On a generalization in quantum theory: Is h Planck constant?

John P. Ralston

Timothy H. Boyer

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) source-free contribution to the general solution of Maxwell's equations. Since classical electrodynamics can be solved while taking the homogenous source-free contribution in the solution as zero or non-zero, 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 non-zero. The textbooks of classical electromagnetism present only the version in which Planck's constant is taken to vanish.

Ronald J. Adler, David Santiago

A. A. Lipovka

In the present work we suggest a non-local generalization of quantum theory which include quantum theory as a particular case. On the basis of the idea, that Planck constant is an adiabatic invariant of free electromagnetic field, we calculate the value of Plank constant from first principles, namely from the geometry of our Universe. The basic nature of the quantum theory is discussed. The nature of the dark energy is revealed.

Friedwardt Winterberg

Lipovka, Anton Anton

In the present work we suggest a non-local generalization of quantum theory which include quantum theory as a particular case. On the basis of the idea, that Planck constant is an adiabatic invariant of free electromagnetic field, we calculate the value of Plank constant from first principles, namely from the geometry of our Universe. The basic nature of the quantum theory is discussed. The nature of the dark energy is revealed.