[Paper Review] Quantum Electromagnetic Rate Theory of the Electron and the Meaning of the Fine-Structure Constant

Paulo R. Bueno|arXiv (Cornell University)|Feb 15, 2023

Mechanical and Optical Resonators4 citations

TL;DR

This paper proposes a quantum electromagnetic rate theory that reinterprets the Planck constant $h$ as fundamentally electromagnetic, derived from Maxwell's equations and the fine-structure constant $\alpha$. It shows that electron ground-state dynamics arise from electromagnetic phase coherence between electric and magnetic quantum rates $\tau_C$ and $\tau_L$, with $\alpha \sim 1/137$ governing quantum uncertainty and wave-particle duality as information loss during perturbations.

ABSTRACT

In a previous work, the meaning of the Planck constant $h = \left( e^2 / 2 α ight) \sqrt{μ_0 / ε_0}$, accomplished by solving Maxwell's electrodynamics laws with specific electric $1 / τ_C = 1 / R_q C_q$ and magnetic $1/ τ_L = R_q / L_q$ quantum rates for the ground-state dynamics, was reinterpreted. $R_q$, $C_q$ and $L_q$ are the resistance, capacitance and inductance quantum of the ground-state dynamics, respectively. Based on this quantum electromagnetic rate approach, here it is demonstrated that the intrinsic massless character that complies with Dirac quantum electrodynamics of the electron in its ground-state energy level is a consequence of a quantum electromagnetic phase coherence between $τ_C$ and $τ_L$ time constants of the oscillatory motion. The quantum mechanical uncertainties associated with $h$ are interpreted to be a consequence of perturbing the inherent electromagnetic phase coherence of the ground state with the loss of half of a byte of electromagnetic information per ``experimental'' perturbation, with the fine-structure constant $α= \sqrt{π/ 2 \left( τ_L / τ_C ight)} \sim 1/137$ playing a prominent role in the phenomenon.

Motivation & Objective

• To reinterpret the Planck constant $h$ as an electromagnetic phenomenon rather than a fundamental quantum postulate.
• To explain the electron's ground-state energy and massless relativistic behavior using classical Maxwellian electrodynamics.
• To resolve the origin of quantum uncertainty as information loss in electromagnetic phase coherence during measurement.
• To unify Dirac quantum electrodynamics with classical electromagnetism through quantum rates $\nu_e$ and $\nu_m$.
• To demonstrate that the fine-structure constant $\alpha$ is the central parameter governing quantum leaps and electron behavior.

Proposed method

• Derives $h = \frac{e^2}{2\alpha}\sqrt{\mu_0/\varepsilon_0}$ from Maxwell’s equations using quantum rates $\nu_e = e^2/(g_e h C_q)$ and $\nu_m = R_q / L_q$, with $C_q$, $L_q$, and $R_q$ as quantum capacitance, inductance, and resistance.
• Applies Faraday’s law to closed-loop electric work $\oint \mathbf{F}_i \cdot d\mathbf{l} = e\varepsilon_i = h\nu_e$, linking it to the electron’s ground-state energy $\sim 13.6$ eV.
• Introduces electromagnetic phase coherence between $\tau_C = R_q C_q$ and $\tau_L = L_q / R_q$ as the origin of the electron’s massless relativistic dynamics $E_{gs} = \mathbf{p} \cdot \mathbf{c}_*$.
• Models quantum uncertainty as loss of half a byte of electromagnetic information per measurement, with degeneracy $g_e = 2$ for electric field.
• Uses the fine-structure constant $\alpha = \sqrt{\pi/2 (\tau_L / \tau_C)} \sim 1/137$ to quantify coherence and perturbation effects.
• Validates the model by showing consistency with Bohr’s energy, Dirac’s relativistic dynamics, and nanoscale electron transport in graphene and electrochemical junctions.

Experimental results

Research questions

• RQ1 How can the Planck constant $h$ be reinterpreted as an electromagnetic quantity rather than a quantum postulate?
• RQ2 What is the origin of the electron’s ground-state energy and its massless relativistic behavior in terms of classical electrodynamics?
• RQ3 How does the fine-structure constant $\alpha$ govern quantum uncertainty and wave-particle duality in this framework?
• RQ4 What role does electromagnetic phase coherence between $\tau_C$ and $\tau_L$ play in electron dynamics?
• RQ5 How does information loss during measurement relate to the uncertainty principle in this quantum electromagnetic rate theory?

Key findings

• The Planck constant is reinterpreted as $h = \frac{e^2}{2\alpha}\sqrt{\mu_0/\varepsilon_0}$, showing its purely electromagnetic origin.
• The electron’s ground-state energy $E_{gs} \sim 13.6$ eV arises from electromagnetic work $\oint \mathbf{F}_i \cdot d\mathbf{l} = e\varepsilon_i = h\nu_e$, consistent with Bohr’s model.
• Electron dynamics in the ground state are massless and relativistic, with $E_{gs} = \mathbf{p} \cdot \mathbf{c}_*$, due to phase coherence between $\tau_C$ and $\tau_L$.
• Quantum uncertainty is quantified as loss of half a byte of electromagnetic information per measurement, with degeneracy $g_e = 2$.
• The fine-structure constant $\alpha \sim 1/137$ governs the coherence and perturbation dynamics, linking $\alpha = \sqrt{\pi/2 (\tau_L / \tau_C)}$.
• Wave-particle duality emerges from the observer’s perspective on coherent vs. perturbed electromagnetic states, with particle behavior arising when coherence is broken by measurement.