This is carried out in detail in my polarizable-vacuum representation of GR paper, available at http://arXiv.org/abs/gr-qc/9909037

Spin 1 interactions are repulsive, so they're not relevant for describing gravitational effects-except as part of supergravity, where they have been studied, in the 1970s. 

Permit me to point a possible (quantum) basis for such a model and to note (up front) that 'there is work to be done' to determine whether the basis qualifies as producing such a formula.

The book "Models for Physics of the Very Small and Very Large" provides a possible analog, for elementary particles, to the periodic table for elements. The book attempts to show how some possible (reasonably well specified yet-to-be-found) elementary particles could 'explain' various cosmology phenomena. (I attach some information about the book.)

The book also opens exploration of the extent to which the quantum basis (that the book features) could lead to alternative models for phenomena that people model today via general relativity. A model for gravitation exhibits parallels to models for electromagnetism. For example, gravity would interact with an energy-and-momentum 4-vector current, much in the way electromagnetism interacts with a charge-and-charge-current 4-vector current. Examples of phenomena the book explores (see section 4.6) include gravitational bending of trajectories of light, gravitational redshifting and blueshifting of light, and perihelia shifts.

The book shows a possible (and simple) basis for perihelia shifts. The basis features a seemingly excessive (compared to a non-shifting orbit) orbital angular momentum. The work does not attempt to provide a formula for the magnitude of the shift.

Book Models for Physics of the Very Small and Very Large (this fi...

Book Models for Physics of the Very Small and Very Large (this fi...

Essentially. This is probably the closest you will get. https://www.researchgate.net/publication/226154456_Polarizable-Vacuum_Approach_to_General_Relativity

Chapter Polarizable-Vacuum Approach to General Relativity

This is carried out in detail in my polarizable-vacuum representation of GR paper, available at http://arXiv.org/abs/gr-qc/9909037

Dear Puthoff,

if your theory solves the issue of the localization of the gravitational energy and relegates the validity of the  EEP only for orbital motion,  it is already a good step.

If it manages to predict that clocks free falling do manifest a relative clock retardation which is the same as the one they would experience if they were at rest in the relevant gravitational field, even better.

The polarizable vacuum approach is a metric theory, so EEP is upheld generally, not just for orbital motion.  See H. E. Puthoff, “Polarizable-vacuum (PV) approach to general relativity,” Found. Phys. 32, 927-943 (2002).

So your theory supports the fact that LLI, LPI and WEP are always satisfied and it should be a different view of the GR integrating gravitation and radiation.

It is strange though that Quantum Vacuum can be modeled by a metric which can be wiped away by a choice of coordinates (maybe I'm wrong). If not, it is an Hypermedium which could match the rest frame of the CMBR.

I've already seen the exponential function in the relation of the metric by other authors, It would be interesting to see what can be point of contact with the other theories.

Stephano, In GR nor PV can the metric simply be wiped away. A trivial metric perhaps, but in reality, the notion of a "local inertial tangent plane" is just an approximation method. That over a small enough region of space-time, the curvature can be approximated as flat. That is not the same as wiping it away with a change in coordinates. Many students get confused in this regard, and many other students proliferate that confusion.  I would recommend you read my latest paper, AN ENGINEERING MODEL OF QUANTUM GRAVITY. It shows a viable, alternate interpretation of GR based on the PV Model and Quantum Electrodynamics. 

https://www.researchgate.net/publication/305501551_AN_ENGINEERING_MODEL_OF_QUANTUM_GRAVITY

Best Regards,

Todd

Article AN ENGINEERING MODEL OF QUANTUM GRAVITY

Todd, I was not able to download your paper.  Can you send it to me at [email protected]?

Tnx

Hal

It's good to hear from you Hal! The paper has been sent to you by email. If you don't receive it, just let me know.

Todd

Many thanks to everyone who has contributed to this fascinating discussion. The Polarizable-Vacuum model looks very interesting - many thanks to Harold for sharing this. However, I'm not entirely sure my original question has been addressed. I wasn't really looking to unify EM and gravity. My point was that there is a well-known (since the time of Heaviside) analogy between electrostatic theory (Coulomb's Law) and Newton's law of gravitation, and that an extension to Newton's (static) law of gravity along the same lines as applied to electrostatics to obtain the equations of electrodynamics should be possible. I have been looking into this over the last few months, starting with the expressions for the electric field generated by an accelerated point charge in orbit around a point charge of opposite sign, as given by appropriate differentiation of the Lenard-Wiechert retarded potentials.

Then, one can make the transformation to a gravitational system of two point masses in orbit around each other, by substituting charge for mass and replacing the electrostatic constant (1/4.pi.eps0) with the negative of the gravitational constant, -G. The electric field then becomes an expression for the gravitational acceleration perceived by one of the masses due to the presence of the other. During the last week, I've carried out some further analysis of the resulting equations of motion and have obtained a precessing elliptical orbit displaying the same perihelion advance as Einstein's result.

The physical principles involved in obtaining the above are (i) conservation of mass (as expressed in a continuity equation), (ii) an assumption that the gravitational field propagates in vacuum with the velocity of light, which requires the use of (iii) retarded potentials. There's no new physics required here :). I suppose I should publish this now :).

Stefano wrote: "Hypermedium which could match the rest frame of the CMBR."

In my completed project and related threads in RG I demonstrated that Polarizable Vacuum of Harold Puthoff and Todd Desiato can be extended to high speed in which the kinetic energy resides in a local field of stress energy expressed as convex curvature, opposing gravity concave curvature as in the Lagrangian Density, and polarizing the local vacuum in a measure equivalent to parameter K in the Puthoff representation.

Albert Einstein recommended development of such a field of kinetic energy in his biographical notes published in 1949. He was not able to complete the work because the CMBR was not discovered in his life time. Einstein had no way to define a zero velocity for his kinetic energy field. With CMBR there is a way to define zero velocity anywhere the observed Temperature of space is the same in all directions. I suggest that this rest frame of the CMBR is in fact the Hypermedium that prevents PV theory from being wiped away by a choice of coordinates.

An added benefit is that the kinetic energy field adds frame dragging to the Polarizable Vacuum model, the lack of which in previous work was the main reason for rejection of PV in the wider research community. My work shows that frame dragging was implied in PV, as Todd pointed out in other discussions, but not expressed explicitly until the velocity terms were added. Kinetic field energy was shown to be necessary and sufficient for expressing the velocity terms.

At first I thought Todd's model was in disagreement with mine until he pointed out that I take measurements in the frame of a traveler, which is likely to occur in deep space at high speed, while he takes his measurement with a distant observer in flat space. With this explanation I stopped using the parameter K for representing polarization derived from kinetic energy, to avoid further confusion, since K in Puthoff's model is a field effect of generators operating without velocity dependence.

How this describes advance of perihelion is not obvious to me except that PV theory when extended with velocity terms can express all of the aspects of General Relativity. It leaves the question on electromagnetics unanswered since the net charge on the planets is not known, but only back calculated to agree with the observed perihelions.

LIGO event GW170817 confirms that gravity does move at light speed. There is no fundamental reason perihelion advance could not be estimated by simpler methods than GR, as long as the method uses gravity traveling at light speed.

My derivation of the advance of the perihelion of Mercury in the PV ansatz is in Section III(c) of my longer PV paper on the archive (see attached).

Dear Harlod,

but how do you obtain that exponential. It is a guess which is obvious from a certain point of view, but at the same time it would invalidate the Schw solution (which is exact, not approximated) for strong fields

It is interesting though that you manage to get the Perihelion advance too.

the way you obtained a unification of gravitation and electrodynamics is interesting, though I challange your "gravito-electrodynamics" to be able to explain the dark matter halo.