Ampere: PhD physicist review
Source note: one document, Assis and Chaib, Ampere's Electrodynamics (2015), text layer, read selectively by Step 1 and re-read by me in Sec. 7.5, 8.2-8.3, 10.8, 14.1, 21.2 and the Weber chapters [read]. Part VII (the 1826 Theorie translation) was not read. The book is partisan (Weber school). No source gap, but Step 1's [memory] items on the bridge literature and Weber are now web-checked below.
Corrections to Step 1
- Claim 3 is framed as the book frames it, and that framing is misleading. In field language, the force on the bridge is the integral of i dl x B, where B is the total field of the whole circuit, including the bridge's own arms. That is the ordinary Biot-Savart-Lorentz calculation, not an "added self-force". The book itself says Grassmann/field forces explain the measured force only when this term is included [read, Sec. 21.2, pp. 267-268]. A later paper by Moyssides reports that the Biot-Savart-Grassmann-Lorentz law agrees with the longitudinal Ampere forces [web: https://link.springer.com/article/10.1140/epjp/i2014-14034-2]. Treat "needs a self-force" as the authors' rhetoric, not a mainstream failure.
- Claim 2 says the bridge "confirmed" k = -1/2. It confirmed a longitudinal force on the bridge. Because the Lorentz force also gives such a force on a closed circuit, the experiment does not pick Ampere over Grassmann. The book's own Sec. 21.2 concedes only that Grassmann's per-element force is zero [read].
- Claim 1 omits that Ampere himself said n = 2 was not proven by experiment: "there is no proof deduced directly from experiment" [read, Sec. 7.5, p. 138]. Only k = (1-n)/2 comes from the null experiment, and n = 2 was assumed.
- facts.json lists "Biot and Savart's deduction contained three errors" as a key claim, but claims.md drops it. This is minor and I do not review it.
- The "same net force on closed circuits" statement is right. I checked it numerically (see claim 1).
- The [memory] medium item about Weber being superseded is now [web]; see claim 5.
Claim 1: Ampere force law (central, 1/r^2, k = -1/2, strong third law)
a. Math: Internally consistent. The book's derivation (eqs 7.22-7.35) requires the torque integrand to be an exact differential, giving k = (1-n)/2 [read]. The exact-differential argument is sound for the stated setup. n = 2 is an input, not derived. My numerical check: take a unit circular loop and a test element at (0.3, 0.4, 0.5). With force = (1/r^2)(cos eps + h cos theta cos theta'), the force from the whole loop on the element has component along the element of 0 (to 1e-15) at h = -3/2 (k = -1/2), and 0.22, 0.65, 1.08 at h = -1, 0, 1. So only k = -1/2 gives the Lorentz-like "force from a closed circuit is perpendicular to the element". But for complete closed circuits the k-dependent part integrates to zero, so total force and torque on closed circuits is the same for every k. Maxwell noted this ("cannot be determined... from experiments in which the active current forms a closed circuit") [web: https://en.wikipedia.org/wiki/Amp%C3%A8re's_force_law]. The three standard forms (Ampere, Grassmann, Biot-Savart-Lorentz) differ only by terms that vanish on closed circuits. b. Experiment: Consistent with every closed-circuit measurement (parallel wires, loops, solenoids, torques). The per-element form is untestable with steady currents in closed circuits by design. c. Tested: Ampere's own 1820-22 experiments, the null (equilibrium) experiments with astatic coils [read]. Later, the longitudinal-force literature (Graneau, Wesley, Moyssides, Peoglos) argues over open-element forces; I only checked abstracts and did not read the papers [web: https://www.sciencedirect.com/science/article/abs/pii/0375960189900893]. Replication of the closed-circuit results is universal; of per-element law, not testable. d. If true as a unique law: nothing changes for closed circuits. As the unique element law, it would require rejecting the Lorentz force law as fundamental for open conductors. Mainstream accepts Ampere's law as a valid but non-unique element form. Verdict: Established for closed-circuit forces. Not testable as stated for the unique per-element form (the k-parameter has no measurable difference on closed circuits).
Claim 2: k = -1/2 from null experiment; collinear elements repel (bridge, 1822)
a. Math: consistent given n = 2 (see Claim 1a). Collinear parallel elements: epsilon = 0, theta = theta' = 0, giving 1 + h = -1/2 (repulsion in Ampere's sign convention) [read, eq 2.x/8.2]. b. Experiment: The mercury-bridge repulsion is real (bridge moves away from the battery whatever the current sign) [read, Sec. 8.2; web: https://researchopinion.in/index.php/jro/article/view/152 describes the same behaviour]. Consistent with the Lorentz force on the whole circuit; see Correction 1. c. Tested: Ampere and de la Rive, Geneva, September 1822 [read]. Reproduced in the literature, including quantitative work by Assis/Bueno, Graneau, Wesley, Moyssides, Peoglos [read for names; I did not read the papers]. The dispute is interpretation, not whether the bridge moves. d. If true: nothing beyond Claim 1; the effect is already accommodated. Verdict: Split. "Bridge shows a longitudinal repulsion": Established. "It singles out k = -1/2 over Grassmann": Not testable as stated (the Lorentz force explains it too, per Moyssides).
Claim 3: field/Grassmann law violates the strong third law and needs the bridge's self-force
a. Math: True that the element-level Grassmann force is not central and not equal-and-opposite (the force on b is perpendicular to b; collinear elements give zero) [read, Sec. 14.1]. Not a contradiction, just a different element law. b. Experiment: No experiment requires the strong third law for open elements. Momentum conservation needs field momentum, which is standard (Poynting). Closed-circuit forces obey the third law in both formulations. c. Tested: Bridge calculations by Assis and others (author-partisan) [read]; Moyssides reports agreement with Lorentz [web, above]. I did not read them. Not independently replicated in a neutral test I could find. d. If true: field momentum would not be needed for steady currents; this would contradict Poynting/momentum accounting that is well tested in radiation pressure and Maxwell stress-tensor calculations [memory, high]. Verdict: Split. "Grassmann element force breaks the strong third law": true by definition, not a flaw. "Needs an extra self-force": Refuted by calculation (the self-field term is part of the standard field calculation); Moyssides' claim is a source, not my own computation.
Claim 4: all magnetism reduces to currents (molecular currents)
a. Math: Consistent. Dipole = small loop, solenoid = magnet [read, Sec. 10.8]. b. Experiment: Consistent with the absence of isolated magnetic monopoles, Gilbert/Barnett-type gyromagnetic effects and the Einstein-de Haas effect [memory, high]. Caveat: electron spin magnetic moments are intrinsic, not classical currents; a magnetic dipole is "as if" a current loop only for field and force purposes. c. Tested: Ampere's solenoid-magnet equivalence verified by Ampere and many later [read]; Einstein-de Haas 1915 [memory, high]. d. Nothing changes. This is standard and already in textbooks. Verdict: Established (as an equivalence for fields and forces). "Unification" is historically important, subsumed by Maxwell.
Claim 5: Weber's law is a better foundation than the field concept
a. Math: Weber's force depends on distance, radial velocity and radial acceleration; it is central, obeys the third law and has a potential energy. Helmholtz's 1847 energy-conservation objection was shown by Weber in 1869-71 to rest on an incomplete version [web: https://en.wikipedia.org/wiki/Weber_electrodynamics]. The negative-inertial-mass objection is disputed. The law is mathematically consistent as a mechanical model. I only read the book's discussion of it, not Weber's papers. b. Experiment: No electromagnetic waves, no retardation (finite-speed propagation), no radiation, no relativistic mass increase or time dilation. Acceleration-dependent and velocity-dependent tests (high-voltage spheres, solenoids, superconductors) found no deviation from Maxwell [web: Weber electrodynamics article, above]. Maxwell/QED reproduces everything Weber does at low speeds and also the above [web, same]. c. Tested: Weber-Kohlrausch 1856 measured the ratio of electric to magnetic units near c, but that is a constant, not a test of Weber's law over Maxwell [memory, medium; not web-checked, not verdict-critical]. Assis and collaborators have argued for tests (e.g. Weber-Maxwell comparisons in the MDPI review) [web: https://www.mdpi.com/2673-9321/2/4/65]; I did not examine results. d. If true: Special relativity and Maxwell's field theory would have to be replaced for electrodynamics, including radiation, which is tested to extreme precision. Verdict: Historically superseded but instructive. For the strong form (better foundation than fields): Tested, not supported (fails to describe radiation and relativistic phenomena that Maxwell/Lorentz does; some of this is calculation-level, so the claim is also refuted as a general foundation).