Kelly-AG: Science Contrarian review (Step 2)

Reviewer role: judge by experimental evidence, build the strongest honest case, examine how the claims were received, and apply the same rigour to the inventor. Tags: [read] from the documents, [web] with URL, [memory] with confidence. Calculations marked [calc] were run in the project venv (numpy).

Source: one paper, A. G. Kelly, "The Sagnac Effect and Uniform Motion" (Kelly_2.pdf, 13 pp., undated, written after 2003; our PDF copy was made 16 Apr 2011, after his death in 2005) [read]. The paper's own results are not new experiments: Kelly performs no measurement in it. Everything experimental is other people's data, so the question for each claim is what those data show and whether his reading of them follows.

Terms for the reader

• Sagnac effect: two light beams sent round a closed loop in opposite directions return at different times if the loop turns. Time difference dt = 4Aomega/c^2, where A is the enclosed area, omega the angular velocity (rad/s), c the speed of light. A rotation of one revolution per second on a 0.1 m^2 loop gives dt of order 10^-17 s, which an interferometer sees as a shift of the fringe pattern (one fringe = one light period).
• Inertial frame: a frame with no acceleration, in which free bodies move in straight lines. A frame fixed to a turntable is not inertial.
• Preferred-frame / Lorentz-ether theories: theories in which light has speed c in one special frame (the "ether", or here the Earth-centred non-rotating frame) and other frames differ. Some are experimentally equivalent to special relativity (SR) for many tests.
• Fringe: one bright band of the interference pattern; "0.23 fringe" means the pattern moved 23% of the band spacing.

Corrections to Step 1

Checked claims.md, facts.json, the deep read and sites.md against the paper text (I read pp.1-13 myself, including pp.6-13 that Step 1 had only as digest).

1. Deep-read note "possible factor-of-10 slip in Sagnac's area (0.86 vs 0.0866 m^2)" is CONFIRMED and sharper than stated. Kelly gives three different areas for the same experiment: "0.86 m^2" on p.1, "666 cm^2" on p.11, while published accounts give 866 cm^2 = 0.0866 m^2, indigo mercury light, 120 rpm, observed shift 0.07 +/- 0.01 fringe [web: search summary of Sagnac 1913 accounts, e.g. https://vixra.org/pdf/2005.0243v1.pdf and https://www.idc-online.com/technical_references/pdfs/mechanical_engineering/The_Sagnac_effect.pdf; I did not open the originals]. [calc] A = 0.0866 m^2, 2 Hz, 436 nm, reversal gives 0.067 fringe, matching 0.07; 0.86 m^2 would give 0.66; 666 cm^2 gives 0.051. So 866 is the number consistent with the observation; 0.86 m^2 and 666 cm^2 are slips.
2. The deep read did not catch that p.6 says the Earth's rotation would shift a 1 m diameter Sagnac disc by "about 1 x 10^-5 fringes at mid-latitudes". [calc] 4AOmegasin(45 deg)/(clambda) with A = pi*(0.5)^2 gives 9.8 x 10^-7 fringe (about 10^-6), a factor of ten smaller. Even a 1 m radius disc gives about 4 x 10^-6. Minor, but it is a second order-of-magnitude slip.
3. Claim 4 in claims.md says ring lasers "confirm the Sagnac formula to better than 1 part in 10^20". This misstates the paper and the experiment. Kelly writes "accuracy of better than 1 part in 10^20" for Bilger et al. (p.7). What the literature reports is a frequency resolution of 1 part in 3 x 10^21 for the Christchurch C-II ring laser (Stedman, Li, Bilger, Applied Optics 1995) [web: search result summary; abstract page https://opg.optica.org/ao/abstract.cfm?uri=ao-34-24-5375 not opened]. That is the stability of the measured beat frequency, not the accuracy of agreement with a formula. [calc] The Sagnac beat for a 0.75 m^2 ring at latitude 43.5 S is about 79 Hz, so a 10^-20 relative accuracy would be a 10^-18 Hz measurement, which is not what is claimed in the literature. Claim 4 should say "frequency resolution" and not "confirms the formula".
4. Claim 1 as written in claims.md ("applies equally to bodies in uniform straight-line motion") is stated without the condition that matters. See Claim 1 below: Wang et al. found a shift in a CLOSED fibre loop whose co-moving source and detector sit on a belt, with segments moving in opposite directions; they did not find a shift for a rigidly translating ring. Step 1's own Investigator note says this; the deep read flagged that pp.6-11 were digest-only. I have now read them.
5. Claim 5's text in claims.md attributes to Kelly that light "does not travel at c relative to a moving disc along the straight segments" and calls this a contradiction of constancy of light speed. Kelly's own wording (p.8) is that the Sagnac/Harress/Pogany tests "also confirm that the light emitted upon a rotating disc, when travelling in a straight line (on a polygonal section), does not travel at the speed c relative to the moving disc". The inference from a round-trip difference to per-segment speed is discussed below.
6. Claim 6: Step 1 (via Wikipedia) found that Einstein wrote about Harress's rotating-prism experiment in 1914. I confirmed bibliographic details: A. Einstein, "Bemerkungen zu P. Harzers Abhandlung 'Ueber die Mitfuehrung des Lichtes in Glas und die Aberration'", Astronomische Nachrichten 199 (1914) [web: https://onlinelibrary.wiley.com/doi/10.1002/asna.19141990104]. A search summary says Harzer's paper on Harress drew two replies from Einstein [web: same search; Wikisource lists "On the Experiment of F. Harress", https://en.wikisource.org/wiki/Translation:On_the_Experiment_of_F._Harress, not opened]. Wikipedia's "Sagnac effect" says Einstein was aware of the effect through Harress's experiments [web: https://en.wikipedia.org/wiki/Sagnac_effect]. Kelly himself cites Harress (p.8) but never mentions this. Note Kelly's claim is specifically that Einstein never referred to the Sagnac tests or the Michelson-Gale test; the 1914 notes do not settle whether Einstein named Sagnac.
7. The deep read says the two circular derivations "use the same equations"; I agree, and it matters for the verdict on claim 2.
8. "Dufour & Prunier repeated it forty years later" vs cited 1937-42 papers; "4250 km" vs 4752 km [calc: 6371 cos 41.77 deg = 4752 km]. Both confirmed.

Claim 1. The Sagnac effect applies to uniform straight-line motion, not only rotation

a. Mathematics. Kelly's own general result is dt = 2D/c^2 with D = closed integral of u dl, where u is the component of the path element's velocity along the light path (pp.11-12). Kelly shows D = 2omegaA for rotation. For a RIGID loop in uniform translation at velocity V, u dl summed round the loop is V . (closed integral of dl) = 0. So by Kelly's own formula a rigidly translating interferometer gives no shift. The conclusion "applies to uniform straight-line motion" holds in his mathematics only for an open segment, or for a closed loop whose parts move with different velocities. His "large disc approximates a straight line" argument (pp.9-10) also fails numerically: for a fixed small loop on a huge disc, A is fixed and omega goes to 0, so 4Aomega/c^2 goes to 0. [calc-by-argument] Post (1967), whom Kelly quotes on p.9, makes exactly this point: a Sagnac device in pure translation gives no shift, and he calls the Galilean-versus-Lorentz asymmetry a "conceptual discontinuity". Kelly reads Post as pointing at a problem for SR; the conventional reading is that translation gives zero shift in both theories and rotation gives a shift in both. Worked example [calc]: a conveyor belt loop with two straight runs of length L = 1 m moving at v = 1 m/s in opposite directions, light traversing the loop in one sense: each run adds 2vL/c^2, total 4vL/c^2 = 4.5 x 10^-17 s. Shifting the whole belt apparatus at 1 m/s changes nothing; only the belt's internal motion matters.

b. Experiment. Wang, Zheng, Yao, Langley, Phys. Lett. A 312, 7-10 (2003): a fibre-optic conveyor, fibre looped round two wheels, with source and detector on the moving fibre. Abstract: "a travel-time difference dt = 2vdl/c^2 in a fiber segment of length dl moving with the source and detector at a speed v, whether the segment is moving uniformly or circularly" [read: research/files/wang-2003-...pdf]. They varied straight-segment length with the same semicircular ends, ran zero-area and figure-8 geometries and found the shift tracks length and speed, not enclosed area; the result was independent of refractive index [read: files; Investigator note]. The 2004 PRL (143901) generalises: each segment contributes 4piv.dl/(clambda) [web: arXiv physics/0609235]. Strong point for Kelly: the zero-area result shows enclosed area is not what matters, and the segment-wise form is just his integral D. I treat this as a genuine, simple, anomaly-flavoured experiment that a "rotation only" textbook statement does not cover. But the physicists who ran it did not claim a conflict with SR; their formula equals the standard SR/Post result for moving media with co-moving source and detector [memory, medium: Post 1967 Rev. Mod. Phys. 39, 475 gives the general form as a line integral of the velocity]. Also note: light in a glass fibre moves at about c/n relative to the fibre, not c relative to the laboratory. The index-independence Wang found is the known Fresnel-drag-compensated outcome of relativistic velocity addition [memory, medium]. It is not predicted by Kelly's rule "light travels at c relative to the lab" with a fibre medium; his treatment applies strictly to vacuum or air paths. Wang's hollow-core fibre test (proposed in their discussion) would address vacuum but I found no report that it was done.

c. Tested? Yes, by one group in the Wang papers (Minnesota universities, FOG on loan from the US Naval Research Laboratory) [read]. Independent replication: I found later papers that cite, analyse or design sensors from the effect (Huang 2021 Eur. Phys. J. D, "One-way interferometer", GSJ analysis) [web via Investigator, titles only]; I did not find a second group reporting the conveyor measurement itself. No test of a rigid translating interferometer by anyone claiming a shift. Null results for pure translation are the standard expectation (Michelson-Morley-type nulls, [memory, high]).

d. If true. Strong form (a rigid ring in uniform translation shows a Sagnac shift) would break the Galilean/Lorentz relativity of inertial frames: a ring could measure its own velocity relative to the lab or ether. That would overturn the null results of Michelson-Morley and all gyroscope/ring-laser work on moving platforms. The weak form (segments moving with co-moving source/detector) changes nothing in mainstream physics.

Verdict (split). Weak form (a moving fibre segment with co-moving source and detector gives dt = 2v*dl/c^2, in a closed loop): Tested, supported by one experiment (Wang et al.), and predicted by mainstream theory; not independently replicated by any source I found. Strong form (uniform translation of an interferometer as a whole produces a Sagnac shift, which is how Kelly's conclusion reads): Refuted by calculation using Kelly's own formula (closed integral of V.dl = 0), and nothing in Wang et al. supports it. Kelly's "that defence is now shown to be groundless" (p.10) overstates Wang.

Claim 2. Light travels at c relative to the laboratory, independent of source speed; this alone reproduces the Sagnac result for any shape

a. Mathematics. Internally consistent: equations (1)-(12) correct (SymPy by the deep reader; I re-derived (3)-(6) by hand). The binomial polygon derivation is correct to second order; second-order terms cancel; the Delta t / 2 Delta t labels on p.12 contradict each other, and prime symbols reverse meaning between p.3 and p.12 [read], but the boxed result is right. Two defects of logic: (i) the second derivation is the same equations as the first, so it is not an independent check; (ii) "if this assumption gives the precise Sagnac result, then this proves... " (p.3) is affirming the consequent. Equal results do not prove the premise when another theory gives the same result. SR with the lab as inertial frame also takes light at c relative to the lab, which is the very premise Kelly uses. So "lab-frame c reproduces Sagnac" is not a result against SR; it is SR's second postulate applied in an inertial lab. Kelly's own phrase "one of the assumptions made by Einstein" (p.4) concedes it. Where Kelly goes beyond: he adds that time and distance on the disc equal lab time and distance (p.12 item 5) and that light is at c relative to an Earth-centred non-spinning frame (Monograph 2, per Investigator [web]). Those additions are the testable difference from SR.

b. Experiment. The Sagnac and Michelson-Gale data fit lab-frame (inertial) c. They also fit every preferred-frame theory in which light is c in the non-rotating Earth-centred frame (Marett 2010 states exactly this reading [web: http://www.conspiracyoflight.com/Michelson-Gale/Michelson-Gale.html]). So Sagnac data cannot discriminate Kelly's theory from SR. Where theories differ is at second order in v/c and in clock rates. Those tests are outside the paper: Ives-Stilwell (Doppler shift of fast ions, second order), Kennedy-Thorndike, muon lifetimes, atomic-clock flights [memory, high for existence; I did not re-verify each in this pass]. "Time and distance are absolute" (Kelly) is in conflict with those, as is the Hafele-Keating confirmation line. Kelly's response is to dispute the Hafele-Keating data (see below). Kelly also needs the light-follows-the-Earth idea to survive stellar aberration; he does not discuss it in this paper [memory, medium: annual aberration of about 20 arcsec is conventionally read as a sign that light is not carried along with the Earth].

c. Tested? The Sagnac consequence: yes, thoroughly (Sagnac 1913, Harress 1911/Knopf 1920, Pogany 1928, Michelson-Gale 1925, ring lasers) [read: Kelly's references]. The discriminating consequences (absolute time) are not tested in this paper. By others yes, with results favouring SR in the standard record [memory, high], but that is outside the documents and I flag it as [memory].

d. If true (absolute time plus lab-frame c): SR's time dilation and relativity of simultaneity would have to be replaced; Lorentz-ether-type theory would be needed to recover Ives-Stilwell and the muon data.

Verdict (split). Narrow form (assuming light at c in the inertial/non-rotating frame gives the Sagnac formula for any loop shape): Established (and equally Established under SR). Broad form (this "proves" Galilean time and distance and rules out SR): Not supported by this paper's evidence, since Sagnac data do not discriminate; the discriminating tests lie elsewhere.

Claim 3. SR has no role in the Sagnac effect; the effect is large and visible at about 13 m/s

a. Mathematics. Correct point: the effect is first order in v/c, and SR's time-dilation correction is second order (v^2/c^2), so the leading result needs no gamma factor. Post says this and Kelly quotes him (p.10). Step 1's "13 m/s per metre of radius" has the scaling backwards: [calc] vr = clambda/(4 pi) = 13.13 m^2/s, so one fringe needs v = 13.13 m/s at r = 1 m, 26.3 m/s at 0.5 m, 6.6 m/s at 2 m. The number is right only at r = 1 m. Weakness: Kelly says "relativity theory cannot possibly have any function" at low speed; but SR was never claimed to give a different first-order term. The 'gamma cancels' remark (p.10) is a misdescription of mainstream derivations, which work in the inertial frame with coordinate time. His own p.4 asymptotics (v approaching c, "speed 2c") stray into a regime he excluded.

b. Experiment. The measured first-order effect agrees with Kelly and with SR. In the GPS system the Sagnac correction (Earth rotation) is applied explicitly alongside SR/GR clock-rate corrections, with the ECI frame as reference, which is what the CCDS/ITU standards Kelly cites (p.9) specify [read: Kelly refs; memory, high for the GPS correction]. Kelly's complaint that SR is "applied daily" to GPS yet "not applied" to Sagnac misses that the two are applied together in one framework; the Sagnac term in GPS is computed from lab-frame c, i.e. the same assumption he uses.

c. Tested? The claim is a statement about scale and attribution; the scale is trivially checkable (above). No test can show "SR has no role" at first order beyond what the formula already says.

d. If true: nothing changes. A reader who accepts it loses nothing from SR. If read as "Sagnac contradicts SR", the claim needs a measurable difference, which Kelly does not give.

Verdict. As a statement about order of magnitude (first-order effect, SR corrections second-order): Established. As a claim that Sagnac contradicts or undermines SR: Not testable as stated (no distinct prediction); the paper's computations coincide with SR's lab-frame calculation.

Claim 4. Michelson-Gale is an ordinary Sagnac test via the projected area (the sin(latitude) factor); ring lasers confirm the Sagnac formula extremely well

a. Mathematics. Consistent and correct. The vertical component of the Earth's rotation vector times the horizontal area is OmegaAsin(latitude); Kelly's projection argument (pp.5-6) is a clear and correct way to see it, and the equator/pole remarks are right. [calc] A = 207,840 m^2, Omega = 7.292 x 10^-5 rad/s, latitude 41 deg 46', lambda = 570 nm: 0.2363 fringe, matching Kelly's 0.236 and Marett's recomputation (0.2364) [web: conspiracyoflight.com above]. Kelly's own spread (+0.55 to -0.05, mean 0.230, "within 3%"; actually 2.5%) and his remark that this scatter may explain the test's low visibility in textbooks are fairly stated [read: p.5]. Slip: "4250 km" to rotation axis should be about 4752 km.

b/c. Experiment. Michelson-Gale 1925 is replicated in kind by ring lasers: the Christchurch C-II reached frequency resolution of 1 part in 3 x 10^21 [web, above] and ring lasers have tracked variations of Earth rotation at about 5 parts per billion [web: search summary]. The consensus reading: these detect rotation relative to local inertial frames. Kelly's reading (rotation relative to the non-rotating Earth-centred frame in which light is c) is observationally the same. This is the strongest-supported claim in the paper.

d. If true: nothing changes; it is the standard account.

Verdict. Established, with corrections: the "1 part in 10^20" is a frequency resolution, not a test of the formula to that precision; "1e-5 fringe" for a 1 m disc is about 1e-6.

Claim 5. Light does not travel at c relative to a moving disc along straight segments of the path (Sagnac, Harress, Pogany); the Sagnac experiments therefore contradict constancy of light speed in the moving frame

a. Mathematics. Kelly's step is: the round-trip time difference proves "the light travels at different speeds in relation to an observer upon the spinning disc" (p.10). This does not follow. The Sagnac observable is the difference of two round-trip times for a closed circuit, measured at one place with one clock. It fixes the sum round the loop of (1/speed_cw - 1/speed_ccw) but says nothing separately about the one-way speed on any single straight segment, because one-way speed depends on how distant clocks are synchronised (a convention), which is exactly what the Sagnac result shows cannot be made consistent round a rotating loop. Mainstream: in rotating coordinates the coordinate speed of light is anisotropic, c +/- omega*r on the rim, and Einstein synchronisation cannot be done consistently round the loop; local observers measuring locally still get c. Kelly writes the same c +/- v, so in coordinate terms his statement is correct and unobjectionable (the deep read agrees: "Galilean closing rate").

b. Experiment. Sagnac, Harress, Pogany all measure closed circuits. They support the coordinate-speed statement but are not a test of per-segment speeds. For the "straight-line" argument (Einstein 1905's polygonal-line clock result on p.8, cited by Kelly): Einstein's polygon argument is about clock rates, second order, and an accelerating polygon is not an inertial path at the corners; Kelly himself notes it is far smaller than Sagnac. His "selectively quote" remark about Einstein's 1916 passage is Kelly's interpretation of a text, not an experiment.

c. Tested? Sagnac-type experiments: yes. A direct one-way speed test on a rotating disc with independent clocks: I found none in the documents; one-way tests are generally convention-limited [memory, medium].

d. If true as a contradiction of SR: SR's local constancy of c would need replacing; but the data do not demand it.

Verdict (split). Coordinate statement (light's speed measured by the disc's coordinate system around the rim differs by direction: c +/- omega*r): Established, and also contained in SR/GR treatments of rotating frames. "Therefore the experiments contradict SR's constancy of light speed": Not testable as stated (one-way speed on a segment has no convention-free measurement), and the inference from a closed-loop difference is a logical overreach.

Claim 6. Einstein never mentioned the Sagnac or Michelson-Gale tests, though they bear on the speed of light (Silberstein 1921, Turner 1979 quoted)

a. Not a mathematical claim. Kelly quotes Silberstein: "As a matter of fact, Einstein himself never entered into the details of this important problem of rotation" and "In fine, the optical circuit experiment may easily become crucial and fatal for Einstein's theory" [read: p.4]. Silberstein was a critic of relativity by 1921 [memory, medium]; Turner and Hazelett's book collects H. E. Ives's anti-relativity papers [memory, medium]. These are interested sources on one side; I record them as such. Kelly adds "This author has located no reference by Einstein to the Sagnac tests" [read: p.4], which is a negative search by one man without a stated method.

b. Record. Counter-evidence found by the Investigator and checked: Einstein wrote at least one, apparently two, 1914 papers in Astronomische Nachrichten on Harzer's analysis of the Harress rotating-prism experiment, which Wikipedia and other [web] sources now class as an early Sagnac-type experiment [web: onlinelibrary.wiley.com asna.19141990104; en.wikipedia.org Sagnac_effect]. Also von Laue is said to have pressed publication of Harress's results (Knopf 1920) and to have given an SR account of the effect [memory, medium; Wikipedia says Knopf's publication was at von Laue's urging]; Langevin gave the SR explanation in the early 1920s [memory, medium]. So the SR community was dealing with rotating-interferometer experiments from 1911 onwards; Kelly's silence charge concerns Einstein personally and by name.

c. Tested? Archival question. Open: whether Einstein ever named Sagnac or Michelson-Gale in letters or papers. A scan of the Collected Papers of Albert Einstein index and Einstein's correspondence would settle it. I have no source either way beyond the 1914 notes.

d. What would change: nothing in physics, since silence is not evidence about nature. At most it concerns the history of how a result was handled.

Verdict. Not testable as stated as physics (a historical claim); as history: partly contradicted (Einstein did address a rotating-interferometer experiment, Harress, in 1914), literal claim about the names Sagnac and Michelson-Gale unresolved.

How these claims were received (rejection analysis)

• Peer-reviewed or serious venues: Kelly's work appeared in Infinite Energy, Galilean Electrodynamics, Physics Essays, Meta Research Bulletin, the Engineers Journal and monographs of the Institution of Engineers of Ireland (IEI) [web: wiki.naturalphilosophy.org/Alphonsus_G_Kelly]. Vigier cited his 1995 monograph in Physics Letters A 234, 75-85 (1997) [web via Google snippet only; full text not opened]. Cowan's In Memoriam (Galilean Electrodynamics 16(6), 2005) says his analyses were "essentially correct" [web via Investigator; Cowan is a sympathetic colleague]. Marett (an amateur experimenter) independently recomputes Michelson-Gale and cites Kelly with Wang [web].
• Hostile record: the Irish Times obituary says he generated "much academic debate, some of it acrimonious" [web: https://www.irishtimes.com/news/pioneering-engineer-who-helped-transform-the-esb-1.482657]. A 1996 letters controversy and an open offer of a public debate "never taken up" are documented in one sympathetic source (Natural Philosophy Wiki / Cowan); the letters themselves have not been located (archive not accessed). I weigh that as documented in one published sympathetic source, not yet corroborated, and not as evidence either way about the physics.
• Was he tested and refuted, or dismissed? On the present record, no controlled test of Kelly's distinctive claims (absolute time, Earth-frame light) is named in the documents, nor a reasoned published refutation. The Sagnac observations were accepted long before him. What was probably dismissed without a rebuttal of substance is his interpretation. I cannot show that from the record; an actual search of 1996 Irish Times letters, of any critics' published responses and of the Infinite Energy 2001 paper is needed. His anomalous-data work on Hafele-Keating is the one place where he publishes raw numbers: per-clock results East -196/-54/+166/-97 ns, West +413/-44/+101/+26 ns against published averages of -59 and +273 ns [web: Investigator, from the USNO 1971 report copy at cartesio-episteme.net]. That scatter (individual clocks differing by hundreds of ns) is real in the raw record and is a fair point for a reanalysis; the standard reply is later, better-controlled confirmations [memory, medium: Alley's 1970s Chesapeake Bay flights, Vessot's 1976 hydrogen maser rocket, NIST optical-clock height tests; not re-verified here]. This is outside the Kelly_2 paper.
• Absence-of-record check: Kelly's works end with his death in 2005; his company (HDS Energy) and Top Tech Ireland leave no trace in the Investigator's search except Google Patents DE1528915A1 (a siphon, 1965 priority). That is a normal pattern for a retired engineer, not an anomaly; nothing here suggests suppression, and nothing in the record shows blocked publication either.

Strongest honest case for Kelly

1. The mathematics is simple, correct and general: dt = 2D/c^2 with D = closed integral of u dl is the same line-integral form the 2004 PRL uses (Wang), and the zero-area/figure-8 conveyor experiments show that "area" is not the fundamental quantity; length and speed of the moving medium are. Kelly anticipated this form in a derivation that avoids the ether and Stokes.
2. His observation that in an inertial lab one needs only "c relative to the lab" is true and is the cleanest route to the formula; the objection "SR does not apply to rotation, so Sagnac is out of its scope" is a weak defence he rightly criticises.
3. The projection argument for sin(latitude) in Michelson-Gale is a good teaching point and correct; he caught that Michelson's early formula was a factor 2 off (via Silberstein) and presents the data scatter honestly.
4. Consistent scepticism of selective inertial-frame choices: the geocentric frame is accepted for GPS but a laboratory on the same Earth is declared non-inertial; Kelly's numbers (pp.9) are order-of-magnitude comparisons of turn angles. This is a fair rhetorical point though it misses that GPS applies the Sagnac correction.
5. Raw Hafele-Keating scatter is genuine.

Kelly's own errors (same rigour)

• Area of Sagnac's apparatus given as 0.86 m^2 and 666 cm^2 (866 cm^2 in the literature); Earth-rotation shift of a 1 m disc 10 times too large; "13 m/s per metre of radius" has the dependence inverted; "forty years" vs 1937-42; "4250 km" vs 4752 km; labelling inconsistencies on p.12; "1 part in 10^20" misdescribes resolution as accuracy.
• Circular logic: a correct prediction "proves" the premise (p.3), while SR makes the same prediction.
• Inferring one-way segment speeds from a closed-loop difference.
• Taking Wang's result as proof for uniform translation of a whole device, which his own integral contradicts.
• Unfalsifiable framing: "SR cannot possibly have any function" and "selectively quote Einstein" cannot be tested by the cited data.
• The paper is undated and unsigned for date of composition; the PDF in our files is a post-death copy.

Investigator findings kept in the record (whatever the verdict)

• Wang et al. 2003 and 2004 (primary basis for claim 1; segment-wise formula; index independence; co-moving source and detector) and the later citing works (Huang 2021; "One-way interferometer"; GSJ analysis).
• Monograph No. 2 (1996): light generated on Earth follows its orbit and gravity, not its spin; absolute time and distance. Note that "c relative to the laboratory" (project paper) and "c in an Earth-centred non-spinning frame" (Monograph 2) differ for a laboratory on the spinning Earth; the claim 4 explanation needs the latter.
• Kelly 2000, Hafele-Keating critique (raw per-clock data); Kelly 2001 (Infinite Energy 39, 24-28), 1998 clock-stations paper, 1999 Bologna paper, 2005 book: not obtained.
• Vigier 1997 (Phys. Lett. A 234, 75-85) citing Kelly's monograph, photon-mass reading of Sagnac; Cowan In Memoriam 2005; Marett 2010 and his own fibre Sagnac work; Klauber 1999; Selleri; Essen 1977.
• Biography: ESB engineer from 1947, PhD 1966, siphon patent; Irish Times obituary 20 Aug 2005; the 1996 Irish Times letters not found; Einstein 1914 Harzer/Harress notes.
• Not reached: isidore.co Vigier PDF, Selleri 1998 proceedings, Irish Times archive, USNO/PTTI proceedings, Infinite Energy.

Verdict table