The Antisymmetry of the Connection, Further Details

This note gives further details for the non-specialist. The basic error in the twentieth century was eq. (26), and this is so glaring that scholarship is needed to find why it was ever made, and why it continued for ninety years.

a138thpapernotes10.pdf

Further Major Errors in Standard Cosmology

These errors again arise from the use of a symmetric connection. The most fundamental one is the incorrect assertion that a connection can always be chosen to be symmetric. If so, the commutator in eq. (4) of the attached vanishes, and the curvature and torsion BOTH vanish, not only the torsion. This is easy to see, yet this error has been perpetrated by dogmatists for ninety years. The connection must be antisymmetric, because the commutator in eq. (4) of the attached must be antisymmetric. Otherwise it is zero. In consequence of the antisymmetry of the connection, there are two different ways of defining the geodesic equation, and these two methods are not equivalent. The geodesic equation many be defined as the path that parallel transports its own tangent vector, and secondly it may be defined as the shortest distance between two points. The geodesic equation was used by Einstein to derive the Newtonian limit, but this is again an incorrect procedure based on an incorrect symmetric connection. Therefore the Einstein methodology is riddled with sequential errors and must be abandoned.

Paper137withmath.pdf

Some Comparisons of the Old and New Field Equations

The new field equations of cosmology are simpler than the now obsolete Einstein field equation. The new field equations are based on the Cartan and Evans Identities of four dimensional Riemannian geometry. These correct the old first Bianchi identity, which neglects torsion. The old Einstein field equation was based on an incorrect second Bianchi identity, as following postings show. The new equations do not use the canonical energy momentum density tensor, but instead use a current density. The mathematical structures of the four field equations of dynamics, cosmology and electrodynamics are the same in ECE theory. The new equations can be applied to obtain new energy from spacetime through spin connection resonance, a concept missing completely from the old Maxwell Heaviside equations. The correct antisymmetry of the connection is used in the new equations, the old Einstein field equation used the wrong connection symmetry, and the old Maxwell Heaviside equations did not use a connection at all, being based on Minkowski spacetime, and being a theory only of special relativity of limited validity.

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.

Abstract
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.

Torsion Approach to Cosmology

This is the only valid approach to cosmology now, the old curvature based approach of Einstein is completely obsolete. Cartan geometry is one way of developing torsion, and there are other ways too. Even the most abstruse and abstract of the curvature based approaches are designed from the beginning to reduce to the incorrect Einstein equation, so none of these approaches are valid. In a recent meeting at the Perimeter Institute it was agreed that a new paradigm shift is needed, and this is already available.

Invariance of the Vector Field Under Coordinate Transformation

This note illustrates this well known property by using the Lorentz boost in the x axis, an undergraduate exercise. It is proven that the B Cyclic Theorem is Lorentz covariant by definition. Great caution should be exercised when reading any claims to the contrary, because these come from known harassers. G. ‘t Hooft allowed a paper into “Foundations of Physics” which was devoted to the incorrect claim that basis vectors are not Lorentz covariant. This is part of the reason why there are demands for ‘t Hooft’s resignation as editor, and from his Chair at Utrecht. Recently ‘t Hooft has allowed another paper into print with the ludicrous claim that the inverse Faraday effect “does not exist”. Google “inverse Faraday effect” to find over nine hundred entries from 1964 onwards by many groups. Finally ‘t Hooft has tried to “unpublish” fifteen ECE papers in “Foundations of Physics Letters”, papers which generated more than thirty positive referees’ reports in the accepted professional manner.

British Civil List Scientist

a138thpapernotes9.pdf

Entry in “Burke’s Peerage and Gentry”

This is now being written up by the editor, William Bortrick, and is to mark achievement of arms on July 8th 2008 for many contributions to science and society, primarily my appointment to the British Civil List on Feb. 28th, 2005, a British National High Honour. A draft of the entry is attached. I think that this will be the 110′th Edition.

Prof. Myron Wyn Evans of Glyn Eithrym, Gent., B. Sc., Ph. D., D. Sc. (Wales).

British Civil List Scientist

BurkesEntry.doc

The Problem of Harassment by Electronic Mail

It is widely known that a campaign of harassment by electronic mail goes on all the time behind the scenes against ECE scientists and others who show that the standard model is incorrect mathematically. Recently the police have cautioned one such harasser, who ceased his activities. He was traced to Barry near Cardiff and used the pseudonym “Arthur Dent”. Upon questioning he was found to be a retired academic. It is also well known that we have traced and identified one harasser to Penn State University, University Park, using our feedback software. He has been sacked from wikipedia, and has ceased his activities. He may also have been disciplined by the university authorities. Harassment by electronic mail is illegal, unprofessional and unethical, and those who indulge in such conduct should be disciplined by the various relevant ethical practices committees of the various professions involved: mathematics, physics, chemistry and engineering. All aggrieved parties are entitled to recourse in law and professional recourse to these committees in complaints filed by all aggrieved parties, individually or in a class action. There are about three or four harassers who spend an inordinate amount of time e mailing all who dare to think about physics. Frequently, their arguments are trivially incorrect, and any missive from such persons, delivered in anonymity or malice, should be reported to the police authorities, lawyers and ethical practices committees by any recipient. Frequently the wording is libelous and abusive. This is wholly unprofessional conduct.

British Civil List Scientist

Consequences of Using the Wrong Connection Symmetry

The consequences are obvious to any bright school pupil: the whole of twentieth century general relativity collapses, and the mathematics associated with using a symmetric connection become meaningless. ECE theory is simpler and mathematically correct within its terms of reference. All solutions of the Einstein field equation are meaningless, as shown in our forthcoming book, “Criticisms of the Einstein Field Equation”. Any development of unified field theory based on the Einstein field equation is incorrect. This includes various string theories and superstring theories which have never been tested experimentally. Journal articles based on the Einstein field equation are meaningless, TV programmes on black holes and dark matter are bad science fiction. The situation is easily remedied by adopting ECE theory, which is a return to the long accepted principles of science, testing against data and simplicity. Academic authority based on trivial errors is false authority, and merit by association must be rejected: appointments made without open competition have no merit. Scholars of science working outside academia produce ideas which can challenge the false authority of academics based in universities of purported merit. Similarly poets and musicians of merit do not have to be based at Oxford and Cambridge and so forth. This is all very obvious at O level. Incorrect dogma is perpetrated in response to peer pressure within certain groupings of individuals. Such groupings have no meaning in a wider societal context.

Civil List Scientist

The Key Point

The key point is given in equation (4) of the attached paper, which proves the Evans Identity of differential geometry. On the left and right hand sides of this equation appear indices mu and nu. If these are the same, both sides of the equation are zero by definition. On the left hand side appears the commutator of covariant derivatives, on the right hand side appears the connection of Riemann geometry. When mu and nu are the same the commutator and connection are said to be “symmetric”. Therefore a symmetric commutator is zero and a symmetric connection is zero. When mu is not the same as nu the commutator and connection are said to be “antisymmetric”. They both change sign by definition when mu and nu are interchanged. So the connection of Riemann geometry is always antisymmetric by definition. The meaningless Einstein field equation used a symmetric connection, leading to numerous sequential errors as shown in the following notes. The situation can only be remedied with an entirely new paradigm such as ECE theory.

Paper137withmath.pdf