## Generally Covariant Unified Field TheoryThis 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 chapers 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 theconditions 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. |

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### Contents

A The RankThree And RankFour Totally Antisymmetric | 21 |

References | 49 |

References | 61 |

Copyright | |

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base manifold Bianchi identity boson Christoffel symbol components covariant derivative covariant uniﬁed ﬁeld deﬁned deﬁnition differential geometry Dirac equation eigenfunction electromagnetic ﬁeld electron energy Euclidean Evans equation Evans Field Evans ﬁeld equation Evans ﬁeld theory Evans Lemma Evans spacetime Evans spin ﬁeld Evans theory Evans uniﬁed ﬁeld Evans wave equation experimentally ﬁrst ﬂat spacetime Found four-vector fundamental gauge ﬁeld theory gauge invariant gravitation and electromagnetism gravitational ﬁeld Hodge dual identiﬁed Lett limit M. W. Evans magnetic ﬁeld mass matter ﬁelds Maxwell Heaviside metric tensor metric vector momentum neutrino non-Euclidean spacetime notation one-form orthonormal particle phase factor photon Phys physical optics polarization potential ﬁeld preprint on www.aias.us quantum mechanics Riemann form rotation Sagnac effect scalar curvature special relativity spin connection spinor standard model Stokes theorem strong ﬁeld tangent bundle tetrad tetrad postulate torsion form torsion tensor two-form Uniﬁed Field uniﬁed ﬁeld theory vielbein weak ﬁeld World Scientiﬁc