Historical research guide · 0806 · 2022
Foundations of Electromagnetism: A Review of Wilhelm Weber’s Electrodynamic Force Law
Christof Baumgärtel · Simon Maher
In one minute
Wilhelm Weber published a force law in 1846, fifteen years before Maxwell’s first paper on electromagnetism, and it takes a different route to the same phenomena: instead of charges making fields and fields carrying the force, charges act on one another directly, through a force that depends only on how far apart they are, how fast that distance is changing, and how that rate itself is changing. Baumgärtel and Maher, at the University of Liverpool, gather what the law has been shown to do. It reduces to Coulomb’s law for charges at rest, gives Ampère’s force between current elements, and in the low-velocity near field it matches the Lorentz force exactly. It was Weber and Kohlrausch, not Maxwell, who first got the speed of light out of an electrical measurement. Swap charges for masses and the same form gives a gravity-like law from which inertia emerges as an interaction with the distant stars. The authors then work through the historical objections and show where the theory still needs development.
Connection
Chapter 10 turns on the idea that the vector potential and direct particle-to-particle action carry real physics the field picture hides; chapter 3 turns on inertia and gravity being effects of a background rather than fundamentals. Weber’s law is the historical version of both arguments in one equation, and this review is the clearest map of what it has already been shown to reproduce.
From the source
Weber’s force between two point charges depends only on their separation, their relative velocity and their relative acceleration; it acts along the line joining them, follows Newton’s third law in the strong form, and conserves energy, linear momentum and angular momentum. Weber proved the energy-conservation point in 1871, and Maxwell then acknowledged in his Treatise that the theory had been criticised mistakenly on that score.Sect. 2, potential (11) and force (13) and (15); Sect. 3.3, second historical criticism
The same single law reduces to Coulomb’s force for charges at rest and yields Ampère’s force between two current elements, including the longitudinal component along the wire that Grassmann’s force lacks; several authors have derived field equations from Weber, and the reverse derivation — Maxwell’s equations yielding a Weber-type formulation once two implicit restrictions are lifted — has also been carried out.Sect. 3.2.1, Coulomb limit (25), Ampère force (26), Wesley’s field derivation (27) to (31)
A direct-action law is not an instantaneous one: the speed of light enters Weber’s formula as a retardation constant, Weber and Kohlrausch measured that constant experimentally in 1856 from Weber’s force — a decade before Maxwell’s wave prediction — and Weber and Kirchhoff each independently derived the telegraph equation for signal propagation from it, so causality is not violated.Sect. 3.2.1, speed-of-light and telegraph-equation paragraphs; Sect. 3.3, propagation-velocity discussion
Weber’s law contains a critical distance below which like charges attract instead of repel, and for electron or positron interaction that distance comes out at the order of the known diameter of the atomic nucleus — which is why the law has been read as a bridge to the strong nuclear force, and why Weber built a planetary model of the atom on it before the electron was discovered.Sect. 3.2.2, opening paragraphs; nucleon-force comparison later in the section
Replace the charges with masses and Weber’s form becomes a gravitational law from which, combined with Mach’s principle, Newton’s second law follows and inertia appears as the body’s interaction with the distant masses — the same route gives centrifugal and Coriolis terms and a frame-dragging effect, and at fourth order in a series expansion of Weber’s force Assis finds an attraction between neutral dipoles that later work reads as containing the Casimir force and a relation to Planck’s constant.Sect. 3.2.2, series expansion (32) and gravitational form (33); Sect. 3.2.3, rotating-shell force (36)
The theory’s sharpest testable prediction is a change in the effective inertial mass of a charge inside a charged spherical shell — a force where standard theory says the field is zero, with an estimate that a shell of 0.5 metre radius at 1.5 megavolts would double an electron’s mass. Mikhailov reported seeing it; refined independent repeats did not, and the Tajmar and Weikert Perrin-tube experiment bounds it two orders of magnitude below the prediction. What is still open is whether a more general Weber-type potential removes the effect from the theory.Sect. 3.2.3, shell force (37) and stationary case (38); Sect. 3.3, Helmholtz criticism and the modern experiments
The way in
https://doi.org/10.3390/foundations2040065How to cite it
Christof Baumgärtel, Simon Maher (2022) Foundations of Electromagnetism: A Review of Wilhelm Weber’s Electrodynamic Force Law doi:10.3390/foundations2040065