Ampere: Science Contrarian review
Reviewer role: Science Contrarian (PhD standard; judges by experiment, not consensus). Source: Assis and Chaib, Ampere's Electrodynamics (Apeiron 2015), a single text-layer PDF. No source gap, but the book is by two partisans of Ampere/Weber, so its statements about what the "mainstream" cannot explain are treated as claims to check, not as data. Passages I read myself [read]: Sec. 8.2-8.3 (bridge experiment and the n>1 experiment), Sec. 21.2 (explanations of the bridge), Sec. 10 (similarity-law equilibrium and Graneau's misdescription of the circuit geometry, around pdftotext lines 8480-8520).
Corrections to Step 1
- claims.md claim 2 merges two separate experiments. Per Sec. 8.3 [read], Ampere first showed in May 1822 with an astatic-coil experiment that n > 1, so k = (1-n)/2 must be negative. The bridge experiment (Sept. 1822, Geneva, with de la Rive) then tested the surprising consequence of negative k. The k = -1/2 value itself came from the null experiment (no continuous rotation), per Sec. 7.5 as summarised in facts.json. The bridge is a confirmation of the sign and of the collinear repulsion, not the origin of the number.
- facts.json's [memory] line says later literature "disputes whether the bridge shows any breakdown of the Lorentz force". That understates the split. [web] Graneau, Moyssides, Pappas, Peoglos and Wesley measured or modelled the bridge force in support of Ampere/Weber, while Moyssides also published that the Biot-Savart-Grassmann-Lorentz law gives longitudinal forces in complete agreement with Ampere's: https://link.springer.com/article/10.1140/epjp/i2014-14034-2 (snippet only; full text not read). Literature on both sides, not one.
- facts.json's remark that Grassmann "gives the same net force as Ampere's on closed circuits for the cases tested in the book" is too weak. It is a general theorem (the two element laws differ by a term that is an exact differential and integrates to zero on a closed circuit) [memory, high]. The bridge matters precisely because the bridge alone is not a closed circuit.
- Not in claims.md: Sec. 21.3 (rotation of a magnet about its own axis, Ampere's motor) is a separate controversy that I did not read in depth; I do not rate it.
- Minor: the book itself shows (Sec. 10) that Graneau and Graneau mis-described Ampere's circuit geometry (vertical vs horizontal planes) [read], a reminder that partisan secondary sources contain errors on both sides.
A quick consistency check I ran (angles formula)
Using the book's form (ii' ds ds'/r^2)(cos(epsilon) + h cos(theta) cos(theta')), h = k - 1 [read]: - k = -1/2 gives h = -3/2. Collinear, same direction: epsilon = theta = theta' = 0, so bracket = 1 - 3/2 = -1/2. Negative means repulsion, matching the claim. - Old expectation k = 0 gives h = -1, bracket = 1 - 1 = 0: no force between collinear elements, matching Ampere's pre-1822 belief [read]. - Side by side parallel (theta = theta' = 90 degrees): bracket = cos(0) = 1, attraction, matching the textbook fact that parallel same-direction currents attract. - n-k relation: k = (1-n)/2 with n = 2 gives -1/2. Consistent.
Claim 1: Ampere's force law (central, 1/r^2, k = -1/2, strong third law)
a. Math: internally consistent; checked above. The family indexed by k all give identical forces on closed circuits [memory, high], so the math alone cannot single out k = -1/2; only element-level experiment can. b. Experiment: agrees with every closed-circuit measurement ever made, as does the Lorentz/Grassmann form. Therefore closed-circuit data (Ampere's balance experiments, solenoids, Biot-Savart wire experiments) do not discriminate. c. Tests: the discriminating tests are those on open or movable parts of a circuit (bridge, wire-explosion longitudinal forces, Graneau). Those were run mainly by advocates; no neutral, controlled comparison is on record in what I read. Not dismissed without testing: mainstream authors did write rebuttals [web, snippet] https://link.springer.com/article/10.1140/epjp/i2014-14034-2 d. If the element law were literally true: textbooks would need a second, non-field description of magnetic force with direct action at a distance; momentum conservation would be a statement about matter alone, with no field momentum. Radiation and relativity are not addressed by the law. Contrarian case: the third law in its strong form is a clean, falsifiable principle, and Ampere reached the law from null experiments, which are the most trustworthy kind of measurement. Against it: Ampere's law is magnetostatic; it cannot describe radiation, and field momentum (Poynting) is independently supported by radiation pressure [memory, high]. Verdict (split): closed-circuit forces from the law: Established. "The true law for isolated current elements, and strong third law is required": Never properly tested (neutral). The law as a complete electrodynamics: Historically superseded but instructive.
Claim 2: k = -1/2 from experiment, and the bridge confirms collinear repulsion
a. Math: consistent (see check; sign chain n > 1, k < 0, repulsion holds). b. Experiment: the bridge moves away from the current source in the stated direction [read, Sec. 8.2; de la Rive quoted]. That motion is not in dispute; the dispute is its interpretation. c. Tests: Ampere and de la Rive 1822 [read]. Repeated by Graneau, who noted mercury being pushed away from the rear faces of the hairpin [web, snippet: https://dflund.se/~snorkelf/Longitudinal/node3.html, and https://www.researchgate.net/publication/376204052_Explanation_to_the_Ampere_Hairpin_Experiment]. Precise force measurements by Moyssides and Peoglos, Moyssides and Pappas [web, snippets only; I did not read the papers]. Confounders I would flag as the researcher-side weakness: the mercury is a current-carrying fluid that experiences its own Lorentz pumping force, and the bridge force depends on how current spreads at the junction. The book's own statement that mainstream cannot explain it ("we do not know of any explanation by Orsted, Biot, Savart, Faraday", [read] Sec. 21.2) is only a statement about 1822. d. If the bridge proves a longitudinal element force: a real extra force beyond Lorentz would be needed, and exploding-wire fragmentation would be a new force effect. If Lorentz explains it, nothing changes. Verdict: bridge motion and collinear repulsion as an observation: Established (replicated). That it discriminates Ampere from Lorentz: Never properly tested by a neutral control (rival computations exist; see claim 3).
Claim 3: the field description fails unless a bridge self-force is added
a. Math: the sub-claim that the Grassmann force gives zero between collinear elements is correct by direct calculation: dF is proportional to ds x (ds' x r), and with ds' parallel to r, ds' x r = 0 [calculation]. Internally consistent. But "the bridge's force on itself" is not an ad hoc patch: in the field picture every segment feels the field of all currents including those in its own conductor, and finite wires have non-zero self-force when the circuit is not closed at that point [memory, medium]. The authors present it as embarrassing; that framing is theirs. b. Experiment: the claim "Lorentz cannot account" is contradicted by Moyssides's published agreement [web snippet, https://link.springer.com/article/10.1140/epjp/i2014-14034-2] and supported by Graneau and Wesley; I could not read either side in full. c. Tests: no neutral third-party experiment found in my search. Note also the authors' own bias: Assis is a Weber/Ampere author [read]. d. If Ampere were right here: field momentum would not carry the missing momentum; the Lorentz force law would need an extra longitudinal term. Verdict (split): Grassmann gives zero collinear force: Established by calculation. Field theory "fails" the bridge: Never properly tested (contested computations on both sides, no neutral controlled test). The self-force requirement being a defect: Not supported.
Claim 4: all magnetism is molecular currents; poles and fluids unnecessary
a. Math: consistent. A magnetic dipole layer equals a current loop (Sec. 10) [read; standard result, Griffiths]. b. Experiment: ferromagnetism and the Earth's field are described well by currents; no magnetic monopole has been confirmed [memory, high]. But electron spin and nuclear moments are intrinsic and not literal circulating current; Ampere's picture needs quantum reinterpretation [memory, high]. c. Tests: this is the most widely corroborated claim in the book (Barnett and Einstein-de Haas gyromagnetic effects relate magnetism to angular momentum) [memory, medium; not web-checked, the verdict does not turn on it]. d. Nothing in mainstream needs to change; it is mainstream. Verdict (split): classical magnetostatics from currents, poles unnecessary: Established. "All magnetism is literal current loops": Historically superseded but instructive (replaced by intrinsic spin).
Claim 5: Weber's law unifies Ampere, electrostatics and induction and is a better foundation
a. Math: Weber's potential reproduces Coulomb's law, Ampere's force and Faraday induction for the cases it was built for [web, https://en.wikipedia.org/wiki/Weber_electrodynamics]. It is not Lorentz invariant [memory, high]. Helmholtz criticised it for a negative effective inertial mass at very small separations and energy problems; Weber and later authors dispute this [web, https://www.mdpi.com/2673-9321/2/4/65 snippet]. b. Experiment: Weber works in slow-charge regimes. It has no built-in retarded propagation or radiation; light, radio waves and fast-particle (relativistic mass increase) data are explained by Maxwell plus special relativity [memory, high; not read in the book]. c. Tests: the strong form (a complete replacement for Maxwell) was effectively judged by the 1888 Hertz radio-wave experiments; nobody ran a controlled head-to-head, the field theory simply explained more. Modernisation attempts exist (e.g. https://www.researchgate.net/publication/370275906_On_the_Modernisation_of_Weber's_Electrodynamics) but I did not assess them. This is "tested by the weight of later evidence", not "dismissed without testing". d. If Weber were the better foundation: relativity-type velocity limits and the field concept would be replaced by action at a distance with a new account of radiation. Verdict (split): reproduces Ampere/Coulomb/induction in slow regimes: Plausible, untested in modern form (the cited derivations are textbook-level mathematics but I did not re-derive them). Better foundation than the field concept: Historically superseded but instructive.
Summary of how it was dismissed
The 1820s Ampere programme was not suppressed; Ampere's force was the leading theory for a generation. Its decline came from Maxwell's Treatise and the Hertz experiments, i.e. on grounds of explanatory reach, not a failed test. The residual contrarian question is the narrow one in claims 2-3: whether anyone has run a neutral, shared-protocol bridge or longitudinal-force test.
Sources used on the web (snippets via search; pages not read in full): see URLs inline above.