[Paper Review] Possible cosmological implications in electrodynamics due to variations of the fine structure constant

J.L. Martínez Ledesma, S. Mendoza|arXiv (Cornell University)|Oct 19, 2002

Relativity and Gravitational Theory1 references3 citations

TL;DR

This paper proposes that a time-varying fine structure constant α implies a modified electrodynamics in vacuum, introducing a new scalar field M alongside standard Maxwell fields. Using differential forms and Hodge decomposition, it derives a generalized Lorentz force that accounts for α variations, predicting measurable deviations from standard electrodynamics if α is not constant, with key implications for cosmological and laboratory-scale electromagnetic interactions.

ABSTRACT

Astronomical observations are suggesting that the fine structure constant varies cosmologically. We present an analysis on the consequences that these variations might induce on the electromagnetic field as a whole. We show that under these circumstances the electrodynamics in vacuum could be described by two fields, the ``standard'' Maxwell's field and a new scalar field. We provide a generalised Lorentz force which can be used to test our results experimentally.

Motivation & Objective

• To investigate the cosmological implications of a time-varying fine structure constant α, as suggested by quasar observations.
• To explore how variations in α affect the fundamental structure of electrodynamics in vacuum.
• To develop a generalized electromagnetic theory that accounts for non-standard charge-current distributions and new scalar fields.
• To derive a modified Lorentz force law that can be tested experimentally to detect deviations from standard Maxwell theory.
• To examine whether the observed α variation (Δα/α ≈ −0.72×10⁻⁵) implies a new physical field M that couples to electromagnetism.

Proposed method

• Uses differential forms and the Hodge decomposition theorem to split the total charge-current 1-form into exact, coexact, and harmonic components.
• Introduces a new scalar field M derived from the harmonic part of the charge-current form, representing a new electromagnetic degree of freedom.
• Applies the generalized continuity equation via the co-differential operator δ, allowing for non-conserved standard charge under varying α.
• Derives a generalized Lorentz force: dP/dτ = (1+η)*F·*Je + M·Je, where η quantifies α variation and Je includes standard and new current components.
• Uses Dirac’s equation with α-dependent coupling to model electron dynamics in a varying-α universe.
• Analyzes the limit η ≈ 0 to show that M vanishes when α is constant, recovering standard electrodynamics.

Experimental results

Research questions

• RQ1 How does a cosmologically varying fine structure constant α affect the fundamental equations of electrodynamics?
• RQ2 What new physical degrees of freedom emerge in vacuum electrodynamics when α is not constant?
• RQ3 Can the observed α variation (Δα/α ≈ −0.72×10⁻⁵) be consistently described within a modified electromagnetic theory?
• RQ4 What is the form of the generalized Lorentz force that accounts for α variations and the new scalar field M?
• RQ5 How can the existence of the scalar field M be tested experimentally in laboratory settings?

Key findings

• A time-varying fine structure constant α implies that the standard continuity equation δJ_std = 0 no longer holds, necessitating a generalized charge-current form Je = J_std + J_n + J_h.
• The electromagnetic field in vacuum can be described by two components: the standard Maxwell field F and a new scalar field M arising from the harmonic part of the charge-current form.
• The generalized Lorentz force is given by dP/dτ = (1+η)*F·*Je + M·Je, where η ≈ Δα/α ≈ −0.72×10⁻⁵, enabling experimental detection of deviations from standard electrodynamics.
• When η = 0, the field M vanishes, and the theory reduces to standard Maxwell electrodynamics, confirming consistency with current observations.
• The harmonic part η_h ≠ 0 leads to a modified force law dP/dτ = (1+η_h)*F·*J_std, implying non-Newtonian deviations in electromagnetic momentum transfer.
• The theory suggests that the field M could be responsible for longitudinal electrodynamic waves, as reported in some experiments, though its strength is small due to the smallness of η.