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:
,
where we define


with, however, . 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:

since . 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 . 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.

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 . 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

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 :


The field equations also determine the locally valid 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 = m_{rest_mass}v/(1 - v²/c²)^1/2. The electroform vector-boson field equations are thought to be locally valid in the metric
,
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
.
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.
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.
Page Images from Gravitation and the Electroform Model, 11th edition.

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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.
Excerpt from the 11th edition deriving the factor of 4 in the solutions of the GR field equations.
[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.

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For more on-line material on the foundations and history of the electroform unified field theory, see