THE SHEARING HYPOTHESIS AND THE ALLAIS ECLIPSE EFFECT

Thomas J. Goodey

Just Two Data Points

Eclipse of 30 June 1954 Eclipse of 2 October 1959

In the 1950s Professor Maurice Allais undertook several marathon experimental series in Paris which involved repeated determinations of the rate of precession of a paraconical pendulum (which he had invented). He detected various periodic anomalies in the motion of this pendulum by using elaborate statistical analysis. However he also serendipitously observed a quite large scale effect which was absolutely unexpected. During two of these experimental series, solar eclipses partial at Paris occurred on 30 June 1954 and 2 October 1959. In both cases a well-defined anomaly was detected in the motion of the paraconical pendulum: its plane of oscillation shifted abruptly. Currently accepted physical theory offers no explanation whatsoever for this phenomenon. It is the only gross anomaly outstanding in the current scheme of physical knowledge.

Allais later shifted his personal emphasis from the field of physics to economic theory, and in 1988 he was awarded the Nobel prize in economics. However, physics remained his first love. He has always maintained that his unexplained pendulum results – both the periodic anomalies and the Eclipse Effect - were genuine and valid. He attributes them both to theanisotropy of inertial space - the title of his recent book on the subject.In this paper I shall confine myself to discussion of the Allais Eclipse Effect.

Attempts to confirm Allais's observations upon the behavior of a pendulum during a solar eclipse have met with varied results: some trials have confirmed the presence of anomalies, while some yielded ambiguous results, and others detected nothing unusual. However none of these experiments used a paraconical pendulum according to Allais's design; nor did the experimenters follow Allais's operational procedures or ask his advice on design of the experiments. Nor – as I shall show – has there ever been any idea of contriving a geometrico-astronomical layout, similar to the layout during the crucial observations of 30 June 1954 and 2 October 1959.

I believe that not enough consideration has been given to the fundamentals: what sort of unusual happening can be hypothesized to have actually taken place during the two eclipses in question? Such considerations suggest important new avenues for exploration. It might well be the case that the Allais Eclipse Effect does not manifest itself at every location during a solar eclipse, or indeed during every solar eclipse; various types of special condition (upon the geometry of the eclipse and upon the position of the observer, for example) might be prerequisites. Such conditions presumably also regulate the intensity of the Effect, and perhaps also determine others of its parameters. By investigating such dependencies we may be able to get a handle on this apparently incomprehensible phenomenon.

The effect Allais observed during the 1954 eclipse was very marked – it has even been described as "brutal". However during the 1959 eclipse the effect was manifested to a much lesser degree. So we have two data points to reason from. The only previous attempt at analysis of the geometry of these eclipses has been Allais's comment that "in 1959 the amount of the solar surface eclipsed (at Paris) was only 36.8% of the surface eclipsed in 1954". It is obviously desirable to go into more detail.

Here are magnified views (taken from Fred Espenak's superb website) of the most relevant portions of the eclipse tracks in 1954 and 1959. The green crosses show Paris, while the stars show the eclipse points at the moment of greatest eclipse and thecorresponding sub-solar points (for definitions, see later), and the arrows show the directions in which those points were moving, relative to the Earth's surface.

30 June 19542 October 1959
gamma=0.61gamma=0.42
G.E.: 60°28' N, 04°10' EG.E.: 20°25' N, 01°26' W
S.S.: 23°12' N, 8°02' WS.S.: 03°24' S, 06°36' W

(Paris is at 48°48' N, 2°20' E.)

(gamma is the minimum distance of the Sun-Moon linefrom the Earth-Moon line
during an eclipse (either solar or lunar)measured in units of Earth radii.)

In factin 1954 the distance between Paris, the experimental location, and the point of greatest eclipse was 1300km, while in 1959 it was 3180km. Moreover, in 1954 the closest the umbral path came to Paris was about the same, 1300km; in other words, the eclipse was maximum at Paris at about the worldwide moment of greatest eclipse. But in 1959 the path of totality came closest to Paris substantially before the moment of greatest eclipse - roughly half an hour before - at a distance of 2790km.Anyway basically Paris was much further from the action in 1959 than in 1954, so a prioriit's no wonder that the eclipse effect was weaker.

But there is another very important difference between the situations in 1954 and 1959:IMHO, not sufficient attention has been paid to the sub-solar point, which is the intersection of the Sun-Earth line with the surface of the Earth. It might well be the case that gravitational effects along this Sun-Earth line interact in combination with gravitational effects along the Sun-Moon line to result in the Allais effect. In 1954 the observer at Paris was positioned between the path of totality (the path of the eclipse point) and the path of the sub-solar point, whereas in 1959 the path of the eclipsepoint passed between the observer at Paris and the path of the sub-solar point. Nowin general, during a total solar eclipse,with respect to the Earth's surface,the eclipsepoint moves eastwards along its path at about 1/2 km/sec while the sub-solar point moves westwardsalong its parallel of latitude at about the same speed(however, the exact speeds vary for each individual case).Thus, if one visualizes the Earth-Sun line as one blade of a scissors and the Moon-Sun line as the other blade, these linesmovetowards, transversely past, and away from one another at a relative speed of about 1km/sec while remaining substantially parallel with one another, rather as scissor blades shear past one another. In 1954 the observer (Allais in Paris) was between these two notional scissor blades around the time of their closest mutual approach, whereas in 1959 he was not.I surmise that this may be the reason why the Eclipse Effect was so much greater in 1954.

The Shearing Hypothesis

Therefore I have formulated the "ShearingHypothesis". This postulates that the Eclipse Effect is somehow due to the Sun-Moon line and the Sun-Earth line momentarily getting close to one another as they shear past one another at the relative speed of about 1km/sec, and that the Eclipse Effect occurs primarily in the region between these lines at the time of their closestmutual approach.

There is a often-deployedcounter-argument against the existence of the AllaisEclipse Effect as follows: If such an effect really existed, and if it appeared close to the Sun-Moon axisat all times, then it would be manifested during the normal course of planetary motion, thus stultifying conventional orbital dynamics. It would also exert an effectupon the orbital movements of satellites. Now, the orbits of the GPS satellites (in particular) are never disturbed in this way; so such an eclipse effect can't exist.

But if the ShearingHypothesis is valid, this counter-argument loses its force. To repeatthisHypothesis,it postulates that the disturbance of pendulum motions, and presumably of other dynamic gravito-inertial processes, is a very transient effect which only occurs in the spatial volume generally between the Sun-Moon line and the Sun-Earth line as they shear past one another at the high relative speed of about 1 km/sec. It only occurs over the period of an hour or so in a restricted cylindrical space whose cross section extends a few thousand kilometers (although its longitudinal dimension is likely very great). It would be reasonable that no significant effect would be exerted upon the orbits of satellites or planetary bodies by such a short-lived effect; it would be unlikely for an orbiting body ever to run into the effect, and certainly the resulting force could never be accumulated in the unique way that a pendulum accumulates small forces over periods of hours.

According to this ShearingHypothesis, therefore, for each solar eclipse, the area where it would be best to locate an experiment for observing the Allais Eclipse Effect is quite restricted: the ideal position (on the Earth's surface) is somewhere on or near the middle portion of the line joining the point of greatest eclipse to the corresponding sub-solar point. Andduring the 1954 eclipse Paris was -quite fortuitously–a very suitable place for observation according to this criterion. Howeverin the 1959 eclipse Pariswas far from being so suitable, so that the effect was less outstanding. Actually the gamma in 1954 was not particularly low (0.61), but nevertheless a remarkably pronounced Eclipse Effect was observed.

Moreover, a matter which has never been considered is the question of the anti-solar-eclipse. If the Shearing Hypothesis is valid, the Allais Effect may well extend right through the Earth to the other (night) side, along the prolongation of the Sun-Moon line. This should be tested – presumably when the eclipse itself is inaccessible, so that a direct experiment for the eclipse itself in the location specified above is in any case difficult or impossible.

Finally, suppose that the portion of the Sun-Moon line which intersects the Earth's surface is its portion between the Moon and the Sun (rather than its portion on the side of the Moon remote from the Sun). In this case a lunar eclipseoccurs. Perhaps the Allais Effect will be manifested near the points of intersection in these cases as well.

Nomenclature

We will consider three straight lines, each of which passes through the centers of two astronomical bodies: the Sun-Moon line ("SML"); the Sun-Earth line ("SEL"); and the Moon-Earth line ("MEL"). At any moment, the point upon the Earth's surface at which the Sun is at the zenith, i.e. one of the points of intersection of the SEL with the Earth's surface, is termed the "Sub-Solar" (abbreviated as "SS"); and the other such point of intersection, at which the Sun is at the nadir, is herein termed the "Anti-Sub-Solar" (abbreviated as "ASS). Here is an illustrative figure:

Similarly the point upon the Earth's surface where the Moon is at the zenith, i.e. one of the points of intersection of the MEL with the Earth's surface, is herein termed the "Sub-Lunar" (abbreviated as "SL"); and the other such point of intersection, where the Moon is at the nadir, is herein termed the "Anti-Sub-Lunar" (abbreviated as "ASL").

On SolarEclipses

An observer located upon the sunlit side of the Earth experiences a total solar eclipse, when (referred to the Sun as stationary) the motions of the Earth and the Moon conspire to bring the Moon momentarily directly in front of the Sun from the point of view of the observer on the Earth's surface, so that the center of the Sun, the center of the Moon, and the observer are momentarily collinear in that order. (This configuration can be abbreviated as CS-CM-O along the SML.)

In other words, the SML is intersecting the surface of the Earth, which is unusual, and the observer is positioned at that one of the intersection points which faces towards the Sun. This point is termed the Eclipse Point ("EP") at that instant; and the other of the intersection points is herein termed the Anti-Eclipse Point ("AEP"). And, at the moment that the SML passes closest to the center of the Earth (so that the distance between them is equal to gamma, and the eclipse is the greatest), the current positions of these points EP and AEP along their tracks upon the Earth's surface are herein termed the points of Greatest Eclipse and Anti-Greatest-Eclipse — GE and AGE.

By the way, during a solar eclipse it is virtually never the case, that the center of the Earth also lies upon the SML; that would require the total eclipse to occur at the observer's local noon, and simultaneously his latitude to be equal to the Sun's current declination. In other words, we can almost forget about the theoretical possibility of all the three celestial bodies being arranged in a straight line; this is illustrated here:

Such circumstances hardly ever come to pass.

However, they will almost come to pass during the eclipse of 22 July 2009, when the center of the Earth comes within less than 450km of the Sun-Moon line. This matter, which is of historic importance, is discussed later.

Digression: it is an odd fact that the angular diameters of the Sun and the Moon, as seen from the surface of the Earth, are almost the same, so that, depending upon the exact distance between the Moon and the Earth at the time of the eclipse (the Moon's orbit around the Earth is not perfectly circular), either the Moon may actually cover the Sun (the eclipse is total), or a ring at the extreme edge of the Sun may remain uncovered (the eclipse is annular). We will assume that this coincidence of angular diameters is just that: a strange coincidence. Any other hypothesis leads us into wild realms of thought which can scarcely be said to be scientific according to any currently imaginable paradigm.

On Lunar Eclipses

In the complementary case that the SML intersects the surface of the Earth, but with the Moon on the opposite side of the Earth from the Sun, then the Moon will be located within the Earth's penumbra at least, if not its umbra, so that a lunar eclipse is taking place. In this case, an observer can see the eclipsed Moon provided that he is positioned anywhere upon the dark side of the Earth. (In this respect, lunar eclipses are quite different from solar eclipses, during which a good view of the eclipse is only available from a very restricted set of locations.)

But if the observer is positioned anywhere upon the sunlit side of the Earth, then he is unable to see the eclipsed Moon:

This may be termed an "anti-lunar-eclipse" situation.

In analogy to the nomenclature for a solar eclipse, that one of the two points at which the SML intersects the Earth's surface during a lunar eclipse, from which the eclipse (the Moon) is visible, will hereinbe termed the Eclipse Point ("EP") [although it has no intrinsic right to this designation]; and the other one of the intersection points (from which the Sun is visible) will herein be termed the Anti-Eclipse Point ("AEP"). And, as before, at the moment that the SML passes closest to the center of the Earth (so that the eclipse is greatest), the current positions of these points EP and AEP upon their tracks will be termed the points of Greatest Eclipse and Anti-Greatest-Eclipse — abbreviated as"GE" and "AGE" [these terms are actually only meaningful in terms of the solar eclipse analogy].

(During a lunar eclipse, no particularlyoutstanding phenomenon is apparentto an observer upon the track of the eclipse point EP, or at the point GE; the eclipse looks much the same from any point. This is quite different from the case of a solar eclipse.)

-o0o-

The remainder of this paper is an attempt to analyze upcoming solar and lunar eclipses over the next few years from the point of view of the Allais Eclipse Effect, and to develop recommendations forexperimental disposition in each case. It should be noted that these recommendationscan never actually lead the experimenter seriously astray, even if the Shearing Hypothesis is fundamentally incorrect. This is because, for each eclipse, the area recommended for experiments will naturally fallquite near to the path of the eclipse point EP, as was the case for the 1954 eclipse in which a pronounced Eclipse Effect was actually observed. However, thebasic recommendationof the Shearing Hypothesis is not to position the experimental pendulum(s)actually in the EP track, but rather to the side of ittowards the sub-solar point.However I consider that, in a suitable case where observations can be freely set up in any desired position, (i.e. where the EPtrackcrosses land), as a cross-check, it would be advisablealso to establish an independentpendulum observation directly upon the EP track.

Relevant solar eclipses

It seems fairly obvious thatthe smaller is the gamma of a solar (or a lunar)eclipse, the stronger will the associated Eclipse Effectbe. Accordingly there is no real imperative to take partial eclipses (where gamma1) into account. However it is considered a matter of course that total, annular and hybrid solar eclipses are all on a par as far as the Eclipse Effect is concerned. (These are collectively termed 'central eclipses').

The following central solar eclipses should be considered:8 April 2005; 3 October 2005; 29 March 2006; 22 September 2006; 7 February 2008; 1 August 2008; 26 January 2009; 22 July 2009; 15 January 2010; 11 July 2010; 20 May 2012; 13 November 2012; 10 May 2013; and 3 November 2013.(No central solar eclipses occur in 2004, 2007, and 2011.)