Builder-G: Arbiter's report

Document under review: G. Builder, "Ether and Relativity", Australian Journal of Physics 11, 279-297 (1958; manuscript received 20 Nov 1957). It is the only document in the project.

Source gap (repeated from Step 1): Ether-And-Relativity-1957.pdf has no text layer. All pages were read from rendered images, and equations were read by eye. Not in the folder and not read by anyone in this review: Dingle's 1957 Nature letter that Builder answers, and Builder's earlier papers (Aust. J. Phys. 10:246 and 10:424). What Dingle argued is known only from Builder's paraphrase and from a web summary (see "Web checks"). Where a conclusion below rests on [memory] alone, it is flagged.

Page numbers: PDF page = journal page minus 278. The claims.md page references mix the two and are sometimes early (Claim 5's clock-slowing section is PDF pp.16-17; the concluding pedagogy section is p.18). This does not change any verdict.

The paper in brief

Builder accepts the premise of H. Dingle (a critic of special relativity, SR) that clock retardation depends on each clock's individual speed. He rejects Dingle's conclusion that SR is therefore wrong. Builder argues instead that SR itself compels a causal role for velocity relative to the universe as a whole (an "absolute" inertial frame, an ether). He holds this is harmless because no dynamical or electrodynamic experiment can measure that velocity. The paper has no data, no new measurement and no numerical example [read]. It predicts the same results as SR, and Builder says so. It is an interpretation argument, and it was published in a mainstream journal, so there is no suppression story in the record.

Points where the reviewers corrected Step 1 (all accepted)

• Builder's equations (6b), (7a), (7b) were checked by all three reviewers and are correct to order v^2/c^2 (v = speed, c = speed of light). Physicist and contrarian checked (7), (8) too. The mathematician checked their structure only. Step 1 had left this unchecked.
• Builder's "absolute velocity" means velocity relative to the universe or the fixed stars (pp.11-12). That is the key to Claim 4 (see below).
• Builder rejects Mach's hypothesis (instantaneous action at a distance). He separates this in a footnote (journal p.291) from Einstein's field-mediated "Mach's principle", which he does not rebut.
• Claim 5's slowing-from-contraction argument is narrower than claims.md states. It is a worked longitudinal light-clock footnote plus an appeal to electromagnetically bound bodies.
• The Nature letter is "The 'Clock Paradox' of Relativity", Nature 179, 865-866 (1957), not "179:866" alone. The physicist and mathematician cited https://www.nature.com/articles/1791071a0, whose ID points to p.1071, not p.865; I treat that URL as unverified. The ID https://www.nature.com/articles/179865a0 matches pp.865-866 but was not fetched either (see QE revision).

What I recomputed (reviewers differed on Claim 3 and Claim 5)

Script: [scratch file], run in the project venv.

1. Claim 3, boost check. Charge q2 at rest, charge q1 moving at v = 0.3c, with q1 at separation r = (1, 2, 0) in the lab frame S (frame at rest with q2). The force on q1 from Builder's (7b) is pure Coulomb: F = (0.08944, 0.17889, 0). I then went to q1's rest frame S', where q2 moves at -v. I used the exact Coulomb field of a uniformly moving charge at its simultaneous-in-S' position, and transformed the force back to S (parallel component unchanged, perpendicular component divided by gamma = 1/sqrt(1-v^2/c^2)). Result: (0.08944, 0.17889, 0). It matches to machine precision. So Builder's two cases ("charge 1 moves" vs "charge 2 moves", same relative velocity, different S-force) are one physical situation described from two frames. The contrarian's analytic argument is confirmed numerically.
2. Claim 5, light clocks at v = 0.6c. Longitudinal clock with contracted length L = L0 sqrt(1-0.36) = 0.8 L0: round trip = L/(c-v) + L/(c+v) = 2.5 L0/c against 2 at rest, so rate ratio 0.8 = sqrt(1-0.36). Transverse light clock with no contraction at all: round trip 2L0/(c sqrt(1-0.36)) = 2.5 L0/c, the same ratio. So the slowing of a light clock is the same factor whether or not the arm contracts (the transverse arm does not). Contraction fixes the longitudinal orientation only. All three reviewers agreed and I agree.
3. Claim 5, Kennedy-Thorndike (KT) logic. Contraction alone makes the longitudinal and transverse round trips equal (Michelson-Morley null), but both equal gamma x the rest value. At beta = v/c = 1e-3 that is a velocity-dependent fractional change of 5.0e-7 in the cavity round trip. This would appear unless the reference clock slows by the same gamma. That is the KT point (confirmed on the web below). It is why "one hypothesis" holds only if every clock and bond obeys the Lorentz factor.

Web checks (remaining medium/low-confidence [memory] facts that verdicts depend on)

Web budget: the search tool was exhausted, so I used fetches only.

Claim-by-claim arbitration

Rule I applied across claims, so verdicts are consistent: - "Internally inconsistent" is used only when Builder's own premise or definition conflicts with his conclusion. - "Refuted by calculation" is used only where I could run a calculation that rules a specific statement out. - "Not testable as stated" is used for the ether-as-hidden-cause reading, which makes no measurable difference from SR.

Contrarian's three categories, as asked. No part of this paper fits "tested and failed" except the dynamical-effect part of Claim 4. For nearly everything else, there is nothing to test against SR, because the paper predicts SR's results. The paper was not dismissed without testing and no suppression is on record (published in the Australian Journal of Physics; no source says otherwise). Pedagogical superiority is never tested (an opinion with no teaching study cited).

Claim 1: clock retardation depends on individual speeds, so it demands a causal role for velocity relative to a unique absolute system

• Agree: The retardation formula (proper time, integral of sqrt(1 - v^2/c^2) dt) is correct SR and invariant. The paper's inference to "demands/compels" does not follow. All three say the causal reading has no measurable difference from SR, and Builder concedes this (p.4).
• Disagree: Only labels. The physicist and contrarian used "Not testable as stated" for the inference. The mathematician stressed the non sequitur.
• Stronger argument: The mathematician's A1/A2. Builder says the explanation "must be sought in the form of the equations" and is the same in every frame (p.3). He then needs one particular frame S0 to supply the cause. His own premise (frame-independence) conflicts with his conclusion (a privileged frame). Proper time is the length of a worldline, a geometric property, as a road's length needs no "interaction with the universe". Worked case: clock B goes out and back at 0.6c for 10 years of lab time; its proper time is 10 x sqrt(1-0.36) = 8 years, the other clock reads 10, and the 2-year difference is the same in every frame. The contrarian's best case for Builder stands: the geometric account does not say why, and Lorentz/Poincare gave a working causal story.
• Final verdict (split):
• Clock retardation as a worldline invariant: Established (Hafele-Keating, CERN muons, replicated [web via reviewers]).
• "SR compels/demands a causal absolute velocity": Internally inconsistent (premise of frame-independence vs conclusion of a privileged frame, p.3; p.15 concedes the ether is not proved).
• Ether as hidden cause of retardation: Not testable as stated (no measurable difference from SR).
• What would settle it: Nothing can settle it empirically, because the two readings predict identical numbers. The logical part is settled by the SR derivation of retardation, which uses no absolute frame.

Claim 2: an absolute system is compatible with and sufficient for SR, because absolute velocities are not measurable dynamically

• Agree: All three: this is the Lorentz-Poincare theory, mathematically equivalent to SR. Builder's formal point that Einstein's 1905 derivation is unchanged if the "stationary frame" is the ether frame is correct. Every ether-drift null result (Michelson-Morley, KT, Ives-Stilwell) is accommodated because the theory is built to accommodate it.
• Disagree: The physicist and mathematician called the weak form "Plausible, untested"; the physicist and contrarian called it "Established". Splitting the word "compatible": it is a mathematical fact, so "Established".
• Stronger argument: The contrarian's "strongest honest case": equivalence is real, and the ether was never refuted by experiment, only made redundant. Builder's "beyond question" (p.14) overstates: sufficiency in prediction is shown, but the ether adds no prediction and requires every force and clock to obey the same compensation. [web: LET indistinguishable from SR, https://en.wikipedia.org/wiki/Lorentz_ether_theory]
• Final verdict (split):
• Compatibility / empirical equivalence with SR: Established (as a mathematical equivalence; also by the null results, e.g. MM-type (4 +/- 8)e-12 [web: https://en.wikipedia.org/wiki/Test_theories_of_special_relativity]).
• Physical existence of an undetectable ether frame: Not testable as stated.
• A detectable ether (drift in light speed or clock rates): Tested, not supported (the null results above). Builder does not claim a detectable one.
• Superiority as a framework: Historically superseded but instructive.
• What would settle it: A statistically significant preferred-frame effect (a sidereal or annual variation in a cavity or clock-comparison experiment). To date none is found at the bounds above; Nagel's ~1e-18 figure is unchecked.

Claim 3: relativistic electrodynamics depends on individual velocities; same relative velocity gives different forces; Newton's third law fails

• Agree: All three: equations (6b), (7a), (7b) are correct to O(v^2/c^2); non-reciprocal forces on isolated moving charges are standard (momentum is carried by the field; Griffiths Sec. 8.2 [memory: high]). The inference to an absolute frame does not follow.
• Disagree: Verdict on the inference: physicist "Not testable", mathematician "Internally inconsistent", contrarian "Refuted by calculation".
• Stronger argument: The contrarian's boost calculation, which I reproduced numerically above. The "different force for the same relative velocity" is one physical situation seen from two frames. The mathematician's point stands too: the dependence on velocity in S is already present in Newtonian physics (kinetic energy). Builder's p.8 remark that all S-observers see the asymmetry means it cannot identify any one frame. I do not use "Internally inconsistent" here, since by my rule that needs a self-contradiction, and Builder's own definition of the relativity principle (same form of laws, p.12) is not contradicted by the S-dependence of force values. The physicist's "not testable" is right for the ether reading, and the contrarian's "refuted" is right for the specific claim that the force difference shows a preferred frame.
• Final verdict (split):
• The equations and the failure of Newton's third law for the particle pair alone: Established (momentum conserved once field momentum is included).
• "The same-relative-velocity force difference is evidence of a privileged frame / compels absolute velocity": Refuted by calculation (Lorentz boost reproduces (7b) from the moving-source field; see the numerical check).
• An ether reading of the dependence on velocity: Not testable as stated.
• What would settle it: Already settled by the boost calculation above. Anyone can repeat it: pick v and r, boost, compare.

Claim 4: absolute acceleration implies an absolute inertial system and absolute velocity; Mach's hypothesis must be rejected; absolute velocity may be kinematically measurable (starlight Doppler)

This claim has four separable parts, and the reviewers disagreed mainly on how to label each.

• (i) Absolute acceleration entails absolute velocity. All three: invalid step (p.10). Newtonian (Galilean) mechanics has absolute acceleration without absolute velocity: a Galilean boost changes velocity and leaves acceleration unchanged. In Minkowski spacetime, proper acceleration is invariant while boosts shift velocity. Builder gets the entailment by defining acceleration as a change in "absolute velocity". Verdict: Internally inconsistent (his own Newtonian and Principia precedent, which he invokes, has the former without the latter; the entailment is circular by his own definition).
• (ii) Mach's instantaneous interaction must be rejected, leaving the ether. The physicist said "Established" for the rejection; the mathematician and contrarian said "Historically superseded". Reconciled: rejecting instantaneous action at a distance is reasonable (it conflicts with finite signal speed). The leap to "only the ether remains" is a false dichotomy that skips the field-mediated Mach's principle, which Builder's own footnote (p.13) notes and leaves unused. Gravity Probe B frame dragging (-37.2 +/- 7.2 mas/yr vs GR -39.2 [web]) is a partial confirmation of the field version (about 20% precision). Verdict: rejection of instantaneous action Established; "therefore ether" Historically superseded but instructive.
• (iii) Absolute velocity (relative to the universe) may be kinematically measurable. All three agree this aged best. The CMB dipole gives the Sun's velocity relative to the CMB frame as 369.82 +/- 0.11 km/s [web: https://en.wikipedia.org/wiki/Cosmic_microwave_background]. The dipole was discovered after Builder wrote [memory: medium, not checked]. Builder's "starlight Doppler" method differs from the CMB method; he calls the limits on measuring absolute velocities "essentially practical rather than fundamental" (pp.12-13), i.e. practically limited for small velocities, not impractical in principle. Verdict: Established for "a cosmic rest frame exists and our velocity relative to it is measurable". Note this is a relative velocity to a matter/radiation distribution, which is not a violation of SR.
• (iv) This frame has dynamical consequences / acts on bodies. The ether-drift and Lorentz-invariance bounds (above) find none. Verdict: Tested, not supported (bounds at the 1e-8 to 1e-12 level in the parameters above; Builder himself does not claim a dynamical detection).
• Where Builder equivocates: he uses "absolute" for both (iii), a frame defined by the matter distribution, and for (iv), a causal ether. The first is vindicated and the second is not. A reader should not credit the CMB result to the second.
• What would settle it: (i) is settled by the Galilean-boost counterexample. For (iv), a dependence of any clock rate, cavity frequency or force on motion relative to the CMB frame would settle it, and the searches so far are null. For Mach: a measurement of frame dragging at percent precision, which GP-B reached only at about 20%.

Claim 5: clock slowing follows from Lorentz-FitzGerald contraction; one hypothesis, not two; the ether presentation is pedagogically superior

• Agree: The longitudinal light-clock footnote is correct (recomputed above, and by all three). Pedagogical superiority is an opinion with no study cited. The "contraction implies slowing" step holds for that geometry only.
• Disagree: The mathematician offered "Refuted by calculation" or "Internally inconsistent" in places and then retreated to "overstated". The physicist said the one-hypothesis claim is correct only given Lorentz covariance. The contrarian rated the one-hypothesis derivation "Established".
• Stronger argument: The physicist and mathematician. My own check shows the slowing is the same factor with no contraction in the transverse orientation, and contraction alone leaves a velocity-dependent 5e-7 fractional change in a cavity at beta = 1e-3. KT therefore needs both contraction and time dilation [web]. "One hypothesis" survives only if you assume the Lorentz factor applies to all clocks and bonds, which is the Lorentz-covariance postulate and carries as much weight as a second hypothesis. I do not call this "Refuted by calculation" or "Internally inconsistent": Builder's own argument already appeals to electromagnetically bound bodies, so it is not self-contradictory, and it is a bookkeeping dispute about what counts as one hypothesis.
• Final verdict (split):
• Light-clock slowing from contraction, longitudinal case, and agreement with all clock/muon tests as a kinematic result: Established.
• "One hypothesis suffices in general (no second assumption)": Not testable as stated as a bookkeeping claim; physically overstated, since KT shows both factors are needed together [web].
• Ether as the cause of the clock slowing: Historically superseded but instructive (Lorentz-Larmor was a reasonable position, equivalent to SR, replaced by the postulate-based/geometric version).
• Pedagogical superiority: Never tested; Not testable as stated (opinion). Bell's "Lorentzian in spirit" teaching approach [web: https://en.wikipedia.org/wiki/Lorentz_ether_theory] shows it is a respectable view, not evidence.
• What would settle it: A controlled teaching study (students taught the Lorentz-ether version vs the geometric version, same assessment). None is cited by anyone.

Corrected claim list

1. Special relativity's clock retardation is a real, replicated, worldline-invariant effect. Builder's claim that it demands a causal role for velocity relative to an absolute system does not follow; his own premise (frame-independence, p.3) conflicts with the conclusion. An ether reading is possible but unobservable.
2. An absolute (ether) frame is mathematically equivalent to SR (the Lorentz-Poincare theory) and so cannot be excluded by any null result. It is also not shown to be needed. A detectable ether has been tested for and not found.
3. Relativistic electrodynamics gives velocity-dependent, non-reciprocal forces on isolated charges (equations 6b, 7, 8 are correct to O(v^2/c^2)). These are frame-dependent descriptions of one situation, as a boost calculation shows, and are not evidence of an absolute frame.
4. Absolute acceleration does not entail absolute velocity. Rejecting instantaneous Machian action is reasonable, but a field-mediated Mach's principle remains open (partly supported by frame dragging). A cosmic rest frame (the CMB frame) exists and our velocity relative to it, 369.82 +/- 0.11 km/s, is measurable. No dynamical effect of that frame has been found.
5. A light clock moving through an ether slows by sqrt(1 - v^2/c^2); for a longitudinal light clock this follows from contraction (Builder's p.16 footnote, aimed at Broad 1923). Explaining all null results with "one hypothesis" requires assuming Lorentz covariance for every clock and force.
6. (Split out of Claim 5 after QE.) Builder says the ether presentation is pedagogically and heuristically superior, and that relativity of simultaneity, constancy of c and reciprocity follow from motion relative to the ether plus the impossibility of one-way light-speed measurement (pp.16, 18). That impossibility is the synchronisation convention; it is what lets an ether theory match SR, and it is a real teaching point. The "superiority" is an untested opinion.

What would settle it (summary)

Open questions

• What exactly did Dingle argue in 1957? The web summary (a logical contradiction from reciprocity) and Builder's paraphrase (retardation depends on absolute velocity) differ, and nobody read Dingle's letter or Builder's earlier two papers. Obtaining Nature 179:865-866 would settle whether Builder answers Dingle fairly.
• Nagel et al. 2015's ~1e-18 Lorentz-invariance bound was cited by the physicist and could not be verified here. It should be checked before it is quoted in the primer; the confirmed bounds are enough for the verdicts.
• Is the CMB discovery date, and the claim that Builder's "Doppler of starlight" is a different method from the CMB dipole, accurate? Both are [memory: medium], not checked.
• Is Builder's p.8 magnet-moving-through-a-loop example an observable at all? The contrarian notes the induced current (the invariant observable) is the same in every frame and Builder gives no number.
• Why the 1957-58 debate (Dingle vs the ether side vs the textbook view) did not converge: is that a philosophy-of-physics matter, or did a missing experiment keep it alive? The documents here cannot tell.

Verdict by claim (summary)

QE revision

Source of this revision: qe.md (verdict MINOR). Evidence used: the OCR text _text/Ether-And-Relativity-1957-51e9ba.txt [read: OCR pp.14-18] and the deep read deep/Ether-And-Relativity-1957-51e9ba.md (pp.5-8, Sonnet). Only one of the three requested deep reads exists (pp.5-8); I did not have separate deep reads for pp.13-15 and 16-18, so the points below on those pages come from my own reading of the OCR prose, which is clean there. No web calls were needed for the changes. Verdicts did not change.

New evidence

1. Magnet-and-conductor, (6a)/(6b) (pp.6-7) [read: deep read]. Builder says that for v much less than c, (6b) reduces to (6a), and that Einstein's 1905 view that relative motion alone is fundamental "must be rejected" (p.7). The deep read derived (6b) from the boosted monopole field and checked it numerically: the residual is O(beta^4) (8.3e-3 at v = 0.4c, 1.7e-6 at 0.05c), whereas (6a) alone is off at O(beta^2) (11% at 0.4c). So (6b) is correct. The same boost argument that dissolves (7a)/(7b) dissolves (6a)/(6b): they are one two-body system in two frames, and the force on a charge is not a frame invariant (perpendicular force scales by gamma). The observable Einstein cared about, the induced current, is the same in every frame; Builder's axial magnet-and-loop "readily verified" claim is asserted, not shown. Ruling: the equations are Established; the inference to an absolute frame is Refuted by calculation, as for Claim 3. His historical remark that Einstein did not use the asymmetry as a premise is fair but does not bear on validity. The third-law gap is field momentum [memory: medium, Griffiths ch.8], which Builder does not mention.
2. One-way speed of light (pp.16, 18) [read: OCR]. Builder writes: "true one-way measurements of light velocity are impossible (so that we can measure only the average value of the light velocity over go-and-return paths)" and then reads the constancy of c and the relativity of simultaneity as effects of motion relative to the ether (p.16). On p.18 he repeats it as the "only other important factor". This is the Einstein-Reichenbach synchronisation convention under another name [memory: medium; I did not fetch a source]. It is how Lorentz ether theory reproduces SR, and it fits my Claim 6 label above. It also exposes a quiet assumption: Builder's ether frame has absolute simultaneity, a convention-dependent choice that no experiment can check, since the same measurements are possible with Einstein synchronisation.
3. Mach 1883 (p.15 of the PDF text) [read: OCR]. Builder reports that Mach himself discussed a space-filling medium and held it "admissible" and "sufficient", but deemed his own hypothesis "more expedient provisionally". This supports the part of Claim 4(ii) where Builder says the ether was open to Mach; it does not rescue "no tenable alternative", since Builder himself leaves out the field-version of Mach's principle.
4. Einstein 1920 (pp.14-15) [read: OCR]. Builder quotes at length: "according to the general theory of relativity space without ether is unthinkable". His footnote adds that Einstein uses "absolute" only to say that space's properties are not affected by anything, and Claim 2's note that Einstein's ether has no state of motion stands. This quote does not support a Lorentz ether, since Einstein's ether has no velocity and so cannot supply an absolute velocity. This is [read] for the quotation and [memory: medium] for my comment on what it implies.
5. Broad (1923) (p.16 footnote) [read: OCR]. Builder names Broad as the source of the "two independent hypotheses" objection. Claim 5 should read as aimed at Broad.
6. "Reality" of relativistic effects (p.18) [read: OCR]. Builder: the effects are "really-observable", and what corresponds to them in nature are real effects caused by motion relative to the ether. This is interpretation, with no test.

Changes

• Dingle URL. Use https://www.nature.com/articles/179865a0 (ID matches Nature 179:865-866). A direct fetch returned HTTP 303 (redirect) and was not followed, so the page contents are unchecked. The 1791071a0 URL is unverified and should not be cited. What Dingle argued is still unknown (see Open questions).
• "Seems impractical" is replaced in Claim 4(iii) by Builder's own wording (limits "essentially practical rather than fundamental"; pp.12-13).
• Label call, Claims 1 and 4(i). I kept "Internally inconsistent" but flag it as a judgment call. A fair alternative label is "non sequitur" (the conclusion does not follow, though no two statements strictly contradict). For Claim 1, Builder's absolute frame S0 is itself one of the frames in which the equations take the same form, so one can argue there is no self-contradiction. My reason for the stronger label: Builder says the cause must lie "in the form of the equations", which is the same in every frame, and then needs one particular frame to supply it. If a reader prefers the weaker label, the practical conclusion is unchanged: the inference does not follow and the ether adds no prediction. (This also applies to my rule near the top, which I applied to Claim 3 and 5 by not using the label there.)
• Claim 3 now carries the (6a)/(6b) ruling above. Claim 5 now says Broad. A new Claim 6 (pedagogy and one-way light speed) is split out of Claim 5 to match claims.md.
• claims.md page note: the arbiter's earlier correction stands (clock footnote at p.16, pedagogy at p.18; Mach material at pp.14-15). claims.md already carries these page numbers.

Verdicts changed: none. The verdict table gained Claim 6 and a (6a/6b) mention in Claim 3, but no label was altered.