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\u2014the Progressing Electric Field<\/strong>\u2014defined as the causal propagation of electric influence from the past positions of charges at finite speed. Magnetic fields, magnetic flux, and Faraday\u2019s 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.<\/p>\n\n\n\n The original article:<\/p>\n\n\n\n Kuan Peng, 2026, \u00ab A Derivation of Faraday’s law from Coulomb’s Law and Relativity \/ 1.The Progressing Electric Field Model \u00bb<\/p>\n\n\n\n https:\/\/www.academia.edu\/146009113\/A_Derivation_of_Faradays_law_from_Coulombs_Law_and_Relativity_1_The_Progressing_Electric_Field_Model<\/a><\/p>\n\n\n\n https:\/\/pengkuanem.blogspot.com\/2026\/01\/a-derivation-of-faradays-law-from.html<\/a><\/p>\n\n\n\n 1. Scope and Intent<\/p>\n\n\n\n This article does not seek to reinterpret Maxwell\u2019s 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.<\/p>\n\n\n\n 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.<\/p>\n\n\n\n 2. Primitive Ontology<\/p>\n\n\n\n The theory is built upon the following primitive entities:<\/p>\n\n\n\n \u2022 Electric charge: a scalar quantity carried by particles.<\/p>\n\n\n\n \u2022 Spacetime: a relativistic spacetime endowed with a universal invariant speed c.<\/p>\n\n\n\n \u2022 Progressing Electric Field (PEF): a causal distribution of electric influence propagated from charges.<\/p>\n\n\n\n No magnetic field, magnetic flux, vector potential, or electromagnetic energy density is introduced at the axiomatic level.<\/p>\n\n\n\n 3. Axioms<\/p>\n\n\n\n Axiom A1 \u2014 Charge as the Sole Source<\/p>\n\n\n\n Electric charge is the only fundamental source of electromagnetic interaction.<\/p>\n\n\n\n Axiom A2 \u2014 Finite Causal Propagation<\/p>\n\n\n\n Any influence produced by a charge propagates through space at a finite invariant speed c. No instantaneous action at a distance exists.<\/p>\n\n\n\n Axiom A3 \u2014 Retarded Local Interaction<\/p>\n\n\n\n At any spacetime point, the electric influence due to a charge depends exclusively on the charge\u2019s position at the corresponding retarded time.<\/p>\n\n\n\n Axiom A4 \u2014 Local Coulomb Structure<\/p>\n\n\n\n The magnitude and radial orientation of the electric influence emitted from a charge at its retarded position obey Coulomb\u2019s law locally with respect to that retarded center.<\/p>\n\n\n\n Axiom A5 \u2014 Superposition<\/p>\n\n\n\n Electric influences from distinct charges combine linearly.<\/p>\n\n\n\n Axiom A6 \u2014 Snapshot Field Representation<\/p>\n\n\n\n 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.<\/p>\n\n\n\n This representation is purely kinematic and does not imply the existence of a global scalar potential.<\/p>\n\n\n\n 4. Definition of the Progressing Electric Field<\/p>\n\n\n\n Definition 1 (Progressing Electric Field).<\/p>\n\n\n\n The Progressing Electric Field E\u209a(x, t) is the spatial field obtained at time t by superposing all Coulomb-type electric influences emitted by charges from their retarded positions.<\/p>\n\n\n\n The field is structured by a continuous family of expanding iso-intensity surfaces whose centers coincide with the past positions of the source charges.<\/p>\n\n\n\n \u2026<\/p>\n\n\n\n For more detail, please read<\/p>\n\n\n\n https:\/\/pengkuanem.blogspot.com\/2026\/01\/axiomatic-formulation-of-derivation-of.html<\/a><\/p>\n","protected":false},"excerpt":{"rendered":" 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\u2014the Progressing Electric Field\u2014defined as the causal propagation of electric influence from … Continue reading Kuan Peng, 21 January 2026, <\/a>\u00ab Axiomatic Formulation<\/a> of \u201cA Derivation of Faraday’s law from Coulomb’s Law and Relativity<\/a>\u201d \u00bb<\/h1>\n\n\n\n
https:\/\/www.academia.edu\/146952831\/Axiomatic_Formulation_of_A_Derivation_of_Faradays_law_from_Coulombs_Law_and_Relativity<\/a><\/h1>\n\n\n\n