1. Charge and mass are different properties of matter.

2. Gravity is different from charge (where one has positive and negative loads) and also different from magnetic fields, which are produced only by dipoles, while gravity sources are monopolist. 

Those two facts make analogies phenomenologically difficult, regardless mathematical tricks about the dimensionality of formulas. 

A big and phantasist question is if by complex induced electromagnetic interactions one can produce (or not) artificial gravitational effects. There is a modern myth (or more a fairy tale) called Philadelphia Experiment, suggesting that such effects are possible. Beyond this ""hint"" we don't know anything.

Yes! If we use first equation of Maxwell... In reality we need formulation of this equation with other criteria... Same exists possibility at the 4th equation of Maxwell...

Dear Mihail Popescu:

1..  Your mention in two points are correct (taking in consideration actual theories)

But we know well the actual gravity theory problem has lot of problems,… The problem comes  from  use of mass and not charge, more precise electron charge... The Galileo Tide explanation was forgotten even if Galileo had right...

Dear Mihai,

Thank you for the first response.

As you rightly point out differences I often focus on analogies after being exposed to heat mass transfer as well as fluid dynamics problems.

Like Fourier equation for heat has analogy in diffusion and some other processes (see [1]) there may be more. My question is an enquiry about possible analogy. The dissimilarities in concepts do not rule out analogies although there are limits to analogies.

The Maxwell equations in my choice of units are not different from the originals but dimensionality indicates that some seemingly distant concepts can be related.

Electric field (EF) is Force/unit_charge. Since unit_charge whatever it might be is legitimately now in m^3/s^2 the EF is now m/s^2 that is acceleration unit. Gravity acceleration in a point in space characterises the strength of the gravity field, so what makes it strange to postulate replacing charge in Maxwell equation with same dimension mass and look at gravity from this perspective. You can apply curl on the acceleration vector field and it must be something on the right side of the equation to match it. But what is it? What is the physiclal interpretation?

When it comes to EM and Gravity relation. Let me draw your attention to US Patent of

Douglas G. Torr and Jose G. Vargas US6891712 B2 where it is stated:

In July 2001, a three-day meeting of the American Institute of Aeronautics and Astronautics (AIAA) was held in Utah. V. Roschin and S. Godin presented a paper: An Experimental Investigation of the Physical Effects in a Dynamic Magnetic System. (American Institute of Aeronautics and Astronautics 2001 Meeting, AIAA-2001-3660). The paper described an assembly of static and rotating magnets, which purportedly achieved a gravitational effect. The authors reported reductions in observed weight ranging up to 35%. However, the paper gave no theoretical basis for the result.

Professor Timir Datta of the University of South Carolina and students and Professor Ming Yin of Benedict University in Columbia, S.C. claim to have observed a gravitational effect in an experiment that placed a test mass in an electric field. They reported a change in weight of up to 6.4 parts in 106. An electric field was produced by an electrode pair comprised of a cone and a flat plate.

Another contribution to the theoretical understanding of gravitational and electromagnetic effects and their interrelation can be found in J. G. Vargas & D. G. Torr, The Cartan-Einstein Unification with Teleparallelism and the Discrepant Measurement of Newton's Constant G, in Foundations of Physics, 29, 145-200 (1999).

[1]T. N. Narasimhan FOURIER'S HEAT CONDUCTION EQUATION' HISTORY, INFLUENCE, AND CONNECTIONS  http://onlinelibrary.wiley.com/doi/10.1029/1998RG900006/pdf

We have one match already:

The Gauss Law

https://en.wikipedia.org/wiki/Gauss%27s_law_for_gravity

https://en.wikipedia.org/wiki/Gauss%27s_law

We must postulate gravitational induction to justify the other Maxwell equations

The ultimate problem is what is c for gravity?

Dear Arno,

Does your approach indicate whether gravitational disturbance is instantaneous or it has some speed limit?

We have still open argument on this due to van Flandren:

http://metaresearch.org/cosmology/speed_of_gravity.asp

http://metaresearch.org/cosmology/gravity/speed_limit.asp

In general relativity, gravitational waves are described with the equations analogous to that used to described electromagnetic waves.

Dear Andrew, (and dear Laszlo)

thank you very much for the impressive literature. I didn't know anything about this patent and the other research. If those things are true, I suppose that meanwhile at experimental level much more is known, but kept secret. 

The problem in my opinion is deeper as just what is c for gravity. It is moreover what is the companion field for gravity. I mean companion field thinking to the pair electricity - magnetism as companion phenomena, as depicted by Maxwell's equations. Maybe gravity is just its own companion field, but should it mean that variation of gravitational field is ... gravitation again? 

The exprimental evidence you produced suggested much more that  variation of magnetic field (by accelerating sources, because rotational movement is automatically accelerated movement) could produce gravitational forces. In this case it is possible that Maxwell's equations are just too much simplified, and that correct equations must contain a field term for every known field, to appear in every equation telling what happens when a particular field varies. Maybe a variation of gravitational field produces also weak electromagnetic waves.

It could be so - but again, we are far away from this ontology, and I am affraid that some dimensional argument alone is really not enough to justify this. Sorry if I am dissapointing you. But I don't write for this sake.

A big theoretical difficulty I see in this context is that the "empty space" assumption chosen to derive the electromagnetic wave formula and the invariancy of c relatively to inertial frames is much more difficult to be assumed if the field is not just electro-magnetic but instead "electro-magnetic-gravitational" or directly "unified". 

Also, if the experimental evidence that you cited is really true, then it didn't make any sense to perform the MM experiment on the surface of Earth, which has an accelerated movement and is a tremendous gravitational source. IF THOSE THINGS ARE TRUE, then the MM experiment must be repeated in imponderability.

I also wonder if the guys had to perform any experiment in order to get the patent. I am affraid that they hadn't, as the patent is just a bureaucratic act. But on the other hand in order to get the patent they had to pay for it, so they were damned convinced of it...

Dear Arno, it seems that you have a mathematical model. Can you please describe it with more detail?

 Dear Yin Zhu

I am not discussing General relativity. I am wondering why classical physics failed to predict gravitational waves. The case of Maxwell equation is an interesting possibility, but if propagation of gravity is instantaneous as you seem to support, then only the Gauss equation that matters I think.

Regarding the title of the question and disregarding the rest of the discussion, see 

A GRAVITATIONAL AND ELECTROMAGNETIC

ANALOGY.

 BY OLIVER HEAVISIDE.

[Part I, The Electrician, 31, 281-282 (1893) and Part II].

This is an approximation of general relativity which takes into account only the four components of the metric tensor with one index equal to 4 ( or 0 depending on your definition).  These four quantities are treated by Heaviside as the analogs of the electromagnetic 4-potential.  It is thus a vector theory of gravitation rather than a tensor one.  This theory can be derived in general relativity as the first post-Newtonian approximation.  But note that Heaviside postulated this theory when Maxwell's electrodynamics was the apex of physics more than twenty years before general relativity!  It remains a useful approximation for low fields and slowly moving particles in a gravitational field.

Thanks Ramzi for your valuable contribution.

This Heaviside work is exactly what I was asking about. I was blissfully unaware of it.

I will have to read this and compare with my raw analogy idea derived from the unified mechanical and electromagnetic units.

 I found "reproduction of Heaviside's article ... an unedited copy of the original. Oleg D. Jefimenko have converted some formulas and all vector equations appearing in the article to modern mathematical notation.

http://serg.fedosin.ru/Heavisid.htm

Also a very interesting Article Gravitation and Special Relativity

by D. H. Sattinger http://math.arizona.edu/~dsattinger/GravSpecRel.pdf

There are suggestions that dark matter theories can be a misunderstanding due to incomplete description of gravity laws.

Andrew, this is the version of Heaviside's article that I have.  It is conveniently in modern notation.  Do you know where we can find Part II of the article?

My apologies.  Part II of Heaviside's article is in the same publication cited previously.

Dear Ramzi,

Thanks to your reference I am finding more interesting views on this subject.

The article:Newtonian Gravitomagnetism and analysis of Earth Satellite Results by

Harihar Behera [1] fully validates my suspicion that gravitation analogy of Maxwell equations is valid with some mas/gravity specific attributes. I attach the snapshot of relevant result. Note that new constants:

ε0g = 1/4πG

µ0g = 4πG/cg2

in my modified kilogram free metric system they become really simple:

ε0g = 1

µ0g = 1/cg2

Where cg is the speed of gravity disturbance.

The conclusion is that if cg is infinite we have no gravitational waves.

[1]Harihar Behera, Gravitomagnetism and analysis of Earth Satellite Results 

 http://arxiv.org/pdf/gr-qc/0510003.pdf

Dear Arno,

I think non-GR approach to gravitational waves is beneficial. It looks like Maxwell equations are relevant to gravitation but the knowledge of the speed of gravitational disturbance propagation is not determined by the equations, so its justification must come from fundamental theories. Heaviside in 1893 was already speculating about speed of gravitational disturbance propagation allowing it to be c or greater.

Dear Arno,

I do not insist on GW I am not instantly dismissing a possibility when it comes of Maxwell equations and of course GR. I respect Tom van Flandern and others' finding which give gravitation disturbance propagation speed ten to the power of ten greater than c and that is being honest to account for experimental error. But I retain openness to other ideas as I would like other people to be open for mine..

I have big doubts about GR GWs  because I know how badly is time interpreted in special relativity, but I have not enough knowledge of GR to tell if that matters or not.

 Yes it can be applied;

Review this transformation x=R^2(x'-vt') t=R^2(t'-vx'/c^2) y=Ry' z=Rz' 

it expresses about the wave-particle duality and the uncertainty principle.

Dear Arno,

I have no my own scientific position on gravitation being of em-nature. I may only  have some heuristic hypotheses and observations:

1 There is a bond between electrical phenomena and gravitation:

• Forces arise from gravitation and EM phenomena and act on masses
• dimensionally consistent similar equations can describe both fields (if my units of measure unification approach is taken seriously)
• Lihgt is bent by gravity 
• US Patent of Douglas G. Torr and Jose G. Vargas US6891712 B2 refers to experiments and theories that support this view

2. Something (gravity) is gonna hold this world all together as one, and that is why anything else is possible (highly speculative and unscientific)

3. I have more than vague indication that the absolute reference frame has mathematical necessity if STR works as it does. Absolute space can then be contemplated as an entity having properties and structure allowing propagation of interactions.

Dear Azzam

Your transformations indicate that relative simultaneity results from them. That makes me skeptic because that distorts the view of temporal relation as it does in naive application of Special Relativity. But saying that STR can still be used if you properly understand temporal concepts distortion it causes. So if you have solid arguments for your transformation this interpretation can be fixed.

Dear Arno,

I do want to read your papers with understanding but I have to focus on my stuff first so it has to wait a bit. What I have already seen looks very interesting but I am not able to comment just yet. 

I thought before that genesis of magnetic field of the Earth has something to do with gravity, but I found there exist planets without magnetic field.

Mars and Venus have no magnetic field

Mars has about 24 hours rotation period and Venus 243 day rotation period

Mars has about 686 days revolutuion period,Venus has about 224.7 days revolution period

So the lack of magnetic field does not seem to be correlated with motion of the planets.

Dear Andrew Wutke,

After reading your last comments perhaps I can have some important suggestions as geologist engineer (without working in my profession last 20 years…)

“I thought before that genesis of magnetic field of the Earth has something to do with gravity, but I found there exist planets without magnetic field.”…- The planetary sciences has same such of accepted theories which makes very hard to understand our planets origin, our planets inner structure… and their evolution (http://planeterosion.blogspot.hu/...) from the mentioned work I can suggest you:

“Mars and Venus have no magnetic field”- Mars is an older planet like Earth it has used its internal source (Core: inner-outer core; Remarks: I do not accept current theory about rocky planets core…- In my assumption the terrestrial planets core are same!)… Because Mars have do not used all inner core: that is why it has gravity field for it has also magnetic field non measurable onto surface… (planetologically can be demonstrated that in past Mars has magnetic field like Moon, too that is  caused by their rotation: causing “moving of its outer core”- analogous with  moving electric charge in a circular electrical conductor-roller) when the gravity field are caused by “ compression of outer” core (https://www.researchgate.net/publication/277364319_Tenyekkel_igazolhato_a_gravitacio_valos_oka -actually i do not have in English, only after in one or two months)      

Venus also has “no magnetic” (is near zero) because has very slowly rotation

 Moon in my concept is a planet (twin planet of our planet) has similarities with Mars…

So come back to  your discussion: negative electric charge moves are causing magnetic field when negative electric charge concentration (presence and their concentration gravity field)- increase of electric negative charge are causing increase of gravity field when decrease are producing decrease of gravity field (see rethink of tide process and tsunami produced by earthquakes) see my question: (https://www.researchgate.net/post/Which_explanation_is_correct_about_tsunami_produced_by_earthquakes_and_tides_of_Earth)     

Article Tényekkel igazolható a gravitáció valós oka

Dear Andrew Wutke,

Review my paper http://vixra.org/abs/1509.0059 

All the problems from Higgs to Galaxies are solved. My transformation gives you the same results of the ether theory, but instead of the Ether theory, it is vacuum energy dependent. Take for example the Sagnac effect. Take the time term in my transformation t=R^2(t'-vx'/c^2). Now according to my transformation space is invariant, and it is only time. In this case we get t+=R^2(t'+vx'/c^2) and t-=R^2(t'-vx'/c^2) thus delta t=R2 (2vL/c2) where R is the Lorentz factor. This result is exactly the same result of explaining Sagnac effect in the framework of Ether theory. Also what about the H&K experiment. It gives you the same result of the Ether theory.  Review this paper also which considering space is invariant in the interpretation of H&K experiment http://arxiv.org/abs/1405.5174

Also review this paper the first section Maxwell’s wave equation http://arxiv.org/pdf/1303.5309v1.pdf

According to my transformation which expressing about the wave-particle duality and the uncertainty principle, gravity is completely quantized. The decrease in the speed of light globally is gravitational potential dependent, not on the the strength of the gravitational. The light bending by gravity, Mercury precession, Pioneer anomaly, and Shapiro delay can be explained completely same the potential retardation, but how can we translated that according to my transformation. That is very simple now to understand that. Also it is vary simple to understand what is the uncertainty and the wave-particle duality and the entanglement. 

Dear Azzam,

As I am interested in alternatives to LT I will have a look at your work in due course. Your claims are interesting.

Dear Andrew Wutke,

Please review this paper 

On the origin of the anomalous precession of Mercury's perihelion, Jaume Giné

http://arxiv.org/abs/physics/0510086v4

The author recovers an ancient work of Gerber in 1898 as a precursor of the retarded theories. In this paper Gerber gave an explanation of the anomalous precession of the Mercury's perihelion in terms of a velocity--dependent potential. In this paper an explanation of the anomalous precession of Mercury's perihelion is given in terms of a simple retarded potential, which, at first order, coincides with Gerber's potential, and which agrees with the author's previous works.

Also this paper 

J D Franson 2014 New J. Phys. 16 065008

doi:10.1088/1367-2630/16/6/065008

In this paper it is calculated that, treating light as a quantum object, the change in a photon's velocity depends not on the strength of the gravitational field, but on the gravitational potential itself. However, this leads to a violation of Einstein's equivalence principle – that gravity and acceleration are indistinguishable – because, in a gravitational field, the gravitational potential is created along with mass, whereas in a frame of reference accelerating in free fall, it is not. Therefore, one could distinguish gravity from acceleration by whether a photon slows down or not when it undergoes particle–antiparticle creation.

Dear Azzam, When you wrote earlier "My transformation gives you the same results of the ether theory, but instead of the Ether theory, it is vacuum energy dependent."

Do you refute the existence of aether and consider vacuum or empty to have energy ?

Dear Albert Roseiro,

I think relative to me it is vacuum energy dependent. And since energy is quantized, then that will lead to completely quantization of gravity by considering the gravitational potential. I see my transformation is the cornerstone between EM, classical physics and quantum theory... how! According to my transformation space is invariant and it is only time. In classical mechanics, a special status is assigned to time in the sense that it is treated as a classical background parameter, external to the system itself. This special role is seen in the standard formulation of quantum mechanics. It is regarded as part of an a priori given classical background with a well defined value. In fact, the classical treatment of time is deeply intertwined with the Copenhagen interpretation of quantum mechanics, and, thus, with the conceptual foundations of quantum theory: all measurements of observables are made at certain instants of time and probabilities are only assigned to such measurements.

That also will explain to us the question in this RG

Aether field rejected by Michelson Morley experiment in 20th century, but now in 21st century Higgs field is accepted. Why is that?

https://www.researchgate.net/post/Aether_field_rejected_by_Michelson_Morley_experiment_in_20th_century_but_now_in_21st_century_Higgs_field_is_accepted_Why_is_that

Dear Azzam, Does your theory considers "time" also as quantize units which its stored energies could eventually be transformed into other forms ?

Dear Albert Roseiro, 

In fact yes! that is when you are dealing with E=mc2 = hv according to my equivalence principle. In this case you deal with the relativistic quantized force as F=dp/dt. The Lorentz factor is potential energy dependent R-1=(1-GM/c2r) . According to my transformation any motion is defined by 4D, and by considering space is invariant, the decrease in the speed of light globally under the gravitational field is given according to c'=(1-GM/c2r)2c , which approximated to c'=(1-2GM/c2r) in case of weak gravitational field. That explains light bending by gravity during the motion in weak gravitational field.

According to my transformation, there is no way to determine the location of the moving object at a certain point in space during the motion because of  the uncertainty principle according to the invariance of the energy momentum four vectors. But if you determine the location of the object at a certain point in space, in this case the wave-function will collapse, and that translated according to my transformation as transforming from 4D during  the motion to 2 a localisation in a certain point in space. In this case at a certain point in space the decrease in the speed of light is given according to 2D where c'=(1-GM/c2r)c and that explains the POUND and REBKA experiment. The motion according to my transformation is defined by the group velocity and during the motion by the vacuum fluctuation, the group and the phase are not equal where that equivalent to the motion in nonlinear dispersion. But at a certain point in space they are equal where that equivalent to the motion in linear dispersion. According to that we can understand the uncertainty principle. Shapiro delay, Mercury precession and the Pioneer anomaly can be solved completely according to that by the wave-particle duality. Also that explains the double slit experiment. https://www.youtube.com/watch?v=A9tKncAdlHQ

Also according to that no need for dark matter or dark energy, and infinities disappeared!!!

https://www.youtube.com/watch?v=A9tKncAdlHQ

Yes, if we take linear gravitational field. This problem has already been taken up long back in my earlier research paper entitled," Unification of generalized electromagnetic and gravitational fields" published in Journal of Mathematical Physics, Vol. 25, (1984) pp 351-354.

Why the Graviton smaller 10^42 times than a Photon, can not travel faster than the speed of light?

Because you were brainwashed by your professors for 100 years, that nothing can travel faster than light!

 “I am the first who understood and explained Gravitation with high speed gravitons v = 1.001762 × 10^17 m/s, with Negative Momentum, Negative Mass and Negative Energy” Adrian Ferent

https://www.researchgate.net/publication/299135595_Ferent_Gravitation_theory

Article Ferent Gravitation theory

So my question seems to be answered 

There is a merit to consider ME for gravity at least in some regime 

Multiple approaches exist since 19th century

The speed of gravity disturbance propagation is controversial 

My heuristic conjecture based on dimensional analysis was not a bad guess 

Further development is General Relativity 

Arno

I only stated why there is no more mainstream interest in ME for gravitation.

It looks with GR there is still no explanation of dark energy.

Dear Thierry De Mees,

As you said:

It appears that the Sun's empirical rotation dynamics matches exactly the Newton gravity equation if we consider that the interaction between gravitons and particles are controlled by Coriolis forces, which is the sole purely mechanical process that can allow an attraction.

My theory and your theory are not too far!!! The problem can be solved completely according to quantum theory ( the Copenhagen school and classical theory. 

In relativity theory of Einstein, if we consider space is invariant and it is only time which related to time dilation, in this case we reach to the unified theory completely. Because in classical mechanics, a special status is assigned to time in the sense that it is treated as a classical background parameter, external to the system itself. This special role is seen in the standard formulation of quantum mechanics. It is regarded as part of an a priori given classical background with a well defined value. In fact, the classical treatment of time is deeply intertwined with the Copenhagen interpretation of quantum mechanics, and, thus, with the conceptual foundations of quantum theory: all measurements of observables are made at certain instants of time and probabilities are only assigned to such measurements.

In this case Lorentz transformation must be modified, and we need a transformation expresses about the wave-particle duality and the uncertainty principle. 

My transformation 

x=R^2(x'-vt') t=R^2(t'-vx'/c^2) y=Ry' z=Rz' expresses also about another explanation of the Coriolis forces according to the wave-particle duality and the uncertainty principle. That explains completely light bending by gravity, Mercury precession, Pioneer anomaly, and Shapiro delay, and by the wave-particle duality there is no energy momentum problem, and no need for dark matter or dark energy and infinities are also disappeared!

I interested too much in the paper of Balwant Singh Rajput in Journal of Mathematical Physics, Vol. 25, (1984) pp 351-354.

If you can draw a connect between Maxwell's equations and Einstien general theory of relativity.

Dear Thierry,

Thanks for bringing Oleg Jefiimenko  into this discussion. I was unaware of his point of view 

https://en.wikipedia.org/wiki/Oleg_D._Jefimenko

Dear Thierry De Mees,

In fact you explained completely my theory in my paper http://vixra.org/abs/1509.0059

The speed of light is locally constant and equals to the speed of light in vacuum. The decrease in the speed of light is observed globally according to the delay in space and time. That will lead completely to quantization of gravity. So what is the difference between my model and the model of Oleg Jefiimenko!!!??

There is no way to remove the paradoxes of SRT without removing the reciprocity... That is the idea of my paper. It explains completely the potential retardation, and according to my model gravity is gauge theory.

The other thing explaining the wave-particle duality, the uncertainty, and the entanglement.

Dear Azzam,

I understand the nature of reciprocity in the STR very well. This is only an apparent effect due to inability to determine the real velocity of objects when isotropic speed of light is assumed and the system speed relative to absolute reference frame is unknown.It may be seen as a heresy to the main stream point of view but this is what it is. So the paradoxes are only apparent as apparent is relative simultaneity.

Dear Andrew, 

In this case you will face a problem in the interpretation of Lorentz transformations according to concept of the delay in space and time. As you know in Lorentz transformation as it is existed time dilation, there must be length contraction. If we want to quit the SRT interpretation, in this case we must back to Lorentz Ether theory. Or we have the Copenhagen school.

Dear Azam

What is true I do not know. I analyse SRT for what it presents against some perception of reality. Length contraction is necessary to match time dilation or when you reverse it it has to go back to normal. The reciprocity is apparent only because moved system is not allowed to use information it has moved. Lt makes its predictions based on motion appearance not on the true knowledge of the situation. This is a bit simplified reasoning but reflects what happens. I say nothing about your theory. I only comment on it.

I am worried that in the theories of gravity the interpretation derived from the STR may be erroneous. Like that of Godel solutions of closed time like curves.

Jefimenko paper:

On the Relativistic Invariance of Maxwell's Equation

http://zfn.mpdl.mpg.de/data/Reihe_A/54/ZNA-1999-54a-0637.pdf

Dear Arno,

I think "rlt" means relativity. Discussing relativity is not a waste of time for me. One day people would like to know why relativity was presented and maintained that way and why and what problems were not understood properly despite of the fact it was overwhelmingly accepted.

Community of physicists is similar to an aquarium. They are gold an angel fish that produce all the beauty and attract all attention, but there are the bottom feeders that nibble on what was left over by them forming a well balanced ecosystem.

Surely some branch of physics move the knowledge forward but reconciling with the past helps to avoid errors in the future.

I am a bottom feeder.

The fact that the Coulomb C can be expressed in term of the others L, M , T is something which really does not convince me. The limits of present theory  is infact the L,M,T in which does not appear any mention to the charge, for example in SR or GRT.

What is usually done is to express L,M,T in terms of c,G,h the three constants...and it is quite interesting to do. Re express evertying in terms of c,G,h but there is always the problem with the charge or with the magnetic field, since c is a ratio between these.

To reason in term of dimensional analisy is always very good, this allowed for example to find interesting relation in fluid dynamics.

I think instead that [L,M,T,C] is the minimum we can have in order to account for a unified theory .The Minkowsky / Einstein space-time has to be replaced by something else of higher order in order to allow the unification of EM and GR , attempted  by Kaluza and Klein without really replacing it.

Yes the unification of generalized electromagnetic field and gravitational field can be obtained, at least mathematically, in higher dimensional space-time or in Quaternionic formulation. A successful attempt of developing Electrodynamics in higher dimensional space-time has been made in our following earlier research papers:

I)  Electro dynamics in Eight-dimensional Space time published in Journal of mathematical Physics, Vol. 26, (1985) pp 208-213

ii) Six-dimensional Electromagnetic Fields published in Prog. Theor. Phys. Vol. 80 (1988).pp 277-293; and Nouvo Cim. Vol. 110A (1988) 297-304

Quaternionic formulation of Generalized  Electromagnetic field has been attempted in our earlier papers published in Lett. Nuovo Cim. Vol. 34(1982) pp 180-182; and Lett. Nuovo Cim. Vol. 37 (1983)pp 325-329

 Thierry, I think unification of gravity and electromagnetism is worth attempting, some call it electrogravitation. The key reason in my opinion, both EM forces or G forces seems wireless or radio phenomaes whatever their strength or amplitude so they should be governed by some extended similar equations.

Dear Thierry,

As you said Stefano, is it useful to unify gravity and electromagnetism? I doubt it because the forces differ so much.

what I see is different if we considered quantum theory and the Copenhagen school. In this case the concept of force is defined according to the wave-particle duality and the uncertainty principle. That is illustrated also in the Cassimir effect. 

Dear Arno,

the unified theory in this case is defining the equivalence principle according to radiation exchange. In this case the gravitational potential plays the rule in the equivalence principle same as in EM, and gravity is gauge theory. The problem here is not related only to EM but also to quantum theory and the Copenhagen school. As we know energy is quantized, and in this case motion in macro world must be described according to quantization of energy. So the quantization of gravity in the right way will lead directly to the unified theory of gravity and EM.

Theirry,

Stefano, is it useful to unify gravity and electromagnetism? I doubt it because the forces differ so much.

the energy is one, and the action principle is one.. so there should be a way to merge the interactions which will eventually justify gravitation and quantum mechanics.

This has been an extensive discussion touching many points.  B   ut sticking to the title of this thread: can electromagnetism and gravitation be unified?  Assume the field theory approach to physics.  Classical non-quantum descriptions are meaningful for long-range interactions only.Then electromagnetism is described accurately by a 4-vector field, that is, a particle (the photon) which has spin 1 and is mass-less because it is long-range.  Gravitation is described by a symmetric second-rank metric tensor.  This is the spin-2 mass-less graviton.  Although general relativity might be approximate, it seems correct in essence.

 Just as electromagnetism can be approximated by a scalar interaction -the electrostatic potential- for slowly moving particles, gravitation can be approximated by a vector field (the post-Newtonian approximation or Heaviside's 1893 theory I referred to previously) for slowly moving particles and weak fields.  The second restriction is needed because of the non-linearity of gravitation which is due to the stress-energy produced by the field and which in turn contributes to it.  

So we have two long-range fields of different natures.  Do we expect to have two fields of the same nature, that is a vector gravitational interaction? Would we be able to distinguish between them? The answer is probably no.  So the existence of two distinct long-range interactions is logical given the experimental data that both electromagnetic and gravitational forces exist.

While the electromagnetic theory has been confirmed experimentally in its quantum version (despite the difficulties arising from renormalization) to a high degree of accuracy, it is still possible that general relativity needs corrections.  This is due to the very weak nature of this force.  Many theories in this direction has been proposed but none has been confirmed.  The basic difficulty in both theories is the assumption of a point particle and the consequent infinities of self-energy.  This is where string theory comes in and into which I will not go.

The remaining question is whether there are other long-range interactions. The first possibility is a 4-scalar interaction.  This would require a spinless, mass-less, neutral particle.  T.D.Lee investigated this fifty years ago but no results came out of it. One may question whether a particle with no mass, charge, or spin is actually meaningful.  The other possibilities are interactions with higher spin.  If experiment dictates their necessity we will have to accept them; but so far there is no evidence for that.

To summarize: the existence of two distinct long-range interactions is dictated by experiment and is reasonable.  Each of these theories can be approximated by a lower spin (zero for electromagnetism and one for gravitation) but this does not invalidate the theories.  Interactions mediated by particles with mass are short-range; a classical theory of these interactions is purely phenomenological and necessarily incomplete so they are beyond the present discussion.. 

Dear Thierry,

I mentioned Heaviside only out of historical interest.  Twenty two years before general relativity (1893) he had the courage to speculate about a vector theory of gravitation as an alternative to Newton's scalar theory. Of course, he was guided by Maxwell's theory of electromagnetism. The proper approach is the post-Newtonian approximation to general relativity which keeps the gmu4 components of the metric tensor and neglects the gij components.  It thus appears as a vector theory very similar to electromagnetism. 

Dear Thierry De Mees

You said; Prof. Oleg Jefimenko has proven that the Lorentz Transformations are exactly obtained by *only* taking into account this retardation of the fields, and so, that the 'relativistic' effect is fully accounted for.

But Lorentz transformation is not only time dilation. It is time dilation with length contraction. In this case in order to Lorentz transformation working good with retardation of the field in this case we must make a rescaling. In this case the speed of light is also unchanged by a rescaling x′ = Sx, y′ = Sy, z′ = Sz, t′ = St where S is any function of v. Combination of this with a Lorentz transformation gives x′ = SR(x − vt), y′ = Sy, z = Sz, t′ = SR(t −xv/c2). Choosing S = R we get: 

x'=R^2(x − vt),  t′ = R^2(t −xv/c2) y'=Ry and z'=Rz and R is the Lorentz factor. 

The rescaling violates “reciprocity”!!!  But in this case all the paradoxes of SRT are disappeared.

This new transformation expresses about the retardation of the field, and at the same time expresses about the wave-particle duality and the uncertainty principle. 

Now the the 'relativistic' effect is fully accounted in gravity. Before!  GR is only an approximation, which accounted only into the classical motion. Because of that the escape velocity in GR is only classical not relativistic. while according to my new transformation, you can define it as relativistic. 

http://vixra.org/abs/1509.0059

Dear Thierry De Mees,

You said "Since Jefimenko found that the retardation of the fields gave identical Lorentz Transformations as Einstein's, it proves the LT correct. However, it is the Special Relativity interpretation which is wrong."

If only the clocks' times can differ, then that is not LT, it is Voigt's transformation, where in Voigt's transformation

x′ = x − v t , t′ = t − x v/c2 , Here t' not equal to t.

In Galilean transformation we know t'=t, and thus there is no difference in time.

Review this paper On the Origin of the Lorentz Transformation, W. Engelhardt

http://arxiv.org/pdf/1303.5309v1.pdf

I agree with you that special Relativity interpretation which is wrong, but in this case according to Jefimenko what is the interpretation of LT!!? Will we back to the Lorentz Ether theory in order to explain LT?

I do not know what Jefimenko names this difference in time? According to LT, as there is a difference in time, there must be a difference in space also, which is named length contraction. We can understand this difference in space and time in LT according to Lorentz Ether theory or SRT. And now if SRT interpretation is wrong, then we must back to Lorentz Ether theory. Or is there third interpretation???

There is no only difference in time in LT. That is only in Voigt's transformation. In LT as there is difference in time, there must be difference in space.

I'm curious to have opinion about these videos and theories described by George Bugh in USA

https://www.youtube.com/watch?v=lB5qG5wHJ_s

Dear Thierry De Mees,

I'm not against  Jefimenko!  I agree with him, but we need to understand how is the retardation according to LT. 

As you said "That's why time doesn't change intrinsically." That means t'=t same as in Galilean transformation..right!? Also according to retardation there is a difference in time. That means t' must not equal to t. So how can we translate that in physics.

Let's propose a plane flies in constant speed v. Now if the observer on the ground on Paris sees the plane now in Paris according to his clock at t=9 Am. Now according to objectivity at this time when the Plane arrives Paris, then it arrives Paris for both the two observers on the ground and on the moving plane. Now if t=9 am according to the clock on the ground. What is time t' now according to the clock on the Plane?

According to your comment, if time doesn't change intrinsically, then t'=9 am also according to the clock on the plane, and in this case t'=t according to Galilean transformation. 

Now if we want to consider retardation in this case  t' must be less than t. And in this case if the plane arrives Paris, then it arrives Paris according to the clock on the ground at t=9 am, while according to the clock on the plane is t' less than 9 am. Here we face a problem in the laws of physics. 

I understand your statement that  time doesn't change intrinsically. That means when the plane arrives Paris at 9 am according to the clock of the ground, then it must arrive Paris at time t'=9 am according to the clock on the plane also. In this case if t' less than t, that will lead to a delay in time with the clock on the plane comparing to the clock on the ground. As a result of this delay in time, there must be a delay in space also. That means if the observer on the ground sees the plane now on Paris at t= 9 am, at this moment, and because of the delay in time on the plane clock, the plane is not yet arrived Paris for the observer on the plane, where t' less than t, and thus at this moment the plane is still approaching to Paris for the observer on the moving plane. This is exactly the Copenhagen school. According to that we get the delay in time and space during the motion in constant speed  given according to

t'=R-1t and x'=R-1x. R is Lorentz factor. That expresses now about Lorentz transformation, the length contraction and time dilation in LT. According to that when the plane arrives Paris at t=9am for the observer on the ground according to his clock, then it will arrive Paris also at t'=9am for the observer on the moving plane. Here t=t' but not at the same time according to the retardation.

This is the same problem we face with SRT when we try to interpret the Sagnac effect.

as in this paper http://arxiv.org/pdf/1404.4075v1.pdf it is written;

Calculating the ensuing travel times of light round the interferometer we find that the LT – due to its linear term x v/c2 – does not predict any Sagnac Effect, but results in c = const also in a rotating system as it does in an inertial system. This explains then why Ashby [6], e.g., uses the Newtonian or Galilean time transformation t’ = t rather than t’ = γ (t - x v/c2) when he calculates the Sagnac Effect in the GPS-System. This was also observed by Carroll Alley in a comment at the end of an engineering presentation on GPS and Relativity.

So the only solution to explain the retardation is we back to the Copenhagen school. But that against objectivity in macro world!!!!!!

Because of that in classical mechanics, a special status is assigned to time in the sense that it is treated as a classical background parameter, external to the system itself. This special role is seen in the standard formulation of quantum mechanics. It is regarded as part of an a priori given classical background with a well defined value. In fact, the classical treatment of time is deeply intertwined with the Copenhagen interpretation of quantum mechanics, and, thus, with the conceptual foundations of quantum theory: all measurements of observables are made at certain instants of time and probabilities are only assigned to such measurements.

Dear Thierry De Mees,

If time is not intrinsic, then there will be a problem with laws of physics. In this case how can we understand that the laws of physics are the same for all observers!!!

In SRT the change in time will meet a change in space, and at the end the laws of physics are the same.

Dear De Mees,

Ok! In this case what about the quantization of gravity? Why do not we consider quantum theory in this case? In this case our world will be close to quantum theory!

About quaternions, not sure if this is related but the initial Maxwell equations were using quaternions algebras. One scientist Dr Terence W. Barrett has used extensively the quaternions approach related to SU(2) topologies to describe classic EM not explainable with standard vectorized EM equations. There are a few papers but also a book but to my knowledge, quaternions have never been any help to describe gravitation as EM effect except Maxwell initially thought his equations based on quaternions with Aether in mind.

https://books.google.fr/books?id=e0-QdLqT-pIC

Dear Arbert Roseiro, 

now quanternions can help to describe gravity according to my quantization of gravity depending on the Maxiwell's ether theory, but instead of Maxiwell's ether theory it is vacuum energy and vacuum fluctuations which is equivalent to acceleration. http://vixra.org/abs/1509.0059

Azzam, If really one can treat gravitation via quanta then I suspect time should be treated also as a quanta. Now this would mean a special link between time-gravitation energies and vacuum energy or ZPF. So far, actual physics model denies the possibility to couple or extract energy from ZPF but the very same physics cannot fuse or generalize the EM with gravitation.

 Dear Mesut Kavak,

I really interested in you paper But I have a question related to the equation in your paper as you said; the momentum and the kinetic energy equations which were derived above change by a rule, and the rule is determined by this energy transformation equation which is

(17). For the light speed c, the equation dances after this as

m=R^2m0 where R is the Lorentz factor.

Here is well known that m=Rm0 not as you wrote it m=R^2m0

In my transformation During the motion 

x=R^2(x'-vt') t=R^2(t'-vx'/c^2) y=Ry' and z=Rz'

This a wave-particle duality and it is vacuum energy dependent. This transformation is a transformation of group.

Here you choose m0c2+mv2=mc2 and I can understand this equation from mv2 as it is resulted from the group velocity not the phase velocity in case of classical motion in case of nonlinear dispersion, and the uncertainty principle in this case plays the rule. Now during the motion by the wave-particle duality there is no at a certain point in space, and in this case what describe the motion is my transformation. When I make a measurement, then I make a measurement at a certain point in space, and in this case the wave-function will collapse. I can't make a measurement without determining this measurement at a certain point in space. In this case the collapsing of the wave-function will lead me to the phase velocity, and in this case at a certain point in space the phase and the group velocities are equal which equivalent to linear dispersion. Thus at a certain point in space, and in case of low velocities I consider the phase velocity and then I back to 1/2mv^2 not  the group mv^2 in case nonlinear dispersion which is the phase multiplied by 2 in case of classical motion. Because of that explaining the Pound and Rebka experiment at a certain point in space in the weak gravitational field is depending on c'=(1-GM/c^2r) which is the phase and in this case the phase and the group are equal (linear dispersion), while during the motion as in case of light bending by gravity in weak gravitational field is depending on the group which is given as c'=(1-2GM/c^2r)c (the phase multiplied by 2 in case of nonlinear dispersion), and in this case the classical velocity is given according to the group not the phase which is given as 2GM/r which is the square of the classical escape velocity.

For me this equation is not clear, because here we have two velocities in case of the wave-particle duality, the phase and the group. And in this equation what you use the phase or the group?