The Dirac Relation, Einstein Coefficients, And The Blackbody Spectrum

Authors

D.W. Schlitt, University of Utrecht

Date of this Version

1973

Citation

Published in Transactions of the Nebraska Academy of Sciences, Volume 2 (1973).

Comments

Copyright 1973 by the author(s).

Abstract

This investigation of some interesting interrelationships in physics was brought about by a mistake. In late 1970 a paper appeared in Physical Review Letters which purported to calculate the effect of the presence of nearby rooms on the emissions and absorption transition probabilities of an atom, (Koutsoyannis 1970). The authors of the paper claimed to show that the usual Dirac relations between these probabilities were altered by collision effects.

It was subsequently pointed out by several physicists that there was a serious mathematical error in the paper which invalidated the results. This was acknowledged in a subsequent erratum. The paper of Koutsoyannis is consequently of no further interest. It is mentioned here only as a historical note on the origins of what follows.

Skepticism about this "result" led me to investigate some of the very fundamental principles behind the Dirac relation and the consequences of its modification. It was found that the black body radiation spectrum would be modified. Experimentally measurable consequences of the modification were than investigated.

The results in themselves are probably not terribly important for physics. They do, however, point out some interesting interrelationships. The recognition of this kind of thing is important for the student of physics.

The general principles of time reversal, detailed balance, and thermal equilibrium place strong requirements on the ratio of the emission and absorption probabilities. Stated in a different way, the modification of the Dirac result W_e/W_a = (n_w+1)/n_w requires a modification of the black body radiation formula. Here n_w is the average number of photons, with frequency w in the radiation field.

To establish this we follow the general outlines of the argument made by Einstein (Bohm, 1951). The probability of absorption can be written

W_a = A_nm I(w)