Einstein–Cartan–Evans theory was an attempted unified theory of physics proposed by Myron W. Evans, which claimed to unify general relativity, quantum mechanics and electromagnetism. The hypothesis was largely published in the journal Foundations of Physics Letters between 2003 and 2005. Several of Evans' central claims were later shown to be mathematically incorrect and, in 2008, the editor of Foundations of Physics published an editorial note effectively retracting the journal's support for the hypothesis.
In the synopsis of his first book, Evans writes:
This book is the first to describe a very successful objective unified field theory which emerged in 2003 and which is already mainstream physics – Einstein Cartan Evans (ECE) field theory. The latter completes the well known work of Einstein and Cartan, who from 1925 to 1955 sought to unify field theory in physics with the principles of general relativity. These principles are based on the need for objectivity in natural philosophy, were first suggested by Francis Bacon in the sixteenth century and developed into general relativity in about 1915. In this year, using Riemann geometry, Einstein and Hilbert independently arrived at an objective field equation for gravitation. Since then there have been many attempts to unify the 1915 gravitational theory with the other three fundamental fields: electromagnetism, the weak and strong fields. As described for the first time in this book, unification is achieved straightforwardly with the principles of standard Cartan geometry and the Evans Ansatz. The latter shows that electromagnetism is spinning spacetime, gravitation is curving spacetime and that they are unified with the structure (or master) equations of Cartan. Quantum mechanics is unified with general relativity using the Evans Lemma and wave equation. Technical appendices and charts are provided which show how all the major equations of physics are obtained from the ECE field theory, and two introductory chapters describe the background mathematics from an elementary level. The mathematical structure of ECE field theory is standard Cartan geometry, also known as differential geometry. The main topics of contemporary physics are covered in individual chapters, which also describe the conditions under which ECE theory reduces to Einstein Hilbert (EH) theory, and to Maxwell Heaviside field theory in classical electrodynamics. The Dirac equation is derived as a limit of the wave equation of ECE theory. The Schrodinger and Newton equations then follow as limits of the Dirac equation. It is therefore shown that ECE field theory provides, for the first time, a structure for the objective unification of field theory in natural philosophy.
Earlier versions of the theory were called "O(3) dynamics".
Evans' claims are not accepted by the mainstream physics community. In an editorial note in Foundations of Physics the Nobel laureate Gerard 't Hooft discussed the "revolutionary paradigm switch in theoretical physics" promised by ECE theory. He concluded that activities in the subject "have remained limited to personal web pages and are absent from the standard electronic archives, while no reference to ECE theory can be spotted in any of the peer reviewed scientific journals".
Several of the published contributions in this theory have been shown to be mathematically incorrect. In response to these demonstrations, 't Hooft's editorial note concludes, "Taking into account the findings of Bruhn, Hehl and Obukhhov, the discussion of ECE theory in the journal Foundations of Physics will be concluded herewith unless very good arguments are presented to resume the matter."
- Evans 2005
- Evans 2006a
- Evans 2006b
- Evans 2007
- Bruhn 2008
- Bruhn, Hehl & Jadczyk 2008
- Rodrigues & Souza 2005
- Trovon de Carvalho & Rodrigues 2001
- 't Hooft 2008
- Anastasovski, P. K.; Bearden, T. E.; Ciubotariu, C.; Coffey, W. T.; Crowell, L. B.; Evans, G. J.; Evans, M. W.; Flower, R.; Labounsky, A.; Lehnert, B.; Mészáros, M.; Molnár, P. R.; Moscicki, J. K.; Roy, S.; Vigier, J.P. (2001), "Explanation of the motionless electromagnetic generator with O(3) dynamics", Foundations of Physics Letters 14 (1): 87–94, doi:10.1023/A:1012085429802
- Alpha Institute for Advanced Studies (AIAS)
- Evans, Myron W. (2005), Generally Covariant Unified Field Theory, Abramis, ISBN 1-84549-054-1
- Evans, Myron W. (2006a), Generally Covariant Unified Field Theory, II, Abramis, ISBN 1-84549-123-8
- Evans, Myron W. (2006b), Generally Covariant Unified Field Theory, III, Abramis, ISBN 1-84549-131-9
- Evans, Myron W. (2007), Generally Covariant Unified Field Theory, IV, Abramis, ISBN 1-84549-248-X
- Bruhn, Gerhard W. (2008), "On the non-Lorentz-invariance of M. W. Evans' O(3)-symmetry law", Found. Phys. 38 (1): 3–6, arXiv:physics/0607186, Bibcode:2008FoPh...38....3B, doi:10.1007/s10701-007-9189-6, MR 2387497
- Bruhn, Gerhard W.; Hehl, Friedrich W.; Jadczyk, Arkadiusz (2008), "Comments on: "Spin connection resonance in gravitational general relativity" by M.W. Evans", Acta Phys. Polon. B 39: 51–58, arXiv:0707.4433, Bibcode:2008AcPPB..39...51B, MR 2372785
- Rodrigues, Waldyr A.; Souza, Quintino A. G. (2005), "An ambiguous statement called the "tetrad postulate" and the correct field equations satisfied by the tetrad fields", Int. J. Mod. Phys. D 14: 2095–2150, arXiv:math-ph/0411085, Bibcode:2005IJMPD..14.2095R, doi:10.1142/S0218271805008157, MR 2218579
- Trovon de Carvalho, A. L.; Rodrigues, W. A. (2001), "The non sequitur mathematics and physics of the "new electrodynamics" proposed by the AIAS group", Random Oper. Stochastic Equations 9 (2): 161–206, doi:10.1515/rose.2001.9.2.161, MR 1832162
- 't Hooft, Gerard (2008), "Editorial note", Foundations of Physics 38 (1): 1–2, Bibcode:2008FoPh...38....1T, doi:10.1007/s10701-007-9187-8
- Alpha Institute for Advanced Study (AIAS), Myron Evans' website.