Authors: David Brown
The empirical successes of Milgrom’s MOdified Newtonian Dynamics (MOND) suggest that there is a serious problem with Newtonian-Einsteinian gravitational theory. Could dark matter have positive gravitational mass-energy and zero inertial mass-energy? Einstein wrote (“The Meaning of Relativity”, 5th edition, page 57) that “A little reflection will show that the law of the equality of the inert and the gravitational mass is equivalent to the assertion that the acceleration imparted to a body by a gravitational field is independent of the nature of the body. For Newton's equation of motion in a gravitational field, written out in full, is (Inert mass) * (Acceleration) = (Intensity of the gravitational field) * (Gravitational mass). It is only when there is numerical equality between the inert and gravitational mass that the acceleration is independent of the nature of the body.” Is it necessarily true that IT IS ONLY WHEN THERE IS NUMERICAL EQUALITY between inertial mass-energy and gravitational mass-energy that THE ACCELERATION IS INDEPENDENT OF THE NATURE OF THE BODY? There is a possibility that the acceleration is independent of the nature of the body but THERE IS A SYSTEMATIC DEVIATION between the inertial mass-energy and gravitational mass-energy. Consider Einstein’s field equations: R(mu,nu) + (-1/2) * g(mu,nu) * R = - κ * T(mu,nu) - Λ * g(mu,nu) — what might be wrong? Consider the possible correction R(mu,nu) + (-1/2 + dark-matter-compensation-constant) * g(mu,nu) * R = - κ * (T(mu,nu) / equivalence-principle-failure-factor) - Λ * g(mu,nu), where equivalence-principle-failure-factor = (1 - (T(mu,nu)/T(max))^2)^(1/2) — if dark-matter-compensation-constant = 0 and T(max) = +∞ then Einstein’s field equations are recovered. Empirical evidence shows that black holes exist. The event horizons of black holes might be figments of the imagination caused by believing in Einstein’s equivalence principle. John P. Lestone’s ideas might suggest that something is wrong with Einstein’s field equations. This brief communication argues that relativistic MOND is the Fernández-Rañada-Milgrom effect.
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