Dear Mozafar, thank you for your answer. Most of what you said is correct, but allow me to point out that there are papers sometime ago which say that explaining mercury anomalous perihelion is possible using cogravity or special relativity.

See for instance Tajmar and de Matos, http://arxiv.org/abs/gr-qc/0304104v1.

And also Behera and Naik, http://arxiv.org/pdf/astro-ph/0306611v1.pdf.

But i don,t find yet derivation of bending of light from special relativity theory. Best wishes

Ok thanks, Mozafar, for your explanations. Best wishes

Hi Victor and Mozafar,

General Relativity yields, in the Minkowskian limit, a set of Maxwell-type equations that can also be found by completing Newton's gravitation theory with some terms that would be absent in the limit of infinite light-speed. For a short historical account of the latter see http://en.wikipedia.org/wiki/Gravitoelectromagnetism

There are indeed many articles following Heaviside's article on the subject, including the ones mentioned. I think the issue is not about the existence of a lorentz-covariant theory of gravitation (although here the literature offers a variety of interpretations and addresses problems), but the issue is about the fact that such a theory is a vector theory, and gravitational waves loose their tensorial character in the Minkowskian limit. While one may think that such a limiting theory could be a good approximation, there are qualitative differences, i.e. features that are lost during the limit, and GR principles may be violated. This does, however, not mean that any study of such a Minkowskian theory of gravitation is useless. On the contrary, we are right now working on some aspects of the vector theory that can be translated to General Relativity by inverting the limiting procedure. In this context you can find many articles and books on teleparallel gravity (you may google this keyword), most of which deal with the Maxwellian form of relativistic gravitational equations in a suitable limit.

Cheers,

Thomas

See my paper: astro-ph /0006423 and references therein

See my paper: astro-ph/0006423, and references therein

I think a problem here from the start entails incentives either for empirical description and prediction verse incentives to capture together what is practical for empirical purposes and a cosmology totally embedded with mathematics. We wind up with negative values in a universe itself that is a special case, absent of zero, in which determinable value is dynamic with age; attempt to unite plural operating causes into a single mathematical frame that ignores a simple accounting from prior accounting, ad-infinitum that delineates the path of emergence and cannot be accomodated to generalized, idealized mathematical description. I think at each intersection (e.g perihelion behavior), for explanation a non zero- bending, non-zero gravitation has to be attributed to all time points to establish a focus on path history; description involving simplified constancy in governing (e.g. the velocity of light in a vacuum) needs rereferal to the time dependent numerical ratio, and an of-itselfness as the existence of volume that is dynamic, heterogeneous in construction that is not highlighted by linear considerations but a prison, volume highlighted by shape/form that is constructed from linear considerations. From Einstein, Newton, Lorenz we can have empirical description that can be accurate but not containing or closed to accept alternate but non-existing possibility.

Our cosmology and math has surfaced to be like our lives in which sacrifice is made from from the set of open possibilites to participate in self established governing law and rules for increased individual certainty among social and physical survival parameters. Really existing only is the heterogeneous entity, an apriorily existing world exclusively of of-itself windup dolls and a terrain that is navigated by accounting that can be flawed in the case of living things depending on particular species and terrains.

If interested I am enclosing as attachments a recent publiction ("Determining the determined state : A sizing of size from aside/the amassing of mass by a mass...") ...the link to a current working manuscript ("Universe or World : Order for action or action for order") is:

http://ssrn.com/abstract=1376065

Hello Victor, regarding Lorentz invariant gravity, I do not think it is a satisfactory theory except as others have pointed out in the weak field approximation. In addition to the difficulties matching all the empirical observations, it shares some weaknesses with GR such as predicting gravitational waves that we should have detected directly and have not. Reconciling gravitational energy loss with the inability to detect the waves is easily done with a fairly benign but non Lorentz invariant theory. If the wavelengths become very long, the detection difficulty is explained.

If anyone is interested, I have put forward what possibly may be the simplest form of such a theory (more complex variants are possible) in a paper published last January in JMP, linked below.

http://www.scirp.org/journal/PaperInformation.aspx?PaperID=27250

I believe that the Yilmaz theory in harmonic coordinates is locally Lorentz invariant. That is one thing that distinguishes it from GR. It first passes to a Lorentz limit before reaching a classical Newtonian low speed limit. But it is not globally Lorentzian. I am prejudiced in favor of anything that eliminates event horizon singularities - and in my opinion, they are not just coordinate singularities. I believe that Yilmaz theory is a viable fundamental theory of particles and fields, however, it needs some attention before it can be applied to a continuum such as a stellar interior. It may be necessary to give up the harmonic coordinates there.

The closest thing to a viable Lorentz-invariant theory of gravity is the RTG of Logunov and Co, see http://arxiv.org/pdf/gr-qc/0210005v2

I personally prefer a variant http://arxiv.org/pdf/gr-qc/0205035v4 which is, as a whole, not Lorentz-invariant.

Dear Thomas, Norbert, Marvin, Robert and Ilja, thanks for your answers. My interest actually is to find a Maxwell-like gravitomagnetic theory which is able to explain properly new experiments such as Podkletnov effect, where general relativity fails to do. So if you know something about that please let me know. Thank you

According to theoretical perspective, it is less motivative. However, if it represents greater achievements, and having violations small, then we may go through with them.

Dear Victor,

I think that the Lorentz-invariant gravitation theory based on the ideas of special relativity. But the modern theory of gravity must use the metric. Therefore based on the Lorentz-invariant gravitation theory was created Covariant Theory of Gravitation. Both theories, general relativity and the Covariant Theory of Gravitation, are derived from the principle of least action. Both theories contain the metric and can explain the perihelion advance, time dilation and other effects.

My answer: not Lorentz-invariant gravitation theory, but the Covariant Theory of Gravitation is a valid alternative to general relativity.

Dear Sergey, thank you for your answer. Do you know url of the Covariant Theory of Gravitaion as you mentioned? And does it explain recent data such as Gravity Probe B? Thank you

Dear Stanley, thank you for your comment. Do you think that event horizon singularity does not exist?

Dear Shamaila, thank you for your comment. Yes it depends on how we perceive gravitation. To me, gravitation may have deep connection with rotating superconductor or rotating superfluidity. I can recall a paper not so long ago explaining connection between general relativity theory and Ginzburg-Landau theory. But i forgot the url of that paper. Best wishes

Dear Victor, see http://en.wikiversity.org/wiki/Covariant_theory_of_gravitation and references there. Some explanation of Gravity Probe B data is there. The theory is developing quickly so it is possible there more accurate results.

General relativity IS Lorentz invariant. To solve the dark matter problem one has

"only" to give up the geometric interpretation of Einstein's theory.

See arXiv 1208.3749 (2012) and later papers.

Gunter Scharf, University of Zurich

@sergey. Thank you, Sergey. Surely i will check your url. Best wishes.

@gunter. Thank you, Gunter. I will read your paper. Is it also possible to solve dark energy using your approach?

@shamaila. For connection between Ginzburg-Landau and general relativity, you can browse papers by Horowitz in google. This may be a good start: http://arxiv.org/abs/gr-qc/0410029. Best wishes

One very simple question.

If you are in the middle of a plate rotating at speed ω you will feel Coriolis force: 2 v x ω m.

You may say that you are at rest and whole universe is rotating around you and induces a constant vector field Ω = 2ω.

Does the integration over the whole universe, of a formulae given in the Lorentz-invariant gravitation theory, give this result for the gravitational torsion field Ω ?

A short clarification concerning the answer by Mozafar and the comment by Gunter:

In my comment I did not imply the usual linearization of GR, but there is another, more direct limiting procedure: formulating GR with Cartan coframes, you can send the Coframes to exact forms. This limit, or rather this restriction also results in Mawell-type equations, but on Minkowski space. The by construction locally Lorentz-covariant theory of general relativity (the remark by Gunter) implies, through the restriction to exact forms, a globally Lorentz-covariant theory (since exactness guarantees the existence of global coordinates), and this global notion was meant in the title of the question. For a short introduction into this limit you may look at Section 7.1. in http://arxiv.org/abs/1103.2016

Does anyone know what Covariant Theory of Gravitation gives us that GR doesn't? I mean in terms of solutions to things that GR fails to address. For example, can CTG be wed with QM better?

@Marshall. That is an interesting question. Please ask Sergey Fedosin. Best wishes

I wished to note that the constant velocity of a free fall fits well with the biological intuition and measurement of a linear mutation rate, x mutations/time. This might be argued to be the only tenible condition for the propogation of life/structure; at one extreme is quick radioactive decay, at the other is loss of definition in proximal frames. Entropy problem is avoided if dependence is on ratios and decreasing volume at each point of perspective....In using the term."linear" I was referring to the need to start with the conservation of momentum rather than (vectorless) energy accounted linearly. In surface plots with time as a constant system variable to witness pair events, e.g. only distances are generated, I get an egg shape when values are generated randomly and uniquely employing pi/10^17 rotations interval 10^14..output values are each unique. This means to me, with respect to causes of "open" surface points that they are maximally diverse in origin, constant (mutation rate) or angular velocity is necessary for continued propagation. I think the problem with Lorenz fixed gravitation field, as in all the inconsistencies describes here, is within the condition "maximally diverse causes" (e.g, longest path length of points forming a discontinuous surface evolved from straight line of progression), the semi-random method used to generate values for plotting function, goal is to relate to actual physical universe.I am reminded of the Rieman inequality that divides the world of quantum mechanics and the macroscopic world. I think tools as quantum mechanics are good for paper exercise, but one must start, in actual beginning with the actual world and work from there, less, starting with imagination, ending with only imagination. In the perihelion problem for instance, distinctly oriented and plural causing surfaces must be involved and would be difficult but not impossible to imagine and test, the same might be true for worst immune diseases, normally accounted elements behaving with temporally disparate motions associatable with distal causes. I think the resemblance in description to action at a distance leads to avoidance of this interpretation, but volumes of space always intercourse regardless of the laws governing them, or whether their existence and nature depends on the same, ad-infinitum. ...from any unique perspective (is no whole perspective as Einstein proposed with a single governing c) is but one unique describable (with a conceivable age), momentum bearing global body in constant change, exists and has a half life in retrospect (2x looking forwards from past) if mutation rate is constant, or (if increasing mutation rate) a predictable 1/2 life of decay(e.g. uranium), the deceasing mutation rate might be visualized to loss of competant orbit energy, lineality, collision on the macro level, failed propagation of macro structure?

Dear Victor:

Thanks. When I'm not spouting off about something, I do try to ask interesting questions, when I encounter something new or out of my depth. Hopefully, Sergey or someone else that knows will see it and comment.

Regards...

Günter, I disagree that the g_mn cannot be measured. We can measure distances and proper time with rulers and clocks. With a sufficient lattice of clocks we can measure all coefficients of g_mn with sufficient accuracy.

I also disagree with "In standard general relativity one puts c = 0." One is free to use nontrivial c in general relativity too.

Then, the dynamics of matter have to be taken into account in GR too.

I also disagree with "We emphasize that these solutions describe different physics

because the corresponding circular velocities squared u(r) are different" If one replaces one radial coordinate r with another r1 = r1(r), all the g_mn will look very different, but the solution remains the same.

You clearly confuse here the arbitrary choice of the radial coordinate r with the physical measurement of the radius.

@Miroslav. Thank you for your question, but I know only a few about torsion or LITG. But regarding Coriolis force, I can cite a paper by myself and Prof. F. Smarandache sometime ago (2007) discussing rotational relativity ( the other name is Q-relativity). As a result of definition of quaternion metric distance, the quaternionic acceleration arises, which includes Coriolis force. Using this new geometry discovered by Alexander Yefremov, we managed to explain Pioneer spacecraft anomaly.

Perhaps you would like to see this paper, available at: http://ptep-online.com/index_files/2007/PP-08-07.PDF. Your comment is welcome. Best wishes

Dear all contributors, thank you so much for all your answers, questions and comments. Allow me to upload a summary of this discussion in pdf file.

More or less successful theories considering gravitation as a field on Minkowski space have been discussed in the 1980s. Two references are

Rastall P.

Can J Phys 57,1979,944

The Newtonian theory of gravity and its generalization

Ya. B. Zel'dovich and L. P. Grishchuk

Usp. Fiz. Nauk 155, 517-527 (July 1988)

The general theory of relativity is correct!

Perhaps you can find an answer there.

For Miroslav Šindler. The gravitational torsion field Ω is similar to magnetic induction field B. You can take the plane with electric charge in rotatation and calculate B. Then change electric charge density by mass density, and B by Ω.

For Marshall Barnes. Covariant Theory of Gravitation has stress-energy tensor of gravitational field. So it is better use the theory in QM.

Thank you, Willem and Sergey, for your answers. Best wishes.

I want add for Miroslav Šindler. Coriolis force is mechanical force from rotating plate on moving body. This force disappears when the body do not touch the plate. But the force of torsion field of rotating plate on the moving body take place in any case.

For Mozafar Karamian.

Lorentz-invariant gravity possibly can explain perihelion advance of planets. For it is necessary to take into account Lorentzian factor gamma^3 and so on. See

Sankar Hajra, Classical Interpretations of Relativistic Phenomena. Journal of Modern Physics, 2012, 3, 187-199.

http://dx.doi.org/10.4236/jmp.2012.32026

Sergey:

Thanks! I'm going to look into that.

Dear Sergey and all. Perhaps you would like to see a comprehensive report on RTG by Logunov. His 255 pages report is available at http://arxiv.org/pdf/gr-qc/0210005v2.pdf. Best wishes

As I see, in RTG by Logunov the gravitational metric is used, which in sum with the metric of Minkowski space gives the metric of General Relativity. So RTG is the metric theory as Covariant Theory of Gravitation and General Relativity. Although RTG is building on the Minkowski space it is not the modified Lorentz-invariant Theory of Gravitation because instead of equations of gravitational field, which must be as Maxwell equations, there is equations for the gravitational metric as a form of gravitational field.

Dear Sergey, thank you for your comments. Yes i think RTG is based on Minkowski space. Best wishes

Sergey, RTG is a Lorentz-invariant theory of gravitation but not THE Lorentz-invariant theory of gravitation you have in mind. This fact suggests that to give THE Lorentz-invariant theoy of gravitation this name was a confusing and therefore bad choice.

Mozafar, criticizing "a variety of versions" of Lorentz-invariant theories of gravity, have you had in mind also RTG? I would be interested in criticism of RTG, because I have proposed a variant of this theory at http://arxiv.org/abs/gr-qc/0205035 .

Bravo, Mozafar!

I want add that Covariant Theory of Gravitation: 1) Is based on the Lorentz-invariant Theory Gravitation. 2) Is not follower of GR. 3) Has Maxwellian equations of gravitational field in covariant form. 4) Is deduced from the principle of least action. 5) Has the stress-energy tensor of gravitational field. 6) Can explain the Pioneer effect on the base of its equation of motion. 7. Can explain other effects of GR in its own way.

Thank you, Ilja, Mozafar and Sergey. Best wishes