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RECENT POSTS IN THIS TOPIC

**Author Frank Martin DiMeglio**: *on* 4/30/11 at 16:14pm UTC, wrote Dr. Corda: You have a very impressive knowledge base, so I am going to...

**Christian Corda**: *on* 4/25/11 at 15:59pm UTC, wrote Dear dreamer, thanks. Yes, I am surely a dreamer too. Best wishes, Ch.

**dreamer**: *on* 4/24/11 at 6:44am UTC, wrote dreamer

**Robert Spoljaric**: *on* 4/10/11 at 1:37am UTC, wrote Dear Dr. Corda, A slightly revised paper (PDF) has now been sent to you...

**Robert Spoljaric**: *on* 4/9/11 at 9:47am UTC, wrote Dear Dr. Corda, Thank you for the opportunity, but first I will try and...

**Christian Corda**: *on* 4/9/11 at 7:18am UTC, wrote Dear Robert, actually, in the email that you sent to me you clarified the...

**Robert Spoljaric**: *on* 4/9/11 at 0:35am UTC, wrote Buongiorno Dr. Corda, Please excuse this post, but it has occured to me...

**Author Yuri Danoyan+**: *on* 3/30/11 at 12:26pm UTC, wrote Gentlemens I wonder why you did not notice or do not want to notice the...

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A "retrocausal" rewrite of physics, in which influences from the future can affect the past, could solve some quantum quandaries—saving Einstein's view of reality along the way.

Figuring out if A causes B should help to write the rulebook for quantum physics.

Finding the universe's wavefunction could be the key to understanding the emergence of reality.

Tests of a rival to quantum theory, taking place in the belly of the Gran Sasso d'Italia mountain, could reveal how the fuzzy subatomic realm of possibilities comes into sharp macroscopic focus.

Combining gravity with the process that transforms the fuzzy uncertainty of the quantum realm into the definite classical world we see around us could lead to a theory of quantum gravity.

FQXi FORUM

October 23, 2016

CATEGORY:
FQXi Essay Contest - Is Reality Digital or Analog?
[back]

TOPIC: From Classical (Analog) to Quantum (Digital) Gravity: The Mystery of Space-Time Curvature and the Secret of the Origin of Mass-Energy by Christian Corda [refresh]

TOPIC: From Classical (Analog) to Quantum (Digital) Gravity: The Mystery of Space-Time Curvature and the Secret of the Origin of Mass-Energy by Christian Corda [refresh]

Towards the goal to quantize gravity, we discuss an intermediate step which consists in extending the picture of standard General Relativity by considering the potential presence of an intrinsic space-time curvature in our Universe, i.e. a curvature which is not due to the mass-energy. The potential existence of an intrinsic space-time curvature is admitted in the framework of Extended Theories of Gravity. In this tapestry, the equations to quantize are not the standard Einstein field equations of General Relativity, but the extended Einstein field equations which take into account the presence of the intrinsic space-time curvature. The traditional relation between mass-energy and space-time curvature, which founds standard General Relativity, results modified in this new picture and, at least at the linearized approximation, variations of this intrinsic space-time curvature generate the mass-energy. Various problems of the Dark Universe, like Dark Energy, Dark Matter and Pioneer anomaly, can be, in principle, solved through this approach, while a definitive endorsement for the effective existence of an intrinsic space-time curvature in our Universe could arrive from the realization of a consistent gravitational wave astronomy. We also discuss the quantization of both mass-energy and space-time curvature in the early Universe by using the process of amplification of vacuum fluctuations which is connected with the primordial production of relic gravitational waves. A future detection of such relic gravitational waves will be an ultimate endorsement for the Digital (Quantum) rather than Classical (Analog) feature of the gravitational interaction.

Christian Corda is a mathematical physicist who works in the research fields of gravitation, astrophysics and cosmology. He received a Ph.D. degree in physics from the Pisa University, Pisa, Italy. He is Editor in Chief and Editorial Board Member of various peer-reviewed international journals in the fields of physics and mathematics.

Dear Dr. Corda.

Congratulations on the birth of baby David. Soon he will, like you, defy gravity and start walking..enjoy every day of parenthood!

I am unqualified to comment on your paper, but I have a request. Can you please give your impression of my earlier 2005 Beautiful Universe paper on which my present fqxi paper is based?

In my model GR would be greatly simplified in a digital universe, reduced to the 'optics' of refraction in a medium of variable density. A geodesic in such a density field will have the curvature due to acceleration with the velocity of the signal varying from universal lattice node to the next node according to its density or potential. Yes my model proposes a varying speed of light with a maximum of c with Lorentz transformations in an ether of nodes spinning in angular momentum of units (h). Apologies for this intrusion but as an expert on GR you can give valuable feedback. Good luck with your research. Avanti!

Thanking you and with kind regards

Vladimir

report post as inappropriate

Congratulations on the birth of baby David. Soon he will, like you, defy gravity and start walking..enjoy every day of parenthood!

I am unqualified to comment on your paper, but I have a request. Can you please give your impression of my earlier 2005 Beautiful Universe paper on which my present fqxi paper is based?

In my model GR would be greatly simplified in a digital universe, reduced to the 'optics' of refraction in a medium of variable density. A geodesic in such a density field will have the curvature due to acceleration with the velocity of the signal varying from universal lattice node to the next node according to its density or potential. Yes my model proposes a varying speed of light with a maximum of c with Lorentz transformations in an ether of nodes spinning in angular momentum of units (h). Apologies for this intrusion but as an expert on GR you can give valuable feedback. Good luck with your research. Avanti!

Thanking you and with kind regards

Vladimir

report post as inappropriate

Dear Vladimir,

thanks for your kind congratulations on the birth of baby David.

I read the abstract of your paper on Beautiful Universe. I think that it could be interesting but you should send it to a peer-reviewed international journal in order to have a concrete scientific feedback.

Cheers,

Ch.

thanks for your kind congratulations on the birth of baby David.

I read the abstract of your paper on Beautiful Universe. I think that it could be interesting but you should send it to a peer-reviewed international journal in order to have a concrete scientific feedback.

Cheers,

Ch.

It is good to you submitted a paper here again. I have not read yours yet, so I can't ocmment much now.

I remember we were considering doing some gravity wave calculations with thermal sources. Yet that got a bit lost in the shuffle.

Cheers LC

report post as inappropriate

I remember we were considering doing some gravity wave calculations with thermal sources. Yet that got a bit lost in the shuffle.

Cheers LC

report post as inappropriate

Hi Lawrence,

nice to meet you again.

Regarding thermal gravitational waves, give a look to this paper by C. Sivaram and Kenath Arun: http://arxiv.org/abs/1005.3431.

I recently accepted it for publication in TOAAJ.

Cheers,

Ch.

nice to meet you again.

Regarding thermal gravitational waves, give a look to this paper by C. Sivaram and Kenath Arun: http://arxiv.org/abs/1005.3431.

I recently accepted it for publication in TOAAJ.

Cheers,

Ch.

Dear Dr. Christian Corda,

as explained in my Essay the derivation of General relativity from the more fundamental canonical theory involves the approximation of the total energy-momentum-stress by the energy-momentum-stress for matter alone. If we relax this approximation and maintain the total energy-momentum-stress, then we do not derive the usual Hilbert & Einstein equations but a generalized equation as the equation 94 in the reference 18 in my Essay.

That generalized equation is your equation 2, except by the notation (T_{ab}(EXTRA) corresponds to T_{ab}(c) in your equation 2) and because the physical interpretation of the new energy-momentum-stress tensor term is somehow different.

In your "Conclusion Remarks", you speculate about how the new equation (2) could, in principle, solve the Dark Energy, Dark Matter and Pioneer anomalies.

We already addressed the issue of Dark Energy in page 53 of the same reference 18. Since we have the explicit form for the new energy-momentum-stress tensor, we compute its value and obtained a cosmological constant of order 10-54 (in Standard Units), which is very close to the last observed value of 10-52. This was then interpreted as an important advance, specially since other approaches to the cosmological constant fail by huge errors. The so called biggest mistake ever in physics!

We did a more accurate computation recently and obtained a value of order 10-52 in complete agreement with observation. This has still to be verified by other experts, but it seems that a natural solution to the Dark Energy problem is already at your hand.

Regarding Dark Matter, we are working in this as well. As said in the same reference 18, first research seems to support the idea that the new theory of gravity also solves the Dark Matter problem. We can already explain observational data that cannot be explained neither by GR+DM, nor by other models as MOND, TeVeS, PCG... Moreover, we can combine both the cosmological and the astrophysical models and then solve some other mysteries, such as why the astrophysical constant a_{0} is numerically close to the Hubble a_{H}. Our new theory predicts a_{0} = 1/8 a_{H}.

I know that some authors consider that the Pioneer anomaly must be related to Dark Matter, because the scale of the anomalous acceleration are very close. I have not studied the Pioneer anomaly enough and cannot say. However, there many other foundational issues that you cite are solved in our approach.

Regards.

Note:

General readers that cannot access to the reference 18 can see the pages 9 and 10 of the associated Executive summary available online for free download.

report post as inappropriate

as explained in my Essay the derivation of General relativity from the more fundamental canonical theory involves the approximation of the total energy-momentum-stress by the energy-momentum-stress for matter alone. If we relax this approximation and maintain the total energy-momentum-stress, then we do not derive the usual Hilbert & Einstein equations but a generalized equation as the equation 94 in the reference 18 in my Essay.

That generalized equation is your equation 2, except by the notation (T

In your "Conclusion Remarks", you speculate about how the new equation (2) could, in principle, solve the Dark Energy, Dark Matter and Pioneer anomalies.

We already addressed the issue of Dark Energy in page 53 of the same reference 18. Since we have the explicit form for the new energy-momentum-stress tensor, we compute its value and obtained a cosmological constant of order 10-54 (in Standard Units), which is very close to the last observed value of 10-52. This was then interpreted as an important advance, specially since other approaches to the cosmological constant fail by huge errors. The so called biggest mistake ever in physics!

We did a more accurate computation recently and obtained a value of order 10-52 in complete agreement with observation. This has still to be verified by other experts, but it seems that a natural solution to the Dark Energy problem is already at your hand.

Regarding Dark Matter, we are working in this as well. As said in the same reference 18, first research seems to support the idea that the new theory of gravity also solves the Dark Matter problem. We can already explain observational data that cannot be explained neither by GR+DM, nor by other models as MOND, TeVeS, PCG... Moreover, we can combine both the cosmological and the astrophysical models and then solve some other mysteries, such as why the astrophysical constant a

I know that some authors consider that the Pioneer anomaly must be related to Dark Matter, because the scale of the anomalous acceleration are very close. I have not studied the Pioneer anomaly enough and cannot say. However, there many other foundational issues that you cite are solved in our approach.

Regards.

Note:

General readers that cannot access to the reference 18 can see the pages 9 and 10 of the associated Executive summary available online for free download.

report post as inappropriate

It seems that there is a problem with the superscript tags. Subscripts are displayed A_{1} but superscripts A^{2} are not.

The above would read T_ab^(EXTRA), T_ab^(c), 10^{-54}, and 10^{-52}.

report post as inappropriate

The above would read T_ab^(EXTRA), T_ab^(c), 10^{-54}, and 10^{-52}.

report post as inappropriate

Dear Dr. Juan R. González-Álvarez,

thanks for your comments.

My best wishes for further developing your approach in extending General Relativity.

Best regards,

Ch.

thanks for your comments.

My best wishes for further developing your approach in extending General Relativity.

Best regards,

Ch.

Dear Dr. Juan R. González-Álvarez,

I would like to invite you to submit your next papers on your approach to extend General Relativity to The Open Astronomy Journal, see http://bentham.org/open/toaaj/index.htm, and/or to The Hadronic Journal, see http://www.hadronicpress.com/edit_board.htm.

These are two international peer-reviewed journal in which I am Editor in Chief.

Best regards,

Ch.

I would like to invite you to submit your next papers on your approach to extend General Relativity to The Open Astronomy Journal, see http://bentham.org/open/toaaj/index.htm, and/or to The Hadronic Journal, see http://www.hadronicpress.com/edit_board.htm.

These are two international peer-reviewed journal in which I am Editor in Chief.

Best regards,

Ch.

Dear Dr. Corda,

You have written a beautiful essay. After the first reading, I was certain that you had gotten your ideas from my essay, but I see by your references that you have a long history of similar innovative concepts. In particular, our essays are complementary on the concepts of intrinsic curvature of global spacetime, the importance of this to DM and DE, how mass-energy is generated by variations of the intrinsic curvature, and that "presence of an intrinsic space-time curvature can generate a model of oscillating Universe". My essay lacks the eloquence and sophistication of yours, as I lack your overall knowledge and experience, so I used a rudimentary conceptual/graphical approach. I have presented a specific General Relativistic mechanism as an alternative to the DM hypothesis and have offered a hypothesis for the formation of structure in which you might be interested. I would be honored if you would read my essay and leave a comment. Congratulations, for in my eyes, you have written a definite winner.

Sincerely,

Dan T. Benedict

report post as inappropriate

You have written a beautiful essay. After the first reading, I was certain that you had gotten your ideas from my essay, but I see by your references that you have a long history of similar innovative concepts. In particular, our essays are complementary on the concepts of intrinsic curvature of global spacetime, the importance of this to DM and DE, how mass-energy is generated by variations of the intrinsic curvature, and that "presence of an intrinsic space-time curvature can generate a model of oscillating Universe". My essay lacks the eloquence and sophistication of yours, as I lack your overall knowledge and experience, so I used a rudimentary conceptual/graphical approach. I have presented a specific General Relativistic mechanism as an alternative to the DM hypothesis and have offered a hypothesis for the formation of structure in which you might be interested. I would be honored if you would read my essay and leave a comment. Congratulations, for in my eyes, you have written a definite winner.

Sincerely,

Dan T. Benedict

report post as inappropriate

Dear Dan,

thanks for your kind words.

I do not know if I have written a definite winner, 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.

I have read your Essay and I find it interesting. In particular, I appreciate your relating the cosmological application of GR to the Mach’s Principle through FPC and your intuitive-geometric vision of the Universe. Some suggestions: you should try to derive the model in a more rigorous way and send it to a peer-reviewed international journal in order to have a concrete scientific feedback. More, you should improve the references. For example, there are more rigorous reference than Wikipedia on the Friedmann–Lemaître–Robertson–Walker Model, examples are L. Landau and E. Lifsits, Classical Theory of Fields (3rd ed.), London: Pergamon (1971) and C. W. Misner , K. S. Thorne, J. A. Wheeler, “Gravitation”, Feeman and Company (1973).

You cold be interested also in two recent works of mine, where, together with my friend H. J. Mosquera Cuesta, we find ways to remove both of the BH's and Universe's Sigularities. These are Mod. Phys. Lett.A25, 2423-2429 (2010) and Astropart. Phys. 34, 7, 587 (2011).

I wish you a lot of luck in the contest.

Cheers,

Ch.

thanks for your kind words.

I do not know if I have written a definite winner, 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.

I have read your Essay and I find it interesting. In particular, I appreciate your relating the cosmological application of GR to the Mach’s Principle through FPC and your intuitive-geometric vision of the Universe. Some suggestions: you should try to derive the model in a more rigorous way and send it to a peer-reviewed international journal in order to have a concrete scientific feedback. More, you should improve the references. For example, there are more rigorous reference than Wikipedia on the Friedmann–Lemaître–Robertson–Walker Model, examples are L. Landau and E. Lifsits, Classical Theory of Fields (3rd ed.), London: Pergamon (1971) and C. W. Misner , K. S. Thorne, J. A. Wheeler, “Gravitation”, Feeman and Company (1973).

You cold be interested also in two recent works of mine, where, together with my friend H. J. Mosquera Cuesta, we find ways to remove both of the BH's and Universe's Sigularities. These are Mod. Phys. Lett.A25, 2423-2429 (2010) and Astropart. Phys. 34, 7, 587 (2011).

I wish you a lot of luck in the contest.

Cheers,

Ch.

Dear Dr. Corda,

Thanks, for your reply and I greatly appreciate your feedback. I'll be the first to admit that my model needs a more rigorous treatment and that some of my references were somewhat weak. I am presently working on just such a revision, among other things. My rough draft started with over 60000 characters, so it went through a major overhaul and the Wikapedia references were last minute additions, requested by FQXI, that I should have taken more seriously. This is my first attempt at writing a scientific paper. Having a support group would have been helpful, as I do want to be considered seriously. Do peer review journals accept papers from anyone? It was my assumption, that you need to be affiliated with a academic institution to obtain consideration.

I look forward to reading your latest works, they sound intriguing. My greatest concern with General Relativity has always been the uncomfortable acceptance of singularities, assuming that QG will someday resolve the issue.

Thanks again and best wishes,

Dan

report post as inappropriate

Thanks, for your reply and I greatly appreciate your feedback. I'll be the first to admit that my model needs a more rigorous treatment and that some of my references were somewhat weak. I am presently working on just such a revision, among other things. My rough draft started with over 60000 characters, so it went through a major overhaul and the Wikapedia references were last minute additions, requested by FQXI, that I should have taken more seriously. This is my first attempt at writing a scientific paper. Having a support group would have been helpful, as I do want to be considered seriously. Do peer review journals accept papers from anyone? It was my assumption, that you need to be affiliated with a academic institution to obtain consideration.

I look forward to reading your latest works, they sound intriguing. My greatest concern with General Relativity has always been the uncomfortable acceptance of singularities, assuming that QG will someday resolve the issue.

Thanks again and best wishes,

Dan

report post as inappropriate

Dear Dan,

actually, it is not needed to be affiliated with ab academic institution to obtain consideration.

Even if such an affiliation is, of course, a vantage, what is really important is to write good research papers.

I would like to invite you to submit your technical papers on your approach to Cosmology to The Open Astronomy Journal, see http://bentham.org/open/toaaj/index.htm, and/or to The Hadronic Journal, see http://www.hadronicpress.com/edit_board.htm.

These are two international peer-reviewed journal of which I am Editor in Chief.

Cheers,

Ch.

actually, it is not needed to be affiliated with ab academic institution to obtain consideration.

Even if such an affiliation is, of course, a vantage, what is really important is to write good research papers.

I would like to invite you to submit your technical papers on your approach to Cosmology to The Open Astronomy Journal, see http://bentham.org/open/toaaj/index.htm, and/or to The Hadronic Journal, see http://www.hadronicpress.com/edit_board.htm.

These are two international peer-reviewed journal of which I am Editor in Chief.

Cheers,

Ch.

Dear Christian

An excellent essay. If we are to find an acceptable route for reality to permeate physics then this will certainly be a strong candidate.

My own work has taken a more physical view but seems otherwise almost entirely equivalent. It is really a case of defining how this 'intrinsic' curvature is manifested in nature at the quantum level. Perhaps I have gone too far too soon, but have been seduced by the trail of 'magic bullets' followed.

I'd be very appreciative of your views on my own essay, http://fqxi.org/community/forum/topic/803 and in particular of your opinion on the relevance of the extended field equations to the physical process described from the empirical evidence.

Best wishes

Peter

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An excellent essay. If we are to find an acceptable route for reality to permeate physics then this will certainly be a strong candidate.

My own work has taken a more physical view but seems otherwise almost entirely equivalent. It is really a case of defining how this 'intrinsic' curvature is manifested in nature at the quantum level. Perhaps I have gone too far too soon, but have been seduced by the trail of 'magic bullets' followed.

I'd be very appreciative of your views on my own essay, http://fqxi.org/community/forum/topic/803 and in particular of your opinion on the relevance of the extended field equations to the physical process described from the empirical evidence.

Best wishes

Peter

report post as inappropriate

Dear Peter,

thanks for your kindness.

It is a big problem defining how this 'intrinsic' curvature is manifested in nature at the quantum level. I realized such a quantization only within the linearized (i.e. at first order) theory in my papers Eur. Phys. J. C 65 1-2, 257 (2010), Astropart. Phys. 30, 209 (2008), Mod. Phys. Lett. A 22, 35, 2647 (2007), Gen. Rel. Grav. 42, 1323 (2010), AIP Conf. Proc. 966, 257 (2008), and Mod. Phys. Lett. A 22, 15, 1097 (2007). I reported the main results in page 9 of my Essay. A better definition implies the quantization of the extended field equations (2) of my Essay, which, based on the strong non linear character of these equations, is a goal very very difficult to realize .

I have read your Essay, it is interesting.

The relevance of the extended field equations is important to the physical process described from the empirical evidence which happen on scales larger than the Solar System scales. Examples are Dark Matter and Dark Energy. In fact, General Relativity is very very well tested within the Solar System. Thus, variations from General Relativity have to be very weak in order to be consistent with the Solar System tests. In my geometric approach this means that the spacial hypersurfaces of the intrinsic curve space-time should have a curvature which manifests only on scales larger than the Solar System scales.

Cheers,

Ch.

thanks for your kindness.

It is a big problem defining how this 'intrinsic' curvature is manifested in nature at the quantum level. I realized such a quantization only within the linearized (i.e. at first order) theory in my papers Eur. Phys. J. C 65 1-2, 257 (2010), Astropart. Phys. 30, 209 (2008), Mod. Phys. Lett. A 22, 35, 2647 (2007), Gen. Rel. Grav. 42, 1323 (2010), AIP Conf. Proc. 966, 257 (2008), and Mod. Phys. Lett. A 22, 15, 1097 (2007). I reported the main results in page 9 of my Essay. A better definition implies the quantization of the extended field equations (2) of my Essay, which, based on the strong non linear character of these equations, is a goal very very difficult to realize .

I have read your Essay, it is interesting.

The relevance of the extended field equations is important to the physical process described from the empirical evidence which happen on scales larger than the Solar System scales. Examples are Dark Matter and Dark Energy. In fact, General Relativity is very very well tested within the Solar System. Thus, variations from General Relativity have to be very weak in order to be consistent with the Solar System tests. In my geometric approach this means that the spacial hypersurfaces of the intrinsic curve space-time should have a curvature which manifests only on scales larger than the Solar System scales.

Cheers,

Ch.

Dear Christian,

Your essay is very interesting and really innovative. In general I agree with the outcome: from analog to digital. In your essay I have found more concepts that seem to support my own (the details in my essay ). For example you claim: “Dark Energy and Dark Matter have to be considered like pure effects of the presence of an intrinsic space-time curvature in the Universe. Considering this point of view, one can think that gravity is different at various scales because of the existence of the intrinsic space-time curvature, which changes at different scales, and there is room for alternative theories.” I am happy - for the first time I have read such innovative view in a public paper. And it is fully compatible with my own view. There are also strong differences. For example I try to prove that gravitational waves do not exist. Moreover in my concept the gravity is an emergent and not fundamental interaction. But I have started out from different assumptions albeit based on geometry as well.

I think I shall read your essey once more to fully understand it.

I look forward to reading your publications and finding out a development of your concepts.

Good luck Christian!

Jacek

http://fqxi.org/community/forum/topic/883

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Your essay is very interesting and really innovative. In general I agree with the outcome: from analog to digital. In your essay I have found more concepts that seem to support my own (the details in my essay ). For example you claim: “Dark Energy and Dark Matter have to be considered like pure effects of the presence of an intrinsic space-time curvature in the Universe. Considering this point of view, one can think that gravity is different at various scales because of the existence of the intrinsic space-time curvature, which changes at different scales, and there is room for alternative theories.” I am happy - for the first time I have read such innovative view in a public paper. And it is fully compatible with my own view. There are also strong differences. For example I try to prove that gravitational waves do not exist. Moreover in my concept the gravity is an emergent and not fundamental interaction. But I have started out from different assumptions albeit based on geometry as well.

I think I shall read your essey once more to fully understand it.

I look forward to reading your publications and finding out a development of your concepts.

Good luck Christian!

Jacek

http://fqxi.org/community/forum/topic/883

report post as inappropriate

Dear Jacek,

thanks for your kind words.

I read your Essay and I agree with you that there are strong differences with respect to mine. In particular, your claiming that gravitational waves do not exist in the way they are conventionally defined is very strong. Actually, gravitational waves are solutions of both the linearized and full Einstein Field Equations in both of Standard General Relativity and Extended Theories of Gravity.

On the other hand, you also claim, verbatim, that "the spacetime has elastic properties". But in that case I think that heavy masses with acceleration should radiate gravitational waves based on such elastic properties. What do you think on this issue?

In any case, I wish you a lot of luck in the contest.

Cheers,

Ch.

thanks for your kind words.

I read your Essay and I agree with you that there are strong differences with respect to mine. In particular, your claiming that gravitational waves do not exist in the way they are conventionally defined is very strong. Actually, gravitational waves are solutions of both the linearized and full Einstein Field Equations in both of Standard General Relativity and Extended Theories of Gravity.

On the other hand, you also claim, verbatim, that "the spacetime has elastic properties". But in that case I think that heavy masses with acceleration should radiate gravitational waves based on such elastic properties. What do you think on this issue?

In any case, I wish you a lot of luck in the contest.

Cheers,

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.”

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

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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.”

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

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I am sorry but I did not read the help on linking sites so I give the the once more. Sorry, the rest of the text is linked to the site.

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Dear Dr. Corda,

Welcome to the essay contest. Since Dr. Elliot McGucken and you are my neighbors in the essays list, therefore I must visit these pages first.

All attempts to quantize gravity have utterly failed, and your attempt to quantize gravity will have the same fate; There are a lot of different Extended Theories of Gravity, including yours, which tries to enlarge the Einstein scheme through an addition of corrective terms, but all these theories are not able to explain inertia, mass and the curvature of spacetime. The complete theory of gravitational interaction must be able to explain inertia, mass, and the curvature of spacetime in the same model. Also the true theory of gravitation must be able to unify gravity with the other forces. Since your variant of Extended Theory of Gravity is not able to do it, then your approach also is wrong and even the quantization of the extended Einstein field equations can not help you.

I agree with you that the intrinsic space-time curvature may be important for Gravity, but not ''by adding an intrinsic space-time curvature to the model''. Instead you must examine how an intrinsic space-time curvature appears and how it works. In other words, you must look for physical solutions rather than for mathematical.

Also, your essay do not show, if you are in the digital or analog party. In general, I don't found any proofs in your essay that the reality is digital, analog, or digital-analog.

Sincerely

Constantin

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Welcome to the essay contest. Since Dr. Elliot McGucken and you are my neighbors in the essays list, therefore I must visit these pages first.

All attempts to quantize gravity have utterly failed, and your attempt to quantize gravity will have the same fate; There are a lot of different Extended Theories of Gravity, including yours, which tries to enlarge the Einstein scheme through an addition of corrective terms, but all these theories are not able to explain inertia, mass and the curvature of spacetime. The complete theory of gravitational interaction must be able to explain inertia, mass, and the curvature of spacetime in the same model. Also the true theory of gravitation must be able to unify gravity with the other forces. Since your variant of Extended Theory of Gravity is not able to do it, then your approach also is wrong and even the quantization of the extended Einstein field equations can not help you.

I agree with you that the intrinsic space-time curvature may be important for Gravity, but not ''by adding an intrinsic space-time curvature to the model''. Instead you must examine how an intrinsic space-time curvature appears and how it works. In other words, you must look for physical solutions rather than for mathematical.

Also, your essay do not show, if you are in the digital or analog party. In general, I don't found any proofs in your essay that the reality is digital, analog, or digital-analog.

Sincerely

Constantin

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Dear Mr. Leshan,

actually, I do not attempt to quantize 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.

On the other hand, I agree with you that the complete theory of gravitational interaction must be able to explain inertia, mass, and the curvature of space-time in the same model. I also agree with you that the true theory of gravitation must be able to unify gravity with the other forces. But, surely, 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!!

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

On the other hand, 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.

I wish you a lot of luck in the contest.

Best regards,

Ch.

actually, I do not attempt to quantize 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.

On the other hand, I agree with you that the complete theory of gravitational interaction must be able to explain inertia, mass, and the curvature of space-time in the same model. I also agree with you that the true theory of gravitation must be able to unify gravity with the other forces. But, surely, 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!!

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

On the other hand, 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.

I wish you a lot of luck in the contest.

Best regards,

Ch.

I clarify my reply to Mr. Leshan on the question "Is Reality Digital or Analog?".

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.

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.

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

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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

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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.

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.

Hello,Christian

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

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

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

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

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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.

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 Christan

Could you please read comments to my Essay?

Thank you for advance.

Yuri

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Could you please read comments to my Essay?

Thank you for advance.

Yuri

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

Steve

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Steve

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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.

nice to see you again too.

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

Cheers,

Ch.

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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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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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

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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

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Dear Sreenath,

thanks for your comment.

Actually, I am shyaway from quantizing gravity because I do not know which is the correct classical theory to be quantized. Is it standard General Relativity or is it an Extended Theory which takes into account the presence of an intrinsic space-time curvature in our Universe? I hope that gravity-waves observations will permit, in the future, to clarify this issue.

Notice that this point could modified the values of both the force of quantum gravity and the Constant of Quantum Gravity that you cited in your Essay.

Wishing success in the competition to you too.

Cheers,

Ch.

thanks for your comment.

Actually, I am shyaway from quantizing gravity because I do not know which is the correct classical theory to be quantized. Is it standard General Relativity or is it an Extended Theory which takes into account the presence of an intrinsic space-time curvature in our Universe? I hope that gravity-waves observations will permit, in the future, to clarify this issue.

Notice that this point could modified the values of both the force of quantum gravity and the Constant of Quantum Gravity that you cited in your Essay.

Wishing success in the competition to you too.

Cheers,

Ch.

quote:

Various problems of the Dark Universe, like Dark Energy, Dark Matter and Pioneer anomaly, can be, in principle, solved through this approach, while a definitive endorsement for the effective existence of an intrinsic space-time curvature in our Universe could arrive from the realization of a consistent gravitational wave astronomy.

end of quote

What do you mean by a "realization of a consistent gravitational wave astronomy ' ?

Thanks

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Various problems of the Dark Universe, like Dark Energy, Dark Matter and Pioneer anomaly, can be, in principle, solved through this approach, while a definitive endorsement for the effective existence of an intrinsic space-time curvature in our Universe could arrive from the realization of a consistent gravitational wave astronomy.

end of quote

What do you mean by a "realization of a consistent gravitational wave astronomy ' ?

Thanks

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Hi Andy,

nice to meet you in this Essay Contest. I am pleasured to discuss with you on physics after our controversy on the Egyptian Conference.

The sentence "realization of a consistent gravitational wave astronomy" means that, first of all, we should resolve various astrophysics sources of gravitational waves and discriminate among them. Second we should give a correct physical interpretation of various different signals.

In other words, detecting gravitational waves should complement observations in the electromagnetic spectrum.

Cheers,

Ch.

nice to meet you in this Essay Contest. I am pleasured to discuss with you on physics after our controversy on the Egyptian Conference.

The sentence "realization of a consistent gravitational wave astronomy" means that, first of all, we should resolve various astrophysics sources of gravitational waves and discriminate among them. Second we should give a correct physical interpretation of various different signals.

In other words, detecting gravitational waves should complement observations in the electromagnetic spectrum.

Cheers,

Ch.

Quote:

Thus, variations of space-time curvature which

generate the production of mass-energy through Eq. (4) result quantized in the relic Universe and

such a quantization generates a number of primordial particles which is given by Eq. (13).

Then, the eective detection of these relic particles (waves) will be a denitive

endorsement for the Digital (Quantum) rather than Classical (Analog) feature of the

gravitational interaction.

end of quote

I have no problem with digital formulation of the particles. What I brought up in my essay was what was the condition of space time prior to formulation of such particles.

In what I wrote, the digital regime was due to embedding of space time / quantum mechanics within a larger non linear theory. AKA t'Hoofts idea of deterministic quantum mechanics.

If that could be done, in the pre Planckian regime, could the process of embedding of space time then becomes an ANALOG process, with a synthesis of reality becoming digital at the end of the flattening of space time?

I would appreciate a serious resonse to this querry

Andrew Beckwith

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Thus, variations of space-time curvature which

generate the production of mass-energy through Eq. (4) result quantized in the relic Universe and

such a quantization generates a number of primordial particles which is given by Eq. (13).

Then, the eective detection of these relic particles (waves) will be a denitive

endorsement for the Digital (Quantum) rather than Classical (Analog) feature of the

gravitational interaction.

end of quote

I have no problem with digital formulation of the particles. What I brought up in my essay was what was the condition of space time prior to formulation of such particles.

In what I wrote, the digital regime was due to embedding of space time / quantum mechanics within a larger non linear theory. AKA t'Hoofts idea of deterministic quantum mechanics.

If that could be done, in the pre Planckian regime, could the process of embedding of space time then becomes an ANALOG process, with a synthesis of reality becoming digital at the end of the flattening of space time?

I would appreciate a serious resonse to this querry

Andrew Beckwith

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Dear Andy,

the key point of your analysis is that "the digital regime was due to embedding of space time / quantum mechanics within a larger non linear theory". Thus, my question is which is such a non linear theory? Is it standard General Relativity or is it an Extended Theory which takes into account the fact that space-time could be intrinsically curve? You could be right in claiming that it could be done in the pre Planckian regime but we need to understand which is the correct non linear theory before quantizing it!

Together with collaborators I realized the quantization of Extended Theories and of space-time curvature but ONLY in the weak field approximation and ONLY in an epoch post Planckian regime, i.e. the Inflationary Era, see pages 8-9 of my Essay.

On the other hand, in principle I agree with t'Hooft's idea of deterministic quantum mechanics, but this will be a successive step with respect to my present analysis.

Cheers,

Ch.

the key point of your analysis is that "the digital regime was due to embedding of space time / quantum mechanics within a larger non linear theory". Thus, my question is which is such a non linear theory? Is it standard General Relativity or is it an Extended Theory which takes into account the fact that space-time could be intrinsically curve? You could be right in claiming that it could be done in the pre Planckian regime but we need to understand which is the correct non linear theory before quantizing it!

Together with collaborators I realized the quantization of Extended Theories and of space-time curvature but ONLY in the weak field approximation and ONLY in an epoch post Planckian regime, i.e. the Inflationary Era, see pages 8-9 of my Essay.

On the other hand, in principle I agree with t'Hooft's idea of deterministic quantum mechanics, but this will be a successive step with respect to my present analysis.

Cheers,

Ch.

It might be that spacetime is not fully quantized in a standard sense. Spacetime physics may be quantized by a a series lagrangian of the form

R + α’R_{abcd}R^{abcd} + α’^2 O(R^4) + …

Where the R is a classical background and the string parameter α’ give corrections in order of the string tension; similar to O(ħ) as the string tension is due to the Heisenberg uncertainty principle. Of course this is a sticking point for the LQG folks, and this background independence issue is the one big card they hold in their hand.

However, a full quantum theory of spacetime in the LQG sense runs into trouble by placing lots of degrees of freedom in spacetime, and by corollary a huge entropy. The classical limit of LQG is not physically tenable. So any quantization of spacetime curvature may simply only work as an effective theory, whether that be with orders in string parameter or with LQG Sen connection terms.

The hyperbolic plane, or the anti de Sitter spacetime, is S-dual to a Thirring fermion field. The horizon limit of an AdS_n spacetime containing a black hole his an AdS_2 ~ H_2. This contains all the conformal machinery of CFT_1, which is the Hartle-Hawking vacuum. The S-dual to the soliton dynamics in H_2 is the Thirring Fermions, which in the interior of the AdS defines the “graviton.” The Thirring field has the Lagrangian

L = {bar-ψ}γ^a∂_aψ + g|ψψ|^2

Where we might think of the graviton as having a substratum of quantized fermions.

Cheers LC

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R + α’R_{abcd}R^{abcd} + α’^2 O(R^4) + …

Where the R is a classical background and the string parameter α’ give corrections in order of the string tension; similar to O(ħ) as the string tension is due to the Heisenberg uncertainty principle. Of course this is a sticking point for the LQG folks, and this background independence issue is the one big card they hold in their hand.

However, a full quantum theory of spacetime in the LQG sense runs into trouble by placing lots of degrees of freedom in spacetime, and by corollary a huge entropy. The classical limit of LQG is not physically tenable. So any quantization of spacetime curvature may simply only work as an effective theory, whether that be with orders in string parameter or with LQG Sen connection terms.

The hyperbolic plane, or the anti de Sitter spacetime, is S-dual to a Thirring fermion field. The horizon limit of an AdS_n spacetime containing a black hole his an AdS_2 ~ H_2. This contains all the conformal machinery of CFT_1, which is the Hartle-Hawking vacuum. The S-dual to the soliton dynamics in H_2 is the Thirring Fermions, which in the interior of the AdS defines the “graviton.” The Thirring field has the Lagrangian

L = {bar-ψ}γ^a∂_aψ + g|ψψ|^2

Where we might think of the graviton as having a substratum of quantized fermions.

Cheers LC

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Dear LC,

yes, maybe you are right.

In any case, I think that the correct Lagrangian, which in my point of view generates the intrinsic space-time, should be the one which obtains the better consistence with astrophysical observations. In that case, the detection of a third polarization of gravitational waves will be the ultimate endorsement for this tapestry.

Cheers,

Ch

yes, maybe you are right.

In any case, I think that the correct Lagrangian, which in my point of view generates the intrinsic space-time, should be the one which obtains the better consistence with astrophysical observations. In that case, the detection of a third polarization of gravitational waves will be the ultimate endorsement for this tapestry.

Cheers,

Ch

Could you please address if you think that particles, of any shape or form could survive a big bang/ big bounce or what have you ?

I.e. could a graviton survive a transition from a prior to the present universe?

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I.e. could a graviton survive a transition from a prior to the present universe?

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Dear Andy,

in my opinion particles of any shape or form could survive a big bang/ big bounce only if we find a solution to the Initial Singularity's problem.

Together with my friend Herman Mosquera Cuesta we recently realized a big bounce model where the Initial Singularity is removed. The paper has been published in Astropart. Phys. 34:587-590, 2011 and it is available in http://arxiv.org/abs/1011.4801

In models like this I think that gravitons and/or other particles should survive a transition from a prior to the present universe.

Cheers,

Ch.

in my opinion particles of any shape or form could survive a big bang/ big bounce only if we find a solution to the Initial Singularity's problem.

Together with my friend Herman Mosquera Cuesta we recently realized a big bounce model where the Initial Singularity is removed. The paper has been published in Astropart. Phys. 34:587-590, 2011 and it is available in http://arxiv.org/abs/1011.4801

In models like this I think that gravitons and/or other particles should survive a transition from a prior to the present universe.

Cheers,

Ch.

Dear Christian,

If in a cloud of hydrogen gas or plasma, particles behave in such a manner that they always feel an equally strong force from all directions, if the force on a particle from one direction, from its own cloud can only increase as it increases as much from the opposite direction, from neighboring clouds, then such clouds can only contract in concert. The energy exchange...

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If in a cloud of hydrogen gas or plasma, particles behave in such a manner that they always feel an equally strong force from all directions, if the force on a particle from one direction, from its own cloud can only increase as it increases as much from the opposite direction, from neighboring clouds, then such clouds can only contract in concert. The energy exchange...

view entire post

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Dear Anton,

if you do not agree with the Standard Big-Bang Model and you propose an alternative one, in my opinion your model has to explain two fundamental issues.

1) The origin of the Cosmic Microwave Background Radiation.

2) A way to avoid Singularity Theorems.

Does your model of continuous creation process explain these two issues?

Best regards,

Ch.

if you do not agree with the Standard Big-Bang Model and you propose an alternative one, in my opinion your model has to explain two fundamental issues.

1) The origin of the Cosmic Microwave Background Radiation.

2) A way to avoid Singularity Theorems.

Does your model of continuous creation process explain these two issues?

Best regards,

Ch.

Dear Christian

Thanks for your response on 17th. I've just read your recent preprint, which I'd now like to cite in an update of a recent paper of mine currently in formal review. Some of the bones are in a recent non mathematical preprint here; "Helical CMBR Asymmetry, Pre-Big Bang State, Dark Matter and the Axis of Evil." http://vixra.org/abs/1102.0016

I believe our work is both complimentary and consistent. You will have seen in the essay (which already over extends for the wordage) that I stop short of the cosmological consequences, but that I'm forced to debunk Eddington's view on diffraction, effectively convicting plasma ions, condensed from the Dark energy field or recycled (and repolarised) by Black Holes, as the culprit for gravitons and curved space time. Page 18 of 19th Feb New Scientist is very interesting.

A you'll gather from the above title, the logical conclusions agree conceptually with the big bounce, and find some good observational (photographic!!) evidence, but also provide a real, local quantum mechanism for sequential 'multiverses'. SR and GR fall neatly into place with QM. There are a surprising number of other consistent essays here, as well as Dan's I'd initially point you to Edwin Klingman, and see his in my threads. I feel it may be time for 'dissenters', which I believe most will still consider you are, to join up and co-support rather more.

I wish you luck here and will help with the score your bravery deserves, and hope you may feel the same of my own. One day you must explain the maths to me! do also please view and comment on my quite short preprint. I may not get to your others yet while reading essays!

Best wishes

Peter

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Thanks for your response on 17th. I've just read your recent preprint, which I'd now like to cite in an update of a recent paper of mine currently in formal review. Some of the bones are in a recent non mathematical preprint here; "Helical CMBR Asymmetry, Pre-Big Bang State, Dark Matter and the Axis of Evil." http://vixra.org/abs/1102.0016

I believe our work is both complimentary and consistent. You will have seen in the essay (which already over extends for the wordage) that I stop short of the cosmological consequences, but that I'm forced to debunk Eddington's view on diffraction, effectively convicting plasma ions, condensed from the Dark energy field or recycled (and repolarised) by Black Holes, as the culprit for gravitons and curved space time. Page 18 of 19th Feb New Scientist is very interesting.

A you'll gather from the above title, the logical conclusions agree conceptually with the big bounce, and find some good observational (photographic!!) evidence, but also provide a real, local quantum mechanism for sequential 'multiverses'. SR and GR fall neatly into place with QM. There are a surprising number of other consistent essays here, as well as Dan's I'd initially point you to Edwin Klingman, and see his in my threads. I feel it may be time for 'dissenters', which I believe most will still consider you are, to join up and co-support rather more.

I wish you luck here and will help with the score your bravery deserves, and hope you may feel the same of my own. One day you must explain the maths to me! do also please view and comment on my quite short preprint. I may not get to your others yet while reading essays!

Best wishes

Peter

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Dear Peter,

which is the journal where you submitted your paper currently in formal review?

Maybe SR and GR fall neatly into place with QM because Einstein was correct and the Final Theory has to be deterministic and not based on uncertainty...

I agree that it may be time for 'dissenters', but it is important that physics remains rigorous and consistent with experiments and observations. Yes, I believe most will still consider me a 'dissenter', but I prefer the term 'Deterministic - Einstenian'.

But I know that there are lots of people within the "mainstream physics" who are changing their positions.

I am going to read page 18 of 19th Feb New Scientist and also to re-read your interesting Essay.

Thanks for help me with the score you think I deserves, I will make the same with you.

Cheers,

Ch.

which is the journal where you submitted your paper currently in formal review?

Maybe SR and GR fall neatly into place with QM because Einstein was correct and the Final Theory has to be deterministic and not based on uncertainty...

I agree that it may be time for 'dissenters', but it is important that physics remains rigorous and consistent with experiments and observations. Yes, I believe most will still consider me a 'dissenter', but I prefer the term 'Deterministic - Einstenian'.

But I know that there are lots of people within the "mainstream physics" who are changing their positions.

I am going to read page 18 of 19th Feb New Scientist and also to re-read your interesting Essay.

Thanks for help me with the score you think I deserves, I will make the same with you.

Cheers,

Ch.

Dear Dr. Corda,

Thanks for your response.You are thinking of which theory,General-Relativity (GR) or Extended Theory of GR (ETGR), stands the test of LISA/LIGO.But for me,it is GR which stands the test if the gravitational wave received is due to gravitational-interaction only.Because it is GR which is designed to explain the gravitational-interaction and it does explain it precisely.If the gravitational wave received confirms ETGR, then the wave sent is as a result of quantum-gravity (QG) effect by a Black-Hole (BH) and hence deviations from GR is to be expected as the metric of GR breaksdown.According to me,all BHs have same intrinsic space-time curvature irrespective of their mass and size (please go to my web-site which I have mentioned in my essay).I think it is the same intrinsic space-time curvature you are talking of in ETGR.According to my view,the arms of all spiral galaxies,which harbour super massive BHs, evolve at the same (constant) angle of nearly 60 degrees in the vicinity of accretion disc and this can be verified from the current data available.From this,the value of Immirzi parameter is also derived.

Thanking you and best regards

Sreenath B N.

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Thanks for your response.You are thinking of which theory,General-Relativity (GR) or Extended Theory of GR (ETGR), stands the test of LISA/LIGO.But for me,it is GR which stands the test if the gravitational wave received is due to gravitational-interaction only.Because it is GR which is designed to explain the gravitational-interaction and it does explain it precisely.If the gravitational wave received confirms ETGR, then the wave sent is as a result of quantum-gravity (QG) effect by a Black-Hole (BH) and hence deviations from GR is to be expected as the metric of GR breaksdown.According to me,all BHs have same intrinsic space-time curvature irrespective of their mass and size (please go to my web-site which I have mentioned in my essay).I think it is the same intrinsic space-time curvature you are talking of in ETGR.According to my view,the arms of all spiral galaxies,which harbour super massive BHs, evolve at the same (constant) angle of nearly 60 degrees in the vicinity of accretion disc and this can be verified from the current data available.From this,the value of Immirzi parameter is also derived.

Thanking you and best regards

Sreenath B N.

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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.

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.

Christian

Thanks. You should read the essay slowly and ensure you take in the implications at each step, I may have understated them but believe they are quite 'earth shattering'. In fact they prove the postulates and principles, but show Einstein was forced to make a wrong 'stipulation'. A little trimming with Occams razor, and a bit more reshaping to QM, and we seem to have a full and falsifiable Quantum Mechanism with Local Reality to drive unified SR and GR. (and 100% deterministic, but with a natural uncertainty element built in, (which I'll have to explain as it's not included).

The NS article is the one about 'atoms' which effectively bounce off the fine structure plasma not the surface itself. It tends to support a prediction I've shied away from making publicly, regarding precisely where the internal reflection mechanism happens,; outside not inside the surface!! That now needs an experiment!

Do you fancy looking over a yet unpublished paper on plasma and refraction? Email the address on the essay if you do, or; peter.jackson53@ymail.com (I'll also let you know which PR journal there).

Best wishes

Peter

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Thanks. You should read the essay slowly and ensure you take in the implications at each step, I may have understated them but believe they are quite 'earth shattering'. In fact they prove the postulates and principles, but show Einstein was forced to make a wrong 'stipulation'. A little trimming with Occams razor, and a bit more reshaping to QM, and we seem to have a full and falsifiable Quantum Mechanism with Local Reality to drive unified SR and GR. (and 100% deterministic, but with a natural uncertainty element built in, (which I'll have to explain as it's not included).

The NS article is the one about 'atoms' which effectively bounce off the fine structure plasma not the surface itself. It tends to support a prediction I've shied away from making publicly, regarding precisely where the internal reflection mechanism happens,; outside not inside the surface!! That now needs an experiment!

Do you fancy looking over a yet unpublished paper on plasma and refraction? Email the address on the essay if you do, or; peter.jackson53@ymail.com (I'll also let you know which PR journal there).

Best wishes

Peter

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Dear Peter,

OK. Let us keep in touch.

Cheers,

Ch.

OK. Let us keep in touch.

Cheers,

Ch.

Christian,

I cannot help but be drawn to the following comment you gave to Anton:

[ if you do not agree with the Standard Big-Bang Model and you propose an alternative one, in my opinion your model has to explain two fundamental issues.

1) The origin of the Cosmic Microwave Background Radiation.

2) A way to avoid Singularity Theorems.

Does your model of continuous creation process explain these two issues? ]

I think my alternative theory has answers for these.

Also, you might find my own essay very interesting in relation to yours.

Rafael

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I cannot help but be drawn to the following comment you gave to Anton:

[ if you do not agree with the Standard Big-Bang Model and you propose an alternative one, in my opinion your model has to explain two fundamental issues.

1) The origin of the Cosmic Microwave Background Radiation.

2) A way to avoid Singularity Theorems.

Does your model of continuous creation process explain these two issues? ]

I think my alternative theory has answers for these.

Also, you might find my own essay very interesting in relation to yours.

Rafael

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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.

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.

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

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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

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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.

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.

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

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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

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Dear Tom,

thanks.

Notice that Equivalence Principle is preserved in those Extended Theories which are also Metric Theories, thus curvature is with and not without inertia. Philosophically, I do not like theories which are not metric.

Cheers,

Ch.

thanks.

Notice that Equivalence Principle is preserved in those Extended Theories which are also Metric Theories, thus curvature is with and not without inertia. Philosophically, I do not like theories which are not metric.

Cheers,

Ch.

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

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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

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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.

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.

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

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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

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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.

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.

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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.

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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.

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

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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

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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.

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 Christian,

It's a definite "yes"! I'm making progress dayly..remember where you heard it first.

Kind regards,

Alan

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It's a definite "yes"! I'm making progress dayly..remember where you heard it first.

Kind regards,

Alan

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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

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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

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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...

view entire post

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...

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Dear Dr. Corda,

You write: ''I am going to reply to your attack''. I saw already your attack on my page; I have a deep suspicion that Darth Sidious is your nickname, I recognize your handwriting and stile. You are able to attack my page with unproven declarations only.

''as the Scientific Community rejects his strange theories, attacks recognized results'' Our majority vote is not qualified to rate scientific theories; A lot of authors vote 10 for the friends and 1 for the Enemy. Since I criticize all papers therefore I'll have low ratings always. In order to have high ratings the author must praise all essays. The science without criticism is not Science. Such majority vote never supports the new advanced theory. I can show you some erroneous essays with high ratings, it mean the Majority is not qualified.Also, people rated by ''good'' some leading essays but I found important errors there. It means our Majority vote is not qualified to rate the scientific essays. Therefore, if the Majority vote rejects ''his strange theories'' it proves nothing. Also, the people rated by ''good'' your essay only because it looks scientifically and have mathematics and professional jargon. However, it is the description of the UNSUCCESSFUL attempt to solve the problems of gravity; it is a story about physics only.

Sincerely,

Constantin

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You write: ''I am going to reply to your attack''. I saw already your attack on my page; I have a deep suspicion that Darth Sidious is your nickname, I recognize your handwriting and stile. You are able to attack my page with unproven declarations only.

''as the Scientific Community rejects his strange theories, attacks recognized results'' Our majority vote is not qualified to rate scientific theories; A lot of authors vote 10 for the friends and 1 for the Enemy. Since I criticize all papers therefore I'll have low ratings always. In order to have high ratings the author must praise all essays. The science without criticism is not Science. Such majority vote never supports the new advanced theory. I can show you some erroneous essays with high ratings, it mean the Majority is not qualified.Also, people rated by ''good'' some leading essays but I found important errors there. It means our Majority vote is not qualified to rate the scientific essays. Therefore, if the Majority vote rejects ''his strange theories'' it proves nothing. Also, the people rated by ''good'' your essay only because it looks scientifically and have mathematics and professional jargon. However, it is the description of the UNSUCCESSFUL attempt to solve the problems of gravity; it is a story about physics only.

Sincerely,

Constantin

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Dear Mr. Leshan,

in all honesty and for the last time, I have not the time to go on your page and attacking you. As I have decided to read the Essays in the order of the Community Ratings it will be very very difficult for me arriving to your one... Maybe there is someone with handwriting and stile similar to mine, but this is not a problem of mine. Really, I am not interested in your Essay and in reading and posting comments in your page.

In any case, again, thank you very very much for your attack. An attack from a person like you implies that my Essay is a good work. Thanks for your interest in my work, I am sure your criticisms will be favourable for me.

Please, stop here this discussion, I am not interested in further discussing with you. I am interested only in scientific discussions.

Best wishes,

Ch.

in all honesty and for the last time, I have not the time to go on your page and attacking you. As I have decided to read the Essays in the order of the Community Ratings it will be very very difficult for me arriving to your one... Maybe there is someone with handwriting and stile similar to mine, but this is not a problem of mine. Really, I am not interested in your Essay and in reading and posting comments in your page.

In any case, again, thank you very very much for your attack. An attack from a person like you implies that my Essay is a good work. Thanks for your interest in my work, I am sure your criticisms will be favourable for me.

Please, stop here this discussion, I am not interested in further discussing with you. I am interested only in scientific discussions.

Best wishes,

Ch.

Dear Dr. Corda,

I trust you and your new family are doing well.

Have you ever taken a ferry across the Adriatic to visit the Croatian coast? It is very nice, but then I have never been to Italy.

Firstly, thank you for such an informative essay. In particular you mention ‘Unified Theory which could, in principle, show the fundamental interactions as different forms of the same symmetry’.

Even though my essay did not make it to ‘the finalists’ stage I was hoping you could take a few moments to read “Is Relativity the Holy Grail of Physics?”

Unlike your own approach of extending GR, the approach I take is to derive a ‘Unified Theory’ referred to as ‘the Light’, which has implications for all of physics. In relation to GR it solves the ‘foundational problem’ of reconciling the Equivalence Principle and the non-uniformity of gravity (tidal gravity).

At this point you probably wish you were on holiday somewhere, so please allow me to mention that my essay is very short, devoid of speculation, and mathematically trivial. The focus is upon foundations alone with ‘the Light’ being the first necessary foundation.

Kind regards,

Robert

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I trust you and your new family are doing well.

Have you ever taken a ferry across the Adriatic to visit the Croatian coast? It is very nice, but then I have never been to Italy.

Firstly, thank you for such an informative essay. In particular you mention ‘Unified Theory which could, in principle, show the fundamental interactions as different forms of the same symmetry’.

Even though my essay did not make it to ‘the finalists’ stage I was hoping you could take a few moments to read “Is Relativity the Holy Grail of Physics?”

Unlike your own approach of extending GR, the approach I take is to derive a ‘Unified Theory’ referred to as ‘the Light’, which has implications for all of physics. In relation to GR it solves the ‘foundational problem’ of reconciling the Equivalence Principle and the non-uniformity of gravity (tidal gravity).

At this point you probably wish you were on holiday somewhere, so please allow me to mention that my essay is very short, devoid of speculation, and mathematically trivial. The focus is upon foundations alone with ‘the Light’ being the first necessary foundation.

Kind regards,

Robert

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Dear Robert,

thanks for your kind message.

I trust you and your family are doing well too, thanks a lot!!

After reading your interesting Essay, I have to tell you that, even if I totally agree with your geometric Einsteinian vision of physics, I need some clarifications.

1) You claims that your theory solves the "foundational problem" of reconciling the Equivalence Principle and the non-uniformity of gravity (tidal gravity). Actually, the non-uniformity of gravity is a global property, while the Equivalence Principle has a local nature, thus, in my opinion, there is not contradiction. Tidal forces emerge exactly when deviations from locality are present. In geometric terms, space-time is locally flat (absence of gravitation and validity of Equivalence Principle) but globally curve (presence of gravitation and non-validity of Equivalence Principle). Thus, in my opinion it is not correct claiming that "Einstein (unrealistically) ignored the non-uniformity of Gravity" but, in an opposite sense, this is exactly the step between Special Relativity and General Relativity in order to realize a relativistic theory of gravitation, i.e. Einstein well understood the non-uniformity of Gravity. On the other hand, in my opinion your Equivalence Identity a=g is only another expression of the Equivalence Principle. More, also mG=mI a priori is only another expression of the Equivalence Principle.

2) Your claims that "relative velocity between matter and antimatter must equal c(2)1/2" and you invoke the Pythagora's Theorem. In my opinion this is not correct. This relation violates Special Relativity and, being velocities, you are using not the Pythagora's Theorem but the classical Galileo's transformation on the sum of velocities which is not correct in relativistic treatments.

3) Which is the role of Uncertainty Principle in your Theory?

Cheers,

Ch.

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thanks for your kind message.

I trust you and your family are doing well too, thanks a lot!!

After reading your interesting Essay, I have to tell you that, even if I totally agree with your geometric Einsteinian vision of physics, I need some clarifications.

1) You claims that your theory solves the "foundational problem" of reconciling the Equivalence Principle and the non-uniformity of gravity (tidal gravity). Actually, the non-uniformity of gravity is a global property, while the Equivalence Principle has a local nature, thus, in my opinion, there is not contradiction. Tidal forces emerge exactly when deviations from locality are present. In geometric terms, space-time is locally flat (absence of gravitation and validity of Equivalence Principle) but globally curve (presence of gravitation and non-validity of Equivalence Principle). Thus, in my opinion it is not correct claiming that "Einstein (unrealistically) ignored the non-uniformity of Gravity" but, in an opposite sense, this is exactly the step between Special Relativity and General Relativity in order to realize a relativistic theory of gravitation, i.e. Einstein well understood the non-uniformity of Gravity. On the other hand, in my opinion your Equivalence Identity a=g is only another expression of the Equivalence Principle. More, also mG=mI a priori is only another expression of the Equivalence Principle.

2) Your claims that "relative velocity between matter and antimatter must equal c(2)1/2" and you invoke the Pythagora's Theorem. In my opinion this is not correct. This relation violates Special Relativity and, being velocities, you are using not the Pythagora's Theorem but the classical Galileo's transformation on the sum of velocities which is not correct in relativistic treatments.

3) Which is the role of Uncertainty Principle in your Theory?

Cheers,

Ch.

Dear Dr. Corda,

I truly appreciate you taking the time to read my paper.

I will answer your questions in order.

1) The first answer is based upon a reply I gave to Peter Jackson on my thread. Bare with me if it is long winded!

Freely falling frames anywhere in our real, gravity-endowed Universe, are equivalent to inertial frames in an idealised, gravity-free universe....

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I truly appreciate you taking the time to read my paper.

I will answer your questions in order.

1) The first answer is based upon a reply I gave to Peter Jackson on my thread. Bare with me if it is long winded!

Freely falling frames anywhere in our real, gravity-endowed Universe, are equivalent to inertial frames in an idealised, gravity-free universe....

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Continue....

If we consider the ‘total energy of a photon’ with the velocity in the range c

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If we consider the ‘total energy of a photon’ with the velocity in the range c

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continue....

If we consider the ‘total energy of a photon’ with the velocity in the range c

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If we consider the ‘total energy of a photon’ with the velocity in the range c

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Dear Dr. Corda,

For some reason I cannot complete my reply on your thread. Therefore I will send the reply to your email.

Kindest of regards,

Robert

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For some reason I cannot complete my reply on your thread. Therefore I will send the reply to your email.

Kindest of regards,

Robert

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Dear Dr. Corda,

As I have not heard back from you, you either went to Croatia for a holiday, or my answers were too long or unclear. :) In case it happens to be the second, please allow me to clarify further.

1) Einstein’s equivalence principle means that we cannot experimentally distinguish between acceleration and a *uniform* gravitational field. But no such *uniform* gravitational field exists in reality. That is, Einstein unrealistically ignored the *non-uniformity* of gravity, for even an arbitrarily small reference frame cannot ignore that non-uniformity according to Ohanian’s paper.

2) The velocity of matter is c in *its* rest frame, and is spatially separated from antimatter by c(root-2) – the hypotenuse of Pythagoras’ triangle. This ‘absolute relationship’ is consistent with Special Relativity, for if that matter is at rest relative to the observer we can ask how many seconds t’ passes for antimatter if the observer counts t = 1 second, and the reciprocal of the time-dilation formula gives us t’ = i. Clearly the ‘absolute relationship’ holds true even if that matter is not at rest relative to the observer.

3) If there is any uncertainty with respect to the position and momentum of matter, it will be due to the nature of matter, rather than *assuming* Heisenberg’s uncertainty principle.

I hope that answers your questions. :)

All the best to you and your family,

Robert

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As I have not heard back from you, you either went to Croatia for a holiday, or my answers were too long or unclear. :) In case it happens to be the second, please allow me to clarify further.

1) Einstein’s equivalence principle means that we cannot experimentally distinguish between acceleration and a *uniform* gravitational field. But no such *uniform* gravitational field exists in reality. That is, Einstein unrealistically ignored the *non-uniformity* of gravity, for even an arbitrarily small reference frame cannot ignore that non-uniformity according to Ohanian’s paper.

2) The velocity of matter is c in *its* rest frame, and is spatially separated from antimatter by c(root-2) – the hypotenuse of Pythagoras’ triangle. This ‘absolute relationship’ is consistent with Special Relativity, for if that matter is at rest relative to the observer we can ask how many seconds t’ passes for antimatter if the observer counts t = 1 second, and the reciprocal of the time-dilation formula gives us t’ = i. Clearly the ‘absolute relationship’ holds true even if that matter is not at rest relative to the observer.

3) If there is any uncertainty with respect to the position and momentum of matter, it will be due to the nature of matter, rather than *assuming* Heisenberg’s uncertainty principle.

I hope that answers your questions. :)

All the best to you and your family,

Robert

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Dear Robert,

thanks for clarifications.

Cheers,

Ch.

thanks for clarifications.

Cheers,

Ch.

Dear Dr. Corda,

I have read the essence of your essay and want to share my thoughts about the intrinsic space-time you have mentioned. If we were to replace space-time with our self (universal I or conscience) we will be able to understand the universe. Please find "Theory of everything" that I have submitted in this contest at your convenience.

Conscience is the cosmological constant

Love,

Sridattadev.

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I have read the essence of your essay and want to share my thoughts about the intrinsic space-time you have mentioned. If we were to replace space-time with our self (universal I or conscience) we will be able to understand the universe. Please find "Theory of everything" that I have submitted in this contest at your convenience.

Conscience is the cosmological constant

Love,

Sridattadev.

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Dear Sridattadev,

I read your "Theory of everything" and I think it is a philosophical theory than a physical theory. Differently from your theory, a physical theory has to be rigorously derived through mathematical equations. As I am a mathematical physicist than a philosopher of science, I cannot judge your theory. I suggest you to send it to some journal of philosophy of science.

Best regards,

Ch.

I read your "Theory of everything" and I think it is a philosophical theory than a physical theory. Differently from your theory, a physical theory has to be rigorously derived through mathematical equations. As I am a mathematical physicist than a philosopher of science, I cannot judge your theory. I suggest you to send it to some journal of philosophy of science.

Best regards,

Ch.

Christian

Interesting conversation with Florin going on, on the Essay Blog. I'm inclined to go with you for publication of the Chromatic Dispersion paper anyway, but it really does need some re-writing first, and I can now be less subtle on the inequalities issue. You mentioned an asst editor, if you'd like to get him to look and comment please do.

Best of luck with the judges.

Peter

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Interesting conversation with Florin going on, on the Essay Blog. I'm inclined to go with you for publication of the Chromatic Dispersion paper anyway, but it really does need some re-writing first, and I can now be less subtle on the inequalities issue. You mentioned an asst editor, if you'd like to get him to look and comment please do.

Best of luck with the judges.

Peter

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Dear Peter,

as the peer-review process of a scientific paper is a very hard work, I prefer to wait that you will send me the final form of your paper before sending it to the asst editor.

Cheers,

Ch.

as the peer-review process of a scientific paper is a very hard work, I prefer to wait that you will send me the final form of your paper before sending it to the asst editor.

Cheers,

Ch.

A close friend of mine has informed me of your insolence to associate my GR with your essay. As you know very well, I find your work lacking any physical validity and think that the mathematical rigor glows by its absence.

I urge you to immediately rectify the many erroneous statements attributed to GR in your Essay and to publish what I actually said about your work, as well as about the books and papers that you sent me.

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I urge you to immediately rectify the many erroneous statements attributed to GR in your Essay and to publish what I actually said about your work, as well as about the books and papers that you sent me.

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The real Albert Einstein told: "Only two things are infinite, the universe and human stupidity, and I'm not sure about the former."

The sentence of this fake shows that the real Albert Einstein was very correct...

The sentence of this fake shows that the real Albert Einstein was very correct...

Gentlemens

I wonder why you did not notice or do not want to notice the radical view that an independent investigator.Remember this name: name,Friedwardt Winterberg

http://bourabai.narod.ru/winter/relativ.htm

http://

bourabai.narod.ru/winter/clouds.htm

Yuri Danoyan

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I wonder why you did not notice or do not want to notice the radical view that an independent investigator.Remember this name: name,Friedwardt Winterberg

http://bourabai.narod.ru/winter/relativ.htm

http://

bourabai.narod.ru/winter/clouds.htm

Yuri Danoyan

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Dear dreamer,

thanks.

Yes, I am surely a dreamer too.

Best wishes,

Ch.

thanks.

Yes, I am surely a dreamer too.

Best wishes,

Ch.

Dr. Corda:

You have a very impressive knowledge base, so I am going to give you some excellent advice so that you may improve, broaden, and consolidate your ideas.

1) Physics is fundamentally/ultimately based upon force (or energy) as it relates to fundamental and stabilized distance in/of space. This truly balances attraction and repulsion. This is key to unifying physics generally.

ULTIMATELY, distance in/of space must be equivalent with force/energy in keeping with space manifesting as gravitational/electromagnetic/inertia energy.

2) Inertia and gravity are fundamentally and truly equivalent ONLY if they are at half strength. Balance and completeness go hand-in-hand, and balance relates to the middle.

3) Combine and include opposites -- as this is a requirement of any truly unified understanding of physics.

4) Quantum gravity requires that opposites be combined and balanced. Inertial and gravitational equivalency fundamentally balances attraction and repulsion and fundamentally stabilizes and balances distance in/of space in conjunction with space manifesting as gravitational/electromagnetic/inertial energy. Quantum gravity requires that space be both visible and invisible, in a balanced fashion. Here we unify gravity and electromagnetism. Quantum gravity requires that space be flattened/contracted AND stretched/expanded in keeping with balanced attraction and repulsion and gravitational/inertial equivalency.

5) Invisible and visible space must be merged and balanced in keeping with balanced attraction and repulsion in order to fundamentally stabilize and balance distance in/of space inertially and gravitationally so that electromagnetism and gravity may be unified.

6) Inertia and gravity must be fundamentally equivalent in order to truly unify gravity and electromagnetism.

7) There is a reduced ability to understand astronomical/telescopic observations BECAUSE they are creations of thought. Try to understand this in relation to both television and dream vision.

Good luck with your work.

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You have a very impressive knowledge base, so I am going to give you some excellent advice so that you may improve, broaden, and consolidate your ideas.

1) Physics is fundamentally/ultimately based upon force (or energy) as it relates to fundamental and stabilized distance in/of space. This truly balances attraction and repulsion. This is key to unifying physics generally.

ULTIMATELY, distance in/of space must be equivalent with force/energy in keeping with space manifesting as gravitational/electromagnetic/inertia energy.

2) Inertia and gravity are fundamentally and truly equivalent ONLY if they are at half strength. Balance and completeness go hand-in-hand, and balance relates to the middle.

3) Combine and include opposites -- as this is a requirement of any truly unified understanding of physics.

4) Quantum gravity requires that opposites be combined and balanced. Inertial and gravitational equivalency fundamentally balances attraction and repulsion and fundamentally stabilizes and balances distance in/of space in conjunction with space manifesting as gravitational/electromagnetic/inertial energy. Quantum gravity requires that space be both visible and invisible, in a balanced fashion. Here we unify gravity and electromagnetism. Quantum gravity requires that space be flattened/contracted AND stretched/expanded in keeping with balanced attraction and repulsion and gravitational/inertial equivalency.

5) Invisible and visible space must be merged and balanced in keeping with balanced attraction and repulsion in order to fundamentally stabilize and balance distance in/of space inertially and gravitationally so that electromagnetism and gravity may be unified.

6) Inertia and gravity must be fundamentally equivalent in order to truly unify gravity and electromagnetism.

7) There is a reduced ability to understand astronomical/telescopic observations BECAUSE they are creations of thought. Try to understand this in relation to both television and dream vision.

Good luck with your work.

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