1) Charge and Electron Transitions - Discovery of blackbody radiation (Planck) in 1900, discovery of the photoelectric effect (Einstein) in 1905, and Bohr's publication of the atomic orbital model in 1913 [1]. When Bohr visited the Institute for Advanced Study in Princeton, T. D. Lee asked him [2]: Why did it take so long to discover the Bohr model that explains the spectrum of the hydrogen atom? Bohr said: You don't understand, at that time no one would have thought that the spectrum was emitted from an atom.

The spectrum of hydrogen atoms contains visible light at wavelengths much larger than the scale of atoms. It is generally believed that this should be a population effect. Bohr argued that the hydrogen spectrum is not produced by vibrations of electrons, i.e. not due to charge acceleration, but that it should be a new mechanism, so that the light source would not have to be larger than the wavelength. According to Bohr's hypothesis electrons operate in discrete orbits . When the electron is in a constant state [2], it does not radiate photons †. When an electron transitions from one state to another, it radiates photons ‡, ΔE=hν . Then we ask, ‘How do Electrons in Atoms Know the Transition Level difference in Advance? †† ; If photons are described by one wave function and electron by another, how do these two wave functions interface? ‡ Should their wave functions describe the same thing?

2) Charge and Stability of Atomic Structure - Inside the atom, electrons do not go into 'death-spiral' due to radiated energy and thus fall rapidly into the nucleus [3], but are stably 'supported' on the outside of the nucleus. This phenomenon reflects two possible facts: firstly, the interaction measured in terms of charge is not working. This means that in this state the charge must have failed, the charge no longer exists, or 'charge' no longer has the meaning of charge. Does the wave function of an electron still contain a charge? Secondly, the motion of an electron, be it a field, a wave or a particle, is no longer the same as in free space, and “accelerated” motion no longer radiates photons. The electron's lack of qualitative change outside and inside the atom would mean that its motion is a constant steady state, like that in inertial space. So is space-time within the atom equivalently flat for electron trajectories? Is the superposition of electron and proton electric fields still linear?

3) Charge and Uncertainty (Causality) - Quantum mechanics suggests that electrons appear probabilistically in different regions of an atom. The inverse relationship between the time domain scale and the frequency domain scale, originating from the Fourier Transform, deviates from its true mathematical meaning here, giving rise to the interpretation of the ‘Uncertainty Principle’ [4], Δx-Δpx>h, and hence Planck physics [6]. The question here is, what is the motion relationship between the charge at this time and the charge at that time, when the electrons with positional probability distribution are the charges with positional probability distribution? Why is it that Bohr's deterministic orbital, which contradicts the uncertainty principle, correctly describes the spectrum, while we have to discard it and interpret the orbital wave function probabilistically? [7]

4) Charge and its Discrete and Conservation - The energy-momentum of a single photon is quantised, E=hν, p=h/λ, but the photon energy-momentum is expressed continuously in its entirety 0 ≤ ν, λ < ∞. However, charge differs from it in that it has only two quantities, q=0, or q=4.8x10-10. Conservation of charge guarantees gauge symmetry, and conservation of energy-momentum guarantees space-time displacement symmetry. Pauli argued that charge conservation and energy-momentum conservation hold equal status [5]. Does this mean that both photons and electrons are fundamental beings? Can't discrete charge be generated in the γγ → e+e- reaction if vacuum excitation is not taken into account?

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Notes

* This is a supplement to question "What is an electric charge? Can it exist apart from electrons? Would it be an effect?" .

https://www.researchgate.net/post/NO44_What_is_an_electric_charge_Can_it_exist_apart_from_electrons_Would_it_be_an_effect?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6InByb2ZpbGUiLCJwYWdlIjoicHJvZmlsZSIsInByZXZpb3VzUGFnZSI6InByb2ZpbGUiLCJwb3NpdGlvbiI6InBhZ2VDb250ZW50In19

** Nobel Laureate Tsung-Dao (T.D.) Lee(1926-2024), died Aug. 4. There is a comprehensive description of his contributions at the link below. He shared the award with Chen Ning Yang for their work on broken symmetry in particle physics. In 1956, they published the paper "Question of parity conservation in weak interactions” [8].

https://www.nature.com/articles/d41586-024-02585-1;

https://www.bnl.gov/newsroom/news.php?a=222034;

† “The main weakness of the theory, as Bohr himself was the first to admit, is that it could offer no good explanation of why these special orbits immunized the electron from radiating its energy away.”

†† “How do Electrons in Atoms Know the Transition Level difference in Advance?”

https://www.researchgate.net/post/NO14How_do_Electrons_in_Atoms_Know_the_Transition_Level_difference_in_Advance?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6InByb2ZpbGUiLCJwYWdlIjoicHJvZmlsZSIsInByZXZpb3VzUGFnZSI6InByb2ZpbGUiLCJwb3NpdGlvbiI6InBhZ2VDb250ZW50In19

‡ "Should all light-emitting processes be described by the same equations?"

https://www.researchgate.net/post/NO11Should_all_light-emitting_processes_be_described_by_the_same_equations?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6InByb2ZpbGUiLCJwYWdlIjoicHJvZmlsZSIsInByZXZpb3VzUGFnZSI6InByb2ZpbGUiLCJwb3NpdGlvbiI6InBhZ2VDb250ZW50In19

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References

[1] Bohr, N. (1913). On the constitution of atoms and molecules. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 26(151), 1-25.

[2] 蓝志成（Chi-Sing Lam，Emeritus Rutherford Professor of Physics, McGill University ；RG @Harry Lam ），2024.8；“The Story of T. D. Lee and Bohr” (李政道与波尔的故事），微信号“科学思维的价值”。

[3] Mason, F. P., & Richardson, R. W. (1983). Why doesn't the electron fall into the nucleus? Journal of Chemical Education, 60(1), 40.

[4] Elias M. Stern, Fourei Analysis: An introduction. 机械工业出版社

[5] Pauli, W. (1936). Space, time and causality in modern physics. In Writings on Physics and Philosophy (pp. 95-105). Springer.

[6] Ng, Y. J. (2003). Selected topics in Planck-scale physics. Modern Physics Letters A, 18(16), 1073-1097.

[7] Born, M. (1955). Statistical Interpretation of Quantum Mechanics. Science, 122(3172), 675-679. https://doi.org/doi:10.1126/science.122.3172.675

[8] Lee, T.-D., & Yang, C.-N. (1956). Question of parity conservation in weak interactions. Physical Review, 104(1), 254.