Abstract
Re-examination of the work of Max Karl Planck has revealed hidden variables in his famous quantum work, consistent with Einstein's famous sentiment that quantum mechanics is incomplete due to the existence of hidden variables. The recent discovery of these previously hidden variables, which have been missing from the foundational equations of quantum theory for more than one hundred years, has important implications for all the sciences as well as for understanding the interactions of electromagnetic radiation with matter. Planck's quantum formula, E = hν, is missing the variable for measurement time. Planck had included the missing time variable in his earlier electromagnetic work, but omitted it in his famous work that sparked the quantum revolution. Restoration of measurement time to Planck's quantum formula produces the more complete, E = ν t. The numerical value Planck calculated for his action constant h takes on new meaning as an energy constant h~ for light. Planck's energy constant is the mean energy of a single oscillation of light, namely 6.626 X 10 -34 J/oscillation. The mean oscillation energy of light is constant , and does not vary with frequency or wavelength. The photon, as historically defined, is a time dependent packet of energy, based on the arbitrary measurement time of one second. An arbitrary, one second increment of energy cannot be a truly indivisible and elementary particle of nature. Omission of the time variable from Planck's quantum formula contributed to numerous paradoxes in quantum mechanics, such as uncertainty relating to formulations involving time, wave-particle duality, the need for normalization of wave functions, lack of dimensions for the fine structure constant, and irreconcilability of quantum mechanics and general relativity (Einstein's gravitational theory). Many of these paradoxes are simplified or eliminated altogether with a re-interpretation of quantum mechanics with Planck's hidden time variable and energy constant.
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