I think that it might be spacetime is quantized only to the 7 loop level. The Calabi-Yau three form induces a Galois cohomology with quotient groups which give loop orders up to 7. There is a moduli for the class of elliptic curves for the qubit system, which leads to multiplicities on the Eisenstein series for string loops. These are the three fold elements 1, 2, 3, which out of 8 dimensions includes the dual to 7, 6 and 5, and self duality gives the 4.

So the graviton, or the heterotic string will have and E_{7(7)} structure for up to 7 loops, and perturbative theory ends, it is cut off. So the graviton may in fact be a 4-fermion condensate or bound system, which in the N = 4 AdS^5xS^5 has an SU(4) structure. So it may be a bit like an extended QCD theory.

One possibility is that the third polarization is an effective mass-state which ends perturbation theory.

Cheers LC

Dear Sreenath,

actually, ETGR are designed to explain the gravitational-interaction at scales which are larger than the Solar System scale, where a weak modify of GR could be needed based on the presence of the intrinsic space-time curvature. Thus, if the gravitational wave received confirms ETGR, then the wave sent is not necessarily as a result of QG. Almost all the astrophysics sources can be treated in a classical way in ETGR exactly like in standard GR. Only the cosmological relic source of pages 8-9 of my Essay needs a quantum treatment. But notice that it needs such a quantum treatment not only in ETGR, but in standard GR too.

Cheers,

Ch.

Dear Rafael,

I have read your interesting Essay, but you do not discuss answers for the origin of the Cosmic Microwave Background Radiation and the way to avoid Singularity Theorems.

On the other hand, you explicitly tells that

"there is the suggestion regarding how the process of gravitation occurs. But the discussions on these are beyond the scope of this essay."

Thus, I think that such answers should arrive in further developments of the theory which will regard how the process of gravitation occurs.

Cheers,

Ch.

Never indeed....but sometimes we see people who interprets bizarely the continuity of our pure reals.They insert also the 0 the - and the infinity in their domains for the physicality....that has no sense about the pure determinism in all localities.

It's a big actual problem in the sciences community these confusions.Eckard has made a beautiful work about the rational road.We need that.

Regards

Steve

Christian,

Well reasoned, well argued.

Personally, I hope you're wrong, because if all the properties of spacetime cannot be determined by matter alone, I think Einstein's program is imperiled rather than extended. I find it easier to live with a singularity than with an extra assumption, especially when it is purely geometric. I realize that you preserve dynamics between spacetime and matter (Table) though it seems to me a bit like putting the cart before the horse.

In any case, though, good luck in the contest.

Tom

    Dear Dr. Corda,

    My theory can explain the curvature of spacetime Physically, but not mathematically. It seems logically argued that the increasing in concentration of holes can slow down time, because in the limiting case, when space is composed of holes only, the time can not exist in general, because all space would be a ''large hole''. There is no duration and extension outside of the Universe.

    Since you are a mathematical physicist who works in the research fields of gravitation, maybe you have any idea how to create the mathematical theory of the space curvature by using holes. In such case our theories meet - Your intrinsic spacetime curvature is just a consequence of appearance of holes in spacetime. I think how to introduce holes in Einstein field equations.

    Sincerely,

    Constantin

    Dear Tom,

    thanks for your kindness and for your comments.

    In my opinion, Einstein's ideas are not imperiled. In fact, there is not an extra assumption, but a modified assumption. It is assumed that the relation between mass-energy and space-time curvature is not equal, but the curvature dominates. The theory remains metric, thus the preserving dynamics between space-time and matter is not a putting the cart before the horse but it implies that the elegant Einsteinian geometrical vision of gravitation remains in the new framework too.

    On the other hand, let me emphasize that Einstein also tried to modify General Relativity in the last years of his life.

    Good luck in the contest to you too.

    Cheers,

    Ch.

    Dear Mr. Leshan,

    thanks for your comment.

    In my opinion, mathematics is the language of physics, thus, we cannot separate them. This is even more important in the Einsteinian geometrical vision of gravitation.

    In any case, if you write a manuscript where you find the way to introduce holes in Einstein field equations, I invite you to send me the paper for a submission for potential publication in the Open Astronomy Journal which is one of the journals where I am Editor in Chief.

    Best regards,

    Ch.

    Christian,

    Very true. I guess I look at it more from the perspective of Einstein as a true classical physicist, wanting to have all the properties of spacetime determined by matter, using some version of Mach's mechanics. That's what he was brought up with, that's what he knew so intimately.

    He didn't grow up with Riemannian manifolds; he was introduced to them when stuck for a geometry that fits the dynamics. A curvature that's prior to the physics seems a bit like "cheating." I mean, the curve might facilitate inertia in a quasi-Euclidean universe, but curvature without inertia requires no dynamics. It really is more epistemologically satisfying, as Einstein said, to not have to introduce geometry to explain mechanics. I'm with Fotini Markopoulou on the proposition that "space does not exist, so time can." Mach's mechanics also treats space as a convenient fiction.

    So the reason I hope you are wrong is merely philosophical, not physical. You still did one great job of theorizing.

    Best,

    Tom

    6 days later

    Dear Christian Corda

    I see that your work is a big project.

    I think that this theory is written in Feynman's lectures on gravity. Are there any differences in your approach? Is this theory background independent, that means that Minkowki space is not the background metric? I have forgotten, but it seems to me that it is background independent? (The backgroud independeny is so important as measurement agreements of GR.) How it is then with quantization of such a theory? Does it give space-time lattice or..?

    I have one theory where elementary particles are superpositions of zero and planck mass black holes. Maybe you have and opinion?

    http://vixra.org/pdf/1103.0025v1.pdf

    I need an endorser on arXiv for publication of my article:

    http://vixra.org/pdf/1012.0006v3.pdf

    It is not speculative one. It is a base for the above article. But the above article is speculative. But I need such a publication that my theories will be read and discussed.

    Yours sincerely

      Dear Janko,

      thanks for you kindness and for your good judgement on my work.

      There are two points of view concerning gravitation: the Einstein's geometric point of view and the Feynman's particle point of view. The Quantum Gravity Theory, if it will be ultimately find, should be the definitive synthesis of them.

      Actually, my research work is based on Einstein's geometric point of view. Which is the correct background metric depends from the scale of the intrinsic curvature. If the scale is not too large the Minkowkian flat space-time remains the background space-time. In fact, Equivalence principle is preserved, thus the space-time, even if globally curve, remains locally flat.

      I regret, I am not an expert of elementary particles and of Feynman's particle point of view, thus, I cannot judge your papers.

      Cheers,

      Ch.

      Dear Dr. Corda,

      congrats for standing 18th on the list and in sight of an assured prize.

      An article I have written on Quantum-Gravity viz. 'New coceptual Foundations for Quantum-Gravity And Quantum-Mechanics' (I have mentioned this in my essay and there I have given the web-site address too ;'http://www.sreenath.webs.com').I want to send it to you for reviewing and would be glad if you accept it for publication in the journal edited by you.In this article,I have derived the basic equation of GR from the basic equation of QG in tensor form.

      Thanking you and looking forward to hearing from you.

      Sreenath.

        Dear Sreenath,

        thanks for your congrats.

        I do not know if I will have an assured prize, this will be judged by the expert panel of judges which will be instructed and I have a total respect in FQXi's merit system.

        You can send me your Quantum-Gravity paper for reviewing at my email

        cordac.galilei@gmail.com

        Cheers,

        Ch.

        Dear Christian,

        Congratulations on your dedication to the competition and your much deserved top 35 placing. I have a bugging question for you, which I've also posed to all the potential prize winners btw:

        Q: Coulomb's Law of electrostatics was modelled by Maxwell by mechanical means after his mathematical deductions as an added verification (thanks for that bit of info Edwin), which I highly admire. To me, this gives his equation some substance. I have a problem with the laws of gravity though, especially the mathematical representation that "every object attracts every other object equally in all directions." The 'fabric' of spacetime model of gravity doesn't lend itself to explain the law of electrostatics. Coulomb's law denotes two types of matter, one 'charged' positive and the opposite type 'charged' negative. An Archimedes screw model for the graviton can explain -both- the gravity law and the electrostatic law, whilst the 'fabric' of spacetime can't. Doesn't this by definition make the helical screw model better than than anything else that has been suggested for the mechanism of the gravity force?? Otherwise the unification of all the forces is an impossiblity imo. Do you have an opinion on my analysis at all?

        Best wishes,

        Alan

        Dear Alan,

        thanks for congratulations.

        Regarding your questions, the fundamental point is that the calculations of the red shift, the time delay in radar echoes from planets,the bending of light, the perihelion shift, and the geodesic effect all support the 'fabric' of spacetime. Can your Archimedes screw model for the graviton explain with the same extraordinary precision these astrophysical tests? If the answer is yes you should continue studies in this direction, if the answer is no, then I suggest you to decline.

        Cheers,

        Ch.

          Dear Dr. Corda

          1) This essay is the description of the UNSUCCESSFUL attempt to solve the problems of gravity: I see no signs that your ETG with intrinsic space-time curvature may explain inertia, mass and unify Gravity with other forces. Does the description of the UNSUCCESSFUL attempt to solve the problems of gravity deserve the prize? In the same way we can support all authors of the Extended Theories of Gravity with similar papers.

          2) According to FQXi rules: ''the essays shall be accessible to a diverse, well-educated but non-specialist audience, aiming in the range between the level of Scientific American and a review article in Science or Nature''. Dr. Corda's essay is too hard to understand for non-specialists and contain too much equations and professional jargon. For example: ''a function of scalar fields in Scalar-Tensor Theories, Ricci curvature scalar, matrix elements, Klein-Gordon equation'' and so on.

          3) About 90 percents of the essay is filled with generally known information about Extended Theories of Gravity, gravitation waves, history of science and so on. Thus, the most part of the essay's physics information was copied from the references. For example he wrote: ''The scientific community hopes in a first direct detection of GWs in next years'' ''From a historical point of view, Einstein believed that'', ''The necessity to produce a correct Quantum Gravity Theory came into existence at the end of 50's of last century''. The essay filled with such information is not original, it is a story about physics and unsuccessful attempts to understand gravity.

          4) This essay has nothing to do with our essay contest because I don't see any speculations about the digital-analog nature of the Universe. In fact Dr. Corda sent us his professional theory by adding only the words ''analog-digital'' to the title of the essay.

          Sincerely,

          Constantin

            Dear Mr. Leshan,

            in all honesty, I am very surprised for this new strong attack. In fact, in your previous message you discussed on a possible collaboration on introducing your holes in Einstein field equations.

            Thus, I am ABSOLUTELY SURE that your new attack is purely personal and due to the fact that your essay is # 157, and, as my Essay is # 18, there are 139 positions between yours and mine...

            In any case, I am very honoured for this new attack by you. It is well known that you are a person who, as the Scientific Community rejects his strange theories, attacks recognized results. This means that I wrote a good Essay, thus, dear Mr. Leshan, THANKS A LOT!!!

            I am going to reply to your attack but this is the last time that I discuss with you because I am interested only in discussions on science, not in lowest discussions and brawls.

            1) I do not attempt to solve all the problems of gravity, I limit myself to discuss intermediate steps like the extension of General Relativity and/or the quantization of Extended Theories in the weak field approximation.

            Even if I agree with you that the complete theory of gravitational interaction must be able to explain inertia, mass and to unify Gravity with other forces in the same model, differently from you, I am not so arrogant and presumptuous to claim that I can find, alone, the complete theory of gravitational interaction. If Albert Einstein and others world's greatest scientists did not find this theory in about 100 years of scientific research, I am absolutely sure that I will not find it being alone!! If you thinks to realize alone such a goal is a problems of yours, not a problems of mine!! Send your "hole theory" to Nature or to Physical Review Letters or to the Gravity Research Foundation Competition, if you are correct you will won the Nobel Prize!!!

            I limit myself to try to give small contributions towards such a goal by following a way that could be the correct one.

            I do not know if my contribution deserves or does not deserve the prize, this will be judged by the expert panel of judges which will be instructed and I have a total respect in FQXi's merit system. Maybe you can support all authors of the Extended Theories of Gravity with similar papers, but I am not interested on your support, at the present time I am interested in the judgement of the FQXi's expert panel of judges. On the other hand, others authors of the Extended Theories of Gravity gave different contributions with respect to my original contribution.

            2) Maybe my essay is too hard to understand for you, but surely it can be understood by diverse, well-educated but non-specialist audience, aiming in the range between the level of Scientific American and a review article in Science or Nature. In fact, the level of Scientific American and a review article in Science or Nature can comprise terms like ''a function of scalar fields in Scalar-Tensor Theories, Ricci curvature scalar, matrix elements, Klein-Gordon equation''. It is well know that various Essays which were awarded in previous FQXi Essay Contests comprised terms like those. What is really important is that there are not high technical computations which use such terms in my Essay. If you do not understands those terms is a problem of yours, not a problem of readers. A non-specialist person like a student who is starting the University, surely understands my Essay. FQXi's Authors who honoured myself with the position # 18 of this Essay Contest SURELY understand my Essay differently from you.

            3) You should read ALL the FQXi rules. In fact, according to them: "While the essay may or may not constitute original research, if the core ideas are largely contained in published works, those works should be the author's."

            It is correct that the most part of the essay's physics information was taken from the references, but these papers were MY PAPERS, published in various international peer-reviewed journals.

            4) I am not so arrogant and presumptuous to claim that the reality is digital, analog, or digital-analog. Even in this case, I recall you that Albert Einstein and others world's greatest scientists did not find the correct answer to this issue in about 100 years of scientific research. Thus, I prefer limit myself to suggest a potential detectable signal, i.e. the relic gravitational waves, which could clarify the digital rather than analog feature of the gravitational interaction. This is absolutely sufficient for me.

            In my opinion, at the present time and at the present status of our scientific knowledge, nobody can claim, with an absolute certainty, that Reality is surely Digital, or surely Analog or surely Digital-Analog. Of course, people have various opinions on this fundamental issue and I respect all the various opinions. I have an opinion too, but I think this is NOT really important. What I think to be really important, at the present status of our scientific knowledge, is the way in which one attempts to arrive to a potential answer to the question, not the question itself.

            I interpreted this beautiful Essay Contest in this spirit and with this spirit I wrote my Essay.

            Best wishes for your "hole theory", even if I think it will be very very difficult that some serious journal of some serious Essay Contest will seriously consider it...

            Best regards,

            Ch.