Lorenz on Light: A Precocious Photon Paradigm

TL;DR

This paper revisits Lorenz's 1867 electromagnetic theory of light, critically analyzing his equations and assumptions, and reinterprets his work using modern notation to enhance understanding of light's wave and particle duality.

Contribution

It provides a modern reinterpretation and critical analysis of Lorenz's original electromagnetic theory of light, clarifying misconceptions and connecting historical ideas to current research.

Findings

Lorenz's theory equates light vibrations with electric currents.

The paper corrects Lorenz's faulty assumptions and presents a proper relation between potentials.

It introduces the concept of magnetoinductive waves as a model for light.

Abstract

In 1867, during the time when Maxwell was publishing his electromagnetic theory, L. Lorenz published his theory equating light vibrations with electric currents. Starting from Kirchhoff's Ohm's law expression, Lorenz introduces scalar potential retardation to obtain an expression for the electric field using retarded potentials. In his theory Lorenz sets the vacuum light speed equal to \sqrt{2}/2 times Weber's measured superluminal value for magnetic induction speed. Using the wave equation Green's function paradigm Lorenz reduces his integral, retarded Ohm's law formulation to a differential formulation for current density. This represents his solution to the electromagnetic action at a distance problem. During the reduction he presents a light like, plane wave solution for current density that can not satisfy initial conditions on the expanding wave front and, using a faulty by parts integration that neglects retardation, he develops the eponymic Lorenz condition. Although generally accepted, this condition relates vector and scalar potentials erroneously. A proper relation is given and major consequences are developed in appendices. As a finale Lorenz suggests a light model that I interpret as magnetoinductive waves. Such waves are only now being studied using Kirchhoff's laws without retardation. I redo this important paper using modern day notation with critical annotations. This elevates the paper to a teaching tool position in the millennial search to understand light's dual nature as wave and corpuscle and brings us full circle, back to Kirchhoff's laws where Lorenz began.