Narrow Results

It is found explicitly 5 Liouville integrals in addition to total angular momentum which Poisson commute with Hamiltonian of 3-body Newtonian Gravity in ${ℝ}^3$ along the remarkable figure-8-shape trajectory discovered by Moore-Chenciner-Montgomery. It is verified that they become constants of motion along this trajectory. Hence, 3-body choreographic motion on figure-8-shape trajectory in ${ℝ}^3$ Newtonian gravity (Moore, 1993), as well as in ${ℝ}^2$ modified Newtonian gravity by Fujiwara et al., is maximally superintegrable. It is conjectured that any 3-body potential theory that admits Figure-8-shape choreographic motion is superintegrable along the trajectory.

We provide a formalism to calculate the effect of the finite size of the sample on hypothetical Yukawa-like corrections to the Newtonian gravitational potential. It is explicitly shown that finite size effect contributions are negligible when the extent of the sample is larger than the range of the Yukawa term. In particular we show that these contributions are small in the configuration of a recent experiment. In the experiment a gold coated sphere was moved across the interface between two materials with different mass densities. In view of these new experimental results, we analyze the situation when the error on the hypothetical correction could result to be significant.

It is widely believed that though pressure resists gravitational collapse in Newtonian gravity, it aids the same in general relativity (GR) so that GR collapse should eventually be similar to the monotonous free fall case. But we show that, even in the context of radiationless adiabatic collapse of a perfect fluid, pressure tends to resist GR collapse in a manner which is more pronounced than the corresponding Newtonian case and formation of trapped surfaces is inhibited. In fact there are many works which show such collapse to rebound or become oscillatory implying a tug of war between attractive gravity and repulsive pressure gradient. Furthermore, for an imperfect fluid, the resistive effect of pressure could be significant due to likely dramatic increase of tangential pressure beyond the "photon sphere." Indeed, with inclusion of tangential pressure, in principle, there can be static objects with surface gravitational redshift z → ∞. Therefore, pressure can certainly oppose gravitational contraction in GR in a significant manner in contradiction to the idea of Roger Penrose that GR continued collapse must be unstoppable.

Classical point particles in Newtonian gravity obey, as they do in general relativity, the universality of free fall. However, classical structured particles, (for instance with a mass quadrupole moment), need not obey the universality of free fall. Quantum mechanically, an elementary “point” particle (in the particle physics sense) can be described by a localized wave packet, for which we can define a probability quadrupole moment. This probability quadrupole can, under plausible hypotheses, affect the universality of free fall. (So point-like elementary particles, in the particle physics sense, can and indeed must nevertheless have structure in the general relativistic sense once wave packet effects are included.) This raises an important issue of principle, as possible quantum violations of the universality of free fall would fundamentally impact on our ideas of what “quantum gravity” might look like. I will present an estimate of the size of the effect, and discuss where if at all it might be measured.

We provide a formalism to calculate the effect of the finite size of the sample on hypothetical Yukawa-like corrections to the Newtonian gravitational potential. It is explicitly shown that finite size effect contributions are negligible when the extent of the sample is larger than the range of the Yukawa term. In particular we show that these contributions are small in the configuration of a recent experiment. In the experiment a gold coated sphere was moved across the interface between two materials with different mass densities. In view of these new experimental results, we analyze the situation when the error on the hypothetical correction could result to be significant.

This work builds on a private communication detailing the potential for a LISA Pathfinder (LPF) test of the inverse square law. Various sources are explored as tests of this law using basic calculations, and plotted with the potential contribution from LPF based on a measurement of the acceleration gradient through the Sun-Earth gravitational saddle point. It is found that an intermediate acceleration range could be filled by this measurement, but would not reach the lower accelerations that other systems have reached.

Newton claimed the influence of gravity is instantaneous; Einstein insisted no influence could propagate faster than the speed of light. Recent experiments to test the speed of gravity have been controversial and inconclusive on technical grounds. Considerable effort is currently expended in the search for a Quantum Gravity; but there is no a priori reason there should be one. We propose that is not the regime of integration which instead occurs in the arena of the Unified Field, UF; further that a completed model of Geometrodynamics inherently includes a Newton/Einstein duality which introduces shock effects in certain arenas. The unified theory predicts that there is no graviton of the usual phenomenal form (an artifact of the incompleteness of Gauge Theory, i.e. gauge theory is only an approximation suggesting new physics). A new Large Scale Additional Dimensional (LSXD) M-Theoretic topological charge alternative is presented. We also attempt to show how the Titius-Bode Law for solar and exoplanetary configurations appears to provide indicia of this multiverse gravitational model. Applications of the dual geometrodynamics formulation include an interpretation of quasar luminosity as the result of gravitational shock waves in a manner countering explanations of large redshift, Z in Big Bang cosmology putatively based on Doppler recession. Instead redshift occurs as the result of a periodic minute photon mass anisotropy caused by periodic coupling to a covariant polarized Dirac vacuum.