Dear Cristian,

You write

---"As distinct from other field theories, like the Electromagnetic Theory, General Relativity is very difficult to quantize. This fact rules out the possibility of treating gravitation like other quantum theories and precludes the unification of gravity with other interactions. At the present time, it is not possible to realize a consistent Quantum Gravity Theory which leads to the unification of gravitation with the other forces."---

If a universe is to create itself without any outside intervention, then its particles must create themselves, each other. If (the properties of) particles then are as much the product as the source of their interactions, their energy exchange, then so is the force between them. This means that a force, in principle, cannot be either attractive or repulsive. That is, particles can only exist, have properties (attract/repulse) if they have some kind of backbone so they can, within limits, absorb energy in an increase of their kinetic energy rather than in a change of identity. That said, if the rest energy of particles ultimately is as much the effect as the cause of their energy exchange, their interactions, of a continuing evolution, then interaction energies never can become infinite at infinitesimal distances, so there's no need for string theory. A universe which finds a way to create itself without any outside intervention can hardly stop doing so: gravity, the contraction of masses and the related expansion of spacetime between the mass concentrations they form, is the expression of this continuing creation process, and hence differs fundamentally from the 'other' forces.

Since according to our present, simplistic ideas particles only are the source of their fields, they either attract or repulse, so the strength of the force between them solely depends on their distance. This belief led to the question how protons can fit in atomic nuclei despite their huge electric repulsion, which is said to be 10^38 times stronger than gravity between them. However, a force never can exceed the counter force it is able to evoke, that is, than the opposition the particles offer to that force: than their inertia. So if we may interpret Einstein's equivalence principle to say that every influence which brings the inertia of a particle to expression as a counter force can be called 'gravity', then there's only gravity. As attractive as it is repulsive, it is much stronger than the weak gravity pulling at Newton's apple, as gravity which is powered by the continuous creation process inherent to a self-creating universe. For details, see my essay the UPDATE 1 post about the strong nuclear force.

Regards, Anton

Dear Anton,

thanks for your comments.

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.

In any case, Einstein's Equivalence Principle is purely geometric as it implies that test masses (particles) have to follow the space-time curvature during their motion. In this geometric vision only mass-energy and curvature are strictly needed. In my attempt to extend General Relativity mass-energy should be produced by variations of an intrinsic space-time curvature. Can this be conciliated with your vision that gravity has to be powered by the continuous creation process inherent to a self-creating universe?

Best regards,

Ch.

    Dear Christian,

    You say: "gravitational waves are solutions of both the linearized and full Einstein Field Equations".

    "Looking at the Einstein equations as a set of second-order partial differential equations it is not easy to predict that there exist solutions behaving as waves. Indeed, and as it will become more apparent in this Section, the concept of gravitational waves as solutions of Einstein equations is valid only under some rather idealized assumptions such as: a vacuum and asymptotically flat spacetime and a linearized regime for the gravitational fields. If these assumptions are removed, the definition of gravitational waves becomes much more difficult. In these cases, in fact, the full nonlinearity of the Einstein equations complicates the treatment considerably and solutions can be found only numerically. It should be noted, however, that in this respect gravitational waves are not peculiar. Any wave-like phenomenon, in fact, can be described in terms of exact ``wave equations'' only under very simplified assumptions such as those requiring an uniform ``background'' for the fields propagating as waves." [link:people.sissa.it/~rezzolla/lnotes/virgo/node9.html]

    You also say: "heavy masses with acceleration should radiate gravitational waves based on such elastic properties"

    I assume that "the matter" is a wave itself. In my view e.g. the electron is a real wave (a local spacetime contraction region moving in a wave form). I know it was also the initial Schrödinger's point of view that the electron is a wave but dismissed after the double slit experiment. That time he could not defend his thesis. According to my concept the matter is only a deformed spacetime so there is nothing to explain about the double slit experiment as the electron is a wave and not only has wave properties. And every "massive" object e.g. the Earth is a gravitational wave itself. And the wave is not traveling outward from the source. There is no source - the Earth is a gravitational wave orbiting the Sun along the geodesic. I know my concept is highly speculative but maybe worth to develop because it delivers a chance to create a GUT.

    Best regards,

    Jacek

    I am sorry but I did not read the help on linking sites so I give the the [link: http://people.sissa.it/~rezzolla/lnotes/virgo/node9.html] once more. Sorry, the rest of the text is linked to the site.

    Dear Dan,

    yes, I confirm you that, exactly like the FQXi, the Gravity Research Foundation has a remarkable merit system. What is really important for them is the quality of the research. When I received an Honorable Mention in the 2009 Competition I had no academic affiliation too.

    I well know that the entry deadline is April 1, I am going to attend this year too. Together with some collegues, we are finishing an Essay on black holes exactly like you.

    Best wishes for this Competition too.

    Cheers,

    Ch.

    Dear Jacek,

    the sentence that you quoted by the paper of Rezzolla reads:

    "... it is not easy to predict that there exist solutions behaving as waves."

    which is different from:

    "... it is impossible to predict that there exist solutions behaving as waves."

    In fact, such solutions of exact equations have been found, see for example

    H. Bondi, F.A.E. Pirani, and I. Robinson, Proc. R. Soc. London A 251, 519 (1959);

    H. Stephani, D. Kramer, M. MacCallum, C. Hoenselaers, and E. Herlt, Exact solutions of Einstein's field equations, 2nd ed. (Cambridge Univ. Press, Cambridge, 2003) Secs. 24 and 31;

    J. Ehlers and W. Kundt, Exact solutions of the gravitational field equations, in: "Gravitation: an introduction to current research", ed. by L. Witten (Wiley, New York, 1962);

    Y. N. Obukhov, J.G. Pereira and G. F. Rubilar, Class. Quant. Grav. 26, 215014 (2009).

    On the other hand, it is true that

    "the concept of gravitational waves as solutions of (linearized) Einstein equations is valid only under some rather idealized assumptions such as: a vacuum and asymptotically flat spacetime and a linearized regime for the gravitational fields."

    But, even if idealized, such assumptions can be realized with an excellent approximation. Take two neighbouring free-falling test masses within a vacuum cylinder in the Earth's gravitational field. For Einstein's equivalence principle they realize a vacuum and locally flat spacetime. This is EXACTLY the principle which is used for detect gravitational waves with interferometers. In fact, test masses suspended to pendulums represent an excellent approximation of free-falling test masses.

    More, the linearized regime is an excellent approximation even for the gravitational field of the Solar System (historically Einstein used the linearized regime to test astrophysical predictions like the light deflection, the gravitational redshift and the precession of the Mercury's perihelion). The gravitational field of a gravitational wave is various order of magnitude lower than the gravitational field of the Solar System, thus, the linearized regime is an absolutely excellent approximation. In fact, high order terms are lower than 10^-42...

    Best regards,

    Ch.

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    • Post #33

    Hello dear Dr Corda, Happy to see you again,good luck ,it's a beautiful essay,congratulations

    Steve

    Hi Steve,

    nice to see you again too.

    Thanks for congratulations, I see that you do not attend to the Essay Contest this year.

    Cheers,

    Ch.

    Dear Christian,

    I have not said it is impossible to predict that there exist solutions behaving as waves. If we try very hard... And it depends on assumptions. I have just assumed another scenario I will try to find another solutions.

    I have only read the paper by Y. N. Obukhov, J.G. Pereira and G. F. Rubilar and found it interesting. They claim:

    1. any exact gravitational wave solution is highly idealized, and is thus probably more of academic interest

    2. As we have seen, the exact plane-wave solution of Einstein's equation transports neither energy nor momentum. This property appears to be quite unusual, since one could expect that a gravitational wave, like any other gravitational field configuration, should be characterized by nontrivial distribution of energy and momentum. In this sense the exact plane wave solution, although being mathematically well defined, appears to be a physical puzzle.

    As you have maybe noticed in my concept e.g. the Earth is a gravitational wave orbiting the Sun along the geodesics. So it transports the energy and momentum and is not a physical puzzle. That is why I think it is worth further research. Maybe the idea is wrong but very simple and beautiful.

    As far it has not been successful to detect gravitational waves with interferometers. I cannot be sure it is impossible. That is only a consequence of my concept.

    Best regards,

    Jacek

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    • Post #36

    Hello,Christian

    What is your opinion about alternative to intrinsic space-time curvature -intrinsic space curvature?

    http://www.fqxi.org/community/forum/topic/946

    Hi Yuri,

    I see in your Essay that the first cited example of physical evidences supporting the Ratio 3:1 is the ratio 3 space-like dimensions - one time-like dimension. It is an interesting Essay, I wish you good luck.

    Concerning your question, I think that the space-time should be globally and intrinsically curve.

    Cheers,

    Ch.

    Dear Jacek,

    in my paper Gen.Rel.Grav.40, 2201-2212 (2008) I released the hypothesis that the whole Dark Energy could be a cosmological gravitational wave. In that case, the frequency of the wave should be minor than the Hubble Constant. The model is consistent with both of the Hubble Law and the Cosmological Redshift.

    Cheers,

    Ch.

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    • Post #39

    your discussion is relevant.

    Dear Christian you say" I released the hypothesis that the whole Dark Energy could be a cosmological gravitational wave. In that case, the frequency of the wave should be minor than the Hubble Constant"

    It's very relevant, do you consider this wave as the first wave?Could you develop a little please?

    Reagrds

    Steve

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    • Post #40

    Hello dear Christian,

    Thanks you are welcome.

    No as habit I am bad organized lol, after all it's not important.You know I will publish probably in the future with a kind of team , humanistic and universal.I need a coach or others I don't know, in all case I am not skilling in management and administration.It's the life.I have problems to focus.But I continue to class all and improve the correlations.

    Regards

    Steev

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    • Post #41

    Christian,

    Congratulations on your accomplishment. Although by the appearance of your entry into this year's contest, it seems only a matter of time before you were given recognition.

    I hope I am able to finish my essay, as it seems as if time is my worst adversary, nowadays. If not, so be it. There's always next year. Too many things to do and learn and not enough time.

    Have a great day!

    Dan

    Hi Dan,

    I am very honoured for your kind words, thanks a lot.

    Maybe we could collaborate in the future.

    Have a great day you too!

    Cheers,

    Ch.

    Steve,

    I applied Eqs. (3), (4) and (5) of my Essay in a cosmological framework. In particular, I released the strong assumption that the mass-energy (4) represents the Dark Energy of the Universe. In that case, the cosmological gravitational wave is the wave-packet (4). Then, the conformally flat line-element (15) becomes the analogous of the FRW line-element. The assumption of homogeneity and isotropy removes the z-dependence in (15). At the end I found consistence with both of the Hubble Law and the Cosmological Redshift.The fact that the frequency of the wave-packet (4) should be minor than the Hubble Constant implies that the length of the cosmological perturbation is longer than the Hubble Radius. This means that cosmological observations remain "frozen" with respect to the cosmological gravitational wave.

    The pre-print of the paper is available in http://arxiv.org/abs/0802.2523

    Cheers,

    Ch.

    Dear Christian,

    I have found your papers to pioneer in the development of the promising and innovative GUT and the first that share my view on the dark matter and energy and on the other hand I feel you could make a few steps forward in the same direction. I am sorry for these words. I will try to explain.

    I have just read your "oscillating universe" on arXive that you have recommended to Steve. I do not understand all the intricacies of the paper due to my partial incompetence in mathematics. I agree with the idea in general and the approach to oscillating universe in the expansion phase.

    Are you acquainted with Sladkowski J. Strongly gravitating empty spaces. arXiv:gr-qc/9906037v1?

    He writes: on some topologically trivial spaces there exist only "complicated" solutions to the Einstein equations. By this we mean that there may be no stationary cosmological model solutions and/or that empty space can gravitate. Such solutions are counterintuitive but we are aware of no physical principle that would require rejection of such spacetimes.

    I fully agree. This is the step in the right direction.

    However later on he writes: Suppose that space-time is only a secondary entity emerging as a result of interactions between physical (matter) fields.

    And in this case I think it is vice versa.

    Finally there is my point. Could you use your approach to the spacetime but make it scale invariant? I mean up to the h scale? I mean to elementary particles? And you should see all interactions unified. Maybe a GUT?

    Best regards,

    Jacek

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    • Post #45

    Dear Dr. Corda,

    I went thro' your lucid essay with ease and entusiasm.The theme of your essay is too clear.But what is perplexing for me is,what makes you shyaway from quantizing gravity/acceleration straight away and try to formulate successful theory of quantum-gravity sothat you can unify all four physical forces? For how to do it,please go through my essay and I hope you will find the solution there.So Iam interested to know how you react to my essay.

    Best regards and wishing success in the competition.

    Sreenath B N