SilverTooth: study primer

Project: Ernest Wilbur Silvertooth, "Experimental detection of the ether", received May 1986 (journal given by Marett as Speculations in Science and Technology 10(1) 3-11 [web: http://www.conspiracyoflight.com/Silvertooth/Silvertooth.html, via the Investigator]). Primer author: Step 4. This primer gives no new verdicts; every verdict below is the arbiter's (arbiter.md).

Source tags: [read] = from the 1986 paper (page given) or a saved file in research/files; [web] = Internet source, URL given; [memory] = recalled, with confidence; [calc] = computed in example.py.

Source note (repeated from claims.md and the arbiter). The project folder holds one five-page paper, a modern retyping with many typing errors, fully readable. It has no raw data, no error bars, no run count, no dates and no place of observation. The sponsor reports it mentions (Rome Air Development Center, DARPA) were not found. What we know about the experiment beyond the paper comes from Silvertooth's own later statements (1976 Applied Optics paper, saved and read; 1989 Electronics & Wireless World article, read by the Investigator from page images) and from other people's reports (Marett 2012; Marinov and Wesley 1987, abstracts only). The inventor's related work outside the folder (1972 JOSA one-way test, recorded as a null by Roberts and Schleif; 1976 Applied Optics; 1989 Electronics & Wireless World; 1992 Physics Essays with C. K. Whitney) was found by the Investigator; only the 1976 paper was read in full. The Investigator's notes on Marett are a reading of his web page; the arbiter checked only a search summary of it.

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1. The idea in one paragraph

Silvertooth was a professional optical engineer (Caltech degree, a 1941 Academy technical award for a Paramount projector condenser, later co-author of a real thin-film standing-wave detector published in Applied Optics in 1983 [web and read, via the Investigator]). He argued that the famous Michelson-Morley experiment could never have detected an "ether" (a medium for light at rest in some absolute frame), because if light goes faster one way and slower the other, its wavelength changes in step and a there-and-back trip hides the difference. He then argued that a different kind of instrument, in which two laser beams meet head-on and form a standing wave, could detect the one-way change in wavelength. He built one, slid part of it 0.25 mm, saw two detector signals go from in-step to opposite, and computed that the laboratory moves through space at 378 km/s, with the largest effect when the constellation Leo was on the horizon. That is close to the 370 km/s motion of the Earth relative to the cosmic microwave background, which also points toward Leo. He went on to say the same effect changes Doppler shifts, with consequences for cosmology, quasars and GPS.

2. What you need to know first

Waves: c = νλ, wavenumber, phase. A wave of frequency ν (cycles per second) and wavelength λ (metres) moves at speed c = νλ. The wavenumber k = 2π/λ is the phase (in radians) the wave gains per metre travelled. If a light path gets longer by ΔL, the phase at the far end changes by kΔL. Interferometers measure such phase differences between two beams. Read: Halliday, Resnick and Walker, Fundamentals of Physics, the chapters on waves and interference; Hecht, Optics, the chapters on interference and interferometers.

Standing waves. Two waves of the same frequency running in opposite directions add to a pattern of fixed bright spots (antinodes) and dark spots (nodes). For two waves with wavenumbers k₁ (going right) and k₂ (going left) the time-averaged intensity at position x is I(x) ∝ 1 + cos(φ_rel(x)), where φ_rel is the relative phase of the two waves at x. Because φ_rel changes by (k₁ + k₂) per metre of x, the nodes are spaced 2π/(k₁ + k₂) apart: λ/2 when both wavelengths are λ. Silvertooth's detector D1 is a photocathode thinner than λ/100 placed inside such a pattern, so it can tell a node from an antinode (about 20,000 : 1 [read: 1989 article, via Investigator; 1983 paper saved in research/files]). Read: any intermediate optics text (Hecht).

Michelson-Morley experiment (MM). Light is split into two perpendicular arms of length L, reflected back and recombined. If light moved at c relative to an ether and the lab moved through it at speed v, the round trip along the motion would take (2L/c)/(1 − v²/c²) and across it (2L/c)/√(1 − v²/c²). The difference is second order in v/c (about (L/c)(v/c)²), and the experiment (1887 onward) found no such difference. Read: Griffiths, Introduction to Electrodynamics, ch. 12 (Electrodynamics and Relativity); Taylor and Wheeler, Spacetime Physics; French, Special Relativity.

Lorentz contraction and special relativity (SR). Lorentz and FitzGerald explained the MM null by saying the arm along the motion shrinks by √(1 − v²/c²). Einstein's SR made the same predictions from two postulates: physics is the same in every inertial (non-accelerating) frame, and light's speed is c. The Lorentz transformation between frames moving at relative speed v is x' = γ(x − vt), t' = γ(t − vx/c²), with γ = 1/√(1 − v²/c²). The term vx/c² in t' is relativity of simultaneity: clocks at the two ends of a rod of length L that are synchronised in the rod's frame differ by Lv/c² as judged from a frame in which the rod moves. Remember this term; it is the same Lv/c² that appears in Silvertooth's Sagnac argument. Read: Griffiths ch. 12; Taylor and Wheeler.

One-way versus two-way speed of light; synchronisation conventions. To time light one way from A to B you need two clocks, one at A and one at B, set to agree. Setting them requires sending a signal, and so assumes a one-way speed. Reichenbach (1928) showed that one may set the outbound speed to c/(2ε) and the return speed to c/(2(1 − ε)) for any ε between 0 and 1; every round-trip measurement still gives c. Einstein's choice is ε = 1/2. This "conventionality of simultaneity" is standard and accepted [memory, high]. Lorentz's ether theory (with a real ether frame, contraction and slowed clocks) makes the same predictions as SR for every experiment; it simply chooses a different ε. Read: the article "One-way speed of light" (Wikipedia) as an entry point; Anderson, Vetharaniam and Stedman, "Conventionality of synchronisation, gauge dependence and test theories of relativity", Physics Reports 295 (1998) [memory, high].

Sagnac effect. Send two beams in opposite directions around a closed loop that rotates at angular speed ω. The co-rotating beam takes longer; the time difference is Δt = 4Aω/c², where A is the area enclosed, and the fringe shift is δ = 4Aω/(cλ) = 4Aων/c². This is the principle of ring-laser and fibre-optic gyroscopes and is well established [memory, high]. It is a property of the closed loop: it equals (2/c²) times the loop integral of the velocity of the path, ∮ v · dl. For a loop that only translates (moves in a straight line, no rotation) the velocity is the same everywhere and ∮ v · dl = 0, so there is no shift. Read: E. J. Post, "Sagnac effect", Reviews of Modern Physics 39, 475 (1967) [memory, high] (Silvertooth cites Post's result in 1976 [read: 1976 p.1101]).

The cosmic microwave background (CMB) dipole. The CMB is slightly hotter in one direction (toward Leo) and cooler in the opposite one, because the solar system moves at 369.82 ± 0.11 km/s relative to the frame in which the radiation is uniform [web: https://www.aanda.org/articles/aa/full_html/2020/12/aa38053-20/aa38053-20.html]. Muller's 1978 Scientific American article on the U-2 radiometer measurements called this "the new aether drift" [web: https://ui.adsabs.harvard.edu/abs/1978SciAm.238e..64M/abstract]. SR allows such a preferred frame of the radiation; it is a fact about the matter and light in the universe, not a frame in which laws of physics differ.

Sidereal time. Time measured by the stars rather than the Sun. A star (or a direction in space such as the CMB dipole) returns to the same place in the sky every 23 h 56 min. An effect tied to a direction in space repeats on sidereal time; an effect tied to the room's heating repeats on solar (clock) time. Over months the two drift apart by about 4 minutes a day, which is how experimenters separate them.

3. The textbook view

Take a lab moving at speed v along x through the CMB frame. Write b = v/c.

3.1 Round trips are blind to the one-way speed. For any one-way speeds c₁ (along +x) and c₂ (along −x) the round-trip time over length L is

t = L/c₁ + L/c₂.

Every round-trip experiment measures only this sum. If c₁ = c/(2ε) and c₂ = c/(2(1 − ε)), then t = 2L/c for every ε. So no round-trip experiment can tell which ε is "real". In SR with Einstein synchronisation ε = 1/2 and c₁ = c₂ = c in every inertial frame.

3.2 Frequency is fixed between co-moving source and receiver. If laser and detector sit on the same table, every crest that leaves the laser arrives at the detector, so the detector counts the same frequency ν the laser emits. On this point Silvertooth and the textbook agree [read: p.1]. Then the wavelength along each direction is λᵢ = cᵢ/ν, and the wavenumbers are kᵢ = 2πν/cᵢ.

3.3 What a phase measurement in the lab sees. An interferometer compares phases. Any phase that a detector in the lab can record is a sum of kᵢ times path lengths along the actual light paths. When the light goes out along +x and comes back along −x, the phase is (k₁ + k₂)L = 2πν(1/c₁ + 1/c₂)L = 2πνt, which is the round-trip quantity of 3.1 and is the same for every ε. The textbook expectation is that every closed comparison of light phases reduces to such round-trip sums, so no tabletop optical experiment, whether it uses travelling waves or standing waves, can find ε. Marett cites Tyapkin (1973) and Lorentz's theorem of corresponding states for this same point [web, via Investigator]; Silvertooth himself cites Tyapkin [read: p.2-3].

3.4 The Lv/c² term. In SR, a rod of length L moving at v has end clocks that, synchronised in the rod's frame, are out of step by Lv/c² as seen from the CMB frame. Multiply by the frequency and this is a phase νLv/c² = (L/λ)(v/c) cycles. It is a bookkeeping difference between two synchronisation choices. It adds up to zero around any closed path in translation, which is why no Sagnac shift appears in translation.

3.5 Doppler shift. For a source receding at speed v_r along the line of sight, the relativistic Doppler formula is ν_obs = ν_source √((1 − v_r/c)/(1 + v_r/c)) [memory, high]. It depends on the source velocity at the moment of emission. Separately, two clocks that accelerate together with acceleration a, separated by L along the acceleration, see a frequency shift aL/c² between them (the equivalence-principle or gravitational redshift; measured by Pound and Rebka in 1960 [memory, high]).

4. Where the inventor departs

The exact point of departure is the third row. Everything that follows (one-way wavelengths, the measurement, the Doppler term) rests on giving the open-segment Sagnac term a physical meaning in straight-line motion. The textbook says that term is the relativity-of-simultaneity offset Lv/c² of 3.4, and that it never shows up in a closed comparison of phases.

The paper also sets aside two earlier one-way tests, the Mössbauer-rotor experiment of Turner and Hill (1964) and the pulsar-timing deductions of Cole (1976), saying they "are defeated through the second order by the argument of Tyapkin" [read: p.2-3; ref. 5, Tyapkin, Lett. Nuovo Cimento 7, 760 (1973)]. The paper gives no argument of its own. Tyapkin's argument is the conventionality point of section 3.3, the same one Marett uses to say a one-way wavelength cannot be measured either, so the citation cuts against Claim 3 as much as against those tests (arbiter, QE revision 4). A mainstream test of the same first-order one-way kind, Gagnon, Torr, Kolen and Chang, Phys. Rev. A 38, 1767 (1988) (a guided-wave experiment), is cited by the Contrarian as the strongest mainstream evidence against Claim 3 [web: https://journals.aps.org/pra/issues/38/4, via Contrarian]; its result was not read in this review, and the arbiter does not rely on it.

It is fair to the inventor to say clearly where he is right. Section 3.1 is his eq. (3): a round trip cannot fix a one-way quantity. He quoted Simon Newcomb's 1881 letter to Michelson making the same compensation point ("when a ray returns on its own path the retardation in one direction is compensated by the acceleration in the other") [read: 1976 p.1101]. His idea that a one-way wavelength could be measured even if a one-way speed cannot is a natural question to ask, because wavelength looks like a purely spatial quantity that needs no clocks. The worked example shows why it fails anyway.

5. Worked example: what should D1 and D2 read after 0.25 mm of travel?

The arbiter's central finding (Claim 3) is that the instrument should give no signal even if Silvertooth's own eq. (5) is true. Here it is step by step. Script: example.py, run with .venv/bin/python review/SilverTooth/example.py; it ran cleanly and its assertions passed.

Step 1. The paper's arithmetic. Inputs: λ = 0.63 μm, Δ = 0.25 mm [read: p.4]. Combining eq. (8), nδ = λ/2 with n = Δ/λ, and eq. (9), δ = λ(v/c), gives Δ(v/c) = λ/2, so

v/c = λ/(2Δ) = 0.63 × 10⁻⁶ / (2 × 0.25 × 10⁻³) = 1.26 × 10⁻³, v = 1.26 × 10⁻³ × 299,792 km/s = 377.7 km/s (378.0 with c = 3 × 10⁵ km/s) [calc].

The slide moves Δ/λ = 396.8 wavelengths. The claimed pattern shift per wavelength of travel is δ = λ(v/c) = 0.79 nm [calc]. Since v ∝ 1/Δ, an uncertainty of ±0.01 mm in Δ gives v between 363 and 393 km/s; ±0.025 mm gives 343 to 420 km/s [calc]. The paper states no uncertainty, so the "378" carries three figures only because the inputs were round numbers.

Step 2. Grant all the premises. Let b = v/c = 1.26 × 10⁻³. Eq. (5) gives wavenumbers

k₊ = 2π(1 + b)/λ for light moving along +x (one way along the slide axis), k₋ = 2π(1 − b)/λ for light moving along −x.

Check: L/λ₁ + L/λ₂ = (L/λ)(1 + b) + (L/λ)(1 − b) = 2L/λ, so eq. (3) holds; their difference is (2L/λ)b, so eq. (4) holds (SymPy residuals 0) [calc]. Note k₊ + k₋ = 4π/λ exactly. That one identity is eq. (3) again, and it decides everything below.

Step 3. Follow the two beams when the slide moves. The slide carries the laser, quarter-wave plate, splitter BS1 and mirror M2. It moves a distance Δ toward the fixed mirror M3 [read: p.3]. Beam A leaves the slide travelling +x toward M3: that leg gets shorter by Δ. Beam B leaves the slide travelling −x toward M1: that leg gets longer by Δ. Every other leg (the fixed mirrors that route both beams onto D1 from opposite sides) is unchanged. So, at D1:

change in phase of beam A = −k₊Δ, change in phase of beam B = +k₋Δ, change in relative phase = k₋Δ − (−k₊Δ) = (k₊ + k₋)Δ = 4πΔ/λ.

The b terms cancel. The paper's own words say the same thing before the sign is lost: moving toward M3 by λ, the wave via M3 "will advance less than a wave (λ₁ > λ)" and the wave via M1 "will retard more than a wave (λ > λ₂)" [read: p.3]. That is, one beam's phase moves λ/λ₁ = 1 − b waves one way and the other's λ/λ₂ = 1 + b waves the other way (using the paper's Fig. 2 labels, which are swapped relative to eq. 5; the swap does not change magnitudes). One beam advances and the other retards, so the changes in their relative phase add: (1 + b) + (1 − b) = 2 waves for every λ of travel, independent of b.

Step 4. Where the standing wave sits. The intensity at D1 depends on the relative phase. The node spacing is 2π/(k₊ + k₋) = λ/2, exactly as with no ether at all. A relative-phase change of 4πΔ/λ moves the pattern by Δ: the whole pattern slides rigidly with the slide. A numerical check in example.py builds the two fields explicitly with b = 1.26 × 10⁻³ and finds the bright spot moves by 205.00 nm modulo λ/2, which is exactly Δ modulo λ/2 [calc].

Step 5. The reference interferometer D2. D2 is a round trip on path p: the out leg and the back leg each change by Δ, so its phase changes by k₊Δ + k₋Δ = 4πΔ/λ. Silvertooth says this himself: D2 "reads a maximum each time Δ changes λ/2" and is "independent of any anisotropy" [read: page image p.3].

Step 6. Compare. After Δ = 0.25 mm both D1 and D2 have gone through 2Δ/λ = 793.65 cycles. Their difference is 0 for every value of b [calc, SymPy: D1 − D2 = 0]. Under Silvertooth's premises the apparatus as described cannot show a phase reversal. The two opposed beams on a slide are, mathematically, a round trip along the slide axis: the same reason MM is blind (section 3.1) makes this instrument blind.

Step 7. Where δ = λ(v/c) came from. If one subtracts instead of adds, (1 + b) − (1 − b) = 2b waves per λ of travel; a standing wave moves by half the relative phase, giving b waves, so δ = λb. The paper gives only the result, not this working [read: p.3-4]; the deep reader reconstructed it this way and the Mathematician showed the subtraction does not match the described geometry.

Step 8. A geometry that would give a signal. Suppose instead both beams' changing legs got longer by Δ, one travelled +x and the other −x. Then the relative phase changes by (k₋ − k₊)Δ = −4πbΔ/λ, which is first order in b. A 180° reversal then needs Δ = λ/(4b), not λ/(2b): for b = 1.26 × 10⁻³ that is 0.125 mm, and at 0.25 mm the phase would be a full cycle, back in step. Read the other way, a reversal at 0.25 mm in this geometry would mean v = 189 km/s [calc]. So even the geometry that gives a first-order signal does not give eq. (9) (arbiter, recomputation 2). Caveat that the arbiter keeps, now narrower: the QE read the Fig. 2 page image and confirmed the opposed-direction geometry used in Step 3 (one changing leg shortens, the other lengthens, and they are traversed in opposite directions) [read: page image p.3, via qe.md]. What remains open is only that the paper gives no dimensions and no derivation of δ = λb; if a correct derivation from the real geometry were produced, the verdict on Claim 3 would revert to "Never properly tested".

Step 9. Ordinary effects of the same size. A reversal at 0.25 mm means a scale mismatch of 1.26 × 10⁻³ between what D1 and D2 count [calc]: - A change during the run in the angle between a beam and the slide axis of 2.9° gives 1 − cos θ = 1.26 × 10⁻³ (a fixed tilt is zeroed out by the procedure) [calc]. Smaller, first-order pointing or twist errors of about λ/4 over the 400 wavelengths of travel are what Sherwin (1989) and Marett proposed [web, via Investigator]. - In the inventor's favour: the whole gain bandwidth of a helium-neon laser (about 1.5 GHz on 4.7 × 10¹⁴ Hz [memory, high]) is 3.2 × 10⁻⁶, several hundred times too small to fake the effect by frequency drift [calc]. (The arbiter and Contrarian round this to "about a thousand"; the order of magnitude is the point.) The refractivity of air, n − 1 ≈ 2.7 × 10⁻⁴ [memory, high], is 4.7 times too small even if it all changed [calc]. - The size of what is claimed: Krisher et al. (1990) set an upper limit of about 100 m/s on a one-way anisotropy with two hydrogen masers on a 21 km fibre link [web: https://pubmed.ncbi.nlm.nih.gov/10012893]; 378 km/s is about 3,800 times that [calc]. Caveat kept by the arbiter: some writers on conventionality argue such two-clock links are themselves synchronisation-dependent.

What the example teaches. The single identity k₊ + k₋ = 4π/λ, which is the round-trip condition that Silvertooth adopted to explain the MM null, also cancels the first-order signal of his own instrument. His 1976 paper reported a related null, in a different setup: not one laser split on a slide, but two free-running lasers whose beat frequency was "held under 3 MHz", sent along oppositely directed paths and sampled at two photocathodes 50 cm apart, 79 cycles expected for a change of v/c of 10⁻⁴ on rotating the granite table, and "No phase shift was observed, thus showing the relative phase between the oppositely directed beams at any pair of locations of detectors to be invarient with v" [read: 1976 p.1101-1102]. The 1986 paper does not mention that experiment.

6. Evidence table

Notes kept in the record whatever the verdicts: - Marett hoped the effect was real and is a dissident-physics experimenter, not an institutional critic [web, via Investigator]. Both halves of his result stand: the signal appeared; he traced it to temperature. - Marinov, Wesley, Whitney and Aspden have their own programmes of absolute-motion detection (interested parties in a positive result); Sherwin and Phipps are critics with their own views. Each is reported as that party's characterisation. - Wesley's ±8 km/s is tighter than the inventor's own ±5% (±19 km/s); its origin is unknown. - The 1989 article's sidebar on suppression ("Suppress, ignore and ridicule") is unsigned; it is the sidebar writer's characterisation. No document of the experiment being blocked was found, and others did repeat it. - The geometry fits in part: from latitude 48.6° N (Olga, Washington, the author's address, not stated as the site) a direction near Leo rises about 10° south of east and sets about 10° south of west, so an E-W axis sees nearly the full component at rising and setting and none at transit, as reported and as Marett saw. But at transit the same direction is 34° up in the south, so a N-S axis should then see about 0.82 of the full effect. The paper does not say when the N-S run was made [calc, Mathematician and Contrarian; the CMB declination of about −7° is memory, medium]. - The 180° criterion cannot tell the sign of the effect, so rising and setting look the same; any 12 h disturbance can mimic the pattern. - The inventor's own later positive claim: Whitney and Silvertooth, "A New Michelson-Morley Experiment", Physics Essays 5(1) 82-89 (1992), report that the standing-wave node spacing inside one Michelson arm departs from λ/2, fitted with c(θ) = c/[1 + (v₀/c)cos θ], v₀ about 378 km/s, θ fixed relative to the stars [web: https://wiki.naturalphilosophy.org/index.php?search=Silvertooth, abstract, via Investigator; paper not read; no verdict given]. In the 1986 model of eq. (5) the node spacing is exactly λ/2 for every b (Check yourself, Q2), so the 1992 claim conflicts with the 1986 model as well as with SR. - The inventor's own earlier one-way results were nulls: the 1972 JOSA test (as recorded by Roberts and Schleif) and the 1976 two-laser test. Marett's 2011 single-laser one-way standing-wave test was also a null. They sit in the record beside the positive 1986, 1989 and 1992 claims. - Open leads kept: a book, "The Silvertooth effect: TETET-99" (S. Silvertooth, D. G. Lahoz, Angel Garcia; Toronto, UNIAM, 1999; ISBN 978-0968308547; authorship and content unknown) [web, via Investigator]; the 1989 article's statement that groups in the USA, West Germany, UK, Italy, France and Austria worked on explaining why the experiment works or should not [web: spirit-science.fr URL above, via Investigator]; Wireless World coverage in November 1986 and November 1989 (not read).

Absence of evidence (from the arbiter). The 1986 paper says the work was "sponsored in part" by the Air Force's Rome Air Development Center and DARPA [read: p.4]. No report or Defense Technical Information Center (DTIC) entry was found, and the University of Arizona experiment that the 1976 paper called "under way" has no known outcome. Competing explanations: informal or in-kind support with no report; reports not indexed or restricted; overstated sponsorship; limited support after an RADC physicist (Newburgh) criticised the 1976 paper in print. The Natural Philosophy Wiki biography says he later did classified work for an Air Force "think tank" associated with the Aerospace Corporation, but gives no source [web: https://wiki.naturalphilosophy.org/index.php?search=Silvertooth, via Investigator]; it bears on the restricted-reports explanation without deciding it. Nothing yet decides between them; a direct DTIC search, AFRL Rome and DARPA archives, FOIA, and the Arizona Optical Sciences Center FY75 report would. Likewise no original data were ever published; the 1986 Nature letter promised details that never reached a refereed journal [web: Forbes/Koberlein, via Investigator].

7. What a learner should take away

Solid. - A round-trip experiment cannot fix a one-way speed or a one-way wavelength. Silvertooth's eq. (5) is a valid way to describe light in a moving lab; it is the Reichenbach choice ε = (1 + b)/2. Newcomb said as much in 1881. - His optics was real. The thin-film standing-wave sensor (1983, with S. F. Jacobs at Arizona) works, and he printed his own null result in 1976. - 378 km/s toward Leo really is close to the measured 370 km/s CMB dipole. That coincidence is why the paper is remembered.

Wrong, and why it is instructive. - The argument for the MM null is circular: the conclusion (round trip independent of v) is the premise. - The step from a rotating loop to a straight segment in translation gives a physical meaning to a quantity that cancels on every closed path. It is the relativity-of-simultaneity term Lv/c² wearing different clothes. A good habit: when a derivation gives a "local" piece of a closed-loop quantity, ask whether the split depends on an arbitrary choice (here, the rotation centre). - The instrument's predicted signal cancels under its own premises, because two opposed beams on a slide add the wavenumbers k₊ + k₋, which is exactly the round-trip sum. A good habit: carry the signs through; "one advances, the other retards" means the relative phase changes by the sum. - He reversed himself on a basic premise (whether frequency or wavelength changes) without saying so. In 1976 he wrote that his own experiment showed the frequency and velocity change, with the wavelength change "a resultant effect" [read: 1976 p.1101]; in 1986 the frequency "cannot change" and only the wavelength does [read: p.1]. The 1986 paper does not mention the 1976 experiment. A good habit: when an author's premise changes between papers, ask what new evidence forced the change; here none is given. - Eq. (10) is undefined as printed (v̄ undefined; the dot of the 1976 acceleration lost), and the 1976 quasar version assumes the acceleration stays constant over a billion-year light flight during which the source orbits several times.

Genuinely open. - Why did Marett, Marinov and perhaps Wesley see a signal at the CMB scale aligned with sidereal time, if the apparatus should be blind? Marett's thermal explanation fits his own data, but a direct test (rotating table, lock-in readout, temperature-controlled and pointing-monitored laser, declared N-S and E-W times, raw data published) has never been done. - Was the real apparatus geometry different from the one reconstructed here? The Fig. 2 drawing matches the reconstruction, but only Silvertooth's dimensioned drawings or his own derivation of δ = λb would settle it. - What did the 1992 Whitney-Silvertooth experiment actually measure? Its claimed departure from λ/2 node spacing is ruled out by the 1986 model itself (Q2), so either the 1992 result has another cause or the model was abandoned; the paper has not been read. - What did the sponsors receive, and did the University of Arizona experiment ever run?

8. Check yourself

1. If the phase reversal had occurred at Δ = 0.20 mm (same λ = 0.63 μm), what speed would eq. (9) give?
2. Using λ₁ = λ/(1 + b) and λ₂ = λ/(1 − b), show that the node spacing of the standing wave formed by two opposed beams of the same frequency is λ/2 for every b. What does this tell you about the instrument?
3. For a Galilean ether (speeds c − v and c + v), what is the round-trip time on an arm of length L along the motion? By how much does it differ from 2L/c at v = 378 km/s, as a fraction? Why does Silvertooth's eq. (5) give no difference at all?
4. Why is a closed Sagnac loop in pure translation free of any fringe shift, and what does Silvertooth's own 1976 paper say about this?
5. The reported effect is a 180° phase reversal. Why can such a criterion not tell whether Leo was rising or setting, and why does that weaken the sidereal argument?

9. Further reading

Mainstream: - D. J. Griffiths, Introduction to Electrodynamics, ch. 12 (Electrodynamics and Relativity). - E. F. Taylor and J. A. Wheeler, Spacetime Physics (relativity of simultaneity, the Lv/c² term). - A. P. French, Special Relativity (MIT Introductory Physics Series): Michelson-Morley and the ether. - E. Hecht, Optics: interference, standing waves, interferometers. - E. J. Post, "Sagnac effect", Rev. Mod. Phys. 39, 475 (1967) [memory, high]. - R. Anderson, I. Vetharaniam, G. E. Stedman, "Conventionality of synchronisation, gauge dependence and test theories of relativity", Phys. Rep. 295, 93 (1998) [memory, high]. - N. Ashby, "Relativity in the Global Positioning System", Living Reviews in Relativity 6 (2003) [memory, high]: how GPS handles Sagnac and synchronisation. - T. P. Krisher et al., Phys. Rev. D 42, 731 (1990) [web: https://pubmed.ncbi.nlm.nih.gov/10012893]. - A. Gagnon, D. G. Torr, P. T. Kolen, T. Chang, Phys. Rev. A 38, 1767 (1988): guided-wave first-order one-way test [web, via Contrarian; result not read]. - R. A. Muller, "The cosmic background radiation and the new aether drift", Sci. Am. 238(5), 64 (1978) [web: https://ui.adsabs.harvard.edu/abs/1978SciAm.238e..64M/abstract].

The inventor and those who engaged with him: - E. W. Silvertooth, "Experimental detection of the ether" (1986), the project paper. - E. W. Silvertooth, "Electromagnetic radiation, relativity, and anomalous red-shifts", Applied Optics 15(5), 1100-1102 (1976): the earlier argument, the two-laser null and the acceleration term (saved in research/files). - E. W. Silvertooth and S. F. Jacobs, "Standing wave sensor", Applied Optics 22(9), 1274 (1983) (saved in research/files). - E. W. Silvertooth, "Motion through the ether", Electronics & Wireless World 95, 437-438 (1989) [web: https://spirit-science.fr/ArchivesScientifiques/1989Silvertooth.pdf]. - E. W. Silvertooth, Nature 322, 590 (1986); "Isotropy of C", JOSA 62, 1330 (1972); Galilean Electrodynamics 1(6) 80 (1990) on GPS; C. K. Whitney and E. W. Silvertooth, Physics Essays 5(1) 82 (1992) (not read in this review). - D. Marett, "A Replication of the Silvertooth Experiment" (2012) [web: http://www.conspiracyoflight.com/Silvertooth/Silvertooth.html]. - D. Marett, "A Single Laser One-Way Speed of Light Experiment using a Standing Wave Interferometer" (2011, null; listed on the same site, not read). - Critiques: C. W. Sherwin, Physics Essays 2(2) 125 (1989); R. G. Newburgh and Ø. Grøn, comments in Applied Optics (1977) (not read). - Related claims by others (characterised by mainstream sources as not accepted; not examined here): S. Marinov (1987), P. Wesley (1987), Navia et al. 2006 (arXiv astro-ph/0608223), De Witte, Cahill.

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Answers

1. v/c = 0.63 × 10⁻⁶ / (2 × 0.20 × 10⁻³) = 1.575 × 10⁻³, so v ≈ 472 km/s.
2. The relative phase of the two beams changes by k₁ + k₂ per metre, with k₁ + k₂ = 2π(1 + b)/λ + 2π(1 − b)/λ = 4π/λ. Nodes are 2π/(k₁ + k₂) = λ/2 apart for every b. The standing wave looks exactly as it would with no ether, and a slide motion moves it rigidly; the instrument is a round trip in disguise and cannot see b. It also means the 1992 Whitney-Silvertooth claim of a departure from λ/2 node spacing cannot follow from the 1986 model (section 6 notes).
3. t = L/(c − v) + L/(c + v) = (2L/c)/(1 − b²). With b = 1.26 × 10⁻³ the excess is b² ≈ 1.6 × 10⁻⁶. With eq. (5), 1/c₁ + 1/c₂ = (1 + b)/c + (1 − b)/c = 2/c exactly: the speeds were chosen so that the round trip comes out isotropic, which is what "no Lorentz contraction needed" amounts to.
4. The Sagnac shift is proportional to ∮ v · dl around the loop. In pure translation v is the same vector everywhere, and the integral of a constant vector around a closed path is zero. Silvertooth agreed in 1976: the segment shift "is simply cancelled in the closed path by the phase shifts in oa and bo" [read: 1976 p.1101].
5. A 180° reversal is the same whether the phase moved +180° or −180°, so the readout sees only the size of the component along the axis, not its sign. At rising and setting the component has opposite signs but equal size, giving a 12 h pattern. Any disturbance with a 12 h period (Marett found one in solar time, tracking room temperature) can produce the same pattern, so a 12 h pattern alone cannot prove a fixed direction in space.