Allais effect and TGDAllais effect is a fascinating gravitational anomaly associated with solar eclipses. It was discovered originally by M. Allais, a Nobelist in the field of economy, and has been reproduced in several experiments but not as a rule. The experimental arrangement uses so called paraconical pendulum, which differs from the Foucault pendulum in that the oscillation plane of the pendulum can rotate in certain limits so that the motion occurs effectively at the surface of sphere. The "/public_html/articles/ Should the Laws of Gravitation Be Reconsidered: Part I,II,III? of Allais here and here and the summary article The Allais effect and my experiments with the paraconical pendulum 19541960 of Allais give a detailed summary of the experiments performed by Allais. A. Experimental findings of Allais Consider first a brief summary of the findings of Allais.
B. TGD inspired model for Allais effect The basic idea of the TGD based model is that Moon absorbs some fraction of the gravitational momentum flow of Sun and in this manner partially screens the gravitational force of Sun in a disk like region having the size of Moon's cross section. Screening is expected to be strongest in the center of the disk. The predicted upper bound for the change of the oscillation frequency is slightly larger than the observed change which is highly encouraging. 1. Constant external force as the cause of the effect The conclusions of Allais motivate the assumption that quite generally there can be additional constant forces affecting the motion of the paraconical pendulum besides Earth's gravitation. This means the replacement g→ g+Δg of the acceleration g due to Earth's gravitation. Δg can depend on time. The system obeys still the same simple equations of motion as in the initial situation, the only change being that the direction and magnitude of effective Earth's acceleration have changed so that the definition of vertical is modified. If Δ g is not parallel to the oscillation plane in the original situation, a torque is induced and the oscillation plane begins to rotate. This picture requires that the friction in the rotational degree of freedom is considerably stronger than in oscillatory degree of freedom: unfortunately I do not know what the situation is. The behavior of the system in absence of friction can be deduced from the conservation laws of energy and angular momentum in the direction of g+Δ g.
2. What causes the effect in normal situations? The gravitational accelerations caused by Sun and Moon come first in mind as causes of the effect. Equivalence Principle implies that only relative accelerations causing analogs of tidal forces can be in question. In GRT picture these accelerations correspond to a geodesic deviation between the surface of Earth and its center. The general form of the tidal acceleration would thus the difference of gravitational accelerations at these points: Δg= 2GM[(Δ r/r^{3})  3(r•Δ rr/r^{5})]. Here r denotes the relative position of the pendulum with respect to Sun or Moon. Δr denotes the position vector of the pendulum measured with respect to the center of Earth defining the geodesic deviation. The contribution in the direction of Δ r does not affect the direction of the Earth's acceleration and therefore does not contribute to the torque. Second contribution corresponds to an acceleration in the direction of r connecting the pendulum to Moon or Sun. The direction of this vector changes slowly. This would suggest that in the normal situation the tidal effect of Moon causesgradually changing force mΔg creating a torque, which induces a rotation of the oscillation plane. Together with dissipation this leads to a situation in which the orbital plane contains the vector Δg so that no torque is experienced. The limiting oscillation plane should rotate with same period as Moon around Earth. Of course, if effect is due to some other force than gravitational forces of Sun and Earth, paraconic oscillator would provide a manner to make this force visible and quantify its effects. 3. What happens during solar eclipse? During the solar eclipse something exceptional must happen in order to account for the size of effect. The finding of Allais that the limiting oscillation plane contains the line connecting Earth, Moon, and Sun implies that the anomalous acceleration Δ g should be parallel to this line during the solar eclipse. The simplest hypothesis is based on TGD based view about gravitational force as a flow of gravitational momentum in the radial direction.
C. What kind of tidal effects are predicted? If the model applies also in the case of Earth itself, new kind of tidal effects (for normal tidal effects see this) are predicted due to the screening of the gravitational effects of Sun and Moon inside Earth. At the nightside the paraconical pendulum should experience the gravitation of Sun as screened. Same would apply to the "nightside" of Earth with respect to Moon. Consider first the differences of accelerations in the direction of the line connecting Earth to Sun/Moon: these effects are not essential for tidal effects proper. The estimate for the ratio for the orders of magnitudes of the these accelerations is given by Δg_{p}(Sun)/Δg_{p}(Moon)= (M_{S}/M_{M}) (r_{M}/r_{E})^{3}≈ 2.17. The order or magnitude follows from r(Moon)=.0026 AU and M_{M}/M_{S}=3.7× 10^{8}. The effects caused by Sun are two times stronger. These effects are of same order of magnitude and can be compensated by a variation of the pressure gradients of atmosphere and sea water. The tangential accelerations are essential for tidal effects. The above estimate for the ratio of the contributions of Sun and Moon holds true also now and the tidal effects caused by Sun are stronger by a factor of two. Consider now the new tidal effects caused by the screening.
The intuitive expectation is that the screening is maximum when the gravitational momentum flux travels longest path in the Earth's interior. The maximal difference of radial accelerations associated with opposite sides of Earth along the line of sight to Moon/Sun provides a convenient manner to distinguish between Newtonian and TGD based models: Δ g_{p,N}=4GM ×(R_{E}/r)^{3} , Δ g_{p,TGD}= 4GM ×(1/r^{2}). The ratio of the effects predicted by TGD and Newtonian models would be Δ g_{p,TGD}/Δ g_{p,N}= r/R_{E} , r_{M}/R_{E} =60.2 , r_{S}/R_{E}= 2.34× 10^{4}. The amplitude for the oscillatory variation of the pressure gradient caused by Sun would be Δgradp_{S}=v^{2}_{E}/r_{E}≈ 6.1× 10^{4}g and the pressure gradient would be reduced during nighttime. The corresponding amplitude in the case of Moon is given by Δ gradp_{S}/Δgradp_{M}= (M_{S}/M_{M})× (r_{M}/r_{S})^{3}≈ 2.17. Δ gradp_{M} is in a good approximation smaller by a factor of 1/2 and given by Δgradp_{M}=2.8× 10^{4}g. Thus the contributions are of same order of magnitude. One can imagine two simple qualitative killer predictions.
D. An interesting coincidence The measured value of Δ f/f=5× 10^{4} is exactly equal to v_{0}=2^{11}, which appears in the formula hbar_{gr}= GMm/v_{0} for the favored values of the gravitational Planck constant. The predictions are Δ f/f≤ Δ p/p≈ 6× 10^{4}. Powers of 1/v_{0} appear also as favored scalings of Planck constant in the TGD inspired quantum model of biosystems based on dark matter (see this). This coincidence would suggest the quantization formula g_{E}/g_{S}= (M_{S}/M_{E}) × (R_{E}/r_{E})^{2}= v_{0} for the ratio of the gravitational accelerations caused by Earth and Sun on an object at the surface of Earth.
E. Summary of the predicted new effects Let us sum up the basic predictions of the model.
To sum up, the predicted anomalous tidal effects and the explanation of the limiting oscillation plane in terms of stronger dissipation in rotational degree of freedom could kill the model. For details see the chapter The Relationship Between TGD and GRT.
