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.
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.
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.
One of the long-standing conundrums of science is the exact mathematical relationship of quantum mechanics to Newtonian physics, as well as to relativistic physics. Herein it is shown to be possible to use the Planck constant as represented by the quantum formula for photon energy, E=hc/λ , where h is the Planck constant, and using an approach similar to Bohr’s classical mechanical solution for the atom, to construct equations that show the mathematical relationship among all three in fundamental terms. This has the possibility of showing how relativity applied to Newtonian physics produces a quantum mechanical result, and may lead to a better understanding of quantum mechanics from a non-statistical approach, as well as possibly allowing a direct calculation of quantum gravity.
Planck's constant h is considered to be a fundamental Universal constant of Physics. And although we can experimentally determine its value to great precision, the reason for its existence and what it really means is still a mystery. Quantum Mechanics has adapted it in its mathematical formalism, as it also has the Quantum Hypothesis. But QM does not explain its meaning or prove its existence. Why does the Universe need h and energy quanta? Why does the mathematical formalism of QM so accurately reflect physical phenomena and predict these with great precision? Ask any physicists and uniformly the answer is that's how the Universe works. The units of h are in energy-time and the conventional interpretation of h is as a quantum of action. But in this brief note we take a different view. We interpret h as the minimal accumulation of energy that can be manifested in our measurements. Certainly the units of h agree with such interpretation. Based on this we provide a plausible explanation for the existence of Planck's constant, what it means and how it comes about. We show that the existence of Planck's constant is not so much dictated by the Universe but rather by Mathematics and the inner consistence and calibrations of Physics.
An interesting case of the complex interaction between theory and experiment can be found in many experiments in quantum physics employing classical reasoning. It is expected that this practice would lead to quantitative inaccuracy, unless the measurements’ results were averaged. Whether or not this inaccuracy is significant depends critically on the details of the particular experimental situation. The example of Millikan's photoelectric experiment, in which he obtained a precise value of Planck's constant, provides a good case for illustrating the process of estimating the inaccuracy resulting from the classical‐quantum discrepancy. In the case of Millikan's experiment, it seems that a significant inaccuracy was avoided because of fortunate coincidences. In general, in the absence of a careful analysis, it is impossible to say whether the use of classical reasoning interferes with the accuracy of a quantum‐physical experiment.
Is the formalism of quantum mechanics complete? Examination of Max Karl Planck's original quantum work suggests the answer is "No".1-3 Retrospective analysis of Planck's foundational quantum derivation suggests that his action constant ("h") is actually the product of an energy constant ("h̃") and a time variable (tm"). Planck's ground-breaking quantum formula, "E = hν" (E is energy and ν is frequency) may more appropriately be denoted as, "E = h̃tmν". The energy constant represents the energy of a single oscillation or wave of electromagnetic (EM) energy, and is constant regardless of frequency, wavelength or photon energy. The time variable (as originally defined by Planck) is the measurement time of the electromagnetic energy. The invariance of the EM energy constant over a change in time or space suggests it represents a universal constant for light. Retrospective evaluation also reveals that Planck inadvertently fixed the EM measurement time (tm) at a value of one (1) second, thereby significantly limiting the time variable's degrees of freedom. Implications appear to be profound for restoring infinite degrees of freedom to the EM measurement time variable. Quantum re-interpretation using the energy constant and measurement time variable suggest conservation of energy, momentum and mass for a single oscillation of light. A deeper layer of foundations in physics may yet need to be built.