In 2004 Chris P. Duif, then at Delft University of Technology, posted a twelve-page paper on arXiv (gr-qc/0408023, fifth version dated 31 December 2004) that asks a narrow question about the Allais Effect: leaving exotic physics aside, does any mundane cause account for what instruments were reported to do during solar eclipses? His answer is that every ordinary explanation proposed up to then fails, either in kind or in size. He is just as clear that this does not prove an anomaly exists. The paper is a single-author preprint that reports no new measurements, and several of its supporting analyses are cited as unpublished or still to appear.
What had been reported
Duif sorts the eclipse reports by the kind of instrument involved.
- Paraconical pendulum. Maurice Allais recorded the swing plane of his Paraconical Pendulum during the eclipses of June 30, 1954 and 2 October 1959. The paper notes that these reports are still regarded as among the most reliable, not least because the two eclipse records resemble each other in shape and size. The plotted quantity is the azimuth of the swing plane in grades (100 grades = 90°); the pendulum was released afresh every 20 minutes, and each point sums up 14 minutes of motion.
- Torsion pendulum. Saxl and Allen reported that the oscillation period of their torsion pendulum changed during the 1970 eclipse in the USA, at a site where the Sun was about 96.5% covered.
- Gravimeters. A Chinese team (Wang and colleagues) reported dips in gravitational acceleration of up to roughly 7 × 10⁻⁸ m/s², falling just before first contact and around last contact rather than at mid-eclipse. Mishra and Rao had earlier published a positive gravimeter result from the 24 October 1995 eclipse in India.
The paper also lists the attempts that found nothing. For torsion pendulums it cites Kuusela's two papers and a further group (Juo, Jianguo, Xuerong, Liakhovets, Lomonosov and Ragyn) as negative replications. For gravimeters it cites Ducarme, Meurers, Mansinha and Tomaschek, all negative. Duif does not dismiss these, but he observes that most repeats used apparatus altered from the originals, and that eclipses vary a good deal in the Sun's elevation, the latitude of the site and the speed of the shadow, differences he says had been largely ignored.
One point needs care. Kuusela appears in the paper twice: as a negative result for the oscillation period of a torsion pendulum, and later as the source of a tilt-like signal from his 1991 measurements in Mexico (see below). The two are not in conflict, because they concern different quantities, and Duif himself uses the pairing to argue that tilt need not alter a torsion pendulum's period.
Do the different instruments show the same pattern in time?
Duif makes a claim about timing that he credits to Robert Latham. Because each of Allais's readings is an accumulation over 14 minutes, Duif fits a smooth curve to the 1954 record and differentiates it to estimate the rate of change. He then presents this curve alongside the Saxl–Allen period change and the Indian gravimeter trace, and adds, in the caption to a tilt record made by Latham in 1974, that this record takes the same shape as the other three once a linear trend is subtracted and the result is turned upside down.
The limits of this claim should be stated plainly. The match is asserted from the plots: the paper describes no other comparison of the curves and offers no statistical test of the resemblance. For Latham's record in particular, the likeness appears only after the detrending and inversion just described. The Saxl–Allen curve is itself Duif's re-plot, using every individual data point instead of the five-point averages those authors published (he says the fitted curve hardly moves), and it comes from a re-analysis he cites as not yet published. Latham's contribution is an internal Imperial College report from 1980.
Which ordinary causes had been proposed?
The paper counts six, each drawn from earlier literature: seismic noise from eclipse-watchers' traffic (Unnikrishnan and co-authors); the gravitational pull of a patch of cooled, denser upper air (Van Flandern and Yang); ground tilt as the soil cools, along with draughts; tilt from the crust flexing under changed air pressure; eclipse-related changes in the geomagnetic field; and faults in the instruments or their analysis (Van Ruymbeke and co-authors). They are easier to weigh when grouped by what they would do to an instrument.
Why Duif finds each one inadequate
Causes that would alter the downward pull
The denser-air model gets the fullest treatment. Duif grants its arithmetic: if air density in the cooled region rose by 0.1% across the whole shadow, an excess of 10¹⁰–10¹¹ kg centred near 10 km altitude could produce an upward pull of about 7 × 10⁻⁸ m/s², matching the Chinese dips. His difficulties lie elsewhere. Air would need to converge at several hundred metres per second; at believable speeds the extra mass would trail the shadow by at least 15 minutes, warming again as it went. A ring of thinned air around the dense patch ought to give deviations of the opposite sign, and the Chinese record shows none down to a tenth of the observed dip. Duif adds that almost nothing is known about the atmosphere at these heights during an eclipse.
His verdict is split. For gravimeters the model remains, in his words, "a reasonable candidate". For pendulums he excludes it, because such instruments hardly respond to changes in vertical gravity: Saxl and Allen had calculated that even a change as large as the tides would be too weak by a factor of 10⁵ to produce their period shift.
Causes that would tilt or shake the instrument
Three proposals share the idea that the instrument's support moved.
Air pressure. The same pressure rise invoked for the dense-air model would also load the crust and tilt it slightly. Duif doubts the size of the rise to begin with: the 0.6% sea-level figure quoted by Van Flandern and Yang is, he says, not confirmed anywhere, against about 0.5 hPa (roughly 0.05%) recorded in Vienna. Using Rabbel and Zschau's work he puts the largest loading tilt at the order of 50 nrad, which he judges too small to matter. The related suggestion that pressure-driven draughts pushed the pendulums of Allais and of Saxl and Allen runs, he argues, against meteorological studies in which the atmosphere responds late and wind speed drops during eclipses.
Cooling ground. Yang and Wang tested this experimentally. For a 2 K temperature drop they found a tilt roughly an order of magnitude short of what the Chinese gravity dips would require. Duif adds soil studies showing that eclipse cooling penetrates only a few centimetres and arrives about 30 minutes behind the shadow, and notes that the temperature gradient is usually no steeper than on an ordinary morning or evening. Allais's pendulum stood in a basement, and Saxl and Allen's apparatus on concrete anchored to rock.
Traffic. The Chinese gravimeter sat in an isolated geophysical station in northern China, kilometres from any road, with the experimenters themselves 200 m from the instrument. Seismic records from Southern Belgium in 1999, a heavily populated region, showed no rise in disturbance. Both points rest on private communications to Duif. He nonetheless recommends recording seismic activity alongside any future measurement.
Causes inside the apparatus or the data
Reported geomagnetic changes during eclipses are at most 10 nT, no larger than the field's ordinary daily swing. Duif describes his analysis here as preliminary and postpones the detail to a later version of the paper.
On instrument error the paper criticises both camps. Duif says that many positive reports come without a statistical analysis or without records long enough to show what a normal day looks like, and that some negative reports display a time window barely wider than the eclipse itself. By his own preliminary estimate the Saxl–Allen signal stands three standard deviations above ordinary daily variation in the period. That figure, like the re-plot above, comes from his unpublished re-analysis and cannot be checked from this paper alone. He concedes that short-lived glitches have many possible causes but argues that they do not reproduce the overall shape of the records.
Tilt of the vertical: what stays open
Duif singles out direct observations of tilt as the part of the puzzle most worth pursuing, and it is the least settled part of the paper.
Two records are discussed. During the 1991 eclipse in Mexico the midpoint of Kuusela's torsion balance, hung on a wire 1.00 m long, deviated by up to 2 mrad (as the paper prints the unit) in one horizontal direction (the paper's y-direction) and showed no such effect in the other. Which way that direction pointed is unclear, because the paper contradicts itself: the main text calls it approximately perpendicular to the shadow's path, while the caption to the accompanying figure says it lay roughly along that path. Duif says only that the deviations seem to be related to the eclipse. In Western Australia on June 20, 1974, Latham's Talyval level registered an east–west tilt of about 5 seconds of arc, which the paper equates to roughly 24 mrad and calls an order of magnitude larger than Kuusela's value. Latham's gyroscope, running at the same time and sensitive enough to detect a real rotation of that size, showed nothing, and he found no change in gravity in the records of the observatory at Mundaring.
Duif's tentative reading is that an eclipse sometimes produces an extra horizontal force. Freely hanging instruments, which he treats both of these as being, would respond to such a force, while a gyroscope and most gravimeters would not. He also allows that Latham's reading may simply have been an instrument error. Two records, one of them possibly faulty, are a thin basis, and the paper does not claim more.
Could tilt of this size explain the pendulum results themselves? For Saxl and Allen the paper leaves the question open. Duif takes Kuusela's records as showing that tilt need not change a torsion pendulum's period, but he adds that the Saxl–Allen pendulum was started by a different mechanism, so that a sensitivity to tilt cannot in principle be excluded for it. He then cites their own later, unpublished test, made a few years after the eclipse, which concluded that a sideways movement of the pendulum disc of 0.1 mm would change the period by 60 ms at most, two orders of magnitude below what they saw during the eclipse. That test covered a far smaller movement than the one at issue: by Duif's figure, a tilt the size of Latham's (about 24 mrad, as the paper prints it) would correspond to a horizontal displacement of roughly 45 mm for the Saxl–Allen pendulum, against the 0.1 mm examined. The paper draws no conclusion from this comparison and does not say that tilt is ruled out for their result. For Allais the question is sharper, because Guérin and Gay had pointed out that his procedure, restarting the pendulum from the last observed angle, is in principle open to tilt errors, whereas Savrov's single-release, ellipse-fitting method is less so. Duif's estimate is that a tilt as large as Latham's would shift Allais's pendulum by, at most, about a tenth of the smallest step Allais could read on his dial. That ratio follows from Duif's two figures and is not a measurement. On that basis he considers it unlikely that tilt of this magnitude produced the 1954 and 1959 curves. Only for Allais does the paper argue that tilt is excluded.
This is a different matter from the distinction drawn at Maurice Allais, where Allais separates static deflections of the vertical from the dynamic effect he claimed. Duif's argument concerns whether a tilting support could corrupt the release-and-read procedure, not whether the direction of the vertical itself was shifted.
What the paper does and does not show
The paper shows that, as of 2004, no single published conventional mechanism matched both the size and the timing of the reported signals across pendulums and gravimeters alike. It does not show that the signals are real. Duif writes that a mixture of small effects and instrument errors, or a conventional cause not yet identified, could still be responsible. His case is built from re-plotted data belonging to others, order-of-magnitude estimates, private communications and unpublished manuscripts, including material from Saxl's archive.
On theory he is brief. He regards gravitational shielding by the Moon as ruled out by existing upper limits, thinks general-relativistic effects too small, and suggests without elaboration that a genuine anomaly would need a theory with preferred-location or preferred-frame effects. That remark points in the general direction of the proposal described at Aether Anisotropy (Allais), though Duif does not endorse it.
His practical advice is that another eclipse run with a single instrument would add little. He asks for several pendulums and gravimeters operated side by side, with seismic activity, ground tilt, pressure, temperature and groundwater level logged together, and for balloon measurements of pressure and temperature near 10 km altitude. For how later campaigns turned out, see Allais Effect Claims vs. Evidence: Positive Reports, Negative Results and the Unpublished NASA Study.
Source notes & attribution
- https://arxiv.org/pdf/gr-qc/0408023