Dear Ram,

Well argued, using the very tools used to construct the GR theory itself.

"on the basis of the general theory of relativity, space as opposed to 'what fills space' has no separate existence".

My view: space is both the content and the container, so I agree what fills space and space itself are the same. You can criticize and fault my essay so I can improve it. Thanks.

    Dear Dr. Vishwakarma,

    Your does illustrate one of the weaknesses with general relativity as a complete theory. In source free regions we can be reasonably sure that solutions with certain symmetries are physically correct, and the Hawking-Penrose energy conditions are upheld. The Einstein field equations though permit all sorts of quirky solutions, including those that are time machines.

    The Kasner solution is a simple case of Mixmaster or Bianchi type cosmologies with anisotropies. The anisotropies are interpreted as due to gravitational waves that behave as if there is a T^{00}, which is a sort of internal energy in a source free region. These models have not been prominent of late, but data involved with CMB anisotropies seem to suggest the early universe may have had properties of this sort. These anisotropies may have been a part of the physics with particle production.

    I think that geometrical or topological decompositions of four manifolds constructs topological quantum field theory, or formalism equivalent to that. The matter which fills spacetime is then equivalent I think to this underlying structure to spacetime. Einstein was dismayed by the apparent asymmetry in physical meaning between G_{ab} and T_{ab}. I think the underlying problem might be addressed by thinking of spacetime has having all the substructure of particle physics. The production of particles in a Mixmaster type cosmology from anisotropy does suggest something of this nature.

    Cheers LC

      Dear Sir,

      Your essay is a brilliant analysis of the current problems facing physics and suggested some solutions. We generally agree with your views. We have analyzed some similar issues in our essay: "INFORMATION HIDES IN THE GLARE OF REALITY by basudeba mishra http://fqxi.org/community/forum/topic/1776" published on May 31. Here we are analyzing your essay from a different perspective.

      The validity of a physical statement rests on its correspondence to reality. This correspondence is communicated or even perceived through reporting in some language, which is the information. Thus, your statement is justified. But we can look at your analysis from a different perspective.

      The mass-energy of the universe that Dark Energy is said to represent has been reduced from 72.8% to 68.3%. At the same time Dark Matter increased from 22.7% to 26.8%. This means the percentage of ordinary matter has gone up from 4.5% to 4.9%. It poses two questions: 1) whether the previous reading was not accurate or 2) whether the balance is actually changing? There can be a third possibility - 3) both the above conclusions are wrong, because our theory or our interpretation of observed phenomena is wrong.

      Dark energy is so named because it does not interact with other bodies (hence dark) and it is smooth and persistent (hence not matter, but energy). Since energy is perceived only through its interactions with matter, the term dark energy is an oxymoron. It is said that it does not interact gravitationally - hence dark. But is gravitation an attractive force? No force can physically "pull" - it can only be a "push" from the opposite direction. We will explain magnetic force separately, as its attraction is not universal, but restricted to magnetic substances only. The gravitational interaction keeps the two bodies in a stable orbit around the barycenter, whose position depends upon the ratio of the masses and the distance between the two bodies. If we take the total area within the orbit and distribute the total mass within that area, we will get the average density. The barycenter represents the ratio of masses of the two bodies in terms of this average density. Thus, the barycenter acts as a base or a ground or a background structure for placement of the bodies. Suppose dark energy is something like that?

      Maxwell's equations are background invariant. Transverse waves are always characterized by particle motion being perpendicular to the wave motion. This implies the existence of a medium through which the reference wave travels and with respect to which the transverse wave travels in a perpendicular direction. In the absence of the reference wave, which is a longitudinal wave, the transverse wave can not be characterized as such. Transverse waves are background invariant by its very definition. Since light is a transverse wave, it is background invariant. Einstein's ether-less relativity is not supported by Maxwell's Equations nor the Lorentz Transformations, both of which are medium (aether) based. Thus, the non-observance of aether drag (as observed in Michelson-Morley experiments) cannot serve to ultimately disprove the background structure. The so-called non-interacting dark energy may be the background structure.

      The universe is not expanding or accelerating, as it is not evident at local galactic scales or less. Had the universe being expanding, such expansion would have been evident in local scales also. Even a spot on the balloon expands. Thus, there is a doubt on the authenticity of the galaxy rotation problem that gave rise to the concept of dark matter. Distant galaxies are rotating around a common galactic center and like the velocities of planets far away from the Sun, their velocities are relatively greater. We can visualize it as a potter's wheel. Compared to a point relatively nearer to the galactic center, the distant objects appear to be moving faster. Since it is a circular orbit, at times they appear as receding (atichaara) while at other times they will appear as approaching (vakra). The measured time span is insignificant in cosmic scales.

      In various threads here we had shown that the equivalence principle is a wrong description of facts and will lead to Russell's paradox of set theory. We have also explained that since space is an interval between objects, the geometry or curvature of space is the actually the curvature of the objects. Yet, the gravitational interaction always moves in curves. This moves the objects in curved paths, which is called the curvature of space. This explains why the space-time metric appears as the field. The energy-stress tensor is a part of the 'dark energy', which is the universal background structure.

      Regards,

      basudeba

        Dear Professor Vishwakarma,

        I read your essay with interest. I liked the term "geometrization of matter" - something I can relate to from my previous work with simplexes. Also the possibility of omitting singularities in the Ozsvath-Schuckling solution agree with my analysis that information might avoid being lost forever in Black Holes.

        Best wishes,

        Antony

          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