The Units of Planck’s Constant Are Wrong, and Photons Do Not Exist [pdf]
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I recommend reading the papers when you get the chance. The author did a great job digging through and summarizing the historical record to help explain how Quantum Mechanics was born at the turn of the 20th century, along with her own contributions. In short: Indeed there are hidden variables in the equations that comprise the fundamentals of quantum mechanics.
1. Planck’s energy equation has a hidden time variable. The equation should be E=htf where h is an energy constant, not an action constant. This implies that each wavelength of light has mass h/c^2 (and therefore momentum), and the fine structure constant has units [cycle x seconds].
2. Planck’s famous black body paper had an undeveloped hypothesis in it that nearly went forgotten. The author calls this the resonance hypothesis. The upshot is that E=Kb x T is missing a term that describes the resonant energy of the system. The equation relating energy directly to temperature via Boltzmann’s constant is in turn only describing the unorderly energy in the system and should be considered a lower bound of the energy of a system of molecules.
Here is what I think is a more modern understanding of the situation. It is true even in classical physics that a circularly polarized electromagnetic field carries angular momentum, and that E = L*omega, where E is the energy, L is the angular momentum, and omega=2*pi*f is the angular frequency of the EM field. See Feynman I-33 last paragraph, https://www.feynmanlectures.caltech.edu/I_33.html
Now, the experimental fact is that L is quantized in multiples of hbar=h/(2*pi). Thus you can derive Planck's results from the assumption that angular momentum is quantized. So the photon is really a quantum of angular momentum, which happens to have a non-quantized energy. But Planck's didn't know that, and worked with quanta of energy proportional to the frequency. (It's not like Planck was wrong. His theory was a necessary step towards the discovery of the deeper result that angular momentum is quantized.) Planck's constant of proportionality has the units of "action", which is the same units as angular momentum but "means" something different. The author starts with energy=action/time and attempts to reverse engineer the energy into quanta of energy, which as far as anybody knows do not exist, instead of starting with energy=angular_momentum*angular_frequency, where the angular momentum is truly quantized.
The author's theory falls apart when you realize that angular momentum in general is really quantized in units of hbar/2 (not for photons but for electrons), in which case her theory of energy being quantized in terms of a full oscillation of light becomes untenable, since you would have to quantize in terms of half an oscillation, at which point why 1/2 and not 1/3 or 1/4? Whereas there are legitimate geometric reasons why an object rotated by 360 degrees would change sign but yield the same physics. See https://www.feynmanlectures.caltech.edu/III_06.html
Can you point me towards an outline of the experiment that shows that angular momentum is quantized in multiples of hbar?
e.g. https://img1.wsimg.com/blobby/go/e266e5e7-739c-437c-89c3-eed...
W. She, J. Yu, R. Feng, Observation of a Push Force on the End Face of a Nanometer Silica Filament Exerted by Outgoing Light, Physical Review Letters, 2008, Vol. 101
Here is a citation in the direction that you want. https://www.researchgate.net/publication/299858388_Roles_of_...
There is no requirement that an electron will jump energy levels if and only if a photon of matching frequency interacts with it. You can use microwaves instead of UV/visible light to the same effect, so long as the microwave resonates with one of the frequencies of the atom
https://img1.wsimg.com/blobby/go/e266e5e7-739c-437c-89c3-eed...