First-Order Fiber-Interferometric Experiments for Crucial Test of Light-Speed Constancy
| Scientific Paper | |
|---|---|
| Title | First-Order Fiber-Interferometric Experiments for Crucial Test of Light-Speed Constancy |
| Read in full | Link to paper |
| Author(s) | Ruyong Wang |
| Keywords | light, speed, Michelson-Morley experiment, Vacuum |
| Published | 2005 |
| Journal | Galilean Electrodynamics |
| Volume | 16 |
| Number | 2 |
| No. of pages | 10 |
| Pages | 23-30 |
Read the full paper here
Abstract
The Michelson-Morley experiment for examining light-speed constancy in paths moving linearly is second-order in speed, so it has never been conducted with paths moving relative to Earth. The Sagnac experiment is a first-order experiment, but it does not address motion that is linear, since its path motion is caused by rotation. The design of an interferometric experiment that is not only sensitive to linear motion, but also first-order in speed, needs two features: 1) optical paths in uniform translational motion, and 2) paths for light return without cancellation of possible effects. Two arrangements with these features are here presented: a conveyor-like arrangement, and a shearing parallelogram arrangement. Both can be implemented with fiber-optic technology. If the entire optical loop is fiber, the light-speed constancy in a moving path of the fiber is examined; if the fiber loop is broken to leave a gap of vacuum (or air), the light-speed constancy in a moving path of vacuum (or air) is examined. According to the same analysis as that for a fiber-optic gyro, translational motion in these arrangements will lead to an increase of optical path length and an increase of the travel time difference, a result falsifying the principle of the light-speed constancy.
Overview
Ruyong Wang's paper is an experiment-design proposal rather than a theoretical argument. Its premise is that the two classic optical tests of light-speed constancy each have exactly one of the two properties a decisive test needs, and neither has both. The Michelson-Morley experiment uses paths in translational motion, but is second-order — its predicted travel-time difference goes as v2/c2, so it is hopelessly insensitive at speeds a laboratory or an aircraft can reach. The Sagnac experiment is first-order and therefore enormously sensitive, but its path motion is rotational, which lets defenders of relativity set the result aside as outside the scope of a theory formulated for uniform translation.
Wang's proposal is to build interferometers that are first-order and translational. He identifies the two design features required — optical paths in uniform translational motion, and a return path that does not cancel the effect — and gives two arrangements that satisfy them: a "fiber-optic conveyor" (FOC) and a "shearing parallelogram", both realisable with existing fibre-optic gyroscope technology. Analysed exactly as a fibre-optic gyro is analysed, both should show a travel-time difference that grows with the length of the translationally moving segment. If it does, Wang argues, light speed is not constant in a uniformly moving path, and the principle of light-speed constancy is falsified. A postscript added before publication reports that the experiment was subsequently performed and gave the predicted non-null result.
The argument
Why Sagnac is first-order and Michelson-Morley is not
Wang's diagnosis is geometric. In the Sagnac arrangement, when the closed path rotates, one beam propagates in the same sense as the rotation everywhere along the loop and the other opposes it everywhere; the contributions add along the whole path and never cancel, so the effect is first-order in the path speed. In the Michelson-Morley arrangement the closed path moves purely translationally, and it is impossible for a beam to travel with the motion over the entire path — if it goes with the motion on one leg it must go against it on another. The two contributions largely cancel and leave a residue of second order.
He is blunt about the consequence: because the residual effect goes as v2/c2, an aircraft at roughly 300 m/s is nowhere near fast enough to decide the question, and a real Michelson-Morley test of a system moving fast relative to the Earth would need something like a space shuttle. No such experiment has been done. "Therefore, the assertion that light speed is still c in a system moving translationally relative to Earth has not yet been verified." He notes he has previously proposed a first-order crucial test using atomic clocks, but argues an interferometric version would be far superior, since an interferometer can resolve time differences shorter than the few-femtosecond period of a light wave.
Wang also records, fairly, that the interpretation of the Sagnac effect is itself contested: some hold it incompatible with light-speed constancy because an observer moving with the path sees two equal-length paths traversed in unequal times; others hold that the motion is uniform circular rather than uniform translational and so falls outside special relativity's remit. Citing Vigier, he treats it as "an unsolved fundamental problem in physics" and concludes the Sagnac experiment therefore cannot serve as the crucial test.
The two arrangements
The fiber-optic conveyor takes the circular path of a Sagnac interferometer, cuts it into two half-circles, and inserts two straight translationally moving segments between them — the fibre is wound around a small conveyor instead of a cylindrical coil, turning a fibre-optic gyro (FOG) into an FOC. One beam then travels with the belt motion and the other against it.
The shearing parallelogram has a top straight path moving uniformly at speed v and a bottom straight path either counter-moving or stationary. Because the bottom path is stationary, any time difference generated in the moving top path is not weakened on the return leg. Extra fibre is needed on the connecting sides, whose lengths change during motion.
The crucial measurement in both cases is a comparison, not an absolute reading. Wang proposes building two conveyors identical in conveying speed and half-circle radius but differing in the length of the translationally moving segment — one of length l1, the other l2 = l1 + l0. Since the total travel-time difference is the sum of the differences contributed by each segment, comparing the two instruments isolates the contribution of the extra moving length l0. If the two conveyors agree, the added uniformly moving path contributes nothing and the counter-propagating beams have equal speeds in it. If they disagree, the beams do not.
The analysis, and its result
Wang derives the expected contribution by applying to the FOC exactly the treatment standardly applied to the FOG, which is based on Fizeau's 1851 result for light speed in a moving medium of refractive index n. He notes that the analysis is in fact better suited to the conveyor than to the gyro, because in Fizeau's experiment the medium moved translationally, as the added FOC paths do, whereas in a gyro it moves circularly.
Following a segment of fibre Δl moving at speed v, with the beam travelling either with or against the motion, and accounting for the displacement of the segment during the transit, he obtains for the FOG the standard result that a fibre arc of given length and given speed contributes a fixed amount to the total travel-time difference "no matter how big the radius R of the arc is" — the contribution depends on arc length and speed, not on curvature. Repeating the calculation for a translationally moving segment yields the same expression. Stated in the postscript and in the figure captions, it is
- Δt = 2v Δl / c2
for a single segment, and N times that for N turns. Two features of this result carry the paper's whole argument. First, it does not contain the refractive index n, so the same prediction holds for a vacuum or air gap as for glass fibre. Second, "if their lengths are the same, a path in uniform translational motion will contribute the same time difference to the total travel-time difference as a path in uniform circular motion" — which is exactly the claim that light speed is not constant in a uniformly moving path.
Vacuum gaps, Earth rotation and sensitivity
Because the predicted effect is independent of n, Wang proposes breaking the fibre loop to leave a gap of vacuum or air, taking the light out, guiding it across the gap and refocusing it on the fibre tips — the arrangement used in Sagnac-interferometer-based Fresnel-drag flow probes. Two otherwise identical conveyors with different gap lengths then isolate the time difference accumulated in the moving gap itself. He notes that the translational motion of a wound coil produces no time difference at all, which is precisely why a FOG senses rotation and not translation, so unused fibre may be left on the coil.
He treats the Earth's rotation explicitly as a systematic. The additional translational velocity it imparts affects both moving paths alike and cancels to first order; the additional angular velocity does not, since it drives the two paths in opposite senses, and contributes a term proportional to the horizontal component of the rotational velocity. He also relays a suggestion by Cynthia Kolb Whitney for a "figure 8" path with zero effective enclosed area, which would be immune to the classic Sagnac effect and to Earth rotation altogether, so that any observed time difference could not be attributed to them.
On sensitivity, Wang notes that many FOGs resolve phase shifts of 10-7 rad, and argues that even if a conveyor were two orders of magnitude worse, 10-5 rad is attainable. With a moving path length of about 180 m, a wavelength of 0.8 µm and a conveying speed of only 1 mm/s, the difference in phase shift between two conveyors should be detectable; for the vacuum-gap version, about 1.8 m of gap at the same wavelength and speed suffices. He stresses that at these speeds Lorentz contraction, a second-order effect, plays no part.
The postscript
Because the journal had a backlog, the paper appeared after the experiment had been done. Wang reports that a travel-time difference Δt = 2vΔl/c2 was indeed found between counter-propagating beams in a fibre segment of length Δl moving with source and detector, "whether the segment moved uniformly or circularly", and that a later run with an air light-guide gave the same non-zero result. His rhetorical argument for expecting this is simple: if the Sagnac contribution of an arc stays finite as the radius grows without limit, "then how can it disappear in uniform motion?" A null result would have amounted to "an unprecedented 'macro quantum jump'".
The postscript also raises a definitional complaint. Speed is measured from a distance and an elapsed time; for a bullet everyone agrees what those are, but Wang says relativists will not supply the corresponding definitions for a light beam and a moving observer. He offers his own: a source and two initially co-located, clock-synchronised observers A and B; light is emitted at t0; only afterwards does B accelerate toward the source and reach constant speed. Both observers then had the same emission time and the same distance at emission, so comparing reception times compares light speeds without invoking the relativity of simultaneity. He points out this can be tested with GPS: two receivers under a geostationary satellite, with B accelerating upward to 20 m/s over 0.7 m in 0.07 s, then 1 m uniformly, both receiving the signal about 0.12 s after emission. Anyone familiar with GPS, he says, would predict B receives it about 6 ns (1.7 m/c) early. Wang consulted Ron Hatch on this point, and the issue is taken up in the accompanying correspondence from Hatch and Tom Van Flandern.
Assessment
The proposal's real merit is that it is a genuine experiment with a definite, falsifiable prediction, made at a scale an ordinary laboratory can build. Wang's structural diagnosis — that Michelson-Morley and Sagnac each supply half of what a crucial test needs — is correct and clearly put, and the design response is elegant: keep the Sagnac loop's non-cancelling return geometry, and replace part of the circular path with a straight moving one. The differential protocol, comparing two instruments that differ only in the length of the moving segment, is good experimental practice, since it cancels most common-mode systematics. So is the explicit treatment of Earth-rotation contamination and the adoption of Whitney's zero-area figure-eight as a cross-check. The continuity argument in the postscript is also a fair challenge to state: the Sagnac contribution of an arc, on the standard analysis, depends on arc length and speed rather than radius, so something must be said about what happens in the limit of infinite radius.
The decisive difficulty is that the predicted result is not, in fact, in conflict with relativity — and this is where the paper's central claim overreaches. Standard relativistic treatment of the Sagnac effect derives the same Δt = 2vΔl/c2 per moving segment, and derives it for a translationally moving segment too, because the quantity being measured is not a one-way light speed but the difference in arrival phase at a detector that is itself moving between emission and reception. In the inertial frame the two beams simply traverse unequal path lengths; in the co-moving description the loop is not a single inertial frame, because a closed circuit of fibre carried on a conveyor cannot be covered by one global inertial coordinate system with consistent clock synchronisation. That failure of global synchronisation — not any variation in c — is the orthodox account of both the Sagnac effect and Wang's conveyor. Wang's own result thus confirms a prediction both theories share, and a shared prediction cannot discriminate between them. His insistence that the result "falsif[ies] the principle of the light-speed constancy" is an interpretive claim laid on top of the measurement, not something the measurement delivers.
The same objection applies to the GPS thought experiment in the postscript. That receiver B, moving toward the satellite, receives the signal about 6 ns early is not disputed by anyone; it follows directly from B having moved 1.7 m closer during the flight time. Wang's proposed definition of light-speed constancy — equal reception times for observers who began equidistant — is a definition under which no theory, relativistic or otherwise, predicts equality once one observer moves. It therefore tests nothing. It is worth noting that Wang's constructive claim is narrower and much stronger than his rhetorical one: he has established that a translationally moving optical path contributes to a Sagnac-type phase difference just as a rotating one does, with no discontinuity in the limit, which is a real and useful result about fibre interferometry regardless of how one interprets it.
Two smaller points. The paper's numerical sensitivity estimates rest on assuming FOC noise performance within two orders of magnitude of a mature commercial FOG, which is plausible but not demonstrated; a moving belt introduces vibration, strain-induced birefringence and thermal gradients in the fibre that a rigid coil does not, and these are first-order noise sources in exactly the band of interest. And the vacuum-gap version, which carries the strongest form of the claim, requires taking light out of fibre and refocusing it onto a tip across a gap whose length varies during conveying — Wang argues correctly that because both beams cross the same gap, small length variations do not affect the first-order difference, but coupling losses and alignment drift are still the practical obstacle, and no measured noise floor for the gap arrangement is reported here.