# TGD and Fringe Physics

Note: Newest contributions are at the top!

 Year 2007

### Fractional Quantum Hall effect in TGD framework

The generalization of the imbedding space discussed in previous posting allows to understand fractional quantum Hall effect (see this and this).

The formula for the quantized Hall conductance is given by

σ= ν× e2/h,ν=m/n.

Series of fractions in ν=1/3, 2/5 3/7, 4/9, 5/11, 6/13, 7/15..., 2/3, 3/5, 4/7 5/9, 6/11, 7/13..., 5/3, 8/5, 11/7, 14/9... 4/3 7/5, 10/7, 13/9... , 1/5, 2/9, 3/13..., 2/7 3/11..., 1/7.... with odd denominator have bee observed as are also ν=1/2 and ν=5/2 state with even denominator.

The model of Laughlin [Laughlin] cannot explain all aspects of FQHE. The best existing model proposed originally by Jain [Jain] is based on composite fermions resulting as bound states of electron and even number of magnetic flux quanta. Electrons remain integer charged but due to the effective magnetic field electrons appear to have fractional charges. Composite fermion picture predicts all the observed fractions and also their relative intensities and the order in which they appear as the quality of sample improves.

I have considered earlier a possible TGD based model of FQHE not involving hierarchy of Planck constants. The generalization of the notion of imbedding space suggests the interpretation of these states in terms of fractionized charge and electron number.

1. The easiest manner to understand the observed fractions is by assuming that both M4 an CP2 correspond to covering spaces so that both spin and electric charge and fermion number are quantized. With this assumption the expression for the Planck constant becomes hbar/hbar0 =nb/na and charge and spin units are equal to 1/nb and 1/na respectively. This gives ν =nna/nb2. The values n=2,3,5,7,.. are observed. Planck constant can have arbitrarily large values. There are general arguments stating that also spin is fractionized in FQHE and for na=knb required by the observed values of ν charge fractionization occurs in units of k/nb and forces also spin fractionization. For factor space option in M4 degrees of freedom one would have ν= n/nanb2.

2. The appearance of nb=2 would suggest that also Z2 appears as the homotopy group of the covering space: filling fraction 1/2 corresponds in the composite fermion model and also experimentally to the limit of zero magnetic fiel [Jain]. Also ν=5/2 has been observed.

3. A possible problematic aspect of the TGD based model is the experimental absence of even values of nb except nb=2. A possible explanation is that by some symmetry condition possibly related to fermionic statistics kn/nb must reduce to a rational with an odd denominator for nb>2. In other words, one has k propto 2r, where 2r the largest power of 2 divisor of nb smaller than nb.

4. Large values of nb emerge as B increases. This can be understood from flux quantization. One has eBS= nhbar= n(nb/na)hbar0. The interpretation is that each of the nb sheets contributes n/na units to the flux. As nb increases also the flux increases for a fixed value of na and area S: note that magnetic field strength remains more or less constant so that kind of saturation effect for magnetic field strength would be in question. For na=knb one obtains eBS/hbar0= n/k so that a fractionization of magnetic flux results and each sheet contributes 1/knb units to the flux. ν=1/2 correspond to k=1,nb=2 and to a non-vanishing magnetic flux unlike in the case of composite fermion model.

5. The understanding of the thermal stability is not trivial. The original FQHE was observed in 80 mK temperature corresponding roughly to a thermal energy of T≈ 10-5 eV. For graphene the effect is observed at room temperature. Cyclotron energy for electron is (from fe= 6× 105 Hz at B=.2 Gauss) of order thermal energy at room temperature in a magnetic field varying in the range 1-10 Tesla. This raises the question why the original FQHE requires so low a temperature? The magnetic energy of a flux tube of length L is by flux quantization roughly e2B2S≈ Ec(e)meL(hbar0=c=1) and exceeds cyclotron energy roughly by factor L/Le, Le electron Compton length so that thermal stability of magnetic flux quanta is not the explanation.

A possible explanation is that since FQHE involves several values of Planck constant, it is quantum critical phenomenon and is characterized by a critical temperature. The differences of the energies associated with the phase with ordinary Planck constant and phases with different Planck constant would characterize the transition temperature. Saturation of magnetic field strength would be energetically favored.

References

[Laughlin] R. B. Laughlin (1983), Phys. Rev. Lett. 50, 1395.
[Jain] J. K. Jain (1989), Phys. Rev. Lett. 63, 199.

For more details see the chapter The Notion of Free Energy and Many-Sheeted Space-Time Concept.

### TGD based vision about new energy technology

The book "TGD and Fringe Physics" contains TGD based models for various anomalies, in particular those claimed by "free energy" community. The earlier chapter The Notion of Free Energy and Many-Sheeted Space-Time Concept gave birth to a new chapter with the title Strange Effects Related to Rotating Magnetic Systems. The new version for "The Notion..." contains besides the models for some "free energy" anomalies fresh material representing an overall view about new energy technologies provided by the TGD based ontology and a discussion of some rather recent evidence for it. Below a short summary about this vision.

The vision about new energy technology has close connections to the basic mechanisms of energy metabolism in living matter in TGD Universe and one cannot avoid even reference to TGD inspired quantum theory of consciousness. The point is that so called time mirror mechanism defines a mechanism of remote metabolism as sucking of energy from remote energy storage, a mechanism of memory as communications with geometric past, and mechanism of intentional action initiating neural activity in geometric past. At the level of technology time mirror mechanism would define a mechanism of energy transfer, communication, and remote quantum control.

1. The new ontology

The ontology of TGD Universe involves several new elements. The notion of many-sheeted space-time means that each physical system corresponds to a space-time sheet, its own sub-universe in geometric sense, and glued to a larger space-time sheet and containing subsystems as smaller space-time sheets glued to it. Many-sheeted space-time leads to the notion of field body distinguishing between TGD and Maxwell's electrodynamics. One can assign to each physical system a field body (or magnetic body) and in case of living matter it acts as intentional agent using biological body as a sensory receptor and motor instrument.

Zero energy ontology states that any physical system has a vanishing net energy so that everything is creatable from vacuum. Zero energy states decompose into positive and negative energy parts. The possibility of negative energy signals is one important implication and a considerable modification of thermodynamics is forced by the fact that different signs of energy correspond to different arrows of geometric time.

Negative energy signals propagating to the geometric past inspire a new vision about communications, energy technology, and remote control. The implications are especially important for the understanding of living matter where both time directions manifest themselves. In neuroscience a radically new view about memory based on the notion of 4-D brain emerges.

The hierarchy of Planck constants implies a generalization of the notions of imbedding space and space-time and macroscopic quantum coherence in all length and time scales at high enough levels of dark matter hierarchy assigned to the hierarchy of Planck constant. The consequences of this hypothesis are powerful: entire cosmos should be in a well-defined sense a living system with dark matter representing higher level conscious entities.

The original motivation for the p-adic physics were the highly successful calculations of elementary particle masses based on p-adic thermodynamics and conformal invariance. The only sensible interpretation of p-adic physics seems to be as physics of cognition and intentionality meaning that cognition is present even at elementary particle level. This implies a profound generalization of space-time concept implying that cognition and intentionality are literally cosmic phenomena but having experimentally measurable correlates in real physics.

2. The new view about energy

The basic idea is that quantum biology could teach us a lot about energy technology. The necessity to carry fuel is one of the drawback of standard energy technologies. Remote metabolism based on sucking of energy by sending negative energy signals to energy storage analogous to a population inverted laser defines what might be called quantum credit card. This is the basic metabolic mechanism of TGD inspired quantum biology. The mechanism could make sense also as an energy technology.

In biological systems the fuel serves as an energy storage and is recycled. Animal cells burn the fuel and plant cells reconstruct it using sunlight as an energy source. Similar recycling of the fuel could make it un-necessary to carry large amounts of fuel. The systems doing the recycling could be seen as primitive life forms and plasmoids are an excellent candidate in this respect. Fuel could be practically any quantum system with two or more states with different energies.

Large Planck constant phases would make it possible to communicate short wave length photons over long distances: say photons with energy of visible photon but having wavelength of EEG photon. This might help to achieve a lossless energy transfer. Topological light rays ("massless extremals") would be in a key role in making possible precisely targeted, dispersion-free and lossless energy and information transfer. They are ideal also for quantum control.

3. Evidence for new ontology

There are surprisingly many well established anomalies supporting the new ontology and these anomalies have been a strong guiding line in attempts to construct a general theoretical framework.

1. There is a considerable support for the notion many-sheeted space-time quantified in terms of p-adic length scale hypothesis. One example is the radiation from interstellar dust having no generally accepted interpretation in terms of molecular transitions. The interpretation in terms of metabolic energy quanta liberated in dropping of electrons or protons to larger space-time sheets makes sense quantitatively.

2. The Bohr quantization of radii of planetary orbits and quantal effects of ELF em fields on vertebrate brain helped considerably to develop the ideas about the hierarchy of Planck constants. Later a lot of further anomalies have emerged supporting the quantization of Planck constant.

3. Living matter is a gigantic bundle of anomalies from the point of view of recent day physics and the notion of field body combined with p-adic length scale hypothesis allows to develop detailed models for how magnetic body controls biological body and receives sensory input from it. The notion of field body leads also to a concrete model for pre-biotic life based on the notion of plasmoid involving magnetic body controlling plasma phase. Recently a considerable empirical support for this notion has emerged.

For details see the chapter The Notion of Free Energy and Many-Sheeted Space-Time Concept .

### Allais effect as evidence for large values of gravitational Planck constant?

I have considered two models for Allais effect. The first model was constructed for several years ago and was based on classical Z0 force. For a couple of weeks ago I considered a model based on gravitational screening. It however turned that this model does not work. The next step was the realization that the effect might be a genuine quantum effect made possible by the gigantic value of the gravitational Planck constant: the pendulum would act as a highly sensitive gravitational interferometer.

One can represent rather general counter arguments against the models based on Z0 conductivity and gravitational screening if one takes seriously the puzzling experimental findings concerning frequency change.

1. Allais effect identified as a rotation of oscillation plane seems to be established and seems to be present always and can be understood in terms of torque implying limiting oscillation plane.

2. During solar eclipses Allais effect however becomes much stronger. According to Olenici's experimental work the effect appears always when massive objects form collinear structures.

3. The behavior of the change of oscillation frequency seems puzzling. The sign of the the frequency increment varies from experiment to experiment and its magnitude varies within five orders of magnitude.

1. What one an conclude about general pattern for Δf/f?

The above findings allow to make some important conclusions about the nature of Allais effect.

1. Some genuinely new dynamical effect should take place when the objects are collinear. If gravitational screening would cause the effect the frequency would always grow but this is not the case.

2. If stellar objects and also ring like dark matter structures possibly assignable to their orbits are Z0 conductors, one obtains screening effect by polarization and for the ring like structure the resulting effectively 2-D dipole field behaves as 1/\rho2 so that there are hopes of obtaining large screening effects and if the Z0 charge of pendulum is allow to have both signs, one might hope of being to able to explain the effect. It is however difficult to understand why this effect should become so strong in the collinear case.

3. The apparent randomness of the frequency change suggests that interference effect made possible by the gigantic value of gravitational Planck constant is in question. On the other hand, the dependence of Δg/g on pendulum suggests a breaking of Equivalence Principle. It however turns out that the variation of the distances of the pendulum to Sun and Moon can explain the experimental findings since the pendulum turns out to act as a sensitive gravitational interferometer. An apparent breaking of Equivalence Principle could result if the effect is partially caused by genuine gauge forces, say dark classical Z0 force, which can have arbitrarily long range in TGD Universe.

4. If topological light rays (MEs) provide a microscopic description for gravitation and other gauge interactions one can envision these interactions in terms of MEs extending from Sun/Moon radially to pendulum system. What comes in mind that in a collinear configuration the signals along S-P MEs and M-P MEs superpose linearly so that amplitudes are summed and interference terms give rise to an anomalous effect with a very sensitive dependence on the difference of S-P and M-P distances and possible other parameters of the problem. One can imagine several detailed variants of the mechanism. It is possible that signal from Sun combines with a signal from Earth and propagates along Moon-Earth ME or that the interferences of these signals occurs at Earth and pendulum.

5. Interference suggests macroscopic quantum effect in astrophysical length scales and thus gravitational Planck constants given by hbargr= GMm/v0, where v0=2-11 is the favored value, should appear in the model. Since hbargr= GMm/v0 depends on both masses this could give also a sensitive dependence on mass of the pendulum. One expects that the anomalous force is proportional to hbargr and is therefore gigantic as compared to the effect predicted for the ordinary value of Planck constant.

2. Model for interaction via gravitational MEs with large Planck constant

Restricting the consideration for simplicity only gravitational MEs, a concrete model for the situation would be as follows.

1. The picture based on topological light rays suggests that the gravitational force between two objects M and m has the following expression

FM,m=GMm/r2= ∫|S(λ,r)|2 p(λ)dλ

p(λ)=hgr(M,m)2π/λ , hbargr= GMm/v0(M,m) .

p(λ) denotes the momentum of the gravitational wave propagating along ME. v0 can depend on (M,m) pair. The interpretation is that |S(λ,r)|2 gives the rate for the emission of gravitational waves propagating along ME connecting the masses, having wave length λ, and being absorbed by m at distance r.

2. Assume that S(λ,r) has the decomposition

S(λ,r)= R(λ)exp[iΦ(λ)]exp[ik(λ)r]/r,

exp[ik(λ)r]=exp[ip(λ)r/hbargr(M,m)],

R(λ)= |S(λ,r)|.

To simply the treatment the phases exp(iΦ(λ)) are assumed to be equal to unity in the sequel. This assumption turns out to be consistent with the experimental findings. Also the assumption v0(M,P)/v0(S,P) will be made for simplicity: these conditions guarantee Equivalence Principle. The substitution of this expression to the above formula gives the condition

∫ |R(λ)|2dλ/λ =v0 .

Consider now a model for the Allais effect based on this picture.

1. In the non-collinear case one obtains just the standard Newtonian prediction for the net forces caused by Sun and Moon on the pendulum since ZS,P and ZM,P correspond to non-parallel MEs and there is no interference.

2. In the collinear case the interference takes place. If interference occurs for identical momenta, the interfering wavelengths are related by the condition

p(λS,P)=p(λM,P) .

This gives

λM,PS,P= hbarM,P/hbarS,P =MM/MS .

3. The net gravitational force is given by

Fgr= ∫ |Z(λ,rS,P)+ Z(λ/x,rM)|2 p(λ) dλ

=Fgr(S,P)+ Fgr(M,P) + ΔFgr ,

ΔFgr= 2∫ Re[S(λ,rS,P)S*(λ/x,rM,P))] (hbargr(S,P)2π/λ)dλ,

x=hbarS,P/hbarM,P= MS/MM.

Here rM,P is the distance between Moon and pendulum. The anomalous term Δ Fgr would be responsible for the Allais effect and change of the frequency of the oscillator.

4. The anomalous gravitational acceleration can be written explicitly as

Δagr= (2GMS/rSrM)×(1/v0(S,P))× I ,

I= ∫ R(λ)×R(λ/x)× cos[2π(ySrS-xyMrM)/λ] dλ/λ ,

yM= rM,P/rM , yS=rS,P/rS.

Here the parameter yM (yS) is used express the distance rM,P (rS,P) between pendulum and Moon (Sun) in terms of the semi-major axis rM (rS)) of Moon's (Earth's) orbit. The interference term is sensitive to the ratio 2π(ySrS-xyMrM)/λ. For short wave lengths the integral is expected to not give a considerable contribution so that the main contribution should come from long wave lengths. The gigantic value of gravitational Planck constant and its dependence on the masses implies that the anomalous force has correct form and can also be large enough.

5. If one poses no boundary conditions on MEs the full continuum of wavelengths is allowed. For very long wave lengths the sign of the cosine terms oscillates so that the value of the integral is very sensitive to the values of various parameters appearing in it. This could explain random looking outcome of experiments measuring Δf/f. One can also consider the possibility that MEs satisfy periodic boundary conditions so that only wave lengths λn= 2rS/n are allowed: this implies sin(2π ySrS/λ)=0. Assuming this, one can write the magnitude of the anomalous gravitational acceleration as

Δagr= (2GMS/rS,PrM,P)×(1/v0(S,P)) × I ,

I=∑n=1 R(2rS,P/n)×R(2rS,P/nx)× (-1)n × cos[nπx×(yM/yS)×(rM/rS)].

If R(λ) decreases as λk, k>0, at short wavelengths, the dominating contribution corresponds to the lowest harmonics. In all terms except cosine terms one can approximate rS,P resp. rM,P with rS resp. rM.

6. The presence of the alternating sum gives hopes for explaining the strong dependence of the anomaly term on the experimental arrangement. The reason is that the value of xyrM/rS appearing in the argument of cosine is rather large:

x(yM/yS))rM/rS)= (yM/yS) (MS/MM)(rM/rS)(v0(M,P)/v0(S,P)) ≈ 6.95671837× 104× (yM/yS).

The values of cosine terms are very sensitive to the exact value of the factor MSrM/MMrS and the above expression is probably not quite accurate value. As a consequence, the values and signs of the cosine terms are very sensitive to the value of yM/yS.

The value of yM/yS varies from experiment to experiment and this alone could explain the high variability of Δf/f. The experimental arrangement would act like interferometer measuring the distance ratio rM,P/rS,P.

3. Scaling law

The assumption of the scaling law

R(λ)=R0 (λ/λ0)k

is very natural in light of conformal invariance and masslessness of gravitons and allows to make the model more explicit. With the choice λ0=rS the anomaly term can be expressed in the form

Δ agr≈ (GMS/rSrM) × (22k+1/v0)×(MM/MS)k × R0(S,P)× R0(M,P)× ∑n=1 ((-1)n/n2k)× cos[nπK] ,

K= x× (rM/rS)× (yM/yS).

The normalization condition reads in this case as

R02=v0/[2π∑n (1/n)2k+1]=v0/πζ(2k+1) .

Note the shorthand v0(S/M,P)= v0. The anomalous gravitational acceleration is given by

Δagr=(GMS/rS2) × X Y× ∑n=1 [(-1)n/n2k]×cos[nπK] ,

X= 22k × (rS/rM)× (MM/MS)k ,

Y=1/π∑n (1/n)2k+1=1/πζ(2k+1).

It is clear that a reasonable order of magnitude for the effect can be obtained if k is small enough and that this is essentially due to the gigantic value of gravitational Planck constant.

The simplest model consistent with experimental findings assumes v0(M,P)= v0(S,P) and Φ(n)=0 and gives

Δagr/gcos(Θ)=(GMS/rS2g)× X Y× ∑n=1 [(-1)n/n2k]×cos(nπ K) ,

X= 22k × (rS/rM)× (MM/MS)k,

Y=1/π ∑n (1/n)2k+1 =1/πζ(2k+1) ,

K=x× (rM/rS)× (yM/yS) , x=MS/MM .

Θ denotes in the formula above the angle between the direction of Sun and horizontal plane.

4. Numerical estimates

To get a numerical grasp to the situation one can use MS/MM≈ 2.71× 107, rS/rM≈ 389.1, and (MSrM/MMrS)≈ 1.74× 104. The overall order of magnitude of the effect would be

Δ g/g≈ XY× GMS/RS2gcos(Θ) ,

(GMS/RS2g) ≈6× 10-4 .

The overall magnitude of the effect is determined by the factor XY.

For k=1 and 1/2 the effect is too small. For k=1/4 the expression for Δ agr reads as

(Δagr/gcos(Θ))≈1.97× 10-4n=1 ((-1)n/n1/2)×cos(nπK),

K= (yM/yS)u , u=(MS/MM)(rM/rS)≈ 6.95671837× 104 .

The sensitivity of cosine terms to the precise value of yM/yS gives good hopes of explaining the strong variation of Δf/f and also the findings of Jeverdan. Numerical experimentation indeed shows that the sign of cosine sum alternates and its value increases as yM/yS increases in the range [1,2].

The eccentricities of the orbits of Moon resp. Earth are eM=.0549 resp. eE=.017. Denoting semimajor and semiminor axes by a and b one has Δ=(a-b)/a=1-(1-e2)1/2. ΔM=15× 10-4 resp. ΔE=1.4× 10-4 characterizes the variation of yM resp. yM due to the non-circularity of the orbits of Moon resp. Earth. The ratio RE/rM= .0166 characterizes the range of the variation ΔyM =ΔrM,P/rM< RE/rM due to the variation of the position of the laboratory. All these numbers are large enough to imply large variation of the argument of cosine term even for n=1 and the variation due to the position at the surface of Earth is especially large.

For details see the chapter The Anomalies Related to the Classical Z0 Force and Gravitation.

### Allais effect and TGD

Allais 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 "../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 1954-1960 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.

1. In the ideal situation (that is in the absence of any other forces than gravitation of Earth) paraconic pendulum should behave like a Foucault pendulum. The oscillation plane of the paraconic pendulum however begins to rotate.

2. 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.

3. 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 changes by Δ f/f≈ 5× 10-4, which happens to correspond to the constant v0=2-11 appearing in the formula of the gravitational Planck constant.

4. There is also quite recent finding by Popescu and Olenici which they interpret as a quantization of the plane of oscillation of paraconic oscillator during solar eclipse (see this).

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 ggg 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 gg.

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/r3) - 3(r•Δ rr/r5)].

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 causes gradually 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.

1. For stationary states the field equations of TGD for vacuum extremals state that the gravitational momentum flow of this momentum. Newton's equations suggest that planets and moon absorb a fraction of gravitational momentum flow meeting them. The view that gravitation is mediated by gravitons which correspond to enormous values of gravitational Planck constant in turn supports Feynman diagrammatic view in which description as momentum exchange makes sense and is consistent with the idea about absorption. If Moon absorbs part of this momentum, the region of Earth screened by Moon receives reduced amount of gravitational momentum and the gravitational force of Sun on pendulum is reduced in the shadow.

2. Unless the Moon as a coherent whole acts as the absorber of gravitational four momentum, one expects that the screening depends on the distance travelled by the gravitational flux inside Moon. Hence the effect should be strongest in the center of the shadow and weaken as one approaches its boundaries.

3. The opening angle for the shadow cone is given in a good approximation by Δ Θ= RM/RE. Since the distances of Moon and Earth from Sun differ so little, the size of the screened region has same size as Moon. This corresponds roughly to a disk with radius .27× RE.

The corresponding area is 7.3 per cent of total transverse area of Earth. If total absorption occurs in the entire area the total radial gravitational momentum received by Earth is in good approximation 93.7 per cent of normal during the eclipse and the natural question is whether this effective repulsive radial force increases the orbital radius of Earth during the eclipse.

More precisely, the deviation of the total amount of gravitational momentum absorbed during solar eclipse from its standard value is an integral of the flux of momentum over time:

Δ Pkgr = ∫ Δ(Pkgr/dt) (S(t))dt,

(ΔPkgr/dt)(S(t))= ∫S(t) Jkgr(t)dS.

This prediction could kill the model in classical form at least. If one takes seriously the quantum model for astrophysical systems predicting that planetary orbits correspond to Bohr orbits with gravitational Planck constant equal to GMm/v0, v0=2-11, there should be not effect on the orbital radius. The anomalous radial gravitational four-momentum could go to some other degrees of freedom at the surface of Earth.

4. The rotation of the oscillation plane is largest if the plane of oscillation in the initial situation is as orthogonal as possible to the line connecting Moon, Earth and Sun. The effect vanishes when this line is in the the initial plane of oscillation. This testable prediction might explain why some experiments have failed to reproduce the effect.

5. The change of |g| to |gg| induces a change of oscillation frequency given by

Δf/f=g• Δ g/g2 = (Δ g/g) cos(Θ).

If the gravitational force of the Sun is screened, one has |gg| >g and the oscillation frequency should increase. The upper bound for the effect is obtained from the gravitational acceleration of Sun at the surface of Earth given by v2E/rE≈ 6.0× 10-4g. One has

|Δ f|/f≤ Δ g/g = v2E/rE ≈ 6.0× 10-4.

The fact that the increase(!) of the frequency observed by Jeverdan and collaborators is Δf/f≈ 5× 10-4 supports the screening model. Unfortunately, I do not have access to the paper of Jeverdan et al to find out whether the reported change of frequency, which corresponds to a 10 degree deviation from vertical is consistent with the value of cos(Θ) in the experimental arrangement.

6. One should explain also the recent finding by Popescu and Olenici, which they interpret as a quantization of the plane of oscillation of paraconic oscillator during solar eclipse (see this). A possible TGD based explanation would be in terms of quantization of Δg and thus of the limiting oscillation plane. This quantization should reflect the quantization of the gravitational momentum flux receiving Earth. The flux would be reduced in a stepwise manner during the solar eclipse as the distance traversed by the flux through Moon increases and reduced in a similar manner after the maximum of the eclipse.

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 night-side the paraconical pendulum should experience the gravitation of Sun as screened. Same would apply to the "night-side" 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

gp(Sun)|/|Δgp(Moon)|= (MS/MM) (rM/rE)3≈ 2.17.

The order or magnitude follows from r(Moon)=.0026 AU and MM/MS=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.

1. Tangential effects on day-side of Earth are not affected (night-time and night-side are of course different notions in the case of Moon and Sun). At the night-side screening is predicted to reduce tidal effects with a maximum reduction at the equator.

2. Second class of new effects relate to the change of the normal component of the forces and these effects would be compensated by pressure changes corresponding to the change of the effective gravitational acceleration. The night-day variation of the atmospheric and sea pressures would be considerably larger than in Newtonian model.

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:

gp,N|=4GM ×(RE/r)3 ,

gp,TGD|= 4GM ×(1/r2).

The ratio of the effects predicted by TGD and Newtonian models would be

gp,TGD|/|Δ gp,N|= r/RE ,

rM/RE =60.2 , rS/RE= 2.34× 104.

The amplitude for the oscillatory variation of the pressure gradient caused by Sun would be

and the pressure gradient would be reduced during night-time. The corresponding amplitude in the case of Moon is given by

Δ |gradpM| is in a good approximation smaller by a factor of 1/2 and given by

Thus the contributions are of same order of magnitude.

One can imagine two simple qualitative killer predictions.

1. Solar eclipse should induce anomalous tidal effects induced by the screening in the shadow of the Moon.
2. The comparison of solar and moon eclipses might kill the scenario. The screening would imply that inside the shadow the tidal effects are of same order of magnitude at both sides of Earth for Sun-Earth-Moon configuration but weaker at night-side for Sun-Moon-Earth situation.

D. An interesting co-incidence

The measured value of Δ f/f=5× 10-4 is exactly equal to v0=2-11, which appears in the formula hbargr= GMm/v0 for the favored values of the gravitational Planck constant. The predictions are Δ f/f≤ Δ p/p≈ 6× 10-4. Powers of 1/v0 appear also as favored scalings of Planck constant in the TGD inspired quantum model of bio-systems based on dark matter (see this). This co-incidence would suggest the quantization formula

gE/gS= (MS/ME) × (RE/rE)2= v0

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.

1. The first prediction is the gradual increase of the oscillation frequency of the conical pendulum by Δ f/f≤ 6× 10-4 to maximum and back during night-time. Also a periodic variation of the frequency and a periodic rotation of the oscillation plane with period co-inciding with Moon's rotation period is predicted.

2. A paraconical pendulum with initial position, which corresponds to the resting position in the normal situation should begin to oscillate during solar eclipse. This effect is testable by fixing the pendulum to the resting position and releasing it during the eclipse. The amplitude of the oscillation corresponds to the angle between g and gg given in a good approximation by

sin[Θ(g,gg)]= (Δ g/g)sin[Θ( gg)].

An upper bound for the amplitude would be Θ≤ 6× 10-4, which corresponds to .03 degrees.

3. Gravitational screening should cause a reduction of tidal effects at the "night-side" of Moon/Sun. The reduction should be maximum at "midnight". This reduction together with the fact that the tidal effects of Moon and Sun at the day side are of same order of magnitude could explain some anomalies know to be associated with the tidal effects. A further prediction is the day-night variation of the atmospheric and sea pressure gradients with amplitude which is for Sun 6× 10-4g and for Moon 1.3× 10-3g.

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 Anomalies Related to the Classical Z0 Force and Gravitation.