1. Abstract

We present an axiomatic formulation of electromagnetic induction based solely on electric charge, Coulomb interaction, and relativistic causality. The theory is built upon a single fundamental object—the Progressing Electric Field—defined as the causal propagation of electric influence from the past positions of charges at finite speed. Magnetic fields, magnetic flux, and Faraday’s law are not assumed as primitives but emerge as derived, effective quantities. This work establishes the axioms, primitive definitions, and core propositions of the theory, providing a foundation for re-deriving induction phenomena without postulating magnetic fields as fundamental entities.

The original article:

Kuan Peng, 2026, « A Derivation of Faraday’s law from Coulomb’s Law and Relativity / 1.The Progressing Electric Field Model »

https://www.academia.edu/146009113/A_Derivation_of_Faradays_law_from_Coulombs_Law_and_Relativity_1_The_Progressing_Electric_Field_Model

https://pengkuanem.blogspot.com/2026/01/a-derivation-of-faradays-law-from.html

1. Scope and Intent

This article does not seek to reinterpret Maxwell’s equations within their own conceptual framework. Instead, it proposes an alternative foundational structure for electromagnetic phenomena. The objective is not to negate existing theories but to identify a deeper causal layer from which standard electromagnetic laws arise as effective descriptions.

The present work constitutes the foundational stage of the theory. Its purpose is to define axioms, construct the primary field object, and demonstrate its essential properties, notably its non-conservative nature and its capacity to induce electromotive effects in conductors.

2. Primitive Ontology

The theory is built upon the following primitive entities:

• Electric charge: a scalar quantity carried by particles.

• Spacetime: a relativistic spacetime endowed with a universal invariant speed c.

• Progressing Electric Field (PEF): a causal distribution of electric influence propagated from charges.

No magnetic field, magnetic flux, vector potential, or electromagnetic energy density is introduced at the axiomatic level.

3. Axioms

Axiom A1 — Charge as the Sole Source

Electric charge is the only fundamental source of electromagnetic interaction.

Axiom A2 — Finite Causal Propagation

Any influence produced by a charge propagates through space at a finite invariant speed c. No instantaneous action at a distance exists.

Axiom A3 — Retarded Local Interaction

At any spacetime point, the electric influence due to a charge depends exclusively on the charge’s position at the corresponding retarded time.

Axiom A4 — Local Coulomb Structure

The magnitude and radial orientation of the electric influence emitted from a charge at its retarded position obey Coulomb’s law locally with respect to that retarded center.

Axiom A5 — Superposition

Electric influences from distinct charges combine linearly.

Axiom A6 — Snapshot Field Representation

At any instant of time, the total electric influence in space may be represented as a spatial field constructed from all retarded contributions corresponding to that instant.

This representation is purely kinematic and does not imply the existence of a global scalar potential.

4. Definition of the Progressing Electric Field

Definition 1 (Progressing Electric Field).

The Progressing Electric Field Eₚ(x, t) is the spatial field obtained at time t by superposing all Coulomb-type electric influences emitted by charges from their retarded positions.

The field is structured by a continuous family of expanding iso-intensity surfaces whose centers coincide with the past positions of the source charges.

…

For more detail, please read