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 = h~ 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.
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 = h~ 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.
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 understanding the interactions of electromagnetic radiation with matter. Planck’s quantum formula (“E = hν”) is missing the variable for measurement time. Restoration of measurement time produces a more complete quantum formula, “E = h ν tm”. Upon balancing, this restored formula reveals that the numerical value of Planck’s constant is actually the mean energy of a single oscillation of light, 6.626 X 10 -34 J/oscillation. Previous definitions of the “photon” relied on a hidden and assumed value for measurement time of “one second”. Quantum chemists of long ago, unaware of this arbitrary value, concluded that the total energy of a “photon” had to be equal to or greater than molecular bond energy, and only “photons” in the visible and ultraviolet regions satisfied this criterion. Infra-red, microwave and radio waves were excluded from study in photochemistry, and were relegated mechanistically to purely thermal processes. An understanding of the restored quantum formula, with its separate time variable and mean oscillation energy constant, reveals that frequency specific effects range through-out the electromagnetic spectrum and are not limited to just the visible and ultraviolet regions. This awareness, in turn, allows the mechanistic explanation of phenomena related to the use of infrared, microwaves and radio waves in the processing, evolution and performance of materials.
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.
In 1900 Max Karl Planck performed his famous black-body radiation work which sparked the quantum revolution. Re-examination of that work has revealed hidden variables, 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 foundational equations for more than one hundred years, has important implications for theoretical, experimental and applied sciences and technologies. Planck attempted to integrate the new "resonant Hertzian (electromagnetic) waves", with existing Helmholtz theories on energy and thermodynamics. In his famous January 1901, paper on black-body radiation, Planck described two significant hypotheses - his well known Quantum Hypothesis, and his more obscure Resonance Hypothesis. Few scientists today are aware that Planck hypothesized resonant electromagnetic energy as a form of non-thermal energy available to perform work on a molecular basis, and that Planck's Resonance Hypothesis bridged the gap between classical Helmholtz energy state dynamics of the bulk macrostate, and energy state dynamics of the molecular microstate. Since the black-body experimental data involved only a thermal effect and not a resonant effect, Planck excluded the resonant state in his black-body derivation. He calculated Boltzmann's constant "kB" using completely thermal/entropic data, arriving at a value of 1.38 ×10-23 J K-1 per molecule, representing the internal energy of a molecule under completely thermal conditions. He further hypothesized, however, that if resonant energy was present in a system, the resonant energy would be "free to be converted into work". Planck seems to have been caught up in the events of the quantum revolution and never returned to his Resonance Hypothesis. As a result, a mathematical foundation for resonance dynamics was never completed. Boltzmann's constant was adopted into thermodynamic theories without its natural companion, the resonance factor ("rf").
The explicit history of the “hidden variables” problem is well-known and established. The main events of its chronology are traced. An implicit context of that history is suggested. It links the problem with the “conservation of energy conservation” in quantum mechanics. Bohr, Kramers, and Slaters (1924) admitted its violation being due to the “fourth Heisenberg uncertainty”, that of energy in relation to time. Wolfgang Pauli rejected the conjecture and even forecast the existence of a new and unknown then elementary particle, neutrino, on the ground of energy conservation in quantum mechanics, afterwards confirmed experimentally. Bohr recognized his defeat and Pauli’s truth: the paradigm of elementary particles (furthermore underlying the Standard model) dominates nowadays. However, the reason of energy conservation in quantum mechanics is quite different from that in classical mechanics (the Lie group of all translations in time). Even more, if the reason was the latter, Bohr, Cramers, and Slatters’s argument would be valid. The link between the “conservation of energy conservation” and the problem of hidden variables is the following: the former is equivalent to their absence. The same can be verified historically by the unification of Heisenberg’s matrix mechanics and Schrödinger’s wave mechanics in the contemporary quantum mechanics by means of the separable complex Hilbert space. The Heisenberg version relies on the vector interpretation of Hilbert space, and the Schrödinger one, on the wave-function interpretation. However the both are equivalent to each other only under the additional condition that a certain well-ordering is equivalent to the corresponding ordinal number (as in Neumann’s definition of “ordinal number”). The same condition interpreted in the proper terms of quantum mechanics means its “unitarity”, therefore the “conservation of energy conservation”. In other words, the “conservation of energy conservation” is postulated in the foundations of quantum mechanics by means of the concept of the separable complex Hilbert space, which furthermore is equivalent to postulating the absence of hidden variables in quantum mechanics (directly deducible from the properties of that Hilbert space). Further, the lesson of that unification (of Heisenberg’s approach and Schrödinger’s version) can be directly interpreted in terms of the unification of general relativity and quantum mechanics in the cherished “quantum gravity” as well as a “manual” of how one can do this considering them as isomorphic to each other in a new mathematical structure corresponding to quantum information. Even more, the condition of the unification is analogical to that in the historical precedent of the unifying mathematical structure (namely the separable complex Hilbert space of quantum mechanics) and consists in the class of equivalence of any smooth deformations of the pseudo-Riemannian space of general relativity: each element of that class is a wave function and vice versa as well. Thus, quantum mechanics can be considered as a “thermodynamic version” of general relativity, after which the universe is observed as if “outside” (similarly to a phenomenological thermodynamic system observable only “outside” as a whole). The statistical approach to that “phenomenological thermodynamics” of quantum mechanics implies Gibbs classes of equivalence of all states of the universe, furthermore re-presentable in Boltzmann’s manner implying general relativity properly … The meta-lesson is that the historical lesson can serve for future discoveries.
A new foundational physics is emerging which radically changes our concepts of electromagnetic waves. The original quantum ideas of Max Planck and Albert Einstein from the turn of the twentieth century, are undergoing an impressive renaissance now at the turn of the twenty-first century. The result is a fundamental physics of electromagnetic waves that is both new and classical. Einstein’s insistence that quantum mechanics was incomplete that “hidden variables” were yet to be discovered was correct. The recent discovery of those variables is the driving force behind this rebirth of the foundations of quantum mechanics and the fundamental physics of electromagnetic (“EM”) waves. The new quantum variables have led to the discovery of new universal constants for EM waves. The new constants have revealed an elegant simplicity in quantum concepts, that requires no paradoxical explanations and imposes no uncertainties or limits. Instead, the new physics provides a more realistic understanding of physical concepts related to EM waves. The old paradigm is disappearing, and yielding to a new paradigm which is both more understandable and more powerful.
Light has the dual characteristics of particles (photons) and electromagnetic waves. The photon has an energy of 𝐸 = ℎ𝜈 (𝜈: frequency, h: Planck constant) and the momentum of 𝑝⃗ = ℎ𝑘⃗⃗ (𝑘⃗⃗: wavenumber and 1|𝑘⃗⃗| is the wavelength). The photon density is proportional to the square of the amplitude of the electromagnetic waves. The fundamental aspect of quantum mechanics is that these characteristics apply to all matters. The properties of matters are described by wave functions. The probability of the existence of the matter is proportional to the square of the associated wave function. When a matter is localized in a limited region, it can only assume discrete values of energy because the wavelength of the matter wave must be an integral division of the region. The phase of the wavefunction has uncertainty on order 1/2 radians; therefore, position and momentum (time and energy) cannot be simultaneously determined. As the size of the localization area of the wavefunction becomes smaller, the minimum kinetic energy becomes larger because of the smaller wavelength (larger momentum uncertainty). The Schroedinger equation was derived based on the idea that the relationship between the frequency and the wavenumber corresponds to that between energy and momentum given by classical mechanics, which makes it possible to obtain the wave functions of matters in the energy eigenstates. Several examples of solutions to the Schroedinger equation are introduced. The mixture between different energy eigenstates and the shift in the energy eigenvalues are induced by electromagnetic fields. The temporal change of the wave function (transition between different energy states) is also obtained using the Schroedinger equation.