Kelly-AG · Source catalogue

A 13-page paper arguing that the Sagnac effect (the time difference between two light beams sent round a closed path in opposite directions on a rotating platform, dt = 4*A*omega/c^2, with A the enclosed area and omega the angular velocity) is not specific to rotation and applies equally to bodies in uniform straight-line motion. Kelly reviews Sagnac's 1913 interferometer on a rotating disc (area given as 0.86 m^2, 2 Hz, reversal doubling the shift), Harress (1911, ten prisms round a disc), Pogany (1928), Dufour and Prunier (repeat tests with the photographic record taken on the disc or from the fixed laboratory, same result), and the Michelson-Gale 1925 test (rectangle 2010 ft x 1113 ft at 41 deg 46' N; mean fringe shift 0.230 against 0.236 predicted, individual readings +0.55 to -0.05). He gives two derivations of dt for a circular path, both assuming light travels at c relative to the laboratory and independent of the source speed, obtaining 4*A*omega/(c^2 - v^2), which reduces to 4*A*omega/c^2; and a general derivation for any polygonal path using a binomial expansion in which second-order terms cancel and the total delay is 2*D/c^2 with D = 2*A*omega. His novel analysis of Michelson-Gale treats it as an ordinary Sagnac test using the projection of the pipe rectangle onto the plane perpendicular to the Earth's axis (hence the sin(latitude) factor). He compares ring-laser results (Macek and Davis 1963; Bilger et al. 1995, 0.75 m^2 ring in New Zealand, better than 1 part in 10^20 per his text) and tabulates how small the 'orbital rotation' is in Hafele-Keating, GPS, Michelson-Gale and Bilger. He argues Special Relativity (SR) has no role in explaining the effect: SR corrections are of order v^2/c^2, far smaller than the effect; Post (1967) is cited for the conceptual discontinuity between Galilean rotation and Lorentz translation; Wang et al. (2003) is cited as showing a Sagnac shift with a straight-line light path on a moving platform; and he notes he found no mention of Sagnac or Michelson-Gale by Einstein (quoting Silberstein 1921 and Turner 1979). Five summary facts close the paper, the last being that time and distance on the spinning disc are identical to the stationary laboratory and to uniform straight-line motion. The deep read (SymPy-checked) finds equations (1)-(12) algebraically correct but notes: the two circular derivations are the same equations under different descriptions; the '13 m/s per metre of radius' for one fringe has the scaling backwards (v = 13.13 m^2/s divided by r); Sagnac's area may be 0.0866 m^2 not 0.86 m^2 [memory, medium; to verify]; 'forty years' for Dufour and Prunier conflicts with the cited 1937-42 papers; the '4250 km' distance to the Earth's rotation axis is inconsistent with R = 6371 km (axis distance about 4752 km at that latitude); and the Delta t / 2 Delta t labels on p.12 contradict each other though the boxed result is right. QE-round additions (pp.6-12, [read: p.N]): (a) p.6-7 Kelly cites Michelson 1913 (ref [9], Astrophys. J. 37, 190-3) as 'a clear confirmation' of his conclusions: light bounced off mirrors rotating at 1800 rpm; he says the fringe shift shows (1) light does not bounce like a tennis ball off a moving racquet, (2) light does not take up the mirror's velocity, (3) 'the light actually ignores the whole rotating apparatus. It moves solely with respect to the laboratory'; accuracy 1:50; Kelly says Michelson made a factor-of-2 error cancelled by a later omission of a similar amount, 'uncovered by a colleague who has been corresponding with this author' (unnamed). (b) p.7 ring laser: beat frequency df = 4*A*omega/(lambda*P) (confirmed from page image; omega = Earth's angular rotation, lambda wavelength, P perimeter); Macek and Davis 1963 'accuracy of 1 in 10^12' on a Sagnac-sized rotating disc; Bilger et al. 1995 square of area 0.75 m^2, He-Ne, latitude 43 deg 29' S, 30 m underground in concrete tied into basalt, 'better than 1 part in 10^20', area smaller than Michelson-Gale by a factor of 277,000 (Anderson et al. 1994); Kelly's observation that the Bilger retardation sense (clockwise viewed from over the South Pole) is opposite to the northern M and G sense. Standing-wave argument: in a ring laser the standing waves 'stay stationary in relation to the laboratory' (text cites 'Martin, 1996' but ref [13] is G. J. Martin, IEEE Spectrum, 1986); when the ring turns, nodes pass an observation post at a rate proportional to rotation rate and dependent on ring shape (square/triangle differ from circle); 'further confirmation of the proposal in this paper, that light, in small scale experiments, travels relative to the laboratory (Anderson, 1986; [14])' (ref [14] Scientific American 254, 86-91). Lock-in: Kelly says the original Sagnac result involved 'a considerable element of luck' because vibration prevented lock-in; a rock-steady rig would have given a null that 'would have been taken as proof positive of SR'. (c) p.8 Kelly quotes Einstein 1905 (clocks along polygonal and curved paths), Einstein 1919 ('The rotating observer notes very well that of his two equivalent clocks, that placed on the circumference runs slower than that placed at the centre') and Einstein 1916 ('special' restricted to uniform translation), and charges that 'authors can selectively quote Einstein's writings, whenever there is a seemingly insurmountable difficulty with SR theory'. (d) pp.9-10 'inertial frame' argument: the Earth's centre is accepted as an inertial frame for GPS and Hafele-Keating, yet the lab is not for Bilger; Kelly's figures for the Earth's orbital turn during each test: Hafele-Keating about 1.6 deg (40 h), GPS signal round the equator 2.9e-6 deg, Michelson-Gale 2.3e-10 deg, Bilger 1.66e-13 deg (on a square of side 0.866 m, 'upon a disc of 8,750,000 m diameter'), Sagnac 2.8e-13 deg; he concludes 'Pretending that SR does not apply to rotation, while at the same time applying it daily to experiments like the Global Positioning System ... is indefensible ... a very biased selection of what is termed an Inertial Frame'. Full Post (1967) quotation on p.9 ('To be consistent with the principle of relativity one has to demand that the Sagnac interferometer and the ring laser cannot lead to a fringe shift or a beat frequency if the equipment is in uniform translational motion ... a disturbing conceptual discontinuity'). (e) p.10 Kelly lists 'the M & G (600m) or Saburi (0.9m) tests' as paths whose deviation from a straight line 'will not be distinguishable'; Saburi is NOT in the reference list. He describes Wang et al. 2003 as sending 'out light in a straight line portion of the light path and back again' on a moving platform, 'Wang achieved the seemingly impossible, by reversing a light beam sent out on a straight line on a moving platform', and concludes the 'rotational-only' defence 'is now shown to be groundless'. (f) p.10 SR vs Sagnac: Kelly 2001 (Infinite Energy 39, 24-28) and Post (1967) on the dilation factor being 'indistinguishable with presently available equipment' and one order smaller than the Doppler correction. (g) p.10-11 'first general derivation of the Sagnac effect which does not assume an ether'; Sagnac's disc 50 cm diameter, enclosed light-path area 666 cm^2 (p.11) versus 0.86 m^2 on p.1. (h) p.12 page image confirms the final formulas: D = 2*omega*A = 4*pi*n*A, 2*Delta t = 2D/c^2 = [8*pi*n*A]/c^2, Delta t = 4*A*omega/c^2; the text-layer '4nA' is an extraction garble of '4*pi*n*A', not Kelly's error. The Delta t / 2 Delta t label wording on p.12 is loose but the boxed result is right. p.12 item 3: Kelly says a lab observer would see 'a very small Doppler effect', and that Sagnac's own camera rode on the disc so there was none.

Key claims

• The Sagnac effect applies to bodies in uniform straight-line translation as well as to rotation.
• Light travels at c relative to the laboratory and independently of the speed of its source, and the Sagnac result (dt = 4*A*omega/c^2) is exactly what that assumption gives for any shape of light path.
• Special Relativity plays no role in the Sagnac effect: the effect is first order in v/c while SR corrections are second order, and the effect is already large at rim speeds of about 13 m/s.
• One fringe shift requires a rim speed of about 13 m/s per metre of radius (the text's wording; the arithmetic gives 13.13 m/s only for r = 1 m).
• The Michelson-Gale 1925 result (0.230 fringe against 0.236 predicted) is a straightforward Sagnac test in which the relevant area is the projection of the pipe rectangle onto the Earth's equatorial plane, explaining the sin(latitude) factor.
• Ring-laser Sagnac measurements (Bilger et al. 1995) agree with theory to better than 1 part in 10^20 on a 0.75 m^2 ring, though the Earth rotates only 1.66e-13 degrees of orbital turn during them, showing that no inertial-frame assumption matters.
• Wang et al. (2003) obtained a Sagnac-type result with a straight-line light path out and back on a moving platform, removing the defence that Sagnac is a rotation-only experiment.
• Because light moves at c relative to the laboratory regardless of platform motion, light does not travel at c relative to a moving disc along straight segments (Sagnac, Harress, Pogany polygon paths).
• Einstein never referred to the Sagnac or Michelson-Gale tests, despite their bearing on the constancy of the speed of light (supported by Silberstein 1921 and Turner 1979).
• In the Sagnac setup, time and distance on the spinning disc are identical to those in the stationary laboratory.
• Michelson's 1913 rotating-mirror test (mirrors at 1800 rpm, accuracy 1:50) shows that reflected light does not take up the mirror's motion and 'moves solely with respect to the laboratory' (Kelly, p.7).
• In a ring laser the standing waves stay stationary relative to the laboratory, and the shape-dependent rate at which nodes pass an observer when the ring turns is further confirmation that light, 'in small scale experiments', travels relative to the laboratory (Kelly, p.7).
• Authors selectively quote Einstein (1905 polygonal-path clocks versus 1916 'special' restricted to uniform translation) when SR meets a difficulty; SR was applied by Einstein himself to curved and polygonal paths (Kelly, p.8).
• Treating the Earth's centre as an inertial frame for GPS and Hafele-Keating but not the laboratory for Bilger et al. is a 'very biased selection', because the Earth turns through orders of magnitude less orbital angle during the Bilger test than in the accepted cases (Kelly, pp.9-10; ratios about 1e10 and 5e6 as stated by Kelly).
• The original Sagnac result owed a 'considerable element of luck' to vibration preventing lock-in; a rock-steady apparatus would have given a null that 'would have been taken as proof positive of SR' (Kelly, pp.7-8).

Relevance: This is the only document in the project and carries all of Kelly's claims. It is a classical-optics paper with derivations that can be checked by hand, centred on whether the Sagnac effect is evidence for a light-speed-relative-to-lab (ether-like, source-independent) picture and against SR, and extends the effect to non-rotating motion. QE-round note: pp.6-12 now carry source-tagged deep-read detail; the ring-laser and Michelson 1913 passages are a second and third line of experimental support offered for claim 2.

Mainstream conflict: Mainstream physics treats the Sagnac effect as fully accounted for by SR (non-rotating inertial frame, c invariant) and general relativity; the first-order result is the same as Kelly's, so the mathematical derivation does not conflict. The conflict is interpretive: Kelly says light has speed c relative to the laboratory (a preferred-frame, Galilean-like reading) and that SR has no role, and that the effect extends to uniform straight-line motion, which mainstream treatments say does not produce a Sagnac shift for a closed path in an inertial frame (the Wang et al. experiment is a separate case that the physicist should assess, including the moving-medium/reflection geometry). Kelly's claim of Einstein's silence also needs checking against Einstein's 1914 note on the Harress experiment [memory, medium]. For Michelson 1913 and the ring-laser standing-wave picture, mainstream accounts cite them against emission (ballistic) theories and describe the ring laser's standing wave as fixed in the inertial frame [memory, medium]; the physicist should say whether they discriminate between Kelly's picture and SR (QE expects they do not).