Constants of quantum physics

Timothy H. Boyer

One should not confuse a physical constant with a theory which incorporates the constant. Planck's constant h can appear in classical or quantum theories.

Paul G. Quincey

The proposed revision of SI units would embed Planck?s constant into the definition of the kilogram, as a fixed constant of nature. Traditionally, Planck?s constant is not readily interpreted as the size of something physical, and it is generally only encountered by students in the mathematics of quantum physics. Richard Feynman?s path integral formulation of quantum mechanics allows a neat visualization of the constant as the circumference of a surveyor?s wheel for measuring action along each path, making Planck?s constant a natural yardstick, almost literally. This approach is shown to have other benefits in the presentation of other basic quantum phenomena.

Miguel Ferrero, Alwyn van der Merwe

Armin Uhlmann

Владик Крейнович, Andrés Felipe Ortiz

For any physical theory, to experimentally check its validity, we need to formulate an alternative theory and check whether the experimental results are consistent with the original theory or with an alternative theory. In particular, to check whether energy is preserved, it is necessary to formulate an alternative theory in which energy is not preserved. Formulating such a theory is not an easy task in quantum physics, where the usual Schroedinger equation implicitly assumes the existence of an energy (Hamiltonian) operator whose value is preserved. In this paper, we show that the only way to get a consistent quantum theory with energy non-conservation is to use Heisenberg representation in which operators representing physical quantities change in time. We prove that in this representation, energy is preserved if and only if Planck's constant remains a constant. Thus, an appropriate quantum analogue of a theory with non-preserved energy is a theory in which Planck's constant can change -- i.e., is no longer a constant, but a new field.