There is a quite recent paper (2011) by Santiago-German which says that the Einstein's general theory of relativity is formally equivalent to the Ginzburg-Landau theory of superconductivity (http://arxiv.org/pdf/1112.1179v1.pdf). He further wrote that this fact lead us to suspect that the superconductivity of gravitation ought to be a real physical process occurring in the outskirts of galaxies.
Such a proposition seems to support previous articles by Horowitz (you can search at google.com), suggesting connection between General Relativity and superconductivity. There is also a paper sometime ago by Kholodenko and Ballard, saying that in dimensions three and higher the famous Ginzburg-Landau equations used in theory of phase transitions can be obtained (without any approximations) by minimization of the Riemannian-type Hilbert-Einstein action functional for pure gravity in the presence of cosmological term. See their paper at http://arxiv.org/abs/gr-qc/0410029.
If such a proposition is correct, then perhaps we can view some problems in cosmology from new angle. Not only dark matter but perhaps the solar system and planets can be viewed as superconductors too. Other possible analogy is between cosmology and condensed matter phenomena such as superfluidity. This analogy has been explored for instance by G. Volovik et al.
So, what do you think? Do you agree that General Theory of Relativity is equivalent to the Ginzburg-Landau theory of superconductivity? Your comments are welcome.
Well, well! I wonder where this one will go to. Let me quote the artist Ad Reinhardt, who said: "The one thing to say about art is that it is one thing. Art is art-as-art and everything else is everything else." You know it isn't really useful to mix everything with everything else and to suspect that there may exist connections between unrelated phenomena. There is no way around understanding gravitation as gravitation and superconductivity as superconductivity! (Incidentally, you might - if you like - look up an old paper by P. W. Anderson wherein he speculates about screening of gravitational interactions by phonons. This is a speculation somewhat related to yours. But it didn't lead anywhere.)
If you had wondered about formal connections between superconductivity and the Higgs mechanism in the theory of weak interactions some reasonable explanations could have been sent to you.
I have'nt read the paper, so I ask: If GR is equivalent to superconductivity, what in gravitation are equivalent to persistent current without any resistance, or Meissner effect or Flux quantization or Josephson tunneling?
Many ideas from superconductivity were borrowed to describe characteristics of particle physics: coherence length, order parameter, thermodynamic transitions similar to Tc, M(Hc). So it makes sense that these concepts of superconductivity can be carried over into systems that GR describes; what are the parameters that describe black holes? Whether GR is the definitive theory or something else will supercede it will depend on how well it describes cosmological physical realities compared to theoretical alternatives. The answer to that question is still unresolved, but tantalizing.
@Arno. Thank you for your answer. Yes i agree with you that it is difficult to predict where the new analogy will bring us. However, it seems that superconductivity offers new experiments which can be explored in microscale, where the general relativity is lacking.
@Patrick. Thank you for your question and comments. Yes if the hypothesis is correct that there is relationship between general relativity and superconductivity, then it seems possible to explore new observational implications of that idea. For example, i think it will be interesting to see if Podkletnov's experiment with rotating superconductor can be explained too using this approach. Best wishes
Thank you, Daniel, for your answer. Yes perhaps we would need new devices to observe implications of superconductor analogy of gravitation. Best wishes
Well, well! I wonder where this one will go to. Let me quote the artist Ad Reinhardt, who said: "The one thing to say about art is that it is one thing. Art is art-as-art and everything else is everything else." You know it isn't really useful to mix everything with everything else and to suspect that there may exist connections between unrelated phenomena. There is no way around understanding gravitation as gravitation and superconductivity as superconductivity! (Incidentally, you might - if you like - look up an old paper by P. W. Anderson wherein he speculates about screening of gravitational interactions by phonons. This is a speculation somewhat related to yours. But it didn't lead anywhere.)
If you had wondered about formal connections between superconductivity and the Higgs mechanism in the theory of weak interactions some reasonable explanations could have been sent to you.
Dear Dr. Jurg Frohlich, thank you for your comments. Yes we are interested to see whether there is formal connection between general relativity and Ginzburg-Landau theory. If you have or know other paper saying otherwise, please inform us. Thank you.
@Igor. Thank you for your comment. But which comment or question you do not agree? Could you please explain? Thanks
@ Jurg. The screening of gravitational interactions by phonons is a speculative physical claim. I was thinking about what verifiable phenomena exist and what are the models that describe them. I see no problem with borrowing models from other disciplines. That would be the description not the art. Do electrons even though in a cloud around nuclei remind us of planetary orbits just a bit? I think so.
@ Arno, @ Victor. If dark matter does lead to falsification of GR, then I agree GR would be a tough place to start from and a bit of a gamble to invest in.
I completely support Jürg Fröhlich's thought that "The one thing to say about art is that it is one thing. Art is art-as-art and everything else is everything else." - The same one can say of the superconductivity and gravity...
Reagrds!
@Daniel. Thanks for your comments. Yes perhaps dark matter and dark energy indicate that we should keep an open mind, especially with cosmology where nobody ever goes beyond the moon. You are from superconductor science, perhaps you would like to read this one: http://arxiv.org/abs/1010.2784.
@Anatolij. Thanks you for your comments. Yes of course they are two different fields, but sometimes there can be cross fertilization between two apparently different fields. Perhaps you would like to read Santiago-German's paper and make comment on where are his faults? Best wishes.
I am very happy to see gravity as superconductor. In my work on Synthetic Physic I use gauge theory and commutators to model gravity by superconductor theory
@Resconi. Btw, do you find new observational implications that should wait for new test? Best wishes
In the 50's Soraj Gupta proved that any massless spin-2 field defined in Minkowski's space-time by the Fierz-Pauli Lagrangian, is equivalent to the linear approximation of Einstein's equations in the appropriate coordinate gauge. Reciprocally, by reversing the linear approximation process he found Einstein's equations (see Gupta PRD 96, 1683 (1954), also S. Deser GRG 1, 9, (1970)). Therefore, if the answer for your question would be a yes, then the Landau-Ginzburg superconductivity theory should be equivalent to a Fierz-Pauli massless spin-2 field in Minkowski space-time.
@M. Maia. Thank you for your comments. Yes it seems possible too. best wishes
Dear Victor,
only a first reaction after your interesting question, I recommend a book:
G. E. Volovik, The Universe in a Helium Droplet (The International Series of Monographs on Physics, 117), Clerendon Press Oxford 2007
Here, he describes the simularities between the superfluid Helium-3 (also releated to Gisnburg_landau) and cosmology but also QCD and other particle physics approaches (casimir energy etc.).
Best wishes
@Torsten. Thank you for your information. Ok i will try to find that book. Best wishes
@Patrick. You are welcome. Best wishes
To all. For all of you who are interested in superconductivity, there is a fine book by Andrei Marouchkine, with title Room temperature superconductivity. The book is available online at http://arxiv.org/pdf/cond-mat/0606187.pdf. Best wishes
Dear Victor Christianto
To see computation in Synthetic Physics you can have a look at the paper
New black hole solutions in a modified gravity arXiv 1109.2928v4 [gr-qc] 14 Dec. 2011 or the same paper in ISRN Astronomy and Astrophysics vol.2011 (2011) Article ID 341919 7 pages.
For the paper Synthetic Pgysical Theory. gauge generalized principle in quantum geometry and gravity Germano Resconi Ignazio Licata you can see the paper Symmetry ISSN 2073-8994. I AM READY TO REPLAY AT ANY QUESTION.
GERMANO RESCONI
@Resconi. Thank you for your answer. With regard to your paper Synthetic Physics, i read it yesterday, but as far as i know you do not mention any single word on superconductor in that paper. Perhaps you can make it more explicit in your next paper. Best wishes
Dear Victor
In the paper Synthetic Physics is not explicitilly named the superconductivity but the three terms Proca Term , Chern-Simon term and Maxwell like terms are all terms relate to the superconductivity as you can see for example in the paper arXiv:1311.7640v2 [hep-th] 2 dec.2013
if you want send to me any message you can use my e-mail [email protected]
>... "The one thing to say about art is that it is one thing. Art is art-as-art and everything else is everything else.....
I all my papers, independentely of there indicated, I have applied GL-theory to nucleons substructure, and based on the values of the monopole (rotating magnetic field) induction , I have derived G, the power radiated (waves-10^22 Hz), the force transmitted to space-time as gravitational force, and which reflected by the object as attraction force. All the data related to gravity (g, gravitational potential of Earth, light deflection, dark matter nature etc.) were calculated without G, which resulted to be related only to Planck lenght. Therefore, there are not gravitons ,
Dear Resconi,
thanks for offering your interesting work. Maybe a stupid question (I have to study your papers) Is synthetic physics related to synthetic differential geometry (a la Kock)? My friend and coauthor Jerzy Krol (also at researchgate) is an expert in model theory and we used it also to describe the exotic smoothness structures of spacetime.
Best wishes
@Panagiotis and @Torsten. Thank you for your comments. Best wishes.
@Stefan. Can you please share your paper as described? Or just give the url. Thanks.
My paper is just now in editing in Prespace Jornal, after publication I will indicate the link, a early version is available on vixra: http://vixra.org/abs/1401.0142
@Stefan. Thank you for the url of your paper. Sure i will read it soon. Best wishes
Prespacetime Journal has just published Volume 5 Issue 1 entitled "Standard
Model, Causal Structure, Modified GR & Origin of Gravity" at
http://prespacetime.com/index.php/pst/issue/view/50
Prespacetime Journal| January 2014 | Volume 5 | Issue 1 | pp. 44-59
Mehedinteanu, S., The Connection between Quantum Mechanics & Gravity
Dear Stefan, i just read at a glance your recent paper in Prespacetime Journal. Since your paper discusses quantum mechanics from quantum fluid, allow me to mention a 1995 paper by prof. Friedwardt Winterberg discussing how to derive quantum mechanics from boltzmann equation using superfluid placnk aether. I can send you his paper if you wish. Best wishes
Dear Torsten Asselmeyer Maluga
Yes the synthetic differential geometry is natually connected with synthetic physics by topos as gauge physic process . The difference is that in syhthetic physics we have a prototype model as Electromagnetic Maxwell equations that represent the universal form or syntesis for Gravity and quantum see my papers Unification of quantum gravity by non classical infromation entropy space ( Resconi , Ignazio). For similar resukt for Brain you can see Geometry for Brain Optimal Control in a Network of adaptiver
In "Theory of superconductivity of gravitation and the dark matter enigma," http://arxiv.org/abs/1112.1179, Wenceslao Santiago-Germ´an states on page 8:
"... It follows that the superconductivity of gravitation is destroyed in a region when there is a sufficiently strong gravitational spatial curvature. Hence, the most probable place to observe the superconducting phenomenon just described is in the outer skirts of galaxies and not near a central region where a supermassive black hole might be present."
In simplistic terms that I can comprehend, this seems to indicate that superconductivity of gravitation can only be found in weak gravitational fields, far from strong gravitational sources. This does not seem at all consistent with the superconductivity of electromagnetism.
I'm compelled to add that galactic dark matter was inferred from discrepancy between observed flat rotation curves of spiral galaxies and expected rotational velocities that diminish as a function of radial distance. However, planar disk distributions of mass can only produce expectations of diminishing velocities when improperly evaluated using two-body equations, with the gravitational force diminished as an inverse square function of the two bodies' separation distance (r).
In evaluations that more properly represent the planar distribution of spiral galaxy disk masses and especially the distribution of their separation distances, no such diminishment of radial velocity is indicated.
Only when attempting to fit the expected diminishing rotation curves to observations does an enormous, extended halo of dark matter seem to be required.
This much simpler assessment does not depend on any complex effects such as superconductivity of the weak peripheral gravitational field produced by exceedingly compound structures consisting of many billions of discrete objects distributed over perhaps hundreds of thousands of light years...
Even if GTR and the Ginzburg-Landau theory of superconductivity are formally equivalent, are the conditions that produce the superconductivity of electromagnetism even approximated by enormous spiral galaxies?
"... It follows that the superconductivity of gravitation is destroyed in a region when there is a sufficiently strong gravitational spatial curvature. Hence, the most probable place to observe the superconducting phenomenon just described is in the outer skirts of galaxies and not near a central region where a supermassive black hole might be present."
BTW - not even a supermassive black hole would curve spacetime to such an extent that it would produce any effect whatsoever at a distance of tens of thousands of parsecs - which would be necessary in order to restrict the proposed (intensified) superconductive gravitational effects to the peripheries of large spiral galaxies.
This seems to be the intent of this specification - to explain why vast planar distributions of mass do not produce rotational velocities that diminish as an inverse square function of radial distance (see prior comment).
@Resconi. Thank you for your comment.
@James. Thank you for your very interesting question. Yes perhaps there is limitation of this analogy. Best wishes.
Dear all contributors: Thank you so much for all your answers and comments. Allow me to share a summary of this discussion in pdf file. Hopefully this discussion will stimulate further experiments.
@Victor Christianto
From the physics point of view the General Theory of Relativity has and can no equivalence to any other physical theory being a strictly mathematical (geometrical) creation, possessing only some, yet not completely explained, physical interpretations... I guess, that the question is slightly misleading the real intrinsic nature of these physical phenomena...
Regards!
Dear Anatolij
In my work on the Synthetic Physics the General Theory of Relativity is only one particular case.
Germano Resconi
@Resconi Germano
To be fully open minded it is necessary still so much to understand what the General ralativity means and its real relation to the Gravity...
Regards!
Gravity is a force that change the kinetic energy of a mass. Kinetic energy is based on the derivative operator that can change for the change of reference. When derivative operator commute we have no problem to create invariance and symmetry. But when the deivative operator does not commute in the ordinary space we cannot create symmetry or invariance ( non holonomic system) In many cases expecially when we have gravitational spin is impossible in an euclidean space to create a coherent theory of gravity. The Einstein idea was to create special curved space where we can have a covariant derivative that locally commute. Now the problem is to define the special reference or space where we can have a commutative property. Now Einstein cannot create a general theory of commutator. Synthetic Physics with the model of Maxwell equation write by commutator a general theory that extend the Einstein equation. Synthetic theory show also that quantum mechanics can have similar commutative general theory. In researchgate at my name Germano Resconi you can found the theory. In this moment I finish to write a new paper where I improve the previous paper. In any case I am ready to reply to your quastions.
Dear Germano, you wrote:
"Gravity is a force that change the kinetic energy of a mass. Kinetic energy is based on the derivative operator that can change for the change of reference...." Yet you, eventully now well that the General Relativity has a very nontrivial problem of existing the energy as a physical property... And this fact is related namely with the intrinsic differential structure of GR... That is a problem lies not in the mathematical formulae, but in the deep physical backgrounds of the GR, which are, to the regret, nowadays very little understood...
Cordial regards!
Dear Anatolij
Now I put you a question. The Coriolis , Centripetal and centrifugal force due to the change of reference and derivates defintions have physical meaning ?
Dear Germano,
NO. Such forces are rendered by mathematical manipulations with reference frames and suitable geometrical interpretations of the resulting kinematics, - you know this very well! If there was no gravity, a mass on orbit would not move with respect to the central force point around the Sun, but would move respectively linearly, and nothing more, as it was stetd by the first Newton law. And I still will remind you that any real force is related with potential energy (Hamiltonian) function, the changes of reference frames are in no way related with real changes of the potential energy, except the scale of its measurement, which is a completely different thing.
With best regards!
Yes but the Hamiltonian function change with reference so reference or point of view is very important. When we have a mass with rotation we can use classical netwtonian rule in the cartesian reference with a lot of difficulty. But if we use rotate reference Newtonian rule is very easy and invariant appear immediatelly. In physics the reference cannot change the physical phenomena but can reduce a lot the non-holonomic difficulty ( non integrability , and so on ). In the Einstein relativity with the Lorenz change of reference we can use Newton law also if the system in the non Lorenz reference does not follow the Newton rules.
Dear Germano, yes, a functional expression is changing, it is true and so natural(!), but it is NOT changing its physical essence. The "non-integrability" and "non-holonomicity" notions have nothing to do with the related physical phenomena, as they only mean some mathematical definitions for some not completely exactly or approximately treated processess. Concerning Newton's laws, they are strongly based on the point-locus interaction physical assumption and are satisfied always, being based on the infinitesimal Lorentz transformations (see for reference: Landau-Lifschitz's manual "Field theory") I have see here really no problem for discusion...
All the best!
Why you are so advers to any Mathematical structure in physics ? All university course in physics use mathematics. Yes Physics is always the same but mathematical model of physics is the instrument by which we can make computation on physics. When we introduce Coriolis forces as virtual forces we can use clssical Newton idea of force and acceleration for rotate system ( non inertial system ). So the change of the meaning of derivative in curved space give us virtual forces that we can use as model to make computation. The same idea I use in the synthetic physic that I built and I hope you can read in my researchgate place
Dear Germano, using mathematics and doing physics are completely different things, - please do not deceive yourself! Mathematics is a strongly deductive logical system based on axioms often very well fitting, as a good formalizing language, for modeling phenomena of other sciences, - yet Physics is NOT a deductive science, it is a mirror of the Nature and is based strongly on our observations and experimental experience... How was nice a conceived math theory of something, it would have no sence, if it had not passed the experimental and practical tests. As P.A.M. Dirac said, "Physical law should have mathematical beauty, but mathematics should not rein physical laws!"
All the best. (And forget about "Coriolis's things... they are misleading yours initially true thinking!) I humbly rest on my side!
Sincerely yours, Anatolij,
Professor of Mathematics and Physics.
I do not want stay in one part or in another part. My research is to build models that we can use to create experiments. I do not like pure mathematics. Now my work on Synthetic Physics is only an hypothesis that can guide experiments. I am not sure if you want read my paper but I hope that you can give me your impression
Dear Germano, sure, I understand you well - math is NOT for love and getting liked, it is for using only! (The only nice girls and women deserve to be loved and granted for sympathy! -:) Please, if you can, send me your paper at email. Is it already published?
Regards,
Anatolij.
P.S. Yet you should take into account that the word "Synthetic" subject to the science Physics is smelling like an "Artificial", not Natural Physics... I am afraid, this name is not much proper and will be strongly misleading potential readaers too...
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