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").
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").
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.
By the end of the nineteenth century all the important elements of classical physics were fully mature. Newton's Laws had been applied with success to everything from industrial machines to planetary orbits. Classical thermodynamics had extended energy conservation arguments into thermal processes, and scientists including J. Willard Gibbs and Ludwig Boltzmann had developed the statistical interpretation of entropy. James Clerk Maxwell had explained all electromagnetic phenomena, from AC generators/motors to light, with the four Maxwell's equations and three material-dependent constitutive relations. There was serious discussion that physics was on the verge of being “finished” – becoming a closed system of knowledge like classical geometry with only essentially routine tasks left of determining how the known laws could be applied to engineering problems. Yet by 1930 the foundations of mechanics, electromagnetics, and atomic-scale systems had been shaken to the core by the new revolutions in the Theory of Relativity, the photon picture of light, and quantum physics. We are still reaping the benefits of the application of these new scientific paradigms in our technology today, including semiconductor electronic devices, lasers, and GPS systems. But the description of reality that these theories provide is still deeply anti-intuitive and disturbing. Nevertheless, quantum physics is one of the most extensively experimentally verified theories that we know. Even when quantum theory and common sense seem to diverge, quantum theory gives the right answers when tested by experiment. In the next chapter we will develop the framework of quantum theory that has been so successful when people “shut up and calculate,” as one scientist suggested as the way through the philosophical thicket of quantum physics. But in this chapter, we will spend a brief time considering the historical development and continuing paradoxical implications of quantum theory. The photoelectric effect and photons In 1905, Albert Einstein, who was a key figure in the revolution of modern physics, was working as a clerk in the patent office in Zurich, Switzerland. Einstein had finished his studies in physics, but had not obtained a coveted position as a university professor. He was intensely interested in the latest developments in classical physics and was aware of a few of the remaining loose ends that were resisting explanation in the classical model.
[概要]量子力学は, 現代の科学技術文明にとってもっとも重要な理論である. 量子なる概念は, 二十世紀初頭に出現した. これを量子革命と称する. われわれは, 本論で量子論の発展過程を見てゆく. とりわけ本論が主題とするのは, 黒体放射の問題がいかに解き明かされてプランクの放射公式に結実したか, ということである. かかる議論の過程で, われわれは, 量子の二重性がどのようにして出現したのかが明確にされるのを見るであろう. 言い替えれば, 量子の二面性の根源が, 完成された理論のどこに潜んでいるかを見いだすであろう. また, 本論は, 量子の認識論に関して, その哲学的含意についても若干の議論をすることになる. [Abstract] Quantum mechanics is the most important theory for the modern scientific and technological civilization. The notion of quantum had been emerged at the beginning of the 20th century that is called quantum revolution. We will see the process of the development of the quantum theory in this paper. Especially, we will see and discuss how the black-body problem had been solved by the Planck's formula for radiation. This discussion will make a clear understanding to the emergence of the so-called wave-particle duality. That is to say, we will see the origins of the quantum duality that are hid behind of the accomplished theory. And we discuss a few philosophical implications that are about the epistemology of quantum.
525. IN preceding chapters we saw how the classical system of mechanics failed to account for certain phenomena of physics, and it became clear that these could only be explained in terms of a new system of dynamics which must be supposed to supersede the old classical system when we have to deal with phenomena conditioned by the fine-scale structure of matter. The first instance of the failure of the classical mechanics was provided by the phenomenon of black-body radiation. On the assumption that black-body radiation represents a state of thermodynamical equilibrium, we found that the observed distribution of radiant energy in the spectrum of an ideal black body could be explained on the supposition that the energy of each part of the radiation-producing mechanism fell into “quanta.” Corresponding to a simple harmonic vibration of frequency v , there was supposed to be an energyquantum of amount hv , where h is Planck's universal constant of which the value has already been given. Calling this energy ∈ , it was found that the energy of vibration could be 0, ∈, 2∈, 3∈,… or any integral multiple of ∈ , but could not contain fractional parts of ∈ . The energy, after retaining one of these values for a certain time, had to be supposed to jump abruptly to some other value, which in turn was retained until another jump occurred.