My slow and crumbled intellect has crept a little forward into understanding the theory of gravity. I am making a comparison between on the one hand the authoritatively established orthodoxy of the Einstein “general theory of relativity”, and on the other hand the relativistic theory of gravity, the latter as investigated by various authors over the years before and since the epochal discoveries of the genius of Albert Einstein. Some of those authors include Henri Poincaré, Hermann Minkowski, Alfred Arthur Robb, Alfred North Whitehead, Nathan Rosen, Robert Harry Kraichnan (who died on 26 Feb 2008), Vladimir Alexandrovich Fock, Suraj N. Gupta, Walter E. Thirring, Richard Phillips Feynman, Steven Weinberg, J.C.W. Scott, Norbert Straumann, and Anatoly Alexeyevich Logunov. I have been guided by the approach of Alfred North Whitehead and Anatoly Alexeyevich Logunov. In particular, I have been reading:
A. Logunov and M. Mestvirishvili, The Relativistic Theory of Gravitation, translated from the Russian by Eugene Yanovsky, Mir, Moscow, 1989.
Anatoly Logunov, Lectures in Relativity and Gravitation: A Modern Look, translated from Russian by Alexander Repyev, Nauka, Pergamon, 1990.
A.A. Logunov, The Theory of Gravity, translated by G. Pontecorvo, Nauka, Moscow, 2001. This can be downloaded from the web for free at http://aps.arxiv.org/PS_cache/gr-qc/pdf/0210/0210005v2.pdf.

Anatolii A. Logunov, Relativistic Theory of Gravity, Nova Science, Huntington, 2001.

For myself, I have found that the relativistic theory of gravity of Logunov and his colleagues is currently the best available guide to understanding the physics of gravity. I would be grateful for further guidance.

In a nutshell: Because of causality, the geometry of physical spacetime is strictly Minkowski, not general Riemannian. Physical spacetime is flat, not curved. This can be understood as follows.

The orthodox “general theory of relativity” of Albert Einstein is expressed in two sets of simultaneous equations, the Hilbert-Einstein equations, and the so-called “coordinate conditions”, taken conjointly. This conjunction is a failure. It fails to provide unambiguous predictions, and cannot be tested empirically. This is because the “coordinate conditions” are arbitrary and fail to express physical laws which are necessary for the physical meaning for the Hilbert-Einstein equations. The orthodox “general theory of relativity”, by itself, without arbitrary supplementary assumptions, does not lead to the parametrised post-Newtonian (PPN) approximation.

For a valid theory of gravity, built on the Hilbert-Einstein equations, the “coordinate conditions” must be replaced by what I like to call the field structure equations, formulated by Logunov and his colleagues as in the above references. These equations are not at all arbitrary, but rather, they express physical laws that are necessary to give physical meaning to the Hilbert-Einstein equations. The conjunction of the Hilbert-Einstein and the field structure equations makes definite and testable predictions. In particular it rigorously and unequivocally leads to the PPN approximation for empirical tests within the solar system. These have strictly and significantly empirically verified the relativistic theory of gravity as formulated by Logunov and his colleagues.

In short, the orthodox “general theory of relativity” and the Logunov relativistic theory of gravity formally share the Hilbert-Einstein equations, but they give entirely different meanings to them. Because of the failure of its “coordinate conditions”, the orthodox “general theory of relativity” is left behind as a half-baked empirically untestable ideology, while the Logunov relativistic theory of gravity, because it uses the correct field structure equations, is sound physics.

The orthodoxy with its nonsensical dogma of curved spacetime weakens the intellectual coherence of scientific discourse in general.

Christopher