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

More documents

Recommendations

Info

There are many short form abbreviations used in physics, but once the definition is understood, a lot is demystified. A is the symbol for a vector named A. It could be the velocity of car A and another vector, B, stands for the velocity of car B. A vector is typically shown as a bold lower case letter. A tensor may use bold upper or lower case so one needs to be aware of context. For a summary of the types of products of vectors and matrices, see the Glossary under “Products.” a• b is the dot product and geometrically means we multiply the value of the projection of a on b times b to get a scalar number. Typically it is an invariant distance and usually the dot is not shown. The dot product is called an inner product in four dimensions. a x b is called the cross product. If a and b are 2-dimensional vectors, the cross product gives a resulting vector in a third dimension. Generalizing to 4 dimensions, if A and B are vectors in the xyz-volume, then vector C = A x B will be perpendicular or “orthogonal” to the xyz-volume. In special relativity this is time; in general relativity this is a spatial dimension. While special relativity treats the 4 th dimension as time, general relativity is as comfortable treating it as a spatial dimension. The wedge product is the four dimensional cross product. It is covered in more detail in Chapter 4 along with more about vectors. 26 Torque calculations are an example of cross products. 8 τ, 9 torque is the turning force. It is a vector pointing straight up. Figure 1-5 shows the torque vector. It points in the 3 rd dimension although the actions appear to be only in the other two dimensions. 8 For a good moving demonstration of the vector cross product in three dimensions see the JAVA interactive tutorial at http://www.phy.syr.edu/courses/java-suite/crosspro.html 9 τ is used for proper time and torque. The context distinguishes them.
At first this seems strange since the vector of the momentum is in the circle’s two dimensions. However, for the torque to be able to be translated into other quantities in the plane of the turning, its vector must be outside those dimensions. Imagine a top spinning on a table. There is angular momentum from the mass spinning around in a certain direction. The value of the momentum would be calculated using a cross product. In relativity, Greek indices indicate the 4 dimensions – 0, 1, 2, 3 as they are often labeled with t, x, y, and z understood. A Roman letter indicates the three spatial indices or dimensions. These are the conventions. 27 Figure 1-5 Torque as an example of a cross product τ = r x F Tau is a vector, the cross product of r and F, also a vector. r, the radius F = force The cross product of r and F is the torque. It is in a vector space and can be moved to another location to see the results. Tensors are similar. When a tensor is moved from one reference frame to another, the distances (and other values) calculated will remain invariant.
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 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 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
Page 70 and 71: frame where measurement is made.) P
Page 72 and 73: Quantum Numbers The equations below
Page 74 and 75: Quantum Gravity and other theories
Page 76 and 77: x time, or momentum x distance, or
Page 78 and 79: 72 E = pc and E = ħ ω and therefo
Page 80 and 81: When the Planck units are used, it
Page 82 and 83:
76 ms is spin quantum number. It is
Page 84 and 85:
experiments and to describe events.
Page 86 and 87:
are the same space; this is a mathe
Page 88 and 89:
82 If a curve is described by y = a
Page 90 and 91:
Scalar, or Inner Product The dot pr
Page 92 and 93:
Figure 4-5 Cross Product a 86 The v
Page 94 and 95:
product produces surfaces that cut
Page 96 and 97:
4-Vectors and the Scalar Product An
Page 98 and 99:
definite - it is a real distance. I
Page 100 and 101:
Einstein is the tensor defined as G
Page 102 and 103:
With some operations one must add t
Page 104 and 105:
Alternately, a set of basis matrice
Page 106 and 107:
Figure 4-12 100 0 2 1 3 q can repre
Page 108 and 109:
Contravariant and covariant vectors
Page 110 and 111:
The scalars, whether real or imagin
Page 112 and 113:
106 2 _ 1 ∂ 2 c 2 ∂ t 2 can be
Page 114 and 115:
Covariant Exterior Derivative D ∧
Page 116 and 117:
Chapter 5 Well Known Equations Intr
Page 118 and 119:
V = IR. A circuit is a completed ci
Page 120 and 121:
The standard definition of magnetic
Page 122 and 123:
Another way of stating this is that
Page 124 and 125:
Figure 5-4 Ampere's and Faraday’s
Page 126 and 127:
Newton’s law of gravitation 120 A
Page 128 and 129:
Figure 5-6 Fields Poisson’s Equat
Page 130 and 131:
This is a differential operator use
Page 132 and 133:
The Evans equations indicate that R
Page 134 and 135:
Compton and de Broglie wavelengths
Page 136 and 137:
Here ħ = h / 2π = Planck’s cons
Page 138 and 139:
Mathematics and Physics To a certai
Page 140 and 141:
Chapter 6 The Evans Field Equation
Page 142 and 143:
Then the wave equation was develope
Page 144 and 145:
138 q ab µν = q a µq b ν q ab
Page 146 and 147:
From the basic structure of equatio
Page 148 and 149:
142 Rµν - ½ Rgµν = kTµν Eins
Page 150 and 151:
original vector - its orientation i
Page 152 and 153:
The electromagnetic and weak fields
Page 154 and 155:
In more mechanical terms, energy an
Page 156 and 157:
Figure 6-8 Abstract Fiber Bundle an
Page 158 and 159:
The other three fields - electromag
Page 160 and 161:
Figure 6-9 The spin connection and
Page 162 and 163:
Evans Field Equation Extensions R =
Page 164 and 165:
The real physical solutions the wav
Page 166 and 167:
160 Another way to look at the equa
Page 168 and 169:
determined by geometry. This makes
Page 170 and 171:
index, it is generally covariant -
Page 172 and 173:
It is also possible to represent bo
Page 174 and 175:
Electromagnetism 168 The B (3) fiel
Page 176 and 177:
Strong force If tetrad index “a
Page 178 and 179:
neutron into other more stable curv
Page 180 and 181:
explanation for the Aharonov-Bohm a
Page 182 and 183:
ORIGIN Einstein / Hilbert (1915) Ev
Page 184 and 185:
then we found it and used it to des
Page 186 and 187:
Very Strong Equivalence Principle T
Page 188 and 189:
Figure 8-2 Separation of Forces PRI
Page 190 and 191:
Note that physics texts often say t
Page 192 and 193:
criteria for dark matter. We know t
Page 194 and 195:
Figure 8-5 Spinning Spacetime The s
Page 196 and 197:
this gives the influence of gravita
Page 198 and 199:
In all the forms of the tetrad, the
Page 200 and 201:
Spacetime curvature in and around p
Page 202 and 203:
The Evans Wave Equation Figure 8-8
Page 204 and 205:
λ is the wavelength. It can be app
Page 206 and 207:
λde B = ħ / p = ħ / mv (6) where
Page 208 and 209:
where ψ a µ is a tetrad. Therefor
Page 210 and 211:
The components of R = -kT originati
Page 212 and 213:
Relationship between r and λ Profe
Page 214 and 215:
Figure 9-4 Curvature and Wavelength
Page 216 and 217:
One may tentatively assume that the
Page 218 and 219:
The first gives us the Principle of
Page 220 and 221:
Chapter 10 Replacement of the Heise
Page 222 and 223:
p b µ = ћ κ b µ (2) The positio
Page 224 and 225:
The volumes here are derived from V
Page 226 and 227:
The Heisenberg uncertainty principl
Page 228 and 229:
Chapter 11 The Evans B (3) Spin Fie
Page 230 and 231:
where g = e/ћ for one photon; e is
Page 232 and 233:
Figure 11-3 shows the circle turnin
Page 234 and 235:
the curvature very slight at the ea
Page 236 and 237:
The magnetic field components are r
Page 238 and 239:
The B (3) field is the fundamental
Page 240 and 241:
The present standard model uses con
Page 242 and 243:
Using Einstein’s index contracted
Page 244 and 245:
unnecessary and it has been shown t
Page 246 and 247:
Figure 12-4 Momentum Exchange p 3 p
Page 248 and 249:
Figure 12-6 Equations in the Tangen
Page 250 and 251:
were still unknown. However it is o
Page 252 and 253:
Consider an experiment where a beam
Page 254 and 255:
Here κ is wave number, ds is the i
Page 256 and 257:
the Evans unified field theory. Sim
Page 258 and 259:
Figure 13-6 Ordinary Stokes is a ci
Page 260 and 261:
Chapter 14 Geometric Concepts Intro
Page 262 and 263:
where φ is the gravitational poten
Page 264 and 265:
Just what equation will be found to
Page 266 and 267:
where e is the charge of the electr
Page 268 and 269:
have quantization of general relati
Page 270 and 271:
The scalar curvature, R, is defined
Page 272 and 273:
Chapter 15 A Unified Viewpoint Intr
Page 274 and 275:
Asymmetry is a combination of symme
Page 276 and 277:
We know energy density increase is
Page 278 and 279:
G q a µ = kT q a µ. Is one formul
Page 280 and 281:
unknowable measurements. ħ is the
Page 282 and 283:
and their respective ratios was,
Page 284 and 285:
It seems inevitable that we will fi
Page 286 and 287:
Quantum mechanics presented us with
Page 288 and 289:
Evans’ equations the electromagne
Page 290 and 291:
A naïve description would be that
Page 292 and 293:
Note that we are still missing some
Page 294 and 295:
Oscillatory Universe The equation m
Page 296 and 297:
We do not have a definite mechanica
Page 298 and 299:
Glossary There are some terms here
Page 300 and 301:
AIAS Alpha Institute for Advanced S
Page 302 and 303:
The B (3) field and O(3) electrodyn
Page 304 and 305:
The calculations to get coordinates
Page 306 and 307:
Connections Circular Basis The equa
Page 308 and 309:
Elie Cartan worked out an approach
Page 310 and 311:
A covariant component is a physical
Page 312 and 313:
Covariant derivative operator (∇
Page 314 and 315:
Curvature at a given point P has a
Page 316 and 317:
Dimension While mathematically well
Page 318 and 319:
Einstein Field Equation The equatio
Page 320 and 321:
Euclidean spacetime Flat geometric
Page 322 and 323:
Fields explain “action at a dista
Page 324 and 325:
Fundamental Particle A particle wit
Page 326 and 327:
Geometric units Conversion of mass
Page 328 and 329:
describes electrodynamics. It is no
Page 330 and 331:
Index Typically Greek letters are u
Page 332 and 333:
Isomorphism A 1:1 correspondence. J
Page 334 and 335:
Local A very small region of spacet
Page 336 and 337:
Another use is with the Dirac and o
Page 338 and 339:
We want a real number to define the
Page 340 and 341:
Time invariance (or symmetry under
Page 342 and 343:
Dual vectors = one forms = covector
Page 344 and 345:
Meson - Any of a family of subatomi
Page 346 and 347:
The Evans phase law is: This is app
Page 348 and 349:
Quantum gravity Quantum gravity is
Page 350 and 351:
Riemann tensor Riemann calculates t
Page 352 and 353:
Schrodinger's Equation ∇ 2 Ψn =
Page 354 and 355:
The spin connection may be best des
Page 356 and 357:
α angular acceleration; fine struc
Page 358 and 359:
Rotation and reflection of a triang
Page 360 and 361:
Next is O(3) electrodynamics which
Page 362 and 363:
Rank is indicated by the number of
Page 364 and 365:
A spin structure is locally a tetra
Page 366 and 367:
q a µ can be defined in terms of a
Page 368 and 369:
The torsion of a curve is a measure
Page 370 and 371:
our real four dimensional spacetime
Page 372 and 373:
Wave or Quantum Mechanics Study of
show all

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

Create successful ePaper yourself

Delete template?

Save as template?