Dear Professor Gopal

I have read your essay with a great pleasure. The reason is not only your style but first of all the geometrization of matter.

I have tried to apply Einstein's geometrization concept (but not his equations) not only to the matter but also to all "force fields" i.e. electromagnetic, strong and weak nuclear. The gravity would then be emergent as a superposition. The job is not easy so I have proposed an experiment to be sure this is not a huge waste of time. As you know Einstein GR failed outside the Solar System distance scale ( so some physicists try to save GR by means of dark things) and Wheeler-deWitt geometrodynamics has the well-known flaws: the problem of time, the problem of Hilbert space and others. QM's Standard Model in turn does not offer any metric. The other theories using canonical approaches (connection dynamics, loop dynamics etc.) or covariant approaches (perturbation theory, path integrals etc.) and string theories also have not acceptable flaws or generate no predictions.

I am looking for that one, universal, distance scale invariant metric (eventually reducing to Einstein GR metric within Solar System distance scale) and having ability to generate predictions. The first prediction of that geometrization concept is my spin experiment outcome. Depending on the outcome we shall look for a proper metric or give up.

GR has no action at a distance and QM has. If we assumed that any spacetime deformation is unlimited (to some extent it deforms the entire spacetime in Gaussian distribution mode, due to its elastic and homeomorphism properties) we have got non-local action! The Gaussian distribution guarantees no singularities for free.

In the contest is more than 100 essays so I would like to draw your attention to Torsten Asselmeyer-Maluga's essay and his publications on the geometrization of matter.

Your essay deserves the highest rating. Good luck!

Best regards

    Greetings Ram Gopal,

    It is good to see your essay here, which I have just begun to read. I had the pleasure to share lunch with you and hear your excellent lecture in Port Angeles, a few years back. I look forward to reading your paper, which I see has already been well regarded, and I will comment once I am done. Good luck!

    All the Best,

    Jonathan

      A very interesting paper Professor Vishwakarma,

      The ideas presented in this essay are indeed worthy of note. People have been so focused on finding a correct formulation for the stress-energy tensor, that they never bothered to examine solutions that make it unnecessary. Very fine work, and a paper well-written and well-enjoyed. I shall be happy to rate this one highly, once my own essay has posted.

      Good Luck!

      Jonathan

      Dear Prof. Vishwakarma,

      I have down loaded your essay and soon post my comments on it. Meanwhile, please, go through my essay and post your comments.

      Regards and good luck in the contest.

      Sreenath BN.

      http://fqxi.org/community/forum/topic/1827

        Dear Dr. Vishwakarma,

        In your highly interesting article, you have argued why the elimination of the term Tik from the basic equation of GR is essential if we are to make sense out of it to explain its recent consequences. Here I consider only the Kasner solution. For me, it appears that the Kasner solution must be applied to the QG field which exists inside black holes and only then it is possible for us to make sense out of it. So Tik points to the existence of QG field but cannot explain it as the metric of GR gik breaks down in the QG field. It is thus possible for us to understand and solve the mystery surrounding the Kasner solution and I think there is no need to eliminate the term Tik from the basic GR equation as it would spoil the formal beauty of the theory. So the effort to retain Tik, lies in finding the basic equation of QG field and from which deriving the basic equation of GR.

        Regards,

        Sreenath

        Dear Vladimir,

        Thanks for your comments and mentioning your relevant work. I have been trying to understand Eisntein's theory (rather than showing anybody wrong). In this process, I found some conceptual problems in GR.

        ___Ram

        Dear Manuel,

        Thanks for your kind remarks. I shall read your paper.

        ___Ram

        Dear Cristinel,

        Thanks for your kind remarks. Riemann tensor can also be non-zero when Ricci tensor is vanishing. That will signify the net energy-momentum-angular momentum of the material and the gravitational fields at a point.

        ___Ram

        Dear Satyavarapu,

        In my essay, there is no problem of the violation of the conservation of energy or matter coming out from nowhere. If you read the article and the references therein, you will note that there are two time scales in the resulting cosmological theory. In terms of one of them, the universe becomes infinitely old without any singularity at any finite time in the past. So, the question of the origin of matter/universe becomes meaningless in this model.

        ___Ram

        Dear Akinbo,

        Thanks for your kind remarks. I shall read your paper.

        ___Ram

        Dear Lawrence,

        Thanks for your kind and knowledgeable comments. It would not be correct to say that all the solutions of Einstein equations are not meaningful. This will create doubt over the general validity of the theory. Then how can we be so sure that Schwazschild solution (for example) represents a meaningful solution. Just because, it seems consistent with experiments? May be, we have been unable to interpret other solutions correctly, which we claim unphysical. As an example, the Kasner solution (which is considered unphysical) in the new paradigm discovered, in the paper, represents a real big bang universe!

        ___Ram

        Dear basudeba,

        Thanks for your wonderful remarks. I shall read your paper.

        ___Ram

        Dear Jonathan,

        Thanks for your kind and inspiring remarks! I look forward to see your essay.

        ___Ram

        Prof. R.G. Vishwakarma,

        Thank you for your reply. You said "Riemann tensor can also be non-zero when Ricci tensor is vanishing.". When Ricci=0, Riemann=Weyl, so we are in complete agreement.

        You mentioned the Kasner solution, and that the matter source (the singularity) exists only at the time t=-1/n, and yet it has effects at other times too. This in fact happens in the Schwarzschild solution as well. The singularity r=0 is not necessarily in the present of an observer affected by the black hole's gravity. This is obfuscated when using the Schwarzschild coordinates, but it is visible for example in the Kruskal-Szekeres coordinates. Another remark: I think something like this happens with the electromagnetic field. Imagine a pair electron/positron attract each other and annihilate. Yet, the electromagnetic field sourced by their charges exists an indefinite time after they were annihilated.

        Best regards,

        Cristi Stoica

        Dear Cristinel,

        Thanks for reminding me that the Weyl tensor (with 10 independent components) can be thought of as containing the information of the Riemann tensor (20 independent components) minus that of the Ricci tensor (10 independent components). So in the case of the vanishing Ricci, Riemann=Weyl.

        I have tried to establish that space and `what fills space' are not two different entities. That is, by considering space means considering the accompanying fields as well. That the matter fields are present in the metric (without taking recourse to the energy-stress tensor), can also be proved by the conventional belief which considers singularity as the source of curvature in the absence of the energy-stress tensor. For this reason, I have considered Kasner, Kerr, Schwarzschild solutions. (For this purpose, I argue that if the source matter is present at the epoch of singularity, it must also be present at other times. That is, the source matter is already present through the metric field, in the Kasner solution.)

        However, we must understand that the singularity is not the sole representative of curvature (in the absence of energy-stress tensor), since the conventional wisdom cannot explain the curvature of the Ozsvath-Schuckling solution (which is singularity-free). Hence the metric field (which has been shown to contain matter and gravitational energy in three cases) must be the real source of curvature.

        Another reason, why the singularity is not an efficient representative of curvature, is the controversial character of the singularity (black hole) in the Schwarzschild solution. There are claims that the black hole mass must be zero [Narlikar & Padmanabhan, Foundations of Physics, Vol. 18, pp.659-668 (2008)].

        The interpretation of the Schwarzschild solution, as a spacetime structure sufficiently away (of course that will be out of the event horizon) from some mass, is fine. In this case, the curvature present at those points can only be explained in terms of the gravitational energy (recalling that GR is a local theory). This is what I have emphasized in the essay.

        The parallel you mention between the GR cases and the electromagnetic one, is interesting. Thanks. It may contain important information.

        ___Ram

        Dear Jacek,

        Thanks for your kind remarks and for your interest in my essay. I also thank you for mentioning Maluga's work on the geometrization of matter. I shall read them in time.

        Best of luck on your ambitious endeavor. The theory based on R^{ik} = 0 might fit in it. It is scale invariant, describes not only the gravitational phenomena in the solar system, but the whole universe, as I have showed.

        Best of luck on your essay.

        ___Ram

        Ram,

        If given the time and the wits to evaluate over 120 more entries, I have a month to try. My seemingly whimsical title, "It's good to be the king," is serious about our subject.

        Jim