The Field Equations of the Electroform Model for Unified Quantum Force Field Theory
The Overthrow of Classical
General Relativity
November 10, 1999, April 13, 2003,
August 2003, January 2004,
October 19, 2013.
by James A. Green

Unified Quantum Field Theory

On-line Study Notes for the 11th edition of GRAVITATION & THE ELECTROFORM MODEL
Introduction - The Overthrow || Language Translation
It is now possible to present both long- and short-range forces in local coordinate form as arising due to the local validity of special relativity and the postulates of quantum mechanics, so that relativistic quantum mechanics is built into the foundation of field theory. That this is not true in general relativity when the field is considered in local coordinates is an indication that general relativity is probably wrong.

General Relativity features forces that are not described by locally Lorentz covariant force field equations, but by field equations guaranteeing local Lorentz covariance for components of the metric tensor only. This leads to a number of troubling paradoxes in connection with the way GR grav-magnetic forces (4 times larger than we expect in special relativity) arise from material currents. All other forces are locally Lorentz covariant in field physics. Magnetic forces in electrodynamics arise from properties of the Lorentz transformation in connection with charged currents, but in General Relativity the grav-magnetic forces arise in connection with off-diagonal elements of the metric tensor guaranteeing geodesic motion. We expect grav-magnetic forces to arise in precisely the same way as ordinary magnetic forces, based on a requirement for process synchronization with a local light-clock, so that the process-synchronization rules are unified for all fields of force. In other words, we expect all force-field effects to synchronize with a local light-clock in a way that guarantees the Principle of Relativity.

Classical General Relativity seems to be vulnerable mathematically to a class of overthrow theorems based on non-self-consistency theorems originating in the non-Lorentz covariance of the gravitational forces when material currents are included. The first signs that non-self-consistency theorems existed appear in an article by Wolfgang Pauli and Fierz [1] communicated by Dirac that was published in 1939, and other signs that non-self-consistency theorems might exist are described in Gravitation by Wheeler, Misner, and Thorne [2]. The best treatment in English of non-self-consistency theorems for GR is probably found in Gravitation & the Electroform Model: From General Relativity to Unified Field Theory , 11th edition, December 2002, by James A. Green [3]. I also worked out the details of the electroform unified field theory based on a symmetric generalization in MKS units (and in classical electromagnetic notation) of vector-boson field theory from elementary particle physics. I managed to rule out General Relativity's field equations in 1993 independently, while investigating its field equations and the geodesic equation of motion according to a treatment presented by Einstein in The Meaning of Relativity [4]. At the same time, he was doing readings on the electroweak model, which unified the electromagnetic field and the weak interaction in the 1970s. This was described in Introduction to Nuclear Physics by Cottingham and Greenwood [5]. I lectured on these discoveries to the Graduate Seminar in Physics at Wichita State University 4 times in the early 1990s. The theory predicted locally valid vector-boson field equations in flat space with a gravitationally time-dilated metric, so that it immediately produced the correct prediction for the gravitational redshift. About 1997, I discovered how to derive the curvature of light around the sun with the GR value from the unified quantum field theory of forces he had developed, so that the radar time-delay predictions of General Relativity were also predicted by his unified quantum field theory of forces. In 1998 I succeeded in deriving the perihelion precession of Mercury with the GR value from the electroform unified field theory also, and produced his 10th edition with the necessary derivations from the foundations of his theory. This was really the final hurdle for the development of the theory, although further development was clearly possible. One-third of the precession of Mercury's orbit was due to the gravitational time-dilation required by the principle of equivalence to preserve synchronization of clocks, the other 2/3 was due to the one-way time-delay in the retarded potentials associated with solutions for the field [3,19]. In the case of the curvature of light around the sun, 1/2 of the effect was due to the spacial variation in the speed of light around the gravitating object, the Einstein-Huygens light-bending effect associated with the wave nature of light that Einstein worked out in 1911. The other half is due to the fall of a photon in a gravitational field like a baseball thrown, which is independent of the spacial variation in the speed of light [3].
James A. Green, 1949-Present Press to display larger cover image
James A. Green, 1949-Present, & 11th edition

The Strong Nuclear Force from the Electroform Unified Field Theory
__Another major milestone that occurred early was the development of the electrostrong theory of the nuclear force by me, Green. It was necessary to derive the properties of the both the weak and the strong interaction, as well as of gravitation and electromagnetism, from one simple set of field equations. The electrostrong model for the strong nuclear force was worked out from the core field equations in 1993-94.[3]. I managed to derive a potential series from his field equations that had virtually all of the expected properties, including the attractive and dominant dipole-dipole "tensor" nuclear force originating in the transport of the nuclear charge by the spinning nucleon and the spin-orbit forces. The major surprise was that the static part of the field was fundamentally repulsive, instead of attractive, as it had initially been visualized by Yukawa. Any other choice of the coupling for the strong nuclear force automatically produces the wrong properties for the other components of the nuclear force, as shown in detail in my Papers on Unified Field Theory.

The Further Development of the Electroweak Model
__The theory of the electroweak force was overhauled and further developed from the initial treatment that had been gleaned from Cottingham and Greenwood [5,3,6]. Cottingham and Greenwood showed how to derive the Fermi coupling constant from the theory [5]. I went somewhat further and derived the Gamow-Teller coupling constant from the electroweak model also [3]. Finally, in 1999 I succeeded in deriving the anti-symmetric properties of the weak decays from his fundamental equations [6].

The Impact on Elementary Particle Physics
__It seemed clear that the electroform unified field theory could also furnish a complete theory of the color force between quarks [7] and the forces between the Rishons in the sub-quark theory developed by Haim Harari at the Weisman Institute in Israel [8,9]. However, this development is not finished, so that a theory of the elementary particles in which the rest masses of the elementary particles have been completely determined by exact solutions of the Dirac equation in the presence of this class of force fields has not yet been definitively obtained. However, this approach is expected to succeed when the effects of vacuum polarization are included. The contact forces associated with heavy-particle interactions, when developed as a consequence of the fundamental vector-boson field equations, should have the right form to produce the mass spectra in a definitive way. Instead of a complete theory in which all properties of the elementary particles are determined by the solutions of wave equations in the presence of specific force fields, we have a sketchier theory that predicts virtually all qualities of such systems [3,8,9] except the exact mass spectrum. In particular, Haim Harari's Rishon model predicts color and flavor characteristics of the elementary particles and the value of the Weinberg angle. However, the precise details of the mass spectrum have not yet been obtained.

The Impact on Experiments and Astrophysical Quantities
__I also developed the consequences of the electroform unified field theory for astrophysics and cosmology. The application of the unified field theory to stellar astrophysics only impacted things where general relativity's curvature of space was concerned, since in the unified quantum field theory space is flat and locally Lorentzian. The differences are in the predictions for the masses of supernova cores and in the mass limits for neutron stars [6,10]. Also, there are formally quantities that can be theoretically measured that are different in the electroform model and in GR. For instance, the total energy of a gravitational wave is larger in GR that in the electroform model, although the part of the energy that is easy to detect corresponding to the "electric" part of the field vector, is the same in both theories. The magnetic part of the field energy is higher in GR, but this difference is impossible to measure with existing equipment. Also, measurements made in the space around an object with a strong gravitational field by a flatlander with a meter stick are different in GR and in the unified field theory, but no one knows how to actually do this experiment at this time. In addition, the unified field theory predicts that gravitational wave amplification is possible with specific apparatus [11], but the effect is tiny and difficult to measure. Other differences exist. In particular, the forces between two gravitating bodies on the y'-axis in the K' system translated along the x-axis of Einstein's special relativistic stationary system K are different in General Relativity and in the electroform unified field theory, the gravitational "magnetic-like" components of the field being 4 times stronger according to Einstein than in the predictions of the electroform unified field theory. But this experiment is difficult and expensive, and so far has not been done. I note that in the electroform unified field theory the B-field forces exist solely due to the time-dilation properties of the Lorentz transformation, just as in relativistic electrodynamics. However, in Einstein's general relativity these magnetic-like forces are 4 times stronger, due to the proposition that motion must be precisely geodesic. Probably in the 21st century the associated experiments will be performed in outer space with special fast robotic spacecraft. Using classical GR, according to an observer in K,
F_magnetic = -4(v/c)2F_grav-static,
so that the forces between two gravitating balls are repulsive for v > c/2, and the observer in K must see the balls drifting away from each other! This would also be true in the moving system K', so that the Principle of Relativity is violated: one can detect what the velocity v is in K' just by doing a Cavendish experiment to measure Newton's constant G in K'. Since we can get the classical GR 2nd-order effects via our alternative model for locally Lorentz-covariant unified quantum field theory, we can save The Principle of Relativity and still compute the perihelion precession of Mercury, the curvature of light around the sun, and the gravitational red-shift, the special tricks that kept us hanging on to classical GR for more than 6 decades.
Another experiment using circulating currents confined in large loops may be arranged as a Cavendish experiment to measure the factor of 4, but this would be more difficult than employing special fast robotic spacecraft, as the torsion in the Cavendish experiment is then proportional to (v/c)2, where v is the velocity of the current in the loop. (In this connection see also the on-line notes on The Balance Point. )

The Impact on Our View of Cosmology
__In the electroform unified field theory, like a line from Charlton Heston at the beginning of The Planet of the Apes, "...time bends, space is...boundless". The magnetic-like components of the field are negligible for the expanding universe in matter-dominated era, and the static component of the field is almost exactly Newton's force of gravity, except that it is defined by a retarded potential, as in electrodynamics. Thus, solutions of the cosmology problem are solutions of

d/dt(dr/dt) = - GM(r)/r2

to a high degree of approximation. The simplest, although not the unique, solution to the cosmology problem is then a universe with
r = a (t)(3/2),

where a is easily determined by substitution into the equation of motion. This corresponds to the case of a universe that collapses from infinity and then bounces back to infinity in an inelastic collision, certainly an approximation. However, the solution is approximately correct for the case of a universe with constant density in the matter-dominated era. However, it holds everywhere, so that when we differentiate this expression and manipulate it to find the Hubble constant, we get H(t) = (2/3)/t. However, this equation describes the Hubble constant locally in meters per second per meter without including the observational time-delay. When this is included, the Hubble constant is H(t,L) = (2/3)/(t - L/c), where L/c is the time-delay to the galaxy being observed. This is supported by measurements of the Hubble constant presented in Cosmology by Micheal Rowan-Robinson, page 51. I mean, a fit to Rowan-Robinson's data shows that this formula for H = H(t,L) works out perfectly at large distances. One of the consequences of this is that when c = HL = (2/3)L/(t - L/c), we have L = (3/5)ct, so that we can only see (3/5) of the way back to the Big Bang at t=0. This effect, due to observational time-delay, makes galaxies at the limits of observation appear to approach velocities near c. Furthermore, it means that at the same time the era of galaxy formation is invisible. More detailed analysis shows that in this case distant galaxies we observe in the Hubble Deep Field are roughly 1/2 as far apart on the average as they are in this neighborhood of the universe. This seems to fit the actual observations made with the Hubble Space Telescope rather well. If the solutions for the case of a collapse of a universe of dead galaxies from some finite maximum height or from infinity is done, and the Crunch-Bang event is reckoned as inelastic due primarily to the photodisintegration of nuclei at collision time, one obtains Squeeze-Boom solutions with oscillating-universe properties. In particular, for the present universe, the cycle time turns out to be approximately 232 billion years. If matter is radiated away over the universe lifetime into space, as the electroform model pictures it, the oscillations go on for some thousands of cycles before the universe burns itself to a cinder in a matter of some 20 trillion years or so. This prediction, however, is dependent on perfect symmetry between matter and anti-matter decays, which have been shown to be violated for some mesons. I note that the electroform model predicts that the maximum energy of a photon that may be generated by a known galactic process is about 120 GeV. This obtained by considering the fall of heavy nuclei into the event horizons associated with supermassive objects. In this case the event horizon condition is
2GM(r)/(c2 r) = 1, so that

GM(mA)/r = [(c2)/2](mA), less than 120 GeV,

where mA is the mass of the heaviest nucleus, so that A is less than 256. For some further notes on ultra-high energy cosmic rays, see The Effect of Gamma Rays on Man-in-the-Moon Marigolds from WeatherVisions19.

The Impact on Our View of the Celestial Sphere
There is an associated theory of the organization of imagery on the celestial sphere, including it's ornamental and wave-mechanical symmetries as well as it's mythic interpretation and pictorial content. Imaging galaxies and imaging nebulae sub-illustrate themes defined by nearby constellations in such a way that the entire scene seems to be a mind-mirror of our life here. However, it is now visible how the mind-mirror effect may be connected with the fundamental mirror-symmetry and long-range order associated with field theory as described by the equations of the electroform model [3].

[1] W.Pauli & M.Fierz, "On relativistic wave equations for particles of arbitrary spin in an electromagnetic field", communicated by P.A.M.Dirac, Proc. Royal Soc. of London, 29 Dec. 1939, pages 211-232.
[2] Misner, Thorne, and Wheeler, Gravitation, W.H.Freeman & Co., 1973.
[3] Green, James A., Gravitation & the Electroform Model: From General Relativity to Unified Field Theory, 11th edition, December 2003 state, Greenwood Research Books & Software.
[4] Einstein, Albert,
The Meaning of Relativity, Princeton University Press, 5th edition, 1974, page 102 shows an electromagnetic-like equation of motion, but the "magnetic" components are strangely 4 times larger than expected for a Lorentz-invariant static field.
[5] Cottingham & Greenwood, Introduction to Nuclear Physics, Oxford University Press.
[6] Green, James A., Thermonuclear Fusion in Stars, Greenwood Research Books & Software, 1999. See the sections on beta decay symmetries and the electroweak model.
[7] Halzen & Martin,Quarks and Leptons, John Wiley & Sons, 1984.
[8] Yuval N'EEman, on the elementary particles.
[9] Harari, Haim, published articles. Click for Haim Harari photo.
[10] Green, James A., Supernova Vignettes, Greenwood Research Books & Software.
[11] Green, James A., Electromagnetic Radiation: Fundamentals and Applications, Greenwood Research Books & Software.
[12] Green, James A., Thermonuclear Fusion in Stars, Chapter 9, Greenwood Research Books & Software, 1999.
[13] Green, James A., Astronomical Maps: The Structure of the Celestial Sphere, Greenwood Research Books & Software.
[14] Green, James A. Cosmology: From General Relativistic to Electroform Cosmology, Greenwood Research Books & Software.
[15] Malin, David, Colours of the Stars, Cambridge University Press, James & Jean [18] in the knee of Orion, Figure 88. Also, in NGC 2264, page 123.
[16] Cherrington, Exploring the Moon with Binoculars and Small Telescopes, Dover Publications, Chart IV.
[17] Ferris, Timothy, Galaxies, Sierra Club. See M51, which Green interprets as the "Beyond Within" theme, in which he leaves heavy Susan in NGC 5194 for a bright romance in Tampa in 1986 in the disco whirl of NGC 5195. Also, M83 seems to caricature a romance from his 1st visit to Tampa in 1983. Note that M83 is situated at the Rump end of Hydra near Heaven's Gate.
[18] Jean in 1988. (See pics.html.) See star names Gienah, Agena, also Corvus, Andromeda, smile in Perseus, the Pleiades, and Aries, Cygnus, eye in Aquila. Lost Horizon.
[19] Roseveare, N.T., Mercury's Perihelion from Le Verrier to Einstein, Clarendon Press, 1983. Chapter 6 on velocity-dependent potentials. I note that Surdin's results on round-trip time-delay had an error of sign [3] that when fixed produces the 2/3 perihelion precession we require from the one-way time-delay associated with a standard retarded potential instead of the round-trip time-delays considered by Surdin as described the end of Chapter 6. When this 2/3 precession is added to the 1/3 from gravitation time-dilation, we get the full perhelion advance [3,12].
[20] See unifiedsummary.html for a quick mathematical overview of one of the non-self-consistency theorems and the electroform unified field theory based on vector-boson field models in MKS units.


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