Alpha Institute for Advanced Studies (AIAS)

Ubi materia, ibi geometria. Lle mae 'na fater, mae 'na geometreg.
Wo Materie ist, dort ist Geometrie. Where there is matter, there is geometry.

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A Discussion of Criticisms of ECE Theory


Einstein-Cartan-Evans (ECE) theory is the first successful unification of general relativity, quantum mechanics and electromagnetism. This unification was accomplished by the Welsh chemist and physicist Myron Wyn Evans (May 26, 1950 – May 2, 2019) and the German physicist Horst Eckardt.

The ECE hypothesis was published in the journal Foundations of Physics Letters between 2003 and 2005, under an objective editor, Prof. Alwyn van der Merwe (who had founded this journal in 1988). The first fifteen foundational papers of ECE theory were published in this journal, and were refereed between forty and fifty times. Unfortunately, the environment changed when the original publisher, Kluwer, became part of Springer.

Dr. Evans, D.Sc., Ph.D. (1977, 1974; University College of Wales, Aberystwyth) then chose to publish the complete Unified Field Theory (UFT) series on the website, in order to present rapid developments efficiently (this series now numbers over 450 papers and books) in an open and comprehensive manner.

Please note that, prior to this research, Dr. Evans had already published over 500 refereed articles and books, in mainstream journals and through mainstream publishers, without controversy (please see the "Omnia Opera" (Collected Works) on

The Alpha Institute for Advanced Studies (AIAS) is an intellectually independent institute of theoretical physics that was founded by Dr. Evans in 1998. Its fundamental philosophy is the pursuit of objective truth through the scientific method, thus its models are required to account for all of the data, instead of being constrained to a predetermined scientific viewpoint.

For the true history of Dr. Myron Evans and his achievements, please see Myron Evans and the Origins of the AIAS.

For a technical history, by theme, with detailed references, please see Introduction to the complete scientific works of Myron Evans.

These two linked articles show that ECE theory did not just turn up one day, but evolved through a lifetime of work by Myron Evans, including countless collaborations with his mentors and international research groups.

In January of 2008, a new editor of Foundations of Physics (which had absorbed Foundations of Physics Letters), Gerard 't Hooft, published his negative opinion about ECE theory in an editorial note (Volume 38, issue 1). In that note, he also stated that he had published, in the same issue, "three papers (G.W. Bruhn, F.W. Hehl, and F.W. Hehl and Y.N. Obukhov) that critically analyze the ECE theory and its claims." (Refutations of these papers and others are provided below.) These papers are:

  1. On the Non-Lorentz-Invariance of M.W. Evans' O(3)-Symmetry Law (Gerhard W. Bruhn);
  2. An Assessment of Evans' Unified Field Theory I (Friedrich W. Hehl); and
  3. An Assessment of Evans' Unified Field Theory II (Friedrich W. Hehl, Yuri N. Obukhov).

This has not impeded the advancement of ECE theory, and 't Hooft's approach has since been called into question, for example:


Convoluted mathematical nonsense has been presented (and periodically repackaged) as critical analysis that gives the impression of mathematical errors in ECE theory where they do not exist. The following are (linked) refutations that address central defects in these papers:

  1. The first refutation addresses Gerhard Bruhn's paper "On the Non-Lorentz-Invariance of M.W. Evans' O(3)-Symmetry Law". The abstract of the current version (as of 2022),, states:

    "… is erroneously premised on the wave number and frequency being invariant under Lorentz transforms. The simple removal of this erroneous premise is sufficient to show that the O(3) symmetry is not Lorentz invariant, and thus is not a valid law of physics. Furthermore, as the O(3) symmetry later became the basic assumption of Evans’ covariant grand unified field theory (CGUFT) [*], recently renamed as the Einstein-Cartan-Evans (ECE) theory), this theory is also physically invalid.”

    [*] Please note that the name is actually Generally Covariant Unified Field Theory (GCUFT).

    These assertions are incorrect for two reasons:

    Furthermore, in Section 10.2.3 of the first volume of the ECE textbook (available as UFT Paper 438), it is shown that the ECE wave equation preserves the frequency omega and wave number kappa of a wave in m space (note that the propagation velocity changes).

    Also, please note that the computer algebra system Maxima has been used to demonstrate the internal consistency of the geometric basis of ECE theory, for example, see the code that is provided with the textbook.

  2. The second refutation addresses Bruhn, G. W., The Central Error of Myron W. Evans’ ECE Theory - a Type Mismatch,

    Bruhn starts by stating that "M.W. Evans constructs his spacetime by a dubious alternative method … Here we sketch the usual method of constructing the 4-dimensional spacetime manifold M”.

    However, the essence of the "usual method” turns out to be the same as the "dubious method”, and Bruhn also rebuts a procedure that does not exist in ECE theory.

  3. The third refutation addresses Waldyr A. Rodrigues Jr. and Quintino A. G. de Souza, An Ambiguous Statement Called ‘Tetrad Postulate’ and the Correct Field Equations Satisfied by the Tetrad Fields,

    (This paper has been referenced by other critics to support their claims.)

    In that paper, Rodrigues and de Souza inexplicably decided to criticize ECE theory by criticizing the long-standing mathematical field of differential geometry itself.

    This refutation shows that the tetrad postulate is a well-established element of standard differential geometry (and even of mainstream physics where, for example, the tetrad is used in standard quantum field theory), and it also discusses relevant aspects of ECE theory.

  4. The fourth refutation addresses Gerhard W. Bruhn, Friedrich W. Hehl, and Arkadiusz Jadczyk, Comments on "Spin Connection Resonance in Gravitational General Relativity”,

    This refutation shows that the traditional Bianchi identity is, in fact, the same as its own tensor formulation, provides help in recognizing a resonance equation, and so on.

    Bruhn, Hehl, and Jadczyk start their Section 2, "General comments on Evans’ paper”, by stating that "The [Evans] paper deals with what the author calls ‘Cartan geometry’. The term is not defined in the paper, so the reader has to guess what the exact meaning is of this term.”

    However, in that Evans paper, the second sentence of the Introduction includes "… of Cartan geometry [1] …”, with [1] being "S. P. Carroll, Space-time and Geometry, an Introduction to General Relativity (Addison-Wesley, New York, 2004)”. (Please note that [1] is the reference that specifies Cartan geometry in the Evans paper that is being criticized by Bruhn, Hehl, and Jadczyk.)

    Another option (to help them gain an understanding of the foundational geometry of the theory that they were attempting to analyze) might have been for Gerard 't Hooft (the editor of Foundations of Physics, from above) to obtain a discount for them from the Springer store ( returns thousands of results for "Cartan geometry”).

  5. The fifth refutation addresses the following two papers that were published in Foundations of Physics 38(1): Hehl, F. W., An Assessment of Evans’ Unified Field Theory I, 7-37; and Hehl, F. W. and Obukhov, Y. N., An Assessment of Evans’ Unified Field Theory II, 38-46.

    This is the most extensive of these five refutations, and (out of necessity) it recapitulates other rebuttals in its eleven appendices.

    In addition to the eleven appendices mentioned above, seven appendices from a separate book, [1], are also referenced. (Please note that [1] is the reference to Generally Covariant Unified Field Theory: The Geometrization of Physics, Vol.1, in Refutation 5.) The first four are from the book proper, and the last three are from a chapter within the book. For convenience, they have been excerpted and linked here: Appendix E, Appendix I, Appendix J, Appendix K, and Appendices A, B and C from Chapter 17.

    In the first paper (on page 28), Hehl states: "Since the publications of Evans and associates are not very transparent to us, we distilled from all their numerous papers and books the "spirit” of Evans’ theory.”

    This refutation shows, in great detail, why these critical papers can be summarized with the first part of that sentence: "The publications of Evans and associates are not very transparent to us”.

Some critics have attempted to disparage ECE theory by claiming that it has been used to "justify the motionless electromagnetic generator” (which these critics claim is a "perpetual motion machine”). Please note that ECE theory and the AIAS do not claim that "perpetual motion” exists, but rather that all energy flows and sources are not known or presented by standard theories.

Unless a device has been replicated and verified by the AIAS, the limit of any theoretical explanation, from the perspective of the AIAS, is "if the device works as described by the inventor, then this is how the operation of that device would be related to physics”.

Furthermore, papers that the critics co-located with that claim (UFT Papers 311, 364, 382, and 383) actually discuss experimental replication, verification, and theoretical explanation of the (external) Ide experiment. (For experiment details, please see the three Ide papers (also available on the AIAS Publications page) that were presented by the author, Osamu Ide, at the 249th American Chemical Society National Meeting & Exposition.)

These critics have even become confused by similar names: "Evans argues that Einstein's theory of general relativity does not take into account torsion, which is included in the Einstein-Cartan theory.”

The problem with the second part of that statement is that the Einstein-Cartan theory is different from Einstein's theory of general relativity.

Furthermore, Einstein-Cartan theory (which is actually that of Dennis Sciama and Thomas Kibble) could not have patched the "torsion hole” because it is based on a modification of the Einstein field equation, plus an additional equation describing spin. Outside of matter, spin vanishes and the theory is identical to the Einstein field equation. In other words, "empty space” is described in the same way as in Einstein’s theory, and matter is introduced as an external source in the form of the energy-momentum tensor. Consequently, all of the criticisms of Einstein's field equation are also applicable to the Einstein-Cartan theory.

Additional Considerations

After a certain point, one has to start to wonder why so much time and energy is being devoted to attacking a theory that critics claim is incorrect and an insignificant footnote to modern physics.

Could the reason be to preclude neutral evaluation by objective scientists of a theory that, among other things (see Advantages of ECE Theory over the Standard Model), removes a foundational element from the structure that supports careers and awards, by identifying the significance of the omission of torsion in general relativity?

As if that were not enough, there are even logical difficulties that are unrelated to general relativity and the torsion problem. For example, the following paper demonstrates that black hole and big bang cosmologies contradict each other (and it does so without using complicated mathematics): Stephen J. Crothers, Black Hole and Big Bang: A Simplified Refutation (2013, 16 pages),

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