The Evans Equations of Unified Field Theory - Alpha Institute for ...

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Contents Introduction .......................................................................................................................1 Don’t Panic............................................................................................................1 General Relativity and Quantum Theory ...............................................................2 Einstein-Cartan-Evans Unified Field Theory .........................................................4 Evans’ Results.......................................................................................................5 The Nature of Spacetime ......................................................................................6 The Four Forces..................................................................................................11 The Particles .......................................................................................................14 What We Will See ...............................................................................................14 Chapter 1 Special Relativity .........................................................................................16 Relativity and Quantum Theory...........................................................................16 Special Relativity .................................................................................................19 Invariant distance ................................................................................................22 Correspondence Principle ...................................................................................24 Vectors ................................................................................................................25 The Metric ...........................................................................................................31 Summary .............................................................................................................32 Chapter 2 General Relativity..........................................................................................34 Introduction..........................................................................................................34 Curved Spacetime...............................................................................................41 Curvature.............................................................................................................44 Concept of Field ..................................................................................................44 Vacuum ...............................................................................................................46 Manifolds and Mathematical Spaces...................................................................47 The Metric and the Tetrad ...................................................................................51 Tensors and Differential Geometry .....................................................................53 Equivalence Principles ........................................................................................54 Chapter 3 Quantum Theory ...........................................................................................56 Quantum Theory .................................................................................................56 Schrodinger’s Equation .......................................................................................61 Vector Space.......................................................................................................61 Dirac and Klein-Gordon Equations......................................................................62 The Quantum Hypothesis....................................................................................63 Heisenberg Uncertainty.......................................................................................65 Quantum Numbers ..............................................................................................66 Quantum Electrodynamics and Chromodynamics ..............................................67 Quantum Gravity and other theories ...................................................................68 Planck’s Constant................................................................................................69 Geometricized and Planck units..........................................................................73 Quantum Mechanics ...........................................................................................74 Summary .............................................................................................................76 Chapter 4 Geometry.....................................................................................................77 Introduction..........................................................................................................77 Eigenvalues.........................................................................................................78 Riemann Curved Spacetime ...............................................................................79 2
3 Torsion ................................................................................................................81 Torsion ................................................................................................................81 Derivatives...........................................................................................................81 ∂ The Partial Differential ......................................................................................82 Vectors ................................................................................................................83 Scalar, or Inner Product ......................................................................................84 Cross or Vector Product ......................................................................................85 Curl......................................................................................................................86 Divergence ..........................................................................................................87 Wedge Product....................................................................................................87 Outer, Tensor, or Exterior Product ......................................................................89 4-Vectors and the Scalar Product .......................................................................90 Tensors ...............................................................................................................90 Some Other Tensors ...........................................................................................93 Matrix Algebra .....................................................................................................95 The Tetrad, q a ....................................................................................................96 Contravariant and covariant vectors and one-forms .........................................102 Wave Equations ................................................................................................104 The Gradient Vector and Directional Derivative, ∇ ...........................................104 Exterior Derivative .............................................................................................107 Covariant Exterior Derivative D ∧ .....................................................................108 Vector Multiplication ..........................................................................................108 Chapter 5 Well Known Equations ................................................................................110 Introduction........................................................................................................110 Newton’s laws of motion....................................................................................110 Electrical Equations...........................................................................................111 Maxwell’s Equations..........................................................................................114 Newton’s law of gravitation................................................................................120 Poisson’s Equations..........................................................................................122 The d'Alembertian □ ..........................................................................................123 Einstein’s Equations..........................................................................................125 Wave equations.................................................................................................127 Compton and de Broglie wavelengths...............................................................128 Schrodinger’s Equation .....................................................................................129 Dirac Equation...................................................................................................131 Mathematics and Physics..................................................................................132 Summary ...........................................................................................................133 Chapter 6 The Evans Field Equation ...........................................................................134 Introduction........................................................................................................134 Einstein Field Equation......................................................................................136 Curvature and Torsion.......................................................................................137 Torsion ..............................................................................................................142 Classical and Quantum .....................................................................................145 The Tetrad.........................................................................................................146 Field Descriptions..............................................................................................151 Summary ...........................................................................................................153 Evans Field Equation Extensions......................................................................156
Page 1: 1 The Evans Equations of Unified Fi
Page 5: 5 Standard Model with Higgs versus
Page 8 and 9: Do keep in mind Einstein’s statem
Page 10 and 11: postulate of general relativity. In
Page 12 and 13: thought were incorrect. Einstein wa
Page 14 and 15: 8 Figure I-1 Spacetime Newton’s f
Page 16 and 17: In order to do calculations in the
Page 18 and 19: 12 Figure I-4 The Four Forces Gravi
Page 20 and 21: The Particles There are stable, lon
Page 22 and 23: Chapter 1 Special Relativity 16 The
Page 24 and 25: unnoticeable, for low velocities, b
Page 26 and 27: The nature of spacetime is the caus
Page 28 and 29: Figure 1-3 Graph of Stress Energy i
Page 30 and 31: An example is shown in Figure 1-4.
Page 32 and 33: There are many short form abbreviat
Page 34 and 35: The cross product is not defined In
Page 36 and 37: form. Given that they are discrete
Page 38 and 39: curvature, but does not allow spinn
Page 40 and 41: Chapter 2 General Relativity Introd
Page 42 and 43: However, acceleration and a gravita
Page 44 and 45: Energy density reference frames T =
Page 46 and 47: infinity - at distances where the c
Page 48 and 49: 42 Figure 2-4 Visualizing Curved Sp
Page 50 and 51: Curvature Curvature is central to t
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We showed that gravitation is curva
Page 54 and 55:
Figure 2-9 Base Manifold with Eucli
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In Figure 2-10 at the top is the te
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We put the object in the tangent sp
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The metric tensor is important in g
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Chapter 3 Quantum Theory Quantum Th
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1930’s when it became well establ
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that we have such accuracy as we ha
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spaces. The formulation is beyond t
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frame where measurement is made.) P
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Quantum Numbers The equations below
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Quantum Gravity and other theories
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x time, or momentum x distance, or
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72 E = pc and E = ħ ω and therefo
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When the Planck units are used, it
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76 ms is spin quantum number. It is
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experiments and to describe events.
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are the same space; this is a mathe
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82 If a curve is described by y = a
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Scalar, or Inner Product The dot pr
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Figure 4-5 Cross Product a 86 The v
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product produces surfaces that cut
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4-Vectors and the Scalar Product An
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definite - it is a real distance. I
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Einstein is the tensor defined as G
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With some operations one must add t
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Alternately, a set of basis matrice
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Figure 4-12 100 0 2 1 3 q can repre
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Contravariant and covariant vectors
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The scalars, whether real or imagin
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106 2 _ 1 ∂ 2 c 2 ∂ t 2 can be
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Covariant Exterior Derivative D ∧
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Chapter 5 Well Known Equations Intr
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V = IR. A circuit is a completed ci
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The standard definition of magnetic
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Another way of stating this is that
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Figure 5-4 Ampere's and Faraday’s
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Newton’s law of gravitation 120 A
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Figure 5-6 Fields Poisson’s Equat
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This is a differential operator use
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The Evans equations indicate that R
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Compton and de Broglie wavelengths
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Here ħ = h / 2π = Planck’s cons
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Mathematics and Physics To a certai
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Chapter 6 The Evans Field Equation
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Then the wave equation was develope
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138 q ab µν = q a µq b ν q ab
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From the basic structure of equatio
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142 Rµν - ½ Rgµν = kTµν Eins
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original vector - its orientation i
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The electromagnetic and weak fields
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In more mechanical terms, energy an
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Figure 6-8 Abstract Fiber Bundle an
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The other three fields - electromag
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Figure 6-9 The spin connection and
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Evans Field Equation Extensions R =
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The real physical solutions the wav
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160 Another way to look at the equa
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determined by geometry. This makes
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index, it is generally covariant -
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It is also possible to represent bo
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Electromagnetism 168 The B (3) fiel
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Strong force If tetrad index “a
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neutron into other more stable curv
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explanation for the Aharonov-Bohm a
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ORIGIN Einstein / Hilbert (1915) Ev
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then we found it and used it to des
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Very Strong Equivalence Principle T
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Figure 8-2 Separation of Forces PRI
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Note that physics texts often say t
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criteria for dark matter. We know t
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Figure 8-5 Spinning Spacetime The s
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this gives the influence of gravita
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In all the forms of the tetrad, the
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Spacetime curvature in and around p
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The Evans Wave Equation Figure 8-8
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λ is the wavelength. It can be app
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λde B = ħ / p = ħ / mv (6) where
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where ψ a µ is a tetrad. Therefor
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The components of R = -kT originati
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Relationship between r and λ Profe
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Figure 9-4 Curvature and Wavelength
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One may tentatively assume that the
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The first gives us the Principle of
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Chapter 10 Replacement of the Heise
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p b µ = ћ κ b µ (2) The positio
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The volumes here are derived from V
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The Heisenberg uncertainty principl
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Chapter 11 The Evans B (3) Spin Fie
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where g = e/ћ for one photon; e is
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Figure 11-3 shows the circle turnin
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the curvature very slight at the ea
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The magnetic field components are r
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The B (3) field is the fundamental
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The present standard model uses con
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Using Einstein’s index contracted
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unnecessary and it has been shown t
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Figure 12-4 Momentum Exchange p 3 p
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Figure 12-6 Equations in the Tangen
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were still unknown. However it is o
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Consider an experiment where a beam
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Here κ is wave number, ds is the i
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the Evans unified field theory. Sim
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Figure 13-6 Ordinary Stokes is a ci
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Chapter 14 Geometric Concepts Intro
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where φ is the gravitational poten
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Just what equation will be found to
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where e is the charge of the electr
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have quantization of general relati
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The scalar curvature, R, is defined
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Chapter 15 A Unified Viewpoint Intr
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Asymmetry is a combination of symme
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We know energy density increase is
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G q a µ = kT q a µ. Is one formul
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unknowable measurements. ħ is the
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and their respective ratios was,
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It seems inevitable that we will fi
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Quantum mechanics presented us with
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Evans’ equations the electromagne
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A naïve description would be that
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Note that we are still missing some
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Oscillatory Universe The equation m
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We do not have a definite mechanica
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Glossary There are some terms here
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AIAS Alpha Institute for Advanced S
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The B (3) field and O(3) electrodyn
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The calculations to get coordinates
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Connections Circular Basis The equa
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Elie Cartan worked out an approach
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A covariant component is a physical
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Covariant derivative operator (∇
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Curvature at a given point P has a
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Dimension While mathematically well
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Einstein Field Equation The equatio
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Euclidean spacetime Flat geometric
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Fields explain “action at a dista
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Fundamental Particle A particle wit
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Geometric units Conversion of mass
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describes electrodynamics. It is no
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Index Typically Greek letters are u
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Isomorphism A 1:1 correspondence. J
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Local A very small region of spacet
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Another use is with the Dirac and o
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We want a real number to define the
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Time invariance (or symmetry under
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Dual vectors = one forms = covector
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Meson - Any of a family of subatomi
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The Evans phase law is: This is app
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Quantum gravity Quantum gravity is
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Riemann tensor Riemann calculates t
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Schrodinger's Equation ∇ 2 Ψn =
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The spin connection may be best des
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α angular acceleration; fine struc
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Rotation and reflection of a triang
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Next is O(3) electrodynamics which
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Rank is indicated by the number of
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A spin structure is locally a tetra
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q a µ can be defined in terms of a
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The torsion of a curve is a measure
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our real four dimensional spacetime
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Wave or Quantum Mechanics Study of
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