Abstract
Newtonian gravity is modified here via Mach's inertia principle (inertia fully governed by universe) and it is generalized to gravitationally quantum bound systems, resulting scale invariant fully relational dynamics (mere ordering upon actual objects), answering to rotation curves and velocity dispersions of the galaxies and clusters (large scale quantum bound systems), successful in all dimensions and scales from particle to the universe. Against the Milgrom’s theory, no fundamental acceleration to separate the physical systems to the low and large accelerations, on the contrary the Newtonian regime of HSB galaxies sourced by natural inertia constancy there. All phenomenological paradigms are argued here via Machian modified gravity generalized to quantum gravity, especially Milgrom empirical paradigms and even we have resolved the mystery of missing dark matter in newly discovered Ultra Diffuse Galaxies (UDGs) for potential hollow in host galaxy generated by sub quantum bound system of the globular clusters. Also we see that the strong nuclear force (Yukawa force) is in reality, the enhanced gravity for limitation of the gravitational potential because finite-range of the Compton wavelength of hadronic gravity-carriers in the nucleuses, reasoning to resolve ultimately, one of the biggest questions in the physics, that is, so called the fine structure constant and answering to mysterious saturation features of the nuclear forces and we have resolved also the mystery of the proton stability, reasonable as a quantum micro black hole and the exact calculation of the universe matter. Tully-Fisher and Fabor-Jackson relations and Fish's and Freeman's laws of the constant central gravitational potential and universalization of Baryonic Fish's law are next paradigms argued here. We don’t play with mathematical functions to set them with empirical results and we don’t simulate the models but the Newton's empirical gravity is returned to its fundamental face logically.
Highlights
Albert Einstein based the theory of relativity regarding to Mach’s mechanics (1960) as noted by Mach that “No one is competent to predicate things about facts
Mach’s mechanics is a fully relational dynamics and the boundary of inertial field equations is defined inertial relationally where the internal inertia is larger than the external inertia as the dominance law of the gravitational quantum bound systems
Tully-Fisher relation has a transition from standard Tully-Fisher in low scale to its very large scale version (M in sun's mass and v in 1 km/s) as: log M 1.75 4log v log M 0.8 4log v (133). This relation is showing the jump in the normalization factor of the standard Tully-Fisher relation to a larger constant which is visible in the reports for galaxies clusters
Summary
Albert Einstein based the theory of relativity regarding to Mach’s mechanics (1960) as noted by Mach that “No one is competent to predicate things about facts. Mach has argued persuasively in his penetrating investigations of this matter” This means that gmn are completely determinable by the mass of bodies, more generally by Tmn. But Einstein general relativity, was not success to obtain a fully connection to Mach’s inertia principle and Einstein field equation (Einstein, 1959) results partial dependency to Mach's inertia principle as Einstein in a letter to de Sitter 1917 states:. Hoyle and Narlikar (1964; 1966) developed a theory of gravitation in context of the Mach’s inertia principle and they used the waves to communicate gravitational influence between particles Another form, for Machian relation, called in the literature as WhitrowRandall relation (Whitrow and Randall, 1951) and Sciama (1953) used electrodynamic type equations for gravity to extract the Machian relation as the Sciama's law of the inertial induction. Milgrom et al, have tried to compensate failures with change of the uncertain parameters similar to mass to light ratio and distance uncertainties but there are serious difficulties, especially in the Bullet clusters and galaxies clusters and globular clusters (Jordi et al, 2009; Baumgardt, 2006; Sollima and Nipoti, 2010; Aguirre et al, 2001; Kent, 1987; Gentile et al, 2011)
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