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

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The Particles There are stable, long-lived constructions that are recognized as the basic building blocks of the universe. There are also fleeting “particles” that exist in accelerator collisions for very short durations. The most organized sense that the particles can be put within is yet to be found. The interrelations among the types of existence is not fully understood. The electron weighs 1/1826 of a proton, but has the exact same charge. The neutron decomposes into an electron, proton, and anti-neutrino in roughly 10 minutes if left outside an atom. A photon can hit an atom and cause the electron surrounding the proton to spread out a bit jumping to a higher orbital – it gives the electron a spatial component. See Glossary for a list of characteristics. We will touch upon the particle puzzles during the course of this book and return to it in the last chapter. What We Will See The first five chapters are introductory review material on relativity, quantum mechanics, and equations that concern both. The next three chapters introduce the Evans equations. The next six cover implications of the unified field equations. Finally, the last chapter is a review with some speculation about further ramifications. Evans has published extensive electromagnetic material that is not covered in this book. 4 The overall subject is too large for a single book. Mathematically there are two ways to describe general relativity and differential geometry. The first is in abstract form – for example, “space is curved”. This is just like a verbal language if one learns the meaning of terms – 4 As this book was being written, it was hard to keep up with developments. For example, explanation of the Faraday homopolar generator which has been a mystery for 130 years has been published. 14
for example, R means curvature. Once demystified to a certain degree, the mathematics is understandable. The second way is in coordinates. This is very hard with detailed calculations necessary to say just how much spacetime curvature exists. In general, it is not necessary to state what the precise curvature is near a black hole; it is sufficient to say it is curved a lot. Any mistakes in this book are the responsibility of this author. Professor Evans helped guide and allowed free use of his writings, but he has not corrected the book. 15 Laurence G. Felker, Reno NV, October 2005
Page 1 and 2: 1 The Evans Equations of Unified Fi
Page 3 and 4: 3 Torsion .........................
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 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
Page 52 and 53: We showed that gravitation is curva
Page 54 and 55: Figure 2-9 Base Manifold with Eucli
Page 56 and 57: In Figure 2-10 at the top is the te
Page 58 and 59: We put the object in the tangent sp
Page 60 and 61: The metric tensor is important in g
Page 62 and 63: Chapter 3 Quantum Theory Quantum Th
Page 64 and 65: 1930’s when it became well establ
Page 66 and 67: that we have such accuracy as we ha
Page 68 and 69: 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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