The Field Equations of the Electroform Model :
From General Relativity to Unified Field Theory

by
James A. Green
Nov.24, 1999; Nov.26-29, 2002; Aug. 2003; May 4, 2005; Dec. 17, 2010, August 12, 2011, October 19, 2013.

Summary for Distribution || Language Translation
This is to introduce the fall of General Relativity's field equations and the electroform model for unified field theory that will replace GR. If one analyzes the system of Einstein field equations plus the equations of motion for the case of weak fields and weak currents in Cartesian coordinates by the method pioneered by Einstein in The Meaning of Relativity, page 102, one obtains source-conjugated Maxwell's equations in 4-potential form:
GR weak-field gravitation 4-potential equations,

where we define


with, however, weak-field GR epsilon and mu values. Note the strange extra factor of 4 in the grav-magnetic permeability of empty space. Further research shows this factor of 4 is also present in exact solutions of the Einstein field equations, such as the Kerr Metric [1].
Straightforward manipulation of the above weak-field GR field equations in 4-potential form with these coupling coefficients yields an invalid form for the equation of continuity:
invalid eqn of continuity with factor of 4

since weak-field GR coupling coefficient product ID. Classical General Relativity shatters on this rock [1]. See also the section on the balance point in [2] below for an analysis of related GR problems involving the Principle of Relativity. Closer analysis reveals that the origin of the problem is that the principle of equivalence does not predict spacial curvature in the static metric, and that the problems are injected by the choice of the Einstein field equations, which set the contracted curvature tensor equal to the source density tensor source density tensor derived from matter tensor. Then the components of the metric tensor are locally Lorentz covariant, but the components of the gravitational force field are not! Instead, the GR grav-magnetic field is derived from artifactual off-diagonal components of the metric tensor in a way that injects the troublesome factor of 4 and spoils the Principle of Relativity from a forces point of view.


Also, we have c = (1/2)(1/μgεg)1/2, half the speed of light one obtains in an electromagnetic-like theory with c = (1/με)1/2. The later speed is really the speed of light we would expect from requiring the local Lorentz covariance of the GR field equations, in fact. But this turned out not to be true. Using Einstein's field equations has the consequence for weak fields that grav-magnetic and electro-magnetic forces would not be synchronized when considering forces between objects on the y-axis translated along the x-axis, as in special relativity, so that the Principle of Relativity would be violated when fields were weak with both fields exhibiting Maxwellian symmetries for like-charges-attract (gravity) and like-charges-are-repulsive (electric) sources, respectively. Thus Max Born asked Einstein early on at a GR lecture what the speed of light would be in the new General Relativity Theory. That the speed of light from the field equations out was not the usual speed of light would be fatal to process synchronism expected from the Principle of Relativity in the weak-field limit. However, this objection cropped up before the internal contradiction involving an invalid form of the equation of continuity became evident. Wags critiqued GR by observing that it was "too clever by half". The Meaning of Relativity exposed the electromagnetic form of the equaition of motion without exposing the factor of 4 anamoly in the grav-magnetic coupling and its consequences, but the "Meaning" of the whole GR business was left in embryonic form in the doorway, visible to analytical minds that could compute forwards a few steps beyond. (Appended August 12, 2011).

On to the true quantum field theory of forces! The foundation of the electroform unified field theory is obtained by insisting on the Lorentz invariance of vector fields with sources whose quanta satisfy Sp.Rel.energy-momentum law. Applying the usual wave-mechanical operators for energy and momentum to this expression, and insisting on Lorentz invariance (synchronism of processes with light-clocks or electromagnetic processes) for this class of fields yields
The Force will be with you...always.
These have solutions in retarded potential form for field bosons of mass m, in which the square brackets indicate evaluation of the density or current at r',t' = t - |r - r'|/c :
4-potential solutions of the electroform field equations

The field equations also determine the locally valid equation of motion The Force of the electroform equation of motion., which can be derived from the field equations in local coordinates. Here F = dp/dt, where p is the usual relativistic momentum p = mrest_massv/(1 - v2/c2)1/2. The electroform vector-boson field equations are thought to be locally valid in the metric
global metric in Cartesian Coordinates,
which is perhaps better given in spherical coordinates, in which case it is approximately the Schwartzschild metric in flat space with gravitational time-dilation only. This gravitational time-dilation is a direct result of applying Einstein's Principle of Equivalence, as easily shown by Einstein's 1911 thought-experiments. That the radial part of the metric is not necessarily curved when the Principle of Equivalence is applied was was described in Gravitation by Misner, Wheeler, and Thorne, and mentioned to me also by Dr. Joseph Strecker in 1975, who also independently noticed it.
The fully developed electroform unified field theory turns out to feature interrelated coupling constants
static coupling coefficients of the electroform model.
The like-charges-repel static field generates details of the nuclear force when we picture spin as giving rise to charge transport and circulating currents. In this case we picture the nucleons as like-charged to get the right form for the dominant dipole-dipole "tensor force" and simultaneously the right form for the spin-orbit force. We can obtain a power-series expansion for the nuclear force directly from the solutions of the electroform unified field theory by introducing a vector identity to clarify the circular charge-transport mechanism in the spinning nucleon. A contact-force representation for the weak part of the field is also derivable from the electroform field equations by a method described by Cottingham and Greenwood, in Introduction to Nuclear Physics.

The precession of the perihelion of Mercury and the curvature of light around the Sun have been obtained from the electroform field equations and flat-space metric given above. Superposition of effects is used to obtain the GR values. The gravitational redshift is also given, simply from the metric. The electroform field equations are set up so that each component of the 4-potential is a representation of the Klein-Gordon equation with sources. In elementary particle physics these vector-boson field equations are typically given in right-hand rule form only, which corresponds to like-charges-repel coupling logic, and in a different notation. The symmetric MKS unit format shown above that brings out the role of the coupling constants and exhibits the "+-" symmetry between like-charges-attract and like-charges-repel logic was developed by James A. Green in the 1990s as well as the the electrostrong model for the nuclear force.
Press to display larger cover image For further details, see Gravitation & the Electroform Model: From General Relativity to Unified Field Theory , 11th edition, by James A. Green, from Greenwood Research Books & Software. See also The Overthrow of Classical GR and the excerpt on deriving the factor of 4.




Footnotes
[1] The factor of 4 has precisely that value in the weak-field problem if the Einstein-Grossman theorem which Laplacianizes and simplifies the linearized field equations is true. Furthermore, the factor of 4 re-appears when we consider exact solutions of the Einstein field equations and examine the case of weak fields and weak currents, just as we would expect if the Einstein-Grossman theorem were true. However, in reality the identical vanishing of the quantity that reduces the linearized field equations to Laplacian form according the result of Einstein & Grossman has resisted my personal attempts to prove it! If it is not assumed to vanish, another non-self-consistency theorem can be derived with similar properties, however, as shown in the 11th edition of Gravitation & the Electroform Model. Furthermore, the field quantities associated with the exact solutions, whose precise coefficients may be obtained by a dimensional analysis of the Kerr solution (following a derivation by Chandrasekhar) lead not only to the factor of 4, but also to the violation of the equation of continuity. It may also be shown in both cases that the GR gravitational B-field quantities do not transform according to the Lorenz transformation in local coordinates, although they vanish in the frame which is stationary relative to the moving source. On the other hand, gravitational B-field quantities in the electromagnetic-like electroform model for forces are in sync with a local light-clock, locally Lorenz covariant, and inject no difficulties.
[2]Supplemental Remarks, Nov.26,2002 - Nov.29,2002:
Dear Physicists and Physics Students,
Please acquire books & software from Greenwood Research online. I particularly recommend the 11th edition of Gravitation & the Electroform Model: From General Relativity to Unified Field Theory by James A. Green, Greenwood Research, 2002, ISBN 1-890121-592, list $48.00.
This book replaces classical General Relativity with a unified quantum field theory of forces in flat space with gravitational time-dilation only that still yields the 2nd-order classical GR effects, such as the perihelion precession of Mercury, the curvature of light around the Sun, and the gravitational red-shift. It turned out that classical GR did not feature locally Lorentz covariant gravitational forces, so that the Principle of Relativity was violated in an inertial frame: it is possible in classical GR to determine if one is moving across the background of space, as gravitational processes in the frame and electromagnetic processes are not then both synchronized with a local light-clock. According to the usual Principle of Relativity, motion against the background of absolute space cannot be determined by any measurement within the system, but in GR this not so, because the field equations do not apply to the force of gravitation, but to the components of the metric tensor. Making the field equations for the components of the metric tensor locally Lorentz covariant does not, however, make the forces locally Lorentz covariant. In fact, from the GR field equations and geodesic equation of motion, one can determine (as Einstein showed in his classic The Meaning of Relativity, pg.102) that
F_grav = m( E_grav + ( v x B_grav)) + (negligible higher-order terms),
but a closer analysis shows that the GR grav-magnetic coupling factor for currents, mu_grav, is 4 times stronger than it would be if the grav-magnetic part of the field were obtained simply from local Lorenz transformations, that is, from synchronization with a local light-clock, as is true for the magnetic field in classical electrodynamics. Thus a Cavendish torsion-pendulum experiment to measure the Newtonian constant of gravitation G could give different results on-board a spacecraft moving with velocity v, according to an external observer, so that from various measurements of G made aboard the spacecraft it would be possible in classical GR to determine the magnitude of the velocity and the direction of travel through absolute space. In fact, at v = c/2 the grav-magnetic force and the gravitational force balance between two spheres on the y'-axis if the motion is in the x-direction, according to an observer in the stationary system. Whether or not GR formally claims that the grav-magnetic force vanishes in the moving system, this violates the Principle of Relativity, introduces local process synchronization problems into our picture of nature, and must certainly be regarded with suspicion.

The Balance Point
To understand this better, it turns out that in classical electrodynamics and in electromagnetic-like gravitation theory the forces between two spheres on the y'-axis of the moving system K' parallel to the stationary system K and moving along the x-axis with velocity v obey
F_magnetic = -(v/c)2F_static.
In General Relativity, however, mu_GR = 4*mu_grav, so
F_magnetic = -4(v/c)2F_static.
Thus in the GR case, the grav_magnetic and the static gravitational forces balance when v = c/2, and for v > c/2 the grav-magnetic force is stronger, forcing the two spheres to move away from each other. That is, classical GR predicts there exists a frame of reference in which two gravitating bodies do not attract each other! Obviously this cannot be true in a locally Lorenz covariant field theory of forces. In this case the spheres must always seem to drift together according to an external observer, except in the limit as v approaches c, when the motion must seem to freeze. As long as forces are described by Lorentz-covariant force-field equations, The Principle of Relativity will be satisfied as Galileo understood it: cannonballs dropped from the top of a mast will strike the deck at the foot of the mast, and the action will always take the same time according to a local observer, although this is not the case in classical General Relativity!
The unified quantum field theory developed in the book introduces classical vector-boson field theory in local coordinates, which yields suitably Lorentz-covariant representations for gravity, electromagnetism, the strong nuclear force, and the weak interaction. Introducing the principle of equivalence as Einstein did in 1911, one imbeds the generalized Maxwellian equations of classical vector boson field theory into a metric with gravitational time-dilation only to describe the forces. The falling-ruler thought experiments sometimes used to justify curvature in the spacial part of the metric do not hold for the stationary rulers described by the GR metric, so this book takes the spacial part of the metric to be flat. This turns out to yield the correct General Relativity 2nd order effects when superposition is used in connection with wave-particle duality effects, and guarantees that the Principle of Relativity holds. In addition to working out these revolutionary details, the book derives the details of the nuclear force from the generalized Maxwell equations, and also introduces the associated cosmology, which is better determined than in classical general relativity, so that it is possible to compute the maximum depth of vision into the expanding Big Bang fireball at about 8.1 billion light-years, the distance at which galactic red shifts hit the Red Limit, because then galaxies seem to be moving away with the speed of light. The "squeeze-boom" cosmology theory also makes it possible to estimate the cycle time of the oscillating universe at about 232 billion years.
On the fermion side of the unified field theory problem, the book introduces the Rishon sub-quarks proposed by Haim Harari and Micheal Shupe, treating the problem of the decay of the proton and deriving neutrino decay events that may be used to prove the Rishon sub-quark theory valid. The Rishon model explains how all quarks are excited or ground states of the U and D quarks. It also provides as many anti-particles as particles in ordinary matter, solving the matter-anti-matter asymmetry problem in Big Bang theory, as first pointed out by Haim Harari. Furthermore, it elegantly and simply explains the origin of color and flavor. A procedure is also proposed in the 11th edition for computing the mass spectrum of the elementary particles in a rigorous manner. Please acquire this seminal and important book for your college library or personal collection. - James A. Green
[3] It is amusing to note that perhaps The Arthurian Legend of The Sword in the Stone is involved in this piece of Einstein & the Holy Grail of space-time research. It seems that the Sword in the Stone is manifested as an enormous golf tee signaling "Relativity" in the great stone head of S.Monocerotis, which seems to show our man drifting with his WUF-resume to the heights, having changed our view of the warp and woof of space-time.

For more on-line material on the foundations and history of the electroform unified field theory, see
The Overthrow of Classical General Relativity

The Units of Unification
The approach used in the 11th edition of Gravitation & the Electroform Model is to avoid the "hints and clues units" commonly found in graduate coursework in elementary particle physics which set h-bar = 1 and c = 1, and then proceed also to set the static field coupling ε = 1 and the magnetic field coupling μ = 1. Of course, setting the field coupling constants to unity along with h-bar and c makes formulae difficult to apply in obtaining results, so that many physicists may be compelled to keep notes in MKSC units and publish them in "natural units" which are actually unnatural and serve mainly to introduce a smokescreen of confusion as a security hoax to keep neophytes under control. The "natural units" approach with force field couplings set to unity has been championed as "the beautiful equations" approach, because there is something slippery and slick about the equations of physics thus stripped, which may then require extra explaining in private sessions when slipped to students, who just cannot seem to compute the numeric answers to problems to save their souls aside from a consultation with a secretive master equipped to deliver a great denouement in person. The French Revolution decisively rejected this approach when it instituted MKSC units, but it has been so many decades ago that secretive practices were finally re-instituted to promote science as a discipline in some fields dominated by obscurantism. As far as I can determine, the blow fell on theoretical physics when Dirac published his brilliant theory of the electron. The advance was so decisive that Dirac won the Nobel Prize, but the consequent gain in prestige allowed his approach for stripping equations of essential constants in order to "beautify" them to dominate editorial boards in physics. We have been stuck with it every since then in order to keep up good press for Nobelist Dr. Paul Adrian Maurice Dirac, who felt that he could not proceed in the French environment without introducing a superfluous element of mystery and disguise repellant to us and worse than useless for purposes of clarification. Now that Dirac is deceased, I propose we give up the element of guile and the disappearing ink that confuses our equations and makes them difficult to apply, though it causes valuable students to cry and come begging for help. Then many could obtain grants to translate material in factually unnatural units into standard undergraduate Meter-Kilogram-Second-Coulomb units, an entertaining business that usually proceeds in secret notebooks for no good reason much of the time. I note that suppressing the force coupling constants blanks out some of the problems discussed above regarding the strange factor of 4 introduced by classical General Relativity into the grav-magnetic coupling μ in the linearized field equations of gravitation in local coordinates. Thus the practice of introducing secretive "hints and clues units" frustrated the advance of theoretical physics in unified quantum field theory by also throwing up a smokescreen defending classical General Relativity against progressive insight. I don't think we should pursue obscurantist standards in physics that make things artificially difficult, as if we were mocking the circumstance that the student seems to need something hard to follow.
- James A. Green, February 26, 2005, updated Dec.19, 2005 and October 19, 2013.
See the associated simultaneous Cloud Vision 93.

A visionary scenario of unitary mythos is associated with the emergence
the unified quantum field theory above: See Orion Sky: Spring, Winter, Summer, Fall.


Above: Jim Green (55) in 2004 with his hair dyed.
I graduated with an undergraduate degree in physics and mathematics from KU in 1973, having taken a readings course in special relativity from Dr. Daniel Ling. After graduation, I decided to change my major to electrical engineering, but I was still interested in relativity and took the time to master classical General Relativity on the side. In 1975 I paid to lecture Dr. Joseph Strecker on classical GR for two semesters, a bit like Professor Barnard in The Day the Earth Stood Still. Dr. Strecker thought perhaps vector-boson field theory should be considered in analysis of alternate field theories of gravitation, and was emphatic that the principle of equivalence did not yield the curvature of space from thought experiments, but only gravitational time-dilation, a viewpoint echoed in Gravitation by Wheeler, Misner and Thorne. Only the imposition of the relatively far-fetched Einstein field equations could introduce spacial curvature into the metric. Dr. Strecker resembled Micheal Rennie (Klaatu in the movie) at the time. By the end of the course I still believed GR was the correct theory, however, because I did not see how the perihelion precession of Mercury and the curvature of light around the Sun could otherwise be derived at that time.
By 1993 I had familiarized myself with vector-boson field theory, and had more proof that classical GR was probably wrong, based on the factor-of-4 difference between the magnetic coupling constant μgrav in electromagnetic-like gravitation vs. its value in classical General Relativity. I had also succeeded in deriving the details of the strong nuclear force and other fundamental forces from one system of ordinary plus mirror-image Maxwell's equations which were very conservatively derived. Finally, in 1998 I succeeded in deriving the perihelion precession of Mercury, the curvature of light around the Sun, and the gravitational redshift all three from my unified quantum field theory, and published it in the 10th edition of Gravitation and the Electroform Model: From General Relativity to Unified Field Theory. Later, I published the 11th edition, attempting to refine my statement of GR overthrow theorems I had discovered. Immediately thereafter, the "Big Eleven" of the Twin Towers at the World Trade Center in New York fell to earth like two columns of clay on September 11, 2001 ... I seemed to many to undercut myself. After some time, the earth stood still again.

Letter: Beyond General Relativity May 4, 2005

Advanced Astrophysics by James A. Green from Greenwood Research.
[1] Gravitation and the Electroform Model, 11th edition, 2002. || Summary.
(3000 BC: Menes unifies Upper and Lower Egypt, and a new capital is erected at Memphis.)
I also point out in this one that the S-quark may be pictured as an excited state of the D-quark, suggesting that the U, D, and S quarks of Gell-Man are not fundamental, but derived from sub-quark rishons T, V as described by Haim Harari and Michael Shupe.
[2] The Electroform Unified Field Theory
[3] Papers on Unified Field Theory
[4] Thermonuclear Fusion in Stars, 2nd edition. || The Sun | Sirius A | ZAMS Sun | Carbon Cycle.
[5] Supernova Vignettes || STAREXP Example: The supernova of Antares.
[6] CHANDRA || Sample white dwarf with iron chemistry.
[7] Cosmology: From General Relativistic to Electroform Cosmology
[8] Galaxy Formation via the He++ to He+ phase transition in the cooling Big Bang fireball.
[9] Astronomical Maps: The Structure of the Celestial Sphere || OrionSky
[10] Free Stellar Astrophysics Downloads Free Stellar Structure Download ZIPS. || Free Stellar Structure Download Web Page thelostchord.html. | 2nd order stellar structure calculations.
[11] Jim Green's Derivation of the Big Bang Helium Abundance.
[12] Jim Green's Derivation of the Limit of Telescopic Vision in the Expanding Universe.
More red limit observations with Galaxy 51.
[13] Sanford, Observing the Constellations.
[14] Burnham, Burnham's Celestial Handbook, vols 1-3, Dover.
[15] Allen, Star Names, Dover.
[16] David Malin and Paul Murdin, Colours of the Stars, Cambridge U. Press, 1984.
[17] Donald D. Clayton, Principles of Stellar Evolution and Nucleosynthesis, McGraw-Hill, 1968. This black-jacketed edition features a Centaur engraved in white on the cover with a drawn bow, suggesting "Star Wars", and is one of my first astrophysics favorites. I have read it several times, a circumstance which thematically synchronizes with the NGC 2264 S.Monocerotis image shown above, in which a figure flying my WUF-resume encounters a black "Centaur". The Centaur head looks like it might weigh a ton, synchronizing with "Clayton" and with my possible first American ancestor, Aderton Greene.
[18] Bowers & Deeming, Astrophysics I: the Stars.
[19] Hong Yee-Chiu, Stellar Physics. || I am a Rock {11} | Chiu solar age 4.5244x109 years.
[20] Martin Schwarzschild, Structure and Evolution of the Stars, Dover.

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Press for The Overthrow of Classical General Relativity.
Green Machine courtesy AlienWare: The Aurora DDR
Background from Mathematical Landscapes by Zarko D. Mijajlovich prepared with Bryce 4.