlet, consisting of an electrified particle vibrating harmonically under the attraction of an oppositely electrified nucleus to which it is held by a force of the usual elastic, proportional-to-the-displacement type. In the enclosure there exist a great number N of these doublets or "oscillators," having their axes fixed in a certain direction, i.e. endowed with one degree of freedom. By an application of the usual equations of the electro-magnetic field.

Planck, however, avoids this by assuming that his oscillators can only emit and absorb discontinuously, and that at any instant the energy of an oscillator can only be an integral multiple of a finite unit or "quantum " of energy, the amount of the unit depending on the frequency. It is to be carefully noted that this does not imply, of necessity, an atomic structure for energy— a view, indeed, repudiated by Planck; it does imply that the oscillator must emit or absorb whole quanta of radiation at one time (at present, be it noted, we are discussing Planck's earlier views). Now such an assumption necessarily involves a modification of Maxwell's distribution law, for that law depends on the possibility of the infinite divisability of the energy among the oscillators, atoms, molecules, and so forth. The point is more easily followed with aid of a "condition-diagram".