The Neglect of Riemannian Torsion – a Catastrophe for Cosmology


This is the title and abstract of an essay invited for a book to be called “The Demise of Big Bang”. The essay is designed to be understood by the intelligent layman.

In this essay it is argued that the Einstein field equation is fundamentally incorrect, a catastrophe for twentieth century cosmology. The reason is the adoption of an incorrect symmetry for the object that introduces torsion and curvature into four dimensional spacetime. This quantity is known as “the connection”, an obscure terminology adopted at the start of the twentieth century when the first papers began to be published on tensor calculus. The torsion and curvature in Riemann geometry are the two fundamental tensors that describe the characteristics of spacetime in four dimensions. The Einstein field equation was based on only one of them, the curvature, because the field equation adopted the wrong type of symmetry for the connection. Recent scholarship has shown that the connection must be antisymmetric in its lower two indices: it must change sign when these two indices are interchanged. This is easy to show, and it is not known why the early protagonists adopted the wrong symmetry. The consequences of this error are catastrophic for cosmology, because all solutions of the Einstein field equation are incorrect and meaningless to physics. These solutions are usually expressed in objects known as metrics. Among these metric solutions are metrics of Big Bang, which is a concept introduced by Hawking and Penrose from the Einstein field equation, specifically from a metric devised in the twenties by Robertson, Walker, Friedmann and Lemaitre. “Big Bang” was a derogatory term introduced by Hoyle to oppose Hawking and Penrose. When the correct antisymmetry of the connection is used, and when the correct , torsion inclusive, geometry is used (the Evans Identity), this metric fails catastrophically. So Big Bang is meaningless in mathematics and physics. Recent scholarship using the Evans Identity shows that all metrics of the Einstein field equation fail the test of this Identity, a rigorous and self checking identity of geometry in four dimensions. The correct field equations are those of Einstein Cartan Evans (ECE) unified field theory, which has replaced the Einstein field equation to great international acclaim. There is no Big Bang, there are no black holes, there is no dark matter. An entirely new cosmology has been devised using ECE theory, one which successfully describes all known orbits, including features that the Einstein field equation is wholly unable to describe (the orbits of stars in spiral galaxies, binary pulsar orbits, solar system anomalies, and so on). Several leading intellectuals of the twentieth century have also criticised the Einstein field equation, for example Schroedinger, Dirac, Eddington and Levi-Civita. It is not known why these criticisms are ignored by current dogmatists. Big Bang has been severely critcised by many scholars for many years. Dogmatists by definition ignore reason, and so dogmatists are not scientists. This is the very essence of the idol of the cave philosophy of Bacon, the basis of all science. The latter must be based on simplicity, reason and observation.


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