[Paper Review] On the Electromagnetic Nature of Planck Constant

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

Experimental and Theoretical Physics Studies4 citations

TL;DR

This paper proposes that Planck's constant (h) has an intrinsic electromagnetic origin, deriving it from fundamental constants of electromagnetism—elementary charge (e), vacuum permittivity (ε₀), and permeability (μ₀)—via a quantum rate concept νₑ defined by electron dynamics at the ground state. The key result is h = (e²/2α)√(μ₀/ε₀), showing h as purely electromagnetic, consistent with Dirac relativistic electrodynamics and Maxwell's equations.

ABSTRACT

In this work, it is demonstrated that there is an additional origin of the electric potential energy of an electron orbiting a nuclei that can be, alternatively to that associated to the elementary `static' charge of the electron as introduced by Bohr, formulated in terms of an electromotive force associated with the closed motion of the electron around the nuclei. This permitted the resolution of the Maxwellian laws of classical electrodynamics within electric $1/τ_C$ and magnetic $1/τ_L$ quantum rate settings for describing the time-dependent oscillatory dynamics of the electron in the ground state, conducting to a reinterpretation of the meaning of $h$ in quantum mechanics. Notably, the quantum electromagnetic rate reinterpretation of the ground state electrodynamics, as introduced in this work, is not only in compliance with Maxwellian laws, but also conforms with the relativistic quantum electrodynamics as proposed by Dirac; hence, it exhibits an inherent massless character of the electron that fulfils both relativistic quantum dynamics and Maxwellian laws of classical electrodynamics.

Motivation & Objective

• To re-express Planck's constant h in terms of fundamental electromagnetic constants (e, ε₀, μ₀), challenging its traditional status as a purely quantum postulate.
• To establish a quantum rate νₑ based on electron orbital dynamics at the ground state, linking it to the von Klitzing constant and quantum capacitance.
• To demonstrate that the electron's ground-state motion complies with massless Dirac fermionic electrodynamics, consistent with relativistic and Maxwellian laws.
• To unify quantum mechanics, electromagnetism, and relativity by showing that h emerges from electromagnetic induction and closed-loop dynamics.
• To resolve the nature of the Josephson flux quantum and the uncertainty principle through induced electromotive force and time-averaged rates.

Proposed method

• Define a quantum rate νₑ = e²/(h C_q) where C_q = 2λε₀ is the quantum capacitance of the ground state, with λ = 2πr being the electron's de Broglie wavelength.
• Introduce the magnetic rate νₘ = 1/τₗ = R_q / L_q, with τₗ = L_q / R_q, linking magnetic dynamics to the quantum capacitance time constant.
• Apply Maxwell’s equations to the closed-loop electron trajectory, deriving induced electromotive force εᵢ = ∮ E·dl = eεᵢ, which relates to the electron’s energy via τ_C εᵢ = h.
• Use the fine structure constant α = c*/c = (1/137) to relate electromagnetic strength to the quantum rate ratio (1/τ_C)/(1/τ_L), enabling derivation of h.
• Derive Planck’s constant as h = (e²/2α)√(μ₀/ε₀), showing its electromagnetic origin through the impedance of free space Z₀ = √(μ₀/ε₀).
• Validate consistency with Dirac’s relativistic theory by showing E_gs = p·c* and m₀ = 0 for the ground state, implying massless behavior.

Experimental results

Research questions

• RQ1 Can Planck’s constant h be derived from fundamental electromagnetic constants rather than being postulated?
• RQ2 What is the electromagnetic origin of the electron’s ground-state energy and its associated quantum rate νₑ?
• RQ3 How do Maxwell’s equations and the Faraday induction law govern the electron’s closed-loop dynamics at the ground state?
• RQ4 Does the electron’s ground-state motion conform to massless Dirac fermionic electrodynamics and relativistic quantum mechanics?
• RQ5 Can the Josephson flux quantum and the uncertainty principle be explained via induced electromotive force and quantum rate dynamics?

Key findings

• Planck’s constant is derived as h = (e²/2α)√(μ₀/ε₀), establishing its purely electromagnetic origin from e, ε₀, μ₀, and the dimensionless α.
• The quantum rate νₑ = e²/(h C_q) is defined via the ground-state electron’s orbital dynamics, with C_q = 2λε₀, linking it to the von Klitzing constant R_k = h/e².
• The induced electromotive force εᵢ = ∮ E·dl leads to τ_C εᵢ = h, where τ_C = 1/(2gₑ νₑ), satisfying the uncertainty principle and Josephson relation Φ_B = h/e.
• The electron’s ground-state dynamics are consistent with massless Dirac fermionic electrodynamics, as E_gs = p·c* and m₀ = 0, implying relativistic invariance.
• The fine structure constant α is reinterpreted as α = cμ₀/(4R_q) = Z₀/(4R_q), linking it to the quantum capacitance and magnetic rate dynamics.
• The derivation confirms compatibility with Maxwell’s equations and classical electrodynamics, showing that quantum mechanics emerges from electromagnetic induction in closed loops.