Summary of the TGD based model of Allais effect

The Allais effect (see this and this) was first reported by Maurice Allais in 1954. It involves an abrupt change in the azimuth of a paraconical pendulum's oscillation plane during the solar eclipse, totaling up to 13.5 degrees.

Empirical findings

Consider first a brief summary of the findings of Allais and others.

1. Paraconical pendulum consists of a rigid rod of \sim 1 meter and a metal ball. The bob, that is the weight at the bottom, has lense like shape. Paraconical pendulum differs from the conical pendulum in that the suspension point of the pendulum is not fixed but is a metal sphere able to roll without sliding in plane. Therefore it has 2 degrees of freedom rather than only one: both swinging and rotation around the vertical axis are possible.
2. In the absence of any other forces than the gravitation of Earth) paraconical pendulum can behave much like a conical or Foucault pendulum. The oscillation plane of the paraconical pendulum turned by 13,5 degrees during 14 minutes (see this). It is difficult to see how the gravitational fields of the Sun and Moon could explain this behaviour by changing the effective value of the Earth's gravitational acceleration.
3. Allais concludes from his experimental studies that the orbital plane approach always asymptotically to a limiting plane and the effect is only particularly spectacular during the eclipse. During solar eclipse the limiting plane contains the line connecting Earth, Moon, and Sun. Allais explains this in terms of what he calls the anisotropy of space.

4. Some experiments carried out during eclipse have reproduced the findings of Allais, some experiments not. In the experiment carried out by Jeverdan and collaborators in Romania it was found that the period of oscillation of the pendulum decreases by Δ f/f∼ 5× 10^-4, which happens to correspond to the constant β₀=2^-11 appearing in the formula of the gravitational Planck constant for the Sun. It must be however emphasized that the overall magnitude of Δ f/f varies by five orders of magnitude. Even the sign of Δ f/f varies from experiment to experiment.
5. There is also the finding by Popescu and Olenici, which they interpret as a quantization of the plane of oscillation of paraconical pendulum during solar eclipse (see this).
6. There is also evidence that the effect is present also before and after the full eclipse. The time scale is 1 hour. Allais emphasized that the effect is a dynamic, not static, phenomenon, connected to the variation of weight or inertia in the space swept by the pendulum during the eclipse. The 10 per cent excessive bending of light is reported during some eclipses (the "residual arc").

Anomalies and their brief explanations

Allais effect raises several problems which do not seem to have answers in the Newtonian and Einsteinian frameworks. The key observations are as follows.

1. Allais effect does not seem to involve any modification of classical gravitation in the sense that a modification of the classical gravitational force is not involved. This allows modification of gravitational potential by an addition of constant and in general relativity the addition of constant to the expression of the time component of the space-time metric.
2. The effect seems to be due to a horizontal force. The orbital plane is changed abruptly, which suggests a new kind of force. If is gravitational, it could be a force caused by the scattering of gravitons from the pendulum. The huge value of gravitational Planck constant implying long length scale quantum coherence and possibility of Bose-Einstein condensates together with the independence of the gravitational Compton length of graviton energy could make this effect large.
3. The fluctuations during the transition are large. This suggests quantum criticality. Classical field equations allow warped space-time surfaces, which are gravitational and gauge vacua and have a flat Minkowski metric with a reduced light-velocity c_#= (1-R²ω²)^1/2.

   This leads to the notion of twisted (or warped) Hamilton-Jacobi structure (see this and this) for which canonically embedded M⁴ is tilted toward M⁴× S¹⊂ H: this allows the generalization of warping to the case of general space-time surfaces as solutions of field equations obeying holography = holomorphy principle (see this and this).

   A thin metal plate serves as an excellent analogy and is a critical system. Same is true for the deformations of canonically embedded M⁴. This universal criticality reflecting itself as fluctuations of c_# could be behind very many forms of quantum criticality.

   See the article Allais effect again or the chapter with the same title.

   For a summary of earlier postings see Latest progress in TGD.

   For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

4. Gravitational Planck constant is expected to play a key role in the Allais effect. It is inversely proportional to a velocity parameter β₀. The identification of β₀ has remained a mystery. The identification β₀= c_# is highly suggestive. This implies that one can talk about reflection, and refraction of waves at the boundaries of two regions with different values of β₀.
5. There are also diffractive effects and also these could be understood if gravitational waves or gravitations cause the transversal effects on the pendulum. Gravitational waves are indeed transversal. The gravitational Compton length λ_gr =GM/β₀ is the same for all gravitons and would characterize the diffraction pattern. Irrespective of the energy of the gravitons (or of any particle). There are several alternative identifications of the large mass M and the value of β₀. Empirical findings suggest a wavelength of 44 m and this scale can be understood rather naturally.
6. By a dimensional argument, the force constant of the gravitational pendulum is proportional to c_#<c. The fluctuations of c_#<c could induce the fluctuations of the pendulum's oscillation frequency. A possible quantum phase transition explaining the upper bound for Δ f/f≤ 2^-11∼ m_e/m_p can identified.

In this article, the earlier model for the effect based on the replacement of the oscillator with its quantum counterpart with very large gravitational Planck constant is discussed. For ℏ_gr the oscillator corresponds to a small oscillator quantum number limit, and this can give rise to large quantum fluctuations of the amplitude as transitions which change this quantum number so that the reason would not be classical gravitation but TGD based quantum theory allowing large quantum gravitational effects.

Are reflection, refraction and diffraction of gravitational waves responsible for the Allais effect?

There is evidence that the Allais effect does not involve screening of classical gravitational force. This raises the question whether reflection, refraction and diffraction type effects assignable to gravitational waves or gravitons are involved and explain the transversality of the effect.

Also diffractive effects are involved and conform with the long wavelengths implied by ℏ_gr. A rather promising model relies on quantum diffraction in the "world of classical worlds" (WCW) consisting of space-time surfaces obeying holography = holomorphy principle and having interpretation as Bohr orbits. Monopole flux tubes can be also interpreted as analogs for flowlines of an incompressible hydrodynamic flow past an obstacle. They can be regarded as quantum particles meaning analogy with quantum diffraction for Schrödinger equation.

The velocity parameter of the gravitational Planck constant as reduced light velocity induced by warping

The pondering of this question led as a by-product to a solution of a longstanding problem concerning the interpretation of the velocity parameter β₀ appearing in the Notale's hypothesis. Field equations allow as solutions warped space-time surfaces, which are flat just like Minkowski space but have reduced light velocity c_#= (g_tt)^1/2= (1-R²ω²)^1/2<c. The identification β₀=c_# is natural. This motivates the notion of twisted (or warped) Hamilton-Jacobi structure allowing to generalize this phenomenon to non-vacuum extremals. Warping as a universal quantum critical phenomenon distinguishing between TGD and GRT, makes it possible to identify a mechanism for the fluctuations of the oscillator frequency in the Allais effect.

The warping only shifts the gravitational potential appearing in g_tt=1-2Φ_gr but the classical gravitational force is unaffected. The reduction of the light velocity caused by the warping resembles that appearing for dielectrics and suggests that the shadow of the Moon involves the reduction c→ c_#. The large value of ℏ_gr and c_#<c suggest that the reflection, refraction and also diffraction of dark gravitons from the pendulum could cause the transversal effects in the transition zones.

The shadow of the Moon would be analogous to a dielectric. This would imply reflection and refraction of dark gravitational radiation from the Sun. Reflection at the surface of the Earth would induce transversal gravitational force amplified by the huge value of gravitational Planck constant and by the fact that the gravitational Compton length for gravitons does not depend on the energy of the dark graviton. The pendulum would become an ideal detector of gravitons. The 10 per cent excessive bending of light is reported during some eclipses (the "residual arc") could be interpreted in terms of reflection for dark photons by the same mechanism.

The reason for huge size of the effect: dark gravitational radiation has always the same wavelength

Sun produces gravitational radiation in the energy range (1--10⁵) eV. The huge value of ℏ_gr scales the wavelength range and makes possible long scale quantum coherence at the gravitational magnetic body amplifying the effect.

Gravitational Planck constant for a massless particle with energy E is GME/β₀. By Equivalence Principle, the expression for the wavelength of the graviton is λ=Λ_gr = GM/β₀=r_S/2β₀ irrespective of graviton energy. All dark gravitons, in fact all dark particles, would have the same Compton wavelength! This could explain why the Allais effect is so huge. The gravitational pendulum could become a detector of gravitons.

For the Earth mass M=M_E and for β_0,E ∼ 1 this gives 5 mm. The replacement β_0,E → β_0,S ∼ 2^-11 assigned with the Sun would give λ=10 m to be compared with 44 m suggested by the experiments. β₀= 2^-13 would give a good fit. For M= M_Sun= 3× 10⁵M_E one has λ = λ_gr,S= 3× 10⁶ m ∼ R_E/2, which is solar gravitational Compton length characterizing Sunspot size scale.

Reduction of the oscillator frequency

From the point of view of General Relativity, the maximal value for the reduction r=Δ f/f∼ 2^-11 of the oscillator frequency is huge. The identification of the fluctuations as being due to the fluctuations of β₀=c_# is natural.

There are several intriguing co-incidences. r equals the velocity parameter β₀ appearing in the expression of the solar gravitational Planck constant and is also near to the electron-proton mass ratio m_e/m_p. Also the velocity of the solar system with respect to the galactic center is of this order of magnitude? Which option is nearer to the truth?

Δf/f≤ m_e/mp could be nearest to the correct interpretation for the maximal reduction of frequency. The mechanism could be the phase transition in which Rydberg atoms with very large size at the magnetic body decay to protons and electrons. The condition that ℏ_gr(H)= ℏ_gr(p) guarantees that H atoms and protons can reside in the same monopole flux tubes: this condition holds true in biology also for base pairs of DNA. This would give β₀(H)/β₀(p) = c_#(H)/c_#(p) =m_p/m_H. The values of Δ f/f< m_e/mp could mean that only a part of the H atoms decay to a proton and electron.

The cautious conclusion would be that the Allais effect does not tell so much about classical gravitational physics than about the new quantum ontology predicting the notion of WCW realizing holography = holomorphy vision, the hierarchy of Planck constants, in particular huge values of gravitational Planck constant, and ZEO. The warping phenomenon distinguishing between General Relativity and TGD would be the central element.

See the chapter Allais effect again or the article with the same title.