The contrasting roles of Planck's constant in classical and quantum theories
Abstract
We trace the historical appearance of Planck's constant in physics, and we note that initially the constant did not appear in connection with quanta. Furthermore, we emphasize that Planck's constant can appear in both classical and quantum theories. In both theories, Planck's constant sets the scale of atomic phenomena. However, the roles played in the foundations of the theories are sharply different. In quantum theory, Planck's constant is crucial to the structure of the theory. On the other hand, in classical electrodynamics, Planck's constant is optional, since it appears only as the scale factor for the (homogeneous) sourcefree contribution to the general solution of Maxwell's equations. Since classical electrodynamics can be solved while taking the homogenous sourcefree contribution in the solution as zero or nonzero, there are naturally two different theories of classical electrodynamics, one in which Planck's constant is taken as zero and one where it is taken as nonzero. The textbooks of classical electromagnetism present only the version in which Planck's constant is taken to vanish.
 Publication:

American Journal of Physics
 Pub Date:
 April 2018
 DOI:
 10.1119/1.5021355
 arXiv:
 arXiv:1710.01616
 Bibcode:
 2018AmJPh..86..280B
 Keywords:

 Physics  General Physics
 EPrint:
 9 pages