Mathematician review: Gift-Stephan

Reviewer role: PhD mathematician (derivations, notation, units, hidden assumptions). Step 2 of the pipeline. Inputs: facts.json and claims.md (Step 1), verified against the sources in source folder: Gift-Stephan (read only).

Source gap (repeated and updated)

• 2001 gravity paper (A_Negation_of_Einsteins_...pdf): text layer garbled. Step 1 saw pages 1-5 and 8. I rendered and read pages 6, 7 and 9 [read: page images p.6, 7, 9]. Page 10 (references) and the derivation-of-field-equation text between eq. 1 and eq. 7 on pages 3-5 were not re-read by me beyond what Step 1 reported. So the Lagrangian/gauge step is taken from Step 1's summary plus eq. 7-10 on p.6, which I did read.
• 2009 magnetism paper (PP-16-03.PDF): I read the text layer from the abstract through section 4.2 (equations 3.1-3.13, Periodic Table, solidity of matter, start of chemical reactivity) and the Greenspan passage. Several symbols are garbled (Greek letters, minus signs), so I read equations in context. I did not read the covalent-bond sections or conclusion in full myself.
• 2018 and 2006 papers: 2018 read in full via text layer except the reference list (equations legible). 2006 not re-read by me; I rely on Step 1's summary and on the same arguments reappearing in 2018 (sections 3, 3.2).
• Not in folder, second-hand through Gift only: Shtyrkov's aberration data, Marmet/Kelly/Sato GPS claims, Aspden's modified force law (eq. 12), Greenspan's simulations. Conclusions about these rest on Gift's account.
• Web checks: the web-search budget was exhausted when I started, so only two WebFetch checks were possible (Nordstrom theory, NIST H2). Other [memory] items remain [memory] and are marked.

Corrections to Step 1

1. The 2001 paper's "three classical tests" are not independently derived. Page 7 (read) shows that perihelion precession and light bending both come from an extra force law (eq. 12, F = (1 + 3v^2/c^2) G M m / r^2) taken from Aspden, not derived from the scalar field equation (7)-(10). Step 1 said these rested on "abstract, conclusion and section 5.4"; in fact they rest on this imported law. The paper itself says (p.6) that light bending and redshift cannot be predicted by the theory alone and are done "heuristically" with a photon mass m_p = E_p/c^2 (eq. 11) [read: page image p.6].
2. Step 1 puts the redshift in "section 5.4 (equations 22-24)". On p.7 the redshift is section 5.3 (eq. 18-21 and on). Minor numbering slip; 5.4 may be a later subsection I did not see.
3. Step 1 did not note the perihelion formula's notation error. Eq. 15 on p.7 reads Delta = 6 pi G m / (a c^2 (1 - e^2)) with "m is the mass of the revolving planet" [read]. The correct GR formula has the Sun's mass M. With the planet's mass the result is smaller by about 1e-7 for Mercury. I treat it as a typo, but it is a defined-symbol error.
4. Step 1 did not record that page 9 (read) has Table II "fundamental interactions" and a claimed unification of spin-0 gravity with pion-mediated strong force. In that table the gravity "strength" is given as G m^2/(hbar c) ~ 3e-42. I computed G m^2/(hbar c) = 5.9e-39 for the proton and 1.75e-45 for the electron [calculation, .venv python]. 3e-42 matches neither. Unclear which mass is meant.
5. Greenspan numbers (2009 paper): Step 1 correctly reports the paper's figures (2.20e14 Hz Coulomb, 1.38e14 Hz "measured") [read]. But the measured H2 vibrational constant is omega_e = 4401.2 cm^-1 [web: https://webbook.nist.gov/cgi/cbook.cgi?ID=C1333740&Mask=1000, the fetched page gave 4401.213 cm^-1], i.e. 4401 x 2.998e10 = 1.32e14 Hz. The fundamental (about 4161 cm^-1, [memory] medium) is about 1.25e14 Hz. Gift's 1.38e14 is about 5% above the standard value. Either Greenspan used a different definition or it is an error; cannot tell without Greenspan's paper.
6. Facts entry for the 2018 paper calls it "27-page"; the text layer I read ends at about p.23 plus references. Not important.
7. Step 1's description of the 2018 Michelson-Morley eq. 17 as "2 l w / c^2" is plausible but the exponent was garbled in my extraction too ("2 l1 w / c c"). Treat as 2 l1 w / c^2 [read, garbled].

Everything else in facts.json that I checked (eq. 1-39 of the 2018 paper, Postulate 1 and eq. 3.1-3.13 of the 2009 paper, eq. 7-11 of 2001) matches the sources.

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Claim 1. Light speed is c - v eastward and c + v westward relative to the rotating Earth, shown by GPS clocks, the GPS range equation, time transfer, and a GPS-clock Michelson-Morley layout (2018)

What the mathematics does (worked check)

Take two clocks A, B a distance l apart on a latitude circle, B east of A, both moving east at surface speed v (about 465 m/s at the equator) relative to an Earth-centred inertial (ECI) frame. In the ECI frame light is assumed to move at exactly c (Gift states this himself, citing IS-GPS-200E, p.4 [read]).

• Light leaves A at time t_I. B has moved on. Closing distance condition: l + v t = c t, so t = l / (c - v) (this is Gift's eq. 24-27 [read]). To first order t = l/c + l v / c^2, which is his eq. 4.
• Gift then divides l by t and calls it "the one-way speed of light relative to the Earth", c - v (eq. 5, 28).

Step by step, that is just the closing speed of a pulse chasing a receding target, in a frame where the pulse speed is set to c at the start. The input (c isotropic in ECI) produces the output (c - v relative to the ground) by arithmetic. The clock times in eq. 1-4 are the CCIR/ITU synchronisation rule, which by construction sets clocks to ECI coordinate time; the term 2 omega A / c^2 is the offset that rule inserts. So the "measured" Delta t = l/c + l v / c^2 is the synchronisation convention, not an independent measurement.

(a) Internal consistency. The algebra is correct. The logic is circular: the anisotropy relative to the ground is derived from an assumed isotropy relative to ECI. Two further inconsistencies:

• ECI is itself moving at about 30 km/s around the Sun. Section 3.2 then uses a different frame (solar-system barycentre) where light is again isotropic at c. A frame moving relative to another cannot also have isotropic c in a Galilean world; light being c in both ECI and barycentric frames is exactly the postulate of special relativity (with Lorentz-type transformations between them). The paper's own conclusion admits "multiple preferred frames" carried by Earth and Sun (p.22 [read]), which is a way of saying c is constant in each frame used, not a single ether.
• If the ether were the CMB frame (which the 2006 paper suggests, claim 3), the Earth moves through it at about 370 km/s [memory] high (CMB dipole). GPS would then show drift of that size. It does not; GPS works with c isotropic in ECI.

The Michelson-Morley layout (eq. 9-22): Gift computes out and back one-way times with GPS clocks. The out-and-back difference along the east-west arm, t1(a) - t1(b) = l1/(c-w) - l1/(c+w) = 2 l1 w/(c^2 - w^2), is first order only because the two legs are timed with separate clocks. The round-trip time is t1(a) + t1(b) = 2 l1 c/(c^2 - w^2), which has no first-order term, exactly why the original experiment is second order. Eq. 17 therefore depends on the clock synchronisation between P and M1. On the north-south arm eq. 19 and 21 are written "approximately l2/c, w << c", which discards exactly the second-order term l2 w^2/(2 c^3) that Michelson-Morley measured. So the GPS version is only first-order and the part that could distinguish theories is dropped.

Time transfer (eq. 34-39): c Delta t = R + v Delta t gives eq. 35 and R/Delta t = c - v cos(theta), but R is the separation at emission, and the receiver has moved. R/Delta t is the closing speed, not the speed of light in the receiver's rest frame.

Numerical check of the 414 ns figure (Kelly via Gift): Sagnac delay for one circuit of the equator, Delta t = 4 Omega A / c^2 with Omega = 7.292e-5 rad/s, A = pi (6.378e6 m)^2 = 1.278e14 m^2, c^2 = 8.988e16: 4 x 7.292e-5 x 1.278e14 / 8.988e16 = 4.15e-7 s = 415 ns [calculation]. So the data are real, and consistent with Gift's c +/- v bookkeeping and with relativity's treatment of rotating frames.

b. Consistent with experiment?

The measured quantity (the Sagnac time difference, 414 ns, Michelson-Gale 1925, Bilger 1995 ring laser) is real and is standard physics, [memory] high; Gift cites Michelson-Gale and Bilger [read]. Special relativity reproduces it to the needed order. Because it is a round-trip (closed path) quantity, it fixes no one-way speed. Modern resonator tests limiting anisotropy to about 1e-17 are cited by Gift himself [read, p.2]. No experiment I know independent of synchronisation convention shows direction-dependent one-way speed [memory] medium.

c. Tested?

The "tests" are re-readings of existing GPS practice (CCIR/ITU formulae, GPS range equation) and published data, not new controlled experiments. No one has run an experiment designed to separate the claim from the convention; and, by Reichenbach/Mansouri-Sexl arguments, none can for a one-way speed with clocks synchronised by the same signal [memory] high. Hatch (cited by Gift, p.22 [read]) attributes the effect to clock bias. Not independently replicated as an ether detection. Marmet, Kelly, Sato not in the folder.

d. What would have to change

If true as ether drift, the isotropy of c in the GPS frame would be false, and SR's second postulate would fail in an observable way; but the GPS system, built on ECI isotropy, works to centimetre level, so it would have to be reinterpreted as an accidentally correct convention. In fact nothing in GPS changes if the claim is read as convention.

Verdict (split)

• The measured numbers (Sagnac delays, GPS synchronisation corrections): Established.
• "These show one-way speed c -/+ v, therefore an ether": Internally inconsistent (circular: assumes ECI isotropy to derive anisotropy; also uses two different isotropic frames) and Not testable as stated (one-way speed is convention-dependent).

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Claim 2. The Earth's orbital motion is detectable from apparatus at rest on Earth: planetary radar ranging, Shtyrkov's geostationary aberration, Roemer (Io) and stellar Doppler

Math

• Radar/ranging (2018 eq. 41-55): the equations (41),(42) are written in the barycentric frame with light at c. With the antenna moving toward the reflector at v, (47) L = (c + v) tau_d follows by the same closing-speed arithmetic as above. Again an assumed isotropic c in the barycentric frame yields c +/- v relative to the antenna. Circular in the same way.
• Roemer/Doppler (2006): Step 1 notes that Gift's final results v/c are the standard first-order SR results [read: facts.json summary of the 2006 paper]; the claim is only that the intermediate speeds c +/- v are "real". To first order, any theory with signal speed c in some frame gives the same fractional period change v/c. Check: Io period T0, Earth receding at v. Successive eclipse signals emitted T0 apart in the ether frame arrive T0 + v T0 / c apart, so T = T0 (1 + v/c). The same result follows in SR to first order; the difference appears at second order, where the SR Doppler factor is sqrt((1+b)/(1-b)) with b = v/c, and ether-with-contraction theories give the same value once clocks slow (Mansouri-Sexl equivalence [memory] high).
• Shtyrkov aberration (2018 p.17-18): Gift states "aberration is independent of both the motion of the source and the distance". This is false for a co-moving source in standard kinematics: stellar aberration arises from the observer's motion relative to the star (angle about v/c = 20.49 arcsec for v = 29.8 km/s, checked: tan(alpha) = 29.8/299792 = 9.94e-5 rad = 20.5 arcsec [calculation]). For a satellite that moves with the observer, the light-time displacement of the source exactly cancels the aberration (planetary aberration = aberration + light-time correction, [memory] high), and no annual signal is predicted in either special relativity or any ether theory in which both objects share the Earth's velocity. A geostationary satellite and ground station share the same orbital velocity about the Sun to excellent approximation. So a seasonal signal at the 20-arcsec level would be a surprise for ether and relativity alike unless the ether wind is the cause, and then the standard first-order cancellation (Lorentz 1895 first-order theorem) must fail; Gift himself quotes that theorem (p.16 [read]).

a. Internal consistency

Radar derivation: algebra correct, assumption circular. Roemer/Doppler: consistent, but does not discriminate. Shtyrkov: the argument that source fixed to Earth shows aberration contradicts the cancellation just described; if the data are correct they would also contradict the paper's own claim that first-order effects cancel for closed paths. Not checkable without the source.

b. Consistent with experiment?

Roemer and stellar Doppler agree with SR and with ether theories (they are the same to first order). Radar ranging: planetary ephemeris and spacecraft tracking (e.g. Cassini, Viking) fit with c isotropic in barycentric coordinates and standard relativistic corrections; Gift notes they need relativistic time corrections [read, p.19]. Shtyrkov's result is not, to my knowledge, reproduced in the mainstream literature [memory] low; I could not verify (search budget exhausted).

c. Tested?

Shtyrkov: one author's data set (Kazan, 1998-99, per Gift [read]); Gift writes "We await confirmation by others" [read, p.18]. No known replication [memory] low. Radar: tested, but not as an ether test.

d. What would have to change

If Shtyrkov is right: aberration kinematics for co-moving sources and first-order Lorentz invariance would fail; a real preferred frame would be required, and GPS/ephemeris would have to reproduce all their present successes with a different explanation.

Verdict (split)

• Roemer and Doppler as ether evidence: Not testable as stated (observationally equivalent to relativity at first order).
• Planetary radar as ether evidence: Refuted by calculation in the sense of reinterpretation: the same closing-speed arithmetic holds without any ether, so it carries no evidential force; "Internally inconsistent" as proof (assumed c isotropic in barycentric frame).
• Shtyrkov: Never properly tested (single unreplicated report; source not in folder; conflicts with standard aberration kinematics, and the paper itself requests confirmation).

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Claim 3. A cosmic ether exists, light-speed invariance and special relativity are invalid, Michelson-Morley was the wrong kind of test because of FLL contraction; the CMB is the ether's thermal radiation

Math

The framework is the generalised Galilean transformation (GGT) of Gagnon et al. with Fitzgerald-Lorentz-Larmor (FLL) contraction and clock slowing (2006 paper [read via facts.json; not re-read]). A theory in which rods contract by sqrt(1 - v^2/c^2) and clocks slow by the same factor relative to an ether frame reproduces all second-order experiments by construction, and with Einstein-type clock synchronisation is observationally equivalent to special relativity (Mansouri-Sexl [memory] high). Therefore, if FLL is true, Michelson-Morley cannot detect it and no experiment can distinguish it from SR, except via one-way speed with ether-based synchronisation, which is not independently measurable. So the logic of the claim is:

1. FLL makes second-order tests blind (true, by design, it was invented for that).
2. First-order tests should show it (Gift's argument): but first-order effects cancel for any closed-path experiment (Lorentz theorem, which Gift cites), and open-path tests are synchronisation-dependent.
3. Therefore SR "invalid". This does not follow: GGT agrees with SR on every measurable quantity.

The statement "SR is invalid" and the statement "the ether is undetectable by construction" are in tension: if the ether were unobservable in principle, the theory is not distinguishable from SR (not falsifiable); if observable, Mansouri-Sexl-type kinematic tests (Michelson-Morley, Kennedy-Thorndike, Ives-Stilwell) constrain it, and they have found nothing [memory] high. The paper's own list shows resonator limits delta c / c < 1e-17 [read, 2018 p.2].

CMB point: the thermal 2.7 K spectrum is a blackbody; calling it "ether radiation" adds a label but no prediction. If it defines the preferred frame, the Earth's speed relative to it is about 370 km/s [memory] high, not 30 km/s; GPS and radar results would then differ from c +/- 30 km/s as claimed in claim 2. Internally the paper then uses an Earth-frame (ECI) and a Sun-frame; neither is the CMB frame.

a. Internal consistency

The kinematic argument (FLL cancels second-order) is consistent but makes the theory unfalsifiable by those tests; the move to "first-order tests" depends on the circular synchronisation step (claim 1), and the multiple-preferred-frames conclusion is contradictory with the notion of a single medium (cf. claim 1, point on two isotropic frames).

b. Consistent with experiment?

Consistent with: all null results (by design). Not supported by: the Kennedy-Thorndike/Ives-Stilwell/Michelson-Morley family and modern resonator tests (Brillet-Hall 1979, Herrmann 2005, Eisele 2009, cited by Gift [read]); Ives-Stilwell is usually read as support for relativistic time dilation [memory] medium. Aberration and Fizeau are explained with or without an ether.

c. Tested?

Michelson-Morley (1887) and many successors (Miller's positive result was attributed to temperature by Shankland et al., which Gift mentions [read]; DeMeo argues Miller was wrongly dismissed, cited in 2018 [read]; I did not evaluate that dispute). Modern resonator experiments: controlled, null at 1e-17. The new GPS "tests" are not independent tests (claim 1).

d. What would change

SR's second postulate and Lorentz invariance of QED and the Standard Model would have to be given up, a preferred frame admitted, and the success of all Lorentz-invariance tests (storage rings, resonators, astrophysical) explained as conspiracy of contractions. The CMB would become a medium, not a relic of early-universe cosmology (which predicts its blackbody spectrum and acoustic peaks, [memory] high).

Verdict (split)

• "SR is invalid because first-order light speed varies": Internally inconsistent (non sequitur; GGT with FLL equals SR in all measurable respects) and Tested, not supported for any detectable preferred-frame anisotropy (resonator limits 1e-17, from the paper's own citations).
• "MM was the wrong kind of test": Not testable as stated (any theory made equivalent to SR escapes second-order tests by definition).
• "CMB is the ether's radiation": Not testable as stated (a relabelling, no distinct prediction).

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Claim 4. The equivalence principle is false (a charge radiates in an accelerating rocket but not hovering above a mass), so GR is invalid; replace it with a Newtonian-type quantum gauge theory with massless spin-0 gravitons that gives Newton's law, redshift, orbit precession, no black holes, no dark matter, no gravity waves (2001)

Math, step by step

Larmor argument (eq. 2-3): P = (1/4 pi eps0)(2/3) q^2 a^2/c^3 gives power from a charge at proper acceleration a = g. Gift says the charge in rocket B (accelerating, free space) radiates and the one in rocket A (hovering) does not, so observers can tell them apart. The mathematical difficulty is that radiation is not an invariant, locally measurable property: whether a uniformly accelerated charge "radiates" depends on the observer (Rohrlich 1963, Boulware 1980, [memory] medium; not web-checked). Local equivalence is claimed only for point-like, small-region experiments; an extended Poynting-flux analysis over the full field region violates that locality condition. Gift mentions Peierls' earlier objection and calls the resolution arbitrary [read]. I did not check that discussion in the page images myself.

Scalar graviton theory (eq. 7-10, p.6 [read]):

• Eq. 7: box A = -m psibar gamma^0 psi A... that is, box A = -m psibar_n gamma^0 psi_n (symbols garbled in the image; I read it as a source built from psibar gamma^0 psi = psi-dagger psi, the number density). This is a scalar Klein-Gordon equation, spin 0, mass 0 [read].
• Eq. 8: identify m psibar gamma^0 psi with a mass density rho_m: box A = -4 pi G rho_m. Eq. 9 static limit: del^2 A = 4 pi G rho_m, Poisson equation; eq. 10: F = G M m / r^2.

Problems:

1. Eq. 8 is written to give Newton. Newton's law is put in by choosing the constant 4 pi G, not derived. The "gauge invariance" label supplies the form box A = source but not the coupling strength.
2. The coupling term m psi-dagger psi A is invariant under any phase change of psi (psi-dagger psi is phase independent). The time-local phase freedom exp(i alpha(t)) is compensated by an A with shift A -> A + (1/m) d alpha/dt (my reconstruction of Gift's section 4.1; Step 1 described the same structure). A field equation box A = -m psi-dagger psi is not invariant under that shift unless box (d alpha/dt) = 0. So the equation of motion breaks the very symmetry used to introduce A. (The identical structure reappears in the 2009 paper.) This is my analysis of Gift's stated construction; the intermediate equations on p.4-5 were not re-read by me.
3. Density psi-dagger psi changes sign for antiparticles, so under this coupling matter and antimatter would repel (my inference; the paper may address it on pages I did not see).
4. The paper admits the coupling is not Lorentz-boost invariant and allows it by postulate (Step 1, [read]).

Light bending and perihelion (p.7 [read]) are the decisive part:

• Gift states the new theory "by itself cannot predict" light bending and redshift (p.6) and uses a heuristic photon mass E/c^2 (eq. 11).
• Perihelion (eq. 12-15): the force law F = (1 + 3v^2/c^2) G M m / r^2 is taken from Aspden, not derived from eq. 8. Check: with v = h u (h = angular momentum per unit mass), F/(m h^2 u^2) gives d^2u/dphi^2 + u = GM/h^2 + 3 G M u^2/c^2. This is eq. 14, an algebraic consequence of the assumed force law [calculation]. And eq. 15 then gives 43 arcsec/century only if M is the Sun's mass (the paper writes the planet's mass, correction 3). The exactly GR number is obtained because the 3 GM u^2/c^2 term is GR's term, put in by hand.
• Light bending (eq. 16-17): Gift drops the GM/h^2 term "since h = infinity" for a photon from infinity. That is wrong: h = r^2 dphi/dt is angular momentum per unit mass and for a photon of speed c passing at distance R it is h = c R, finite. Retaining the term in his own eq. 14: u'' + u = G M/(c^2 R^2) (1 + 3 cos^2 phi). Particular solution: u = cos(phi)/R + (G M/(c^2 R^2)) (5/2 - (1/2) cos 2 phi). Setting u = 0 at phi = pi/2 + epsilon: epsilon = 3 G M/(c^2 R), total deflection delta = 6 G M/(c^2 R), i.e. 3 times Newtonian (2 G M / c^2 R) and 1.5 times GR's 4 G M/(c^2 R). For the Sun, GR gives 1.75 arcsec; this gives about 2.6 arcsec [calculation: ratio 6/4 x 1.75]. So Gift's own equations, treated consistently, overshoot observation by about 50%, whereas dropping the term reproduces GR only by an unjustified step. (Check by the same method: only the 3 cos^2 term gives epsilon = 2 G M/(c^2 R), delta = 4 G M/(c^2 R), matching his eq. 16-17; only the Newtonian term gives delta = 2 G M/(c^2 R).)
• Redshift (eq. 18-21): photon loses energy GM m/R with m = h nu / c^2 (eq. 11), giving delta nu/nu = GM/(R c^2). This is the Newtonian energy bookkeeping, correct to first order. It uses gravitational mass E/c^2 for a photon, which is the equivalence of gravitational and inertial mass in disguise, the principle he is rejecting.

Standard scalar gravity for comparison [web: https://en.wikipedia.org/wiki/Nordstrom%27s_theory_of_gravitation]: Nordstrom's scalar theory predicts zero light bending and a perihelion lag of about -7 arcsec/century (opposite sign, 1/6 the GR magnitude) instead of +43. A pure scalar graviton field of the kind in eq. 7-9 inherits this, which is why Gift needs the added force law and photon mass.

Table II (p.9 [read]): strength column 3e-42 for gravity does not match proton or electron (see Correction 4).

a. Internal consistency

Not consistent: (i) A shift symmetry not respected by the field equation; (ii) GR-matching results come from imported ad hoc terms; (iii) the discarded GM/h^2 term gives 6 GM/(c^2 R) not 4; (iv) redshift derivation uses E/c^2 gravitational mass; (v) notational error in eq. 15.

b. Consistent with experiment?

• Equivalence principle: composition-independent free fall tested at about 1e-13 (torsion balances, lunar laser ranging; MICROSCOPE satellite about 1e-15) [memory] medium; not web-checked.
• Light bending 1.75 arcsec solar limb (VLBI to ~1e-4) and Shapiro delay (Cassini 2003) match GR [memory] high. Gift's theory needs the photon-mass heuristic; the scalar-only version gives zero (Nordstrom, web).
• Mercury 43 arcsec/century [read: Gift's own text, p.7].
• Gravitational waves: LIGO 2015 onward; Hulse-Taylor orbital decay matches GR quadrupole formula to about 0.2-1% [memory] medium. Gift says the decay is accounted for "qualitatively" [read; Step 1]; no calculation seen.
• Black holes and dark matter: observational evidence not discussed in detail by Gift (Step 1 [read]); I did not evaluate it.

c. Tested?

The equivalence principle has been tested extensively (above); Gift's theory has not been tested beyond his own derivations. Gift says "modern tests" will be reported later (p.6 [read]); no sign they were. No replication.

d. What would have to change

If the equivalence principle failed, GR (and metric theories generally) would fail, and torsion-balance and lunar-ranging results at about 1e-13 would need an unexplained cancellation. Light bending would need a coupling that does not exist in the scalar theory without extra assumptions.

Verdict (split)

• "The equivalence principle is false because accelerated charges radiate differently": Tested, not supported (EP tests) and the Larmor argument is a known observer-dependence subtlety, not a refutation [memory] medium.
• "A scalar-graviton gauge theory gives Newton, redshift, precession, light bending": Internally inconsistent (gauge construction; ad hoc imported force law; light-bending step uses an unjustified h = infinity) and Refuted by calculation as stated (pure scalar theory gives zero light bending and retrograde precession; with Gift's own added terms the bending comes out 6 G M/(c^2 R), not 4).
• "No black holes / dark matter / gravity waves": Tested, not supported for gravity waves (LIGO detection; binary-pulsar decay). Black holes and dark matter: not assessed here; marked unknown.
• Newton's law and redshift alone: Established (but not in dispute; they are Newtonian/weak-field GR results).

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Claim 5. Magnetism is a fundamental interaction separate from electromagnetism, mediated by massless spin-1 "magnatons", arising by relaxing Lorentz covariance; it supposedly explains Pauli exclusion and chemical bonding (2009)

Math, step by step

• Eq. 3.1: rho = div(m)-type "magnetic charge" (garbled in the text layer), with m the magnetic moment. Eq. 3.3: phase transformation exp(i alpha rho). Eq. 3.5: alpha = alpha(x) is allowed to depend on space but not time. Eq. 3.6: add a 3-vector A_k coupled to psibar gamma^k psi, with A_k -> A_k + d alpha / d x^k (eq. 3.7 as I read it, garbled) [read].
• Eq. 3.8: box A_k = (coupling) psibar gamma_k psi, a 3-vector Klein-Gordon equation. Eq. 3.10-3.12: identify psibar gamma_k psi with a current J_k, so del^2 A_k = -mu J_k, "the Poisson equation for magnetostatic potentials which contains all of classical magnetism". Eq. 3.13: dipole force F = 3 mu1 mu2/(4 pi r^4)-type [read].

Problems:

1. The gauge transformation (3.7) shifts A_k by a gradient d alpha / d x^k. A pure gradient has zero curl, so the transformations the theory is built on never generate a magnetic field B = curl A. A field with non-zero curl is not produced by the symmetry; the gauge-invariant field strength is zero. The "gauge principle" does not give the field its content.
2. Eq. 3.8 is not invariant under the shift A_k -> A_k + d_k alpha unless box d_k alpha = 0 (same defect as in claim 4).
3. The source psibar gamma_k psi is the ordinary (electric) Dirac current density J_k. A coupling "magnetic charge x J_k A_k" is formally the QED coupling j.A with a different constant. Equation 3.12 is simply classical magnetostatics, which the photon field already contains. So nothing distinguishes magnatons from the spatial part of the photon: no new prediction beyond what Maxwell's equations give.
4. A massless spin-1 field with only three spatial components (no time component) has 3 polarisations. A massless vector particle has 2 physical helicities; the third (longitudinal, plus the missing time component) is removed in QED by gauge invariance and Lorentz covariance. Abandoning covariance (Postulate 1) removes that protection, so the theory has an unphysical or unconstrained mode; the paper does not address this. (Standard QFT [memory] high.)
5. Eq. 3.13 is an ordinary classical dipole-dipole result. The paper says its 1/r^3 potential "becomes dominant at short distances" (p.15). Check against energy scales: two electron magnetic moments (Bohr magneton 9.27e-24 J/T) side by side at 1 angstrom: U = (mu0/4 pi) mu_B^2 / r^3 = 1e-7 x (9.27e-24)^2 / (1e-10)^3 = 8.6e-24 J = 5.4e-5 eV [calculation]. The H2 bond energy is about 4.5 eV [memory] high, and exchange/Pauli effects are of order eV. So the magnetic dipole term is about 1e5 times too small to be the "Pauli force" or the bond. It also averages away over orientations. That is a quantitative refutation of the explanatory claim, using Gift's own eq. 3.13.
6. The claimed attraction between anti-parallel spins and repulsion between parallel spins: side-by-side dipoles do behave this way, but head-to-tail dipoles do the opposite, and bond electrons are not fixed side by side; and an attraction for anti-parallel pairs cannot explain Pauli exclusion (which forbids two electrons in the same state regardless of the size of any force): the standard account is antisymmetry of the many-electron wave function (spin-statistics theorem, [memory] high), which produces an effective "exchange" repulsion without a new force.
7. Greenspan's simulations (as described, p.16 [read]): classical dynamics with an assumed attractive force between the bonding electrons reproduces vibrational frequencies and bond lengths. That shows a fitted attractive interaction can mimic a bond in a classical model; it does not identify that force as magnetic or compute its size from eq. 3.13, which (item 5) is far too small. The paper's "measured" H2 value 1.38e14 Hz disagrees with the NIST omega_e 1.32e14 Hz (Correction 5).

a. Internal consistency

Not consistent (items 1-4 above: gradient-only gauge field; non-invariant field equation; coupling identical to the photon's; unphysical polarisation count).

b. Consistent with experiment?

Classical magnetostatics: yes, but it is the same as Maxwell. New content (a separate quantum, distinct from photon, giving effects at short range): no experiment cited other than Greenspan's classical simulations, which do not test magnatons. Photon-mediated magnetic interactions are tested by QED to about 1 part in 1e10 on g-2 [memory] high, a result in which the magnetic coupling is already included. The paper cites Barut's remarks on unexplained resonances in e+e- scattering as possible evidence [read]; I could not check these claims or whether they hold.

c. Tested?

No direct test of magnatons reported in the paper or known to me. No particle experiment has seen one [memory] medium (Step 1 says the same). Not replicated (nothing to replicate). Published in Progress in Physics (accepted within about 10 weeks [read]) [journal reputation: memory low].

d. What would have to change

QED would need a second massless spin-1 field coupled to magnetic moments; Lorentz invariance of the Standard Model would be abandoned, contradicting Lorentz-invariance bounds (about 1e-17 or tighter for many parameters, [memory] medium); the spin-statistics theorem's explanation of Pauli exclusion would need to be replaced with a force.

Verdict (split)

• Magnaton gauge construction: Internally inconsistent (gradient-only shift gives zero field strength; field equation breaks its own symmetry; same coupling as photon).
• Magnaton as separate particle: Never properly tested (no experiment designed to look for it; the sole "confirmation" is classical simulation).
• Explains Pauli exclusion and chemical bonding: Refuted by calculation (dipole-dipole energy about 5e-5 eV at 1 angstrom against eV-scale bond/exchange energies, using the paper's own eq. 3.13).
• Classical magnetism restated as Poisson equation: Established, but not new.

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Summary table

Sources used

• [read] all four PDFs in source folder: Gift-Stephan (see source gap for coverage).
• [web] https://en.wikipedia.org/wiki/Nordstrom%27s_theory_of_gravitation (zero light bending; perihelion lag about -7 arcsec/century vs +43).
• [web] https://webbook.nist.gov/cgi/cbook.cgi?ID=C1333740&Mask=1000 (H2 omega_e = 4401.2 cm^-1).
• [calculation] Sagnac 415 ns; stellar aberration 20.5 arcsec; Bohr-magneton dipole energy 5.4e-5 eV; light-bending integral (6 G M/c^2 R); G m^2/(hbar c) for proton and electron.
• [memory], not web-checked because the search budget was exhausted: Mansouri-Sexl equivalence (high); CMB dipole speed about 370 km/s (high); planetary aberration cancellation for co-moving source (high); observer dependence of radiation from accelerated charges, Rohrlich/Boulware (medium); EP test precision 1e-13 and 1e-15 (medium); Hulse-Taylor agreement 0.2-1% (medium); H2 bond energy about 4.5 eV (high); Shtyrkov replication status unknown (low).