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This Concept Map, created with IHMC CmapTools, has information related to: Gravitational anomalies.cmap, POSSIBLE GRAVITATIONAL ANOMALIES 3. Anomalous time dila- tion due to warping of space-time. a) Sub-manifold gravity predicts warping of the space-time. The warping of flat 2-surfaces - bend- ing without stretching is familiar for 2-dimensio- nal surfaces. For a flat 2-D surface z=f(x,y) the imbedding depends on say linear coordinate, say x, can be arbitrary function of the coordina- te. b) Also M^4 can have this kind of warped flat imbeddings. The induced metric however codes for the time dilation (say for Phi= ω×t, where Phi is angular coordinate for geodesic circle of CP_2. One therefore ob- tains time dilation in ab- sence of gravitational fields., POSSIBLE GRAVITATIONAL ANOMALIES 2. The dependence of effective light-velocity on space-time sheet. a) Dependence of light-velo- city on space-time sheet is basic effect predicted by sub- manifold gravity and might become visible when the no- tion of effective space-time fails. b) This effect could become visible if light from distance object can arrive along seve- ral paths identified as space- time sheets. The distance and thus also the time for travel along light-like geode- sic depends on space-time sheet. c) The measurements of Hubble constant give rise to two different results. This could be due to the fact that light can arrive along diffe- rent space-time sheets. d) It has been found that the time taken for laser light to travel to Moon and back seems to change as if Moon were receding. The explana- tion could be that the time used in measurements corre- sponds to that assignable to distant start and in good ap- proximation to cosmological time. This time unit is how- ever proportional to sqrt(g_tt) for cosmological metric and depends on cosmic time. This would cause apparent in- crease of the distance of Moon. The predicted size of the effect is correct., POSSIBLE GRAVITATIONAL ANOMALIES 1. Background: During years I have conside- red models for various claim- ed gravitational anomalies. a) The basic assumption has been that the anomalies are modellable in terms of sub- manifold gravity and many- sheeted space-time. b) Also large gravitational Planck constant has been considered and could be reduced to the h_gr= GMm/v_0, v_0/c≈2^(-11) applied to elementary par- ticles to obtain h_eff=h_gr of reasonable size. Compton length does not depend on the mass m of the particle. c) The anomalies should re- flect the failure of the as- sumption that the space-ti- me of GRT provides effecti- ve description of TGD. This notion is discussed in sepa- rate context and is implied naturally by many-sheeted space-time., POSSIBLE GRAVITATIONAL ANOMALIES 6. Anomalously strong gravi- magnetism. a) It has been observed that the mass of Cooper pair as deduced from Thomson mag- netic field associated with su- perconductor is slightly higher than the sum of electron mas- ses instead of being smaller than the sum by the binding energy of Cooper pair. The dis- crepancy is of order Δm/m ≈ 10^(-4). b) Also Tajmar et al have do- ne experiments. They suggest that the effect might be due to a small contribution from gravimagnetism to the effecti- ve Thomson magnetic field. Thomson field is to a square of the ratio of gravitons Comp- ton wavelength λ_g and imagi- nary gravimagmnetic penetra- tion depth λ_L. Graviton mass is assumed to result from cos- mological constant and is so- mething like 10^(-55) kg). The outcome is by about factor 10^(-28) too small. Authors argue that graviton mass should be by factor 10^(14) higher. c) TGD suggests that it is h_gr associated with Cooper pair and Earth, which increases λ_g by a factor h_gr(2e,E)/h. The sca- ling factor of B_gr would be (h_gr/h)^2, h_gr= 2GM_Em_e/v_(0,E). v_(0,E) can be estimated from the con- dition that it corresponds to a typical velocity, now the ve- locity of the rotation of Earth around its own axis. The resul- ting scaling factor is 3.6× 10^(14) and happens to have correct order of magnitude! d) The value of h_gr is of same order of magnitude as obtained from the condition that EEG photons are dark photons with energies of bio-photons. h_eff= h_gr implies that the energy of cyclotron photons does not depend on the mass of ion., POSSIBLE GRAVITATIONAL ANOMALIES 4. Could the sheets of many-sheeted spa- cetime be revealed somehow? a) One could dream of demonstrating the sheets of many-sheet- ed space-time in an experimental situation where two sheets are present such that the sheets carry em field. If the second sheet is of finite length or the- re is sequence of copi- es of this sheet, the interactions of test particle could reveal the presence of the sheets b) This kind of experi- ment has been indeed performed using mag- netic field of strength .2 Gauss, which hap- pens to be same as the strength of endo- genous magnetic field in TGD inspired biolo- gy. The effect is seen as variation of the fre- quency of cyclotron ra- diation., POSSIBLE GRAVITATIONAL ANOMALIES 5. Allais effect and TGD. a) Allais effect is observed during solar eclipse when Moon is between Sun and Earth. The rotation plane of the pendulum begins to rotate as observed first by economy Nobelist Allais. The sign and magnitude of the effect vary in wide limits, as if it would depend very sensitively on precise relative distances of Sun, Moon and pendulum. b) Suggests interference effects and this in turn that large values of gra- vitational Planck constant h_gr are involved. h_gr =h_eff can make sen- se for elementary particles and Equi- valence Principle allows the reduct- ion of the situation to elementary particle level. c) Assumption:gravitational force corresponds to a transfer of radial four-momentum along gravitational massless extremal (ME) connecting particle and Sun or Moon. The force is integral over wavelengths of mo- dulus squared of an amplitude mul- tipied by transferred momentum gi- ven in terms of wavelength using generalization of standard expres- sion. This fixes the from of the am- plitude. d) By EP only gravitational accelera- tion matters so that one can consi- der either pendulum or elementary particles forming it and sum the forces in this case. e) Interference occurs with the gra- vitational MEs from Moon and Sun are parallel. f) The large value of h_gr for Moon- pendulum and Sun-pendulum sys- tems implies that the effect is high- ly sensitive to the relative distances. Gravitational interferometer results., POSSIBLE GRAVITATIONAL ANOMALIES 3. Anomalous time dila- tion due to warping of space-time. a) Sub-manifold gravity predicts warping of the space-time. The warping of flat 2-surfaces - bend- ing without stretching is familiar for 2-dimensio- nal surfaces. For a flat 2-D surface z=f(x,y) the imbedding depends on say linear coordinate, say x, can be arbitrary function of the coordina- te. b) Also M^4 can have this kind of warped flat imbeddings. The induced metric however codes for the time dilation (say for Phi= ω×t, where Phi is angular coordinate for geodesic circle of CP_2. One therefore ob- tains time dilation in ab- sence of gravitational fields.