In relativity theory , the spacetime is curved by the presence of massive bodies.The curve of spacetime effects to the motion

No medium is necessary. Spacetime can be curved, even in the absence of matter-there exist vacuum solutions of Einstein's equations, that aren't Minkowski spacetime. It depends on the boundary conditions.

It should be kept in mind that GR is a classical theory, but it is possible to study quantum matter in a curved spacetime.

The quantum vacuum=vacuum state of a quantum theory, doesn't consist of virtual particles-it is the state that doesn't have any particle. People persist in confusing the average value of the number of particles-which is zero-with the fluctuations of the number of particles about its average value, which (a) don't vanish and (b) need not be Gaussian, therefore don't provide a unique description of the distribution.

However the vacuum state of quantum matter in a curved spacetime isn't unique-as is the case in flat spacetime. So, yes, spacetime curvature is a way of expressing the non-uniqueness of the vacuum state of quantum matter.

Dear Sergei Eremenko

I suppose that your question is not about Einstein’s spacetime but about the modern interpretation of “the medium space”.

The known properties of space – in relation to the observable phenomena – are the universal (quantum) fields that exist everywhere during the whole evolution of the universe. These universal fields are the Higgs field and the electric field + corresponding magnetic field (electromagnetic field). Gravity seems to be an emergent force field because there were times that there was no matter in the universe. The consequence is that gravitation is mediated by the universal (quantum) fields.

The attempts to implement Einstein’s curved spacetime into QFT have resulted in new hypotheses about space itself. It is proposed that space itself has a structure – so it is build up by units with a volume and a boundary that tessellate the volume of our universe – and it is termed “Discrete space”. These models of space itself are “filled up” with the properties of the universal (quantum) fields. Thus every unit has one scalar of the Higgs field. Etc. The idea is not new because it was already proposed by the ancient Greek philosophers some 2500 years ago.

With kind regards, Sydney

Dear Sergey,

First, it must be taken into account that GR requires continuity to works, at a quantum level, space is discontinuous and GR is useless.

Then you have to take into account that matter and universe (space-time) are the same. Let me explain, all the matter in the universe is what gives it its hyperspheric shape, if we divide from there between groups of galaxies, galaxies, planetary systems, planets, objects, molecules, atoms, nuclei, electrons (see how I'm going reducing the scale). All this encompasses the universe (space-time), however, the spaces between the nucleus and the electrons, for example, are not part of the universe, nor of space-time. There is a discontinuity there and GR is not applicable.

In short, the medium that GR refers to is the matter itself.

Dear Stam Nicolis ,

"Spacetime can be curved, even in the absence of matter-there exist vacuum solutions of Einstein's equations"

That is not possible, can you give an example?

Dear Sydney Ernest Grimm ,

You are still with the fields .. You still don't want to understand, that the fields and their associated particle do not really exist, they are an approximation.

There is no logical reason for its existence. There is a Higgs field, created by a Higgs boson. That's it.

But what about that field and that boson? where did they come from? how have they been created? There is no answer (and that's not taking into account the part about typical field physics problems).

Never use fields to explain concepts because you will wrong.

Sergei Eremenko ,

your question is quite interesting.... GR is just a partial view on gravitation, it tells us that something has curve in order to account for several phenomena (not all) the theory it is able to predict to a very good degree of accuracy.

GR deals with "metric" which is changed from flat to curved but it does not account at all for any physics behind such distortion, it misses the physical ontology, the picture given is quite unsatisfactory, that distortion forcibly mimics something deeper still unknown. The big issue with GR is that it cannot cope with an energy density and gravitational potential energy (Gullstrand was the first to notice this fact in 1920) . This tells us that something significative is missing and that limitates a lot GR's prediction power, being one of the reason of proliferation of alternative theories.

Quantum Field Theory: QED and QCD need a background with huge energy hence the potential energy is an indispensable ingredient. Also these theories have huge prediction power but as Dirac himself said: " renormalization is quite unsatisifactory, just hides something deeper which has still to be understood"

Dear Stefano Quattrini ,

"GR deals with" metric "which is changed from flat to curved but it does not account at all for any physics behind such distortion, it misses the physical ontology, the picture given is quite unsatisfactory"

Behind such distortion is the matter that curves space-time does not lose any physical ontology.

"The big issue with GR is that it cannot cope with an energy density and gravitational potential energy (Gullstrand was the first to notice this fact in 1920)"

I do not know this point, could you explain it better with an example?

spacetime itself is the “medium” that is curving. When we think of a medium for the transmission of waves we think of something like air or water which exists within Spacetime. The medium of Spacetime is different in the sense that Spacetime itself is curving in a way described by the Einstein equations of GR.

This medium of Spacetime supports curvature and gravitational waves. I also think that Spacetime is the medium for the wave propagation of light and other electromagnetic waves as explained here:

Data Prerecording of Conference Presentation on the Unification of Physics

Richard

Dear Sergio Garcia Chimeno

The concept of Discrete space doesn't mean that all the changes in our universe are quantized. Discrete space is a continuum with topological properties although the continuum has a spatial structure. The consequence of the topological changes is that every observable change has a duration and can be thought as a "flux" of infinite small changes.

Planck's constant - the fixed amount of energy - represents a fixed amount of change (energy) of all the mutual relations between the observable phenomena. In other words, you are mixing different concepts.

With kind regards, Sydney

Dear Sydney Ernest Grimm ,

I am not mixing different concepts, GR and differential geometry need a continuous and differentiable surface to work

Sergio Garcia Chimeno ,

the space-time is just an "artifact" by itself, if you feel satisfied to distort an artifact, help yourself...

https://www.researchgate.net/post/Field_energy_density_and_Potential_energy_in_gravitation_missing_in_Einstein_F_E_are_the_reasons_for_a_missing_unification_of_the_interactions

Dear Stefano Quattrini ,

Spacetime is not "an artifact", spacetime is the universe itself that changes according to how its masses are distributed.

I still don't understand what you mean by the link. Explain it in your own words, you must always bear in mind the authority bias, it is indifferent whoever says A or B.

Hi Dr Sergei Eremenko . In general relativity, spacetime is not 'flat' but is curved by the presence of massive bodies. This artistic representation visualises spacetime as a simplified, two-dimensional surface, which is being distorted by the presence of three massive bodies, represented as coloured spheres. See the link: https://sci.esa.int/web/lisa-pathfinder/-/56434-spacetime-curvature

Also, see the following link: https://www.britannica.com/science/relativity/Curved-space-time-and-geometric-gravitation

Kindly, see the following link too: https://books.google.com.om/books?id=bU4xUMuJlukC&pg=PA54&lpg=PA54&dq=What+media+is+curving+in+General+Relativity?&source=bl&ots=G1UDHTjSrF&sig=ACfU3U1be2uqLZLeN93rUj57lysDppXVpQ&hl=en&sa=X&ved=2ahUKEwj5poKX3dvzAhUn4YUKHSOABI8Q6AF6BAggEAI

The assumption of the question is that the "spacetime" in the General Relativity (GR) field equation is actually (meaning real component of the universe) a "medium". This conception has the possibility in uniting GR with quantum observations - legitimately linked to light interference. I think this is the one of keys conception (paradigm shift) needed for unification. But note that it entails the idea the "spacetime" (the media) exerts a force on matter. But if this is correct, then the "energy-momentum" tensor is not energy but force. So, the GR equation becomes force creators (such as gravitation mass) warps the media and the media gradient exerts a force on matter. This is better (IMHO) model to think about uniting the Big and the Small.

Now the remaining issue is a simpler model on how these forces are created and how they interact with matter. Note for simplicity this must entail that there is only 1 type of force (the gradient of the medium). The 4 forces in the quantum realm must reduce to one force on matter.

Scalar Theory of Everything (STOE) unites the big, the small, and the four forces (GUT) by extending Newton's model

https://www.researchgate.net/publication/344442808_Scalar_Theory_of_Everything_STOE_unites_the_big_the_small_and_the_four_forces_GUT_by_extending_Newton's_model

http://intellectualarchive.com/?link=item&id=2414

https://www.youtube.com/watch?v=0YlJGdTvuTU

Sergio Garcia Chimeno ,

space-time is just the math outcome of the Galilean equivalence of IRFs, with the additional constraint of a limited speed in coordinate transformations. That made necessary to mix space with time and give birth to something which so far did not have a satisfactory experimental evidence: missing the relativity of simultaneity which is what is directly implied by the IRFs equivalence....

The intrinsic hierarchical nature of gravitation is quite against such equivalence and dynamics too is hierarchical...that equivalence is an abstraction which can hold only to a first order approximation....

Gentlemen, Attempts to explain gravity with the help of familiar bodies and phenomena familiar to us from the experience of terrestrial laboratories is a useless exercise. Gravitational forces are fundamentally different from the bodies and electromagnetic fields we are used to. The gravitational field cannot be contained or shielded from it. This resembles the curvature of space, this is the curvature of space. This is easy to verify. In addition, gravity is not limited to the attraction of bodies. The gravitational field has energy and momentum, changes spatial and temporal scales. Whether it's ether or quantum fields, they can be shielded - gravity cannot be shielded. The rest was said by Einstein in 1920:

Dear Stefano Quattrini ,

And speed is just the math outcome of deriving the space between time. Is speed also an artifact?

Dear Valery Borisovich Morozov ,

Well, electromagnetism is also a curvature of space-time just like gravity. You can use fields as approximations

Sergio Garcia Chimeno , No electromagnetic field is described by Maxwell's covariant equations in flat space. Of course, these equations also exist in a gravitational field, i.e. Riemann space. Gravity and electromagnetism are different theories, their nature is different.

Einstein's gravity is incomplete. Einstein's equations do not enforce strict conservation laws.

It can be fixed:

Preprint Gravitational Field Equation and the Structure of Black Holes

Preprint Уравнение гравитационного поля и структура черных дыр

Dear Valery Borisovich Morozov ,

Electromagnetism is also described with the electromagnetic stress-energy tensor and Einstein's equations. And it causes curvature the same as gravity, but covariant in 4D

https://en.wikipedia.org/wiki/Electromagnetic_stress%E2%80%93energy_tensor

Dear Valery Borisovich Morozov ,

"Einstein completes the work by adding a value to the equation2 which makes it one which satisfies the law on the conservation of matter but does not the system of matter and gravitational fields. The conservation law is preserved but is true only for the closed systems"

You know that the passage from the Riemann tensor to the Einstein tensor is done precisely for the conservation of energy, but here you are making a mistake "but does not the system of matter and gravitational fields" and it is by thinking about fields. I repeat it again, the fields do not exist, they are only approximations, and matter and gravity are really the same, they are curvatures of space-time, Einstein's equations are fine as they are because notice that they use mass density, they can calculate the curvature causing the earth at any distance only by increasing the volume

Sergio Garcia Chimeno "You know that the passage from the Riemann tensor to the Einstein tensor..."

It seems to me that you do not quite understand the meaning of the words that you say. Einstein's equations are undoubtedly good, but they do not work in strong fields and do not provide a conservation law.

Preprint Gravitational Field Equation and the Structure of Black Holes

Preprint Уравнение гравитационного поля и структура черных дыр

Preprint Exact equation of gravity field based on Einstein's separati...

Preprint Точное уравнение гравитационного поля на основе эйнштейновск...

Dear Valery Borisovich Morozov ,

You would agree with me that applying the Bianchi identities to the Riemann tensor to convert it into the Einstein tensor has the objective of precisely the conservation of Energy, right? It is that if you do not know that, little we can talk more because you lack information .. Einstein's equations do not come out of nowhere, you must know how to deduce them and you must know why they are deduced that way.

dear Sergio Garcia Chimeno

it is just a rate and it works fine in all applications of classical Physics. Until somebody shows that relativity of simultaneity holds (to some astonishment never experimentally verified in 100 years) the space-time is just an artifact, giving some results.

There are no media that are curving within the framework of general relativity. Our perception of the world as a 3-dimensional body is solely due to the fact that our physical bodies and all their parts (fragments) are also perceived as 3-dimensional. This perception of the surrounding world is due to the activity of its integral part  the brain. The gravitational field of attraction does not bend the surrounding space: it is just that this body attracts a body of lesser mass that has fallen into its sphere of influence. The fields of attraction include the Newtonian field and its 4-dimensional relativistic generalization  the Schwarzschild field created by a solitary mass. The result of the interaction of a gravitating body and a body caught in its field depends on the value of the gravitational potential of the source of ol and the kinetic energy of the passing body. There are 3 possible cases, depending on the magnitude of the source field and the direction and speed of the passing body: 1) it will fall on the attracting tree; 2) become his companion; 3) will fly away from the body along a slightly curved trajectory. So here general relativity only makes it possible to obtain more accurate calculation results than Newton's theory.

Without any theory, we simply see the firmament with the stars located on the inner surface of the celestial sphere stretching over us, rotating around the tilted axis. inclined to the celestial equator at an angle of 23.5 degrees. We measure solar and sidereal time by observing the uniform movement of this sphere. But where is GRT here? And its influence on knowledge about the structure of the Universe should be sought exclusively in the study of the structure of Time as the most important source that creates our world. The makings of this knowledge are laid down in the SRT, the main figure of which is the Minkowski cone. It consists of the upper Cone of the Future, the lower Cone of the Past and the starting point - the Moment of the Present. Actually, our whole life is a continuous chain of events in the Present. It is this very moment that should be investigated to understand the nature of Time. Ravda in SRT this point is just a mathematical concept, but in GRT a cone can rotate and gravitate, and the present is a 3-surface at every moment of time. In this case, the Past and the Future are two rotating hypersurfaces rotating in opposite directions. In other words, our world (the Space of the Present) is the result of the processing of our Future into our Past. But in order to study this world, one should turn to the Cosmos, the particles of which are the Earth and we together with it. Our world is the planet Earth, the axis of rotation of which is the axis of the cone, and its apex is a point in the sky, located near the Polar Star from the constellation Ursa Minor. It is in it that the Past of everyone on Earth will be transformed into his Future. The energy received by the planet is distributed among all the inhabitants of the planet and its environments. Therefore, it is high time to pay attention to the numerous experiments of various researchers of Time, most often independent (from modern science). However, life on the planet began to change at an accelerated rate, so you should at least ask what is happening with the planet and with us.

Thanks, colleagues. I obviously know geometrical meaning of GR, and would like to focus on the question - whether Quantum Vacuum (of virtual particles), Zero-Point field or Higgs field seemingly permeating the whole space can be that 'media' that curve in GR? Or these fields with nonzero energy have nothing to do with GR?

Quantum gravity is a dummy. Quantum fields interact with matter. The gravitational field "does not notice" the substance penetrates it without interaction.

“…GR geometric meaning of curved spacetime lacks explanation what physical media really curves. Can quantum vacuum of virtual particles be that media? Does curvature of spacetime means uneven distribution of that quantum vacuum?…”

- GR geometric meaning of curved spacetime is fundamental meaning just of only curved spacetime, and of nothing else; and so doesn’t require any explanation what physical media really curves – the fundamental base of GR is just the postulate that interactions in systems “mass-spacetime mass” are real, and all material objects are impacted by the “curved spacetime” so, that they move in corresponding “geodesics”.

GR, though, by no means explains – how/by what way/by what force the spacetime impacts on matter, say, how forces Earth to move around Gun,

- what is quite natural, the postulated interaction above fundamentally cannot exist, and any rational explanations are impossible.

Gravity fundamentally for sure is the “fourth”, though non-existent in official physics now, fundamental Nature force, which in a number of traits is similar to the fundamental Nature E/EM force, and acts as other Forces, at least as E/EM Force, act: there is corresponding Gravity charge “gravitational mass”, the charge radiates Gravity mediators “gravitons”, which impact, at least at statics in accordance with Newton law, on other charges – as that electrically charged bodies interact. Note, however, that Gravity and E/EM Forces are fundamentally different.

As well as so that

“…Electromagnetism is also described with the electromagnetic stress-energy tensor and Einstein's equations. And it causes curvature the same as gravity, but covariant in 4D….”

- is in certain sense a bit correct – since G and E/EM Forces are similar, they indeed are similarly described, including, by using stress-energy tensors; however the claim that Electromagnetism causes curvature the same as gravity is too strange claim even in GR, see above - “curvature” in GR is caused fundamentally only by “masses”. And is fundamentally wrong at all – nothing, including Electromagnetism, in Matter can impact on the Matter’s really fundamentally absolute, fundamentally flat, and fundamentally Euclidian, [5]4D spacetime with metrics (cτ,X,Y,Z,ct).

“…. Until somebody shows that relativity of simultaneity holds (to some astonishment never experimentally verified in 100 years) the space-time is just an artifact giving some results…”

- the Matter’s spacetime above is absolutely fundamentally real, Matter can exist and change absolutely fundamentally only in its concrete spacetime and nowhere else [more see yesterday SS post in https://www.researchgate.net/post/Is_time_quantized2],

- and relativity of simultaneity is well observed on Earth; say, if some light flash is directed in two opposite directions along Earth 30 km/s velocity on equal distances, say, L, where some photons’ detectors and synchronized clocks are placed,

- then photons, according to the both clocks’ showings arrive in both simultaneously, in spite of evidently the photons, that propagate along Earth velocity direction, pass larger L distance , since the “forward” detector and clock move, with the speed 30 km/s, on the additional to L space interval in the photons time propagation interval;

- whereas photons that propagate in opposite direction pass lesser distance , since the “back” detector and clock move toward each other with the speed 30 km/s.

And just because of the “relativity simultaneity” the measured on Earth time intervals are equal, the measured distances are equal, and the speed of light is the same in both directions. That was known soon 200 years ago; and was quantitavely rigorously estimated by Voigt yet in 1887 as the Voigt-Lorentz decrement –Vx/c2, including -VL/c2 in this case.

More about what are space/time/spacetime [and Gravity] see the Shevchenko-Tokarevsky’s informational physical model, for first reading see https://www.researchgate.net/publication/342600304_The_informational_physical_model_some_fundamental_problems_in_physics http://dx.doi.org/10.13140/RG.2.2.12325.73445/3

“…Quantum gravity is a dummy. Quantum fields interact with matter. The gravitational field "does not notice" the substance penetrates it without interaction. ….”

- quantum Gravity absolutely fundamentally really exists, and Gravity field is “quantum field”, and Gravity evidently “notices the substance”, just because of the noticing any body’s mass is lesser on the mass defect comparing with the case when the bodies components are infinitely distanced.

The SS posts in https://www.researchgate.net/post/Do_you_think_that_general_relativity_needs_modifications_or_it_is_a_perfect_theory are relevant to this thread question as well, a couple of the posts are on the visible page now.

Cheers

In general relativity, "environment" is 4-space. There is no need to disfigure the theory, to invent ether. The only thing more stupid than that is to ascribe the properties of familiar environments. Einstein's space has neither elasticity nor speed. The long-established mechanics of continuous media does not work in a vacuum. This was understood back in the 19th century.

It makes no sense to deal with quantum gravity in such a primitive way. This is indicated by numerous articles about nothing i.e. about quantum gravity.

A quantum theory of gravity is needed. But she's not there. And nobody knows where to start.

“…The long-established mechanics of continuous media does not work in a vacuum. This was understood back in the 19th century….”

- that isn’t really so. Just in the 19th century the Maxwell electrodynamics was developed, and well worked in, for the continuous media “ether”; that is another case that this ED turned out to be incompatible with Galileo transformations, which are based on the Newton’s – and any other normal human, though, absolute Matter’s space/time/spacetime; and in late 19th century it was experimentally shown that the ED works so, that the physical effects of some ether, which would be fixed in corresponding absolute space, aren’t observable, and so the Galileo-Poincaré relativity principle appeared;

- and Poincaré claimed that absolute space/time/spacetime is principally non-observable; however really the absolute motion is observable and absolute velocity of Sun system can be measured, see https://www.researchgate.net/publication/259463954_Measurement_of_the_absolute_speed_is_possible DOI: http://dx.doi.org/10.5281/zenodo.48709.

However form that something isn’t observable by no means follows that it doesn’t exist; and, besides, really some media is, in fact, introduced in classical ED till now – since it has quite concrete parameters “vacuum permittivity” and “vacuum permeability”.

For any normal human it looks as would be something strange in that concrete physical parameters of the space/time/spacetime, which is nothing else than only [really [5]4D] “empty container”, has; however that is postulated in official physics from 1905;

- and so, say, in that further in 1916 for this empty container a lot of other properties and effects, which by no means the emptiness can have fundamentally, was postulated as well; etc.; more see the SS post above and links in the post. Including in this post it is pointed, that the interactions, where really are fundamentally nothing else than the “fourth” fundamental Nature force “Gravity” acts, absolutely fundamentally are quantum interactions, and so the quantum Gravity theory fundamentally can be, and so must be, developed.

So though that

“…It makes no sense to deal with quantum gravity in such a primitive way. This is indicated by numerous articles about nothing i.e. about quantum gravity….”

- is quite correct, existent and quite legitimate in official physics “Quantum Gravity” theories really are too strange mental constructions; however that

“…A quantum theory of gravity is needed. But she's not there. And nobody knows where to start.

……”

- is really incorrect, the base of the really scientific Gravity theory is developed in the Shevchenko-Tokarevsky’s informational physical model, see 2007 initial Gravity and E/EM fundamental Nature forces models in

https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics ; https://arxiv.org/abs/0707.4657 , section 2.9 “Mediation of the forces in complex systems”,

- including in the model the experiments, where the quantum nature of Gravity Force really can be observed and measured, was proposed yet in 2007 as well, see https://www.researchgate.net/publication/215526868_The_informational_model_-_possible_tests ; http://arxiv.org/abs/0706.3979 DOI 10.5281/zenodo.34963 ; at least the section 2.1.2. “Monochromatic photon beam distortion” and

https://www.researchgate.net/publication/245583444_On_the_photon_spectrums_of_some_monochromatic_beams_in_Earth_gravitation_field https://arxiv.org/vc/arxiv/papers/0707/0707.4657v2.pdf

Though yeah, QM Gravity practically for sure will be developed basing on “classical” gravitodynamics, as that was made by Schrödinger and Dirac for QM electrodynamics, however that fundamentally will not be a theory of “Gravitational Field Equations in General Relativity”; since, again, the postulated in GR interactions in the systems “mass-spacetime-mass” fundamentally cannot, and so don’t exist.

Cheers

Where did you get this information ... It's not like that.

The statement about the fallacy of general relativity is also absurd. Quantum gravity doesn't fit into the experimental database.

In the main work of Maxwell, the term "ether" is not used. Do not read Atsukovsky, he is an idiot.

SPACE AS "JELLO": Spacetime is normally thought of as three dimensions of space and one of time. But I like to think of it as four dimensions of space, where space is "squishy." That is, you have a lump of jello in your hand; shake, and it tends to "jiggle" -- it expands and contracts in different regions (the fourth spacial dimension). It is stressed, and there are compression waves, accompanied by expansion waves, so that our portion of the Universe can be thought of as being in a region of expansion.

“…Where did you get this information ... It's not like that…. Makkulling.djvu

… In the main work of Maxwell, the term "ether" is not used. Do not read Atsukovsky, he is an idiot..”

- again, in whole 19-th century, including in Maxwell theory, EM physical effects were considered as some disturbances in some ether, and just this “luminiferous ether” was cancelled by Einstein in 05 year of 20-th century. The linked Makkulling.djvu is only one of innumerous publications, where the authors tell about how bad some ethers are, and so how true the cancelling was;

- whereas in 1905 paper it was necessary to cancel ether since any reliable ether is fixed in absolute space, which was cancelled in the paper for principal reason – only in this case the postulate about constancy of the speed of light becomes be so fundamental that can be the fundamental base of a fundamentally new theory;

- where, really, the “speed of light” indeed was postulated as some omnipotent essence, and for its constancy lengths of moving bodies must contract, moving clocks must slow tick rates, etc.,

- and all that happens because of the once more SR postulate, which is based on the cancelling of the absolute spacetime - that all/every inertial frames are absolutely completely equivalent and legitimate; whilst any existence of the absolute Matter’s spacetime makes the new theory rather questionable.

However from the last postulate any number of senseless physical, logical, biological, etc., consequences follow, utmost evident and known is the Dingle objection to the SR; and “twin paradox”, which was known seems yet from 1906, and which really is two times applied Dingle objection: if all frames are absolutely equivalent and legitimate, then when the twin-traveler comes back, both twins must be simultaneously older and younger each other; what is evident biological absurdity.

The twin paradox was numerously “solved” in framework of the SR, though these “solutions” mostly used some tricks, besides only one – and very popular solutions, which is inevitably senseless, the Dingle objection [and any number of others] is fundamentally true; more see https://www.researchgate.net/publication/322798185_The_informational_model_twin_paradox http://vixra.org/pdf/1801.0415v2.pdf http://dx.doi.org/10.13140/RG.2.2.34064.51201/1

Unlike the numerous quite legitimate in official physics “solusers”, Einstein seems understood that the twin paradox cannot be solved in the SR, and sketched a solution basing on the GR, which was developed by Tolman; which, of course, is only a next strange mental construction, see the links above.

From this fact completely rigorously by the completely rigorous “proof by contradiction” it follows that Matter’s spacetime is absolute, that there exist the preferred frames that are at absolute rest in the absolute 3D space, etc.; more see the SS posts above and papers that are linked in the posts;

- And this space/time/spacetime fundamentally cannot be transformed by anything in Matter, including by the speed of light constancy; and by some strange in this case “masses” in the GR.

Correspondingly in that

“…The statement about the fallacy of general relativity is also absurd. Quantum gravity doesn't fit into the experimental database.… …."

- both claims are fundamentally senseless; since that is already few times quite clearly explained in the SS posts above; and, though, that continuous changes on microscale are logically, i.e. absolutely fundamentally, prohibited was completely rigorously proven more 2500 years ago by Zeno, in his really brilliant outstanding aporias – more see the posts and links in the posts.

Cheers

"It is stressed, and there are compression waves"

There is a lot of nonsense written in popular literature about gravity waves. But even there they do not speak of compression waves. Usually they talk about waves of distortion of 3D space. In fact, everything is much more complicated. It is correct to write waves as waves of anisotropy of the speed of light.

It is impossible to talk about the elasticity of spaces. There are no analogues among the bodies around us. Read what Einstein wrote about it 100 years ago.

According to Einstein, space is a collection of clocks and rulers.

Sergey Shevchenko ,

I have already told you that you do not know physics very well. I will add that the history of physics is also not your strongest side. Hence your strange ideas about general relativity. Einstein and Maxwell never considered space in their theories as something incorporeal, or vice versa as an elastic medium. They both came from experimental results. Maxwell used mainly the results of Faraday, his explanation with the help of "lines of force" of most of the phenomena. As a result, Maxwell introduced the tension tensor into physics. In relativistic form, it is the energy-momentum-tension tensor. Taking place both in mechanics and in electrodynamics and in general relativity. These are three different tensors describing different physical objects. But all of them, including two different spaces of Maxwell and Einstein, have energy density, energy flow. Moreover, both theories have equations of motion (each has its own equation), and field equations.

Read the 1920 article (I quoted it above.) In Russian, this is the last article in volume 1 of Einstein's collected works. http://eqworld.ipmnet.ru/ru/library/books/Einstein_t1_1965ru.djvu

You are doing what you do not understand. Hence the distortion of the problems of general relativity. The main problem of general relativity is the departure of the energy-momentum tensor and a full-fledged conservation law.

This task has been solved.

Preprint Точное уравнение гравитационного поля на основе эйнштейновск...

Preprint Exact equation of gravity field based on Einstein's separati...

Preprint Уравнение гравитационного поля и структура черных дыр

Preprint Gravitational Field Equation and the Structure of Black Holes

Present equations having been made of terms that are NOT exact expressions for Fields , A different analytical form is felt necessitated for the quantum field components, which is not to be found equivalent to existing relations . Hence intensity does NOT reduce exactly with distance squared.

Moreover , an effective relativistic quantum field theory, including weakfield quantum general relativity , does NOT bring out the interchangeability of spatial architectonics whose dynamics would necessarily support classical groups as of the elliptic genera .

Well, yes, the interaction in gravity is not proportional to the inverse square of the distance. This is not the only effect of general relativity. There is no quantum theory of gravity. These are all ugly hypotheses that partially work.

There is no need for hypotheses that don't work. While there is a full-fledged theory.

Dear Valery Borisovich Morozov,

- you next time repeat here some strange claims, whereas, including, in the SS posts above it is already quite clearly explained – why these claims are strange; and make that too vividly. So again

“……Einstein and Maxwell never considered space in their theories as something incorporeal, or vice versa as an elastic medium…”

- Maxwell, and all other physicists till 1916, never considered in their theories as something incorporeal, or vice versa as an elastic medium. In those time the medium for propagating E/EM fields was some “ether”, which, again – see the SS posts above – had some concrete material properties, i.e. “vacuum permittivity” and “vacuum permeability”, which by no means were some properties of “space”, that was ether in space;

- and, what is quite natural, in those times a number of ethers’ models existed, which, again, existed till 1905/ 1908, when all etherswere cancelled in 1905 SR version, and the space/time/spacetime obtained quite material properties - quite really “contracted space” quite really contracts material bodies’ lengths, quite really “dilated time” quite really slows real clock tick rates, etc.; and 1916 it was claimed that “curved spacetime” forces, say, Earth to rotate around Sun.

All these space/time/spacetime “materializations” were – and are, of course, till now – fundamentally illusory fantastic suggestions, which were postulated in the SR/ GR because the authors didn’t understand what are space/time/spacetime, since these fundamental phenomena/notions were/are fundamentally transcendent/uncertain/irrational in mainstream philosophy and sciences; and so “materializations” hadn’t - and haven’t till now any rational explanations – why/how that happen,

- nonetheless, since the transcendence above exists in the mainstream till now, the SR/GR are standard theories in physics.

Really, again, what are absolutely fundamental phenomena/notions “Space” and “Time”, and their actualization as the Matter’s spacetime, can be, and are, scientifically defined only in the Shevchenko-Tokarevsky’s “The “Information as Absolute” conception and informational physical model, the links see above.

And just therefore Einstein after 1916 attempted to develop of the “Theory of Everything”, “uniting” two known in his times “GR-Gravity” and Maxwell theory; however quite naturally failed; and this fact shows, that he was, nonetheless, professional physicist, and understood, that everything that turns out looks too strange to be a physics.

“ These are three different tensors describing different physical objects. But all of them, including two different spaces of Maxwell and Einstein, have energy density, energy flow. Moreover, both theories have equations of motion (each has its own equation), and field equations. ”

- again, there is no any “spaces of Maxwell” which “has energy density”; and there is no “field equations” in the GR, because of the physical notion [fundamental in this case] “field”, as that is rigorously defined in the SS&VT model above, relates only to fundamental Nature forces, and, though in official there exist numerous fantastic “fields”, say, “Higgs field” , “inflaton”, etc., nonetheless even in these cases the fields exist in space, and by no means are “spaces” – and so in the GR there is no Gravity “field”, since observed gravitational effects are caused/determined by space/time/spacetime.

“…the interaction in gravity is not proportional to the inverse square of the distance. This is not the only effect of general relativity. There is no quantum theory of gravity. These are all ugly hypotheses that partially work. …”

- the interactions in Gravity at statics really are proportional to the inverse square of the distance, and deviations from this Newton’s law appear only if in a system of gravitationally coupled bodies the bodies are moving. In this case the gravito-magnetic force appears, inertial mass changes in Lorentz factor, etc.; however, again, all that must be taken into account on the indeed scientific theory of the fundamental Nature force “Gravity” in the Matter’s fundamentally absolute, fundamentally flat, and fundamentally Euclidian, [5]4D spacetimewith metrics (cτ,X,Y,Z,ct), which fundamentally cannot be – and so really isn’t - “contracted”, “dilated”, “curved”, have some “energy-momentum-tension tensors”, etc.

And to

“…I have already told you that you do not know physics very well. I will add that the history of physics is also not your strongest side. …”

- yeah, that was so; and in that case in corresponding SS post it was explained, that such claims are indeed very popular bazaar practice, where [in bazaars] the main rule in any discussion is “who first said “you are the fool”” wins in the discussion;

- and now this practice is rather popular in recent scientific community, so a lot of “outstanding” physicists, who really only composed/compose full stop physics, have became be outstanding by using this rule. In this case you attempt to claim yourself as some “outstanding” one, whereas really writes some too questionable physics; and when it is explained that this physics is strange, use another bazaar discussion rule – write vividly posts shifting the explanations from visible page.

Cheers

Dear Sergei Eremenko,

What media is curving in General Relativity? Nothing is curved. The Ricci tensor partial differential equation of GR includes time. Changes in momentum are non-linear and curves over time as you implied. As to your questions:

Your questions: "Can quantum vacuum of virtual particles be that media? Does curvature of spacetime means uneven distribution of that quantum vacuum?"

A better name for the quantum vacuum is the Zero Point Field (ZPF), The field is made up of particulates vastly smaller than virtual particles. Virtual particles are the largest particulates of this field. And yea, the curvature of spacetime does mean the uneven distribution of the ZPF. In particular it means density variations and flows of this field surrounding matter. The ZPF density and field pressure surrounding all matter is less than it is away from matter. This density difference pushes matter together. The atmospheric-like pressure of the field is 6.6743015 × 10−11 Newtons. This is the force factor of the gravitational constant G.

Forrest Noble

the Zero Point Field (ZPF) is no more than Phantasmagoria .

Most Respectfully

REZA

Dear Reza Sanaye,

"Phantasmagoria," cool word. I could see that it had the root-word fantasy within it.

Your quote: "the Zero Point Field (ZPF) is no more than Phantasmagoria,

Most Respectfully"

Of course we know the ZPF is real. As Zero Point Energy we have been observing it and have accepted its reality for more than 70 years. As to its virtual particles, we have been observing and acknowledging them for about 40. As to it being a particulate field of even smaller particles, is presently a hypothesis, but IMO this hypothesis will eventually become mainstream theory,. And because of the evidence as to its physical, aetherial nature, not just an energy field, it will also be realized as fact IMO.

https://www.universeofparticles.com/an-aether-of-zero-point-particles/

https://en.wikipedia.org/?title=Zero_point_field&redirect=no

Dear Sergey,

The theory has never been created not on the basis of any model. Only experiments formed the theory. So it was with the electromagnetic theory, so it was with general relativity, and so it will be in the future.

Tellingly, modern inventors of media know little about the physics of gravity. R. Feynman (undoubtedly one of the greatest physicists) gave a lecture on quantum gravity, which was published in a book. But the author took the wrong path. Thousands of ugly models appeared that were not suitable for creating a full-fledged theory. Rubbish. As a result, we are as far from creating a quantum theory of gravity as we were a hundred years ago.

At this time, classical general relativity is developing. It successfully gets rid of serious flaws. Preprint Exact equation of gravity field based on Einstein's separati...

Preprint Gravitational Field Equation and the Structure of Black Holes

The quantum theory of gravity should be a continuation of general relativity. To do this, you need to know the classic well. Unfortunately, an army of ignoramuses is engaged in this.

"Zero Point Field" well studied and not suitable for the role of the carrier of gravity. The interaction with the substance of the physical vacuum (as it is called) is too strong in comparison with gravity. This interaction is well measured with high precision. But the main thing is this field is easily screened, which follows from the experiments of the Casimir force. By the way, this topic is very popular, Feynman laid the foundation. But Feynman himself, after giving lectures, never returned to this topic. It doesn't take a genius to understand - it's a dead end.

Very good question points to a weakness in epistemological issue with GR.

There may be progress if they are able to answer more concretly why a priori concepts like space and time (Kant) should bend with matter.

How about old fashioned aether?

As to "nothing curves" sounds logical, but is an evasion.

Start explaining why one would write (ds)^2 = g(i,j) dx(i) dx(j) to begin with.

Dear Valery Borisovich Morozov,,

Yes, at the quantum scale the ZPF is relatively strong. But IMO at the distance scale of GR the atmospheric-like pressure of the ZPF on all matter is 6.6743015 × 10−11 Newtons, the force factor of the gravitation constant G. This is the only certain background field in existence. All others are hypothetical, and most of these don't even exist IMO, examples being dark matter, dark energy, the Higgs field etc.. Others have their basis primarily in the mathematical modeling of quantum physics.

Sergei, - Paraphrasing, you ask: Can the quantum vacuum be the media that is being curved in General Relativity? In 1955, John Wheeler proposed that the quantum vacuum is a locally violent sea of Planck length vacuum fluctuations that he named "quantum foam". These fluctuations creates both vacuum zero-point energy and the uncertainty principle. If this model is assumed, the quantum vacuum becomes a very stiff elastic medium that propagates waves at the speed of light. If the fluctuations are predominantly at Planck frequency, then this medium has quantifiable impedance and bulk modulus.

This model of the quantum vacuum makes falsifiable predictions discussed in the article below. For example, this model predicts that the gravitational force between two electrons is closely related to the electrostatic force between these two electrons. This prediction is proven correct by showing how both the gravitational and electromagnetic forces are distorting the quantum vacuum in related ways.

www.researchgate.net/publication/353049276

If something is curved, there should be something deformed. So, one has to get involved in theory of elasticity. I think, the Sakharov's view of gravitation as the elasticity of space sheds light on this point, and it needs to be further improved.

Dear Güngör Gündüz ,

Very well! But the elasticity of space-time is not related to gravity (except gravitational waves), it is related to light and its energy.

A photon is generated when an atom goes from a state of more energy (more curvature of space-time) to less energy (less curvature) that elasticity is what generates light moving as an impulse through the 4 dimension.

Here is the calculation of the wave function (chapter 2.6):

https://doi.org/10.13140/RG.2.2.19015.96168

And here the photon energy calculated using classical physics

https://doi.org/10.13140/RG.2.2.19090.27846 (chapter 2.2 and chapter 2.5)

“…The theory has never been created not on the basis of any model. Only experiments formed the theory. So it was with the electromagnetic theory, so it was with general relativity, and so it will be in the future…..”

- that the base of any scientific theory must be only experimental results – that is fundamental law. However at that it is necessary to understand, that at experiments only some material interactions of studied material objects and material objects “instruments” happen, including digits on monitors that indicate measurements results are nothing else than some interactions of EM pulses with concrete material objects, say, LED screen.

Correspondingly the experimental results aren’t some digits, the results are always only “digits+interpretations”, the last are in framework of concrete theory, hypothesis, model, etc.,

- and the interpretations can be really fantastic, but adequate to the reality; the theory that Sun rotates around Earth was in whole accordance with experiments, and worked well enough, Columbus using this theory at navigation well had traveled from Europe to America and back.

Though in this case there are [at least] the couple of exclusions – the SR and GR, where basing on experiments that discovered that moving in 3D space material bodies are contracted, and intrinsic processes in moving bodies are slowed, postulated that these effects are caused by Matter’s space/time/spacetime impacts,

- in spite of the observed physical effects happen with concrete material objects, and at that any just “space contraction”, “time dilation”, etc., never was observed, whereas any body evidently isn’t a “space”, and any clock isn’t “time”; and the illusions appeared only because of the authors didn’t understand – what are [absolutely] fundamental phenomena/notions “Space” and “Time”, and their concrete actualizations in concrete informational system “Matter” as the Matter’s concrete spacetime.

Correspondingly the SR/GR are really completely ad hoc illusory mental constructions, which really have no any experimental confirmation; but are standard official physics theories, and are rather vividly “corrected” in a lot of “modifications”, including that are on RG and this thread,

- where the postulated in the SR/GR fantastic “material” interactions of the space/time/spacetime and material objects are postulated as well,

- in spite of such interactions are fundamentally impossible; that is rigorously proven in the Shevchenko-Tokarevsky’s “The Information as Absolute” conception https://www.researchgate.net/publication/260930711_the_Information_as_Absolute DOI 10.5281/zenodo.268904, and

the informational physical model, which is based on the conception, for first reading see https://www.researchgate.net/publication/355361749_The_informational_physical_model_and_fundamental_problems_in_physicsand more in detail see

https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics , https://vixra.org/abs/2109.0045 ; https://arxiv.org/abs/0707.4657

Correspondingly that

“…Tellingly, modern inventors of media know little about the physics of gravity. Thousands of ugly models appeared that were not suitable for creating a full-fledged theory. Rubbish. As a result, we are as far from creating a quantum theory of gravity as we were a hundred years ago.…..”

- is correct, and that is quite logically inevitable fact, since existent numerous “Quantum Gravity theories” are developed only as some attempts to “quantize” the GR, what is fundamentally impossible, and so these mental constructions are evidently senseless – but are quite legitimate now in official physics, in spite of fundamentally have no any experimental base.

“…If something is curved, there should be something deformed. So, one has to get involved in theory of elasticity. I think, the Sakharov's view of gravitation as the elasticity of space sheds light on this point, and it needs to be further improved. …”

- again – see above – nothing can be “curved”, “transformed”, etc., in the Matter’s fundamentally absolute, fundamentally flat, and fundamentally Euclidian, [5]4D spacetime with metrics (cτ,X,Y,Z,ct),

- where the utmost fundamental Matter’s “material base” – “ether”, which is the [5]4D dense lattice of [5]4D fundamental logical elements [FLE] is placed, and practically everything in Matter is determined by the logical construction and properties of FLEs.

This lattice isn’t elastic, etc., everything in Matter is/are some disturbances in the lattice, which propagate with 4D speed of light in the lattice in accordance with a small number of logical links; as, say that would be in a 3D hard disk, where memory bits flip each other in any direction by some program [though the Matter’s lattice is 4D hard dick, and Matter is fundamentally automation – see 2-nd link above]

More see the SS posts above and links in the posts; though last time in the thread rather strange scientifically, but vivid, posting appeared, nonetheless for the reads it is enough a few mouse clicks on “Show previous answers” option, and for convenience the basic links are repeated here.

Cheers

Dear Sergey Shevchenko ,

Rigorously proven does not mean writing a collection of bullshit without a single equation.

Rigorously proven means giving anyone the necessary tools, in this case mathematics, so that they can verify it.

You are light years away from rigorously proven and something minimally related to science.

The electromagnetic wave model was created in the middle of the 19th century. Then people were more educated and understood that the electromagnetic "ether" has the property of quasi-elasticity (Boltzmann's model). True, this model does not explain Coulomb's law.

That is why electrodynamics in combination with the special theory of relativity accurately describes the motion of charged bodies and electromagnetic waves. With a modified interpretation, Maxwell's equations work in quantum mechanics.

Article On the question of the electromagnetic momentum of a charged body

Dear Stefan Bernhard Rüster ,

From the point of view of a mathematician, Λ is the integration constant of the Einstein equation. It is related to the boundary conditions, but not to the mass of the attracting center. Of course, the field and its energy density change from the boundary conditions.

You know very well that Einstein's equations are not exact. There is a good replacement for this equation. It changes almost nothing in weak fields.

Preprint Gravitational Field Equation and the Structure of Black Holes

Stefan Bernhard Rüster

When we take them seriously PHYSICALLY , then we come across many falsities and paradoxes ..........

respectfully

REZA

Stefan Bernhard Rüster,

The gravitational field equation is a system of partial differential equations. To solve it, it is necessary to set the initial and boundary conditions. In stationary problems, g00 = 1-1/r is given at infinity. as a result, we have a solution with Λ=0. We always obtain such a solution if we have the Minkowski space in the limit. Therefore, the Λ term is omitted in the Einstein equation. It is not in my equation either.

Dear Stefan,

you can easily check this by looking at the limit at infinity of your solution to the Einstein equation with Λ. It is different from the Schwarzschild limit.

Best regards, Valery

Stefan Bernhard Rüster

do you mean we have tinier than the Schwarzschild limit ??

Dear Stefan,

"But who tells, that the Schwarzschild limit is correct?"

Schwarzschild solved the problem and solved it. You also set a problem and solved it. Physics consists of problems and their solutions. It remains to compare the solutions with what we observe in nature. If something does not agree, everyone forgets about the decision. If the efficiency of the process is 0.01, this is good.

Best regards, Valery

I want to draw your attention. For any Λ, the covariant divergence Mki,k =0

I think people know what causes curvature and what mathematics in GR

reflects this.

The question of what curves is still not answered.

The spacetime interpretation claims that it is spacetime itself which is curved. Other interpretations are not allowed in the mainstream. While the situation in quantum theory is too confused that now discussing different interpretations is allowed, discussing different interpretations of GR remains anathema.

This is polemical? Yes, of course. But it is the result of the experience. I have defended the Lorentz ether interpretation of relativity and extended it to gravity. No freak nonsense, but published in a peer-reviewed mainstream physics journal:

Schmelzer, I. (2012). A Generalization of the Lorentz Ether to Gravity with General-Relativistic Limit. Advances in Applied Clifford Algebras 22(1), 203-242, resp. arxiv:gr-qc/0205035.

The reaction is complete ignorance, attempts to contact mainstream scientists by mail remain unanswered, presentations in forums handled like as this would be nonsense of the typical ether freaks. No argumentation about the content.

Whatever answer differs from "the medium curved is spacetime itself" will be ostracized too. While the mainstream answer is obviously metaphysical, thus, there is no empirical evidence which would allow to distinguish it from the Lorentz ether or possibly other interpretations, you have to accept it without any questioning if you want to do physics in the mainstream. Such is life.

And as long as there is no independence of scientists, which would require some minimal job security for physicists, this will remain so. Developing alternative approaches is a luxury which can afford only those who don't have to apply for grants to survive.

The Lorentz ether interpretation is relevant for this question because it shows that the medium can be a quite classical one, following the basic equations of classical condensed matter theory - continuity and Euler equations.

Ilja Schmelzer ,

Everything is correct. This is the reaction to your childish pranks.

Valery Borisovich Morozov

without any justification of your claim, it is your claim which qualifies as a childish prank.

Dear Stefan,

If I am not mistaken, the solution to the problem of the field of a point source for nonzero Λ diverges at infinity. This is true?

Best regards, Valery

Dear Stefan,

I'm pretty sure your work is applicable to describing the rotation of galaxies. But the asymptotic behavior with nonzero Λ shows that not everything is clear at this point.

I think it's a good idea to use Einstein's equation (or some other equation) to describe the motion of stars in galaxies.

Best regards, Valery

A friend of mine from Haifa who deals with issues close to general relativity, read my article and wrote - "Wonderful work. You once again proved that all ingenious is not simple but very simple."

HI Stefan Bernhard Rüster , you kindly provided classical GR geometrical interpretation (two purely mathematical tensors), but the question is deeper - about the essence of a 'medium' of space. Can GR curvature be associated with uneven distribution of Quantum Vacuum, Zero-point energy field, or anything else? What space is 'made of'? If space is empty it seems nothing to 'curve'

Hi Ilja Schmelzer - after your 2012 publication, how your views evolved regarding the core question what space is made of and what is curving? Space seems holds energy (via Quantum Vacuum states, Zero-point energy or maybe Higgs field?); how this energy distribution related to purely geometrical GR interpretations?

A good question that provokes fundamental issues in physics. Space-time, like matter, has two dual aspects. I made an answer to part of your question which you may read at

Preprint Matter aspect of the space-time: A viscous fluid

Thanks, professor A. I. Arbab for your ideas of spacetime fluid model. By this discussion, I am trying to find the physical meaning for 'Atomic Solitons' - Article Atomic solitons as a new class of solitons

Conference Paper Atomic String Functions and Spacetime Quantization

Ilya, Stefan

Well, you give me the usual answer, it is space time itself curves, reflected

in the metric tensor g(i,j). That anyone questioning this will be banished from Physics for X number of years.

The trouble with this is to explain a possible distortion in the energy background,

which would explain gravity better.

For example two objects which float on the surface of still water are cause to attract. (Or that the distortion causes a price in energy, that must be lessened)

Therefore this explanation revolving around spacetime alone seems not suficient.

If you cannot use energy, what other variable must be minimized.? I think Hilbert

managed something like this.

Know something?

Concepts that seem to be unclear:

GR has nothing to do with any quantum concept of vacuum or energy, much less with fields.

GR shows that fields do not exist, everything is due to geometry, matter and gravity are curvatures. Relativity is incomplete because it does not take into account the gravitational field?

Absurd, you have not understood anything, there is no gravitational field.

A hose bends, right? What is it that bends in a hose? The matter. But how is it possible that it bends if I am the size of an atom and I see several holes without matter? Because on a larger scale it also curves. Do you see a void between Earth and Mars? On a scale of Galaxies, this void does not exist, Matter and gravity are only curvatures

I recently entertained a model where the universe is filled with a scalar field governed by the Klein-Gordon equation. Such a matter content can allow a quantum vacuum to be prevailing and parameterized by a cosmological constant (vacuum). The conformal Einstein equations bring about an additional contribution that could act as residual energy attributed to the vacuum. You can read this at

https://www.researchgate.net/publication/355757221_Scalar_field_and_particle_dynamics_in_conformal_frame

Stefan Bernhard Rüster , "I found both, the energy-momentum density tensor of the gravitational field and the conservation law!"

Me too.

Best regards, Valery

Thanks, A. I. Arbab . Is it Higgs scalar field , as per https://www.insidescience.org/index.php/news/two-physicists-share-nobel-prize-higgs-discovery and https://sitn.hms.harvard.edu/flash/2012/issue125b/ "...permeates the entire universe"? How is your scalar field related to Higgs?

Dear Sergei Eremenko

not much has changed. Except that I now think that gravity with EEP appears in many very different physical systems. One has to look at the proof of the EEP to see this: Take a flat Newtonian background and put something (whatever it is) inside. Assume a Lagrange formalism. Then look at the Euler-Lagrange equations for the preferred coordinates (Cartesian for space and absolute time). Assume translational invariance for these coordinates, and you have conservation laws. Assume that the Lagrangian has also O(3) invariance for Euclidean rotations, and, even more, preserves also some 4D quadratic form so that the full symmetry of the Lagrangian is O(3,1) or O(4). This makes the stress-energy-momentum tensor T^mn found in the conservation laws a symmetric 4D tensor.

Then, simply define the gravitational field by g^mn sqrt |g| = T^mn. You make the transformation of the coordinates so that beyond this the preferred coordinates remain unchanged and everything else becomes "matter fields". This should not change the Lagrangian itself, and also preserve the Euler-Lagrange equations for them. So we have a Lagrangian for gravity and matter fields and know the Euler-Lagrange equations for the preferred coordinates - they are the harmonic condition. But the harmonic condition does not depend on the matter fields, thus, the Euler-Lagrange equation for the matter fields will not depend on the preferred coordinates too - action equals reaction. That's the EEP.

So, the gravitational field with EEP will appear in almost everything. All you need is to identify the stress-energy-momentum tensor for translations in the background and name it the gravitational field. I'm actually writing a paper where I extend this to quite general lattice theories embedded into a continuous Newtonian background space. The situation appears similar. The lattice theory becomes one where the preferred coordinates are defined on nodes and the gravitational field by a scalar on edges. Dual to the Regge formalism - it is the g^mn sqrt |g|, not the g_mn, which are defined on the edge. They define the d'Alembert operator on the lattice, and box x^m(n) will be the harmonic condition.

So, even for lattice theory the derivation works, and almost nothing is necessary to prove this. But this means that simply based on the equations of the gravitational field and the fact that the EEP holds one can say almost nothing about the medium itself.

Juan Weisz

" I think people know what causes curvature and what mathematics in GR

reflects this.

The question of what curves is still not answered. "

very Dear Juan

It will never be answered

there is NO spacetime curvature

respectfully

REZA

Ilja Schmelzer

" Schmelzer, I. (2012). A Generalization of the Lorentz Ether to Gravity with General-Relativistic Limit. Advances in Applied Clifford Algebras 22(1), 203-242, resp. arxiv:gr-qc/0205035.

The reaction is complete ignorance, attempts to contact mainstream scientists by mail remain unanswered, presentations in forums handled like as this would be nonsense of the typical ether freaks. No argumentation about the content. "

very dear Iljaa !

I feel VERY proud of you

It was a wondrous piece of rationalistic science

I congratulate you for possessing the mind capable of writing such articles ...................

yours

REZA

It is not so clear to me that energy density is a purely quantum concept, after all

you find it also in EM.

Hilbert minimized someting callled h, what is it?

Hmmm. On the visible page 2 days ago posts are, what quite-quite differs from the case, when after unique in last days rational SS post 3 days ago now the vivid bazaar – i.e. as aggressive and unscientific spamming – posting appeared, and this post was shifted from the visible page in 5 hours.

So more see the SS post 3 days ago now, here only note that the last posting is again based on the fundamentally non-adequate to the reality GR postulate that gravitational interactions are caused and determined by mystic interactions in the systems “mass-spacetime-mass” , and that is standard postulate till now in official physics;

- because of for the author of GR , and for standard physicists, the fundamental phenomena/notions “Matter”, “Space”, “Time” were, and are, completely transcendent/uncertain/irrational, and so prescribing for these phenomena/notions some transcendent properties and effects was, and is, logically completely inevitable fact. A couple of examples:

“…GR shows that fields do not exist, everything is due to geometry, matter and gravity are curvatures. Relativity is incomplete because it does not take into account the gravitational field?

Absurd, you have not understood anything, there is no gravitational field.….”

- that is quite clear official physics claim about what “GR shows”, whereas really GR shows nothing, it completely ad hoc, having really no any rational and/or experimental grounds, postulates the strange things in the quote above; whereas any rational grounds in this case fundamentally cannot exist,

- nothing can happen “due to geometry” really, and that “matter and gravity are curvatures” looks as too strange claim even in official physics, where matter is some “curvature” only in so evidently strange mental constructions [“string”, “loop-quantum”, “M-“, etc. theories] that these constructions, though are quite legitimate in official physics, aren’t standard theories.

Again, the Matter’s fundamentally absolute, fundamentally flat, and fundamentally Euclidian, [5]4D spacetime with metrics (cτ,X,Y,Z,ct), fundamentally is nothing else than [5]4D empty container, where Matter as a whole, and every material object – particles, fields, bodies, etc., exists and constantly changes at the objects’ interactions, which are determined by fundamental Nature forces and the corresponding Forces’ fields. Including Gravity completely fundamentally is nothing else than the “fourth” fundamental Force, which is mediate gravitational interactions by its field.

Again, the emptiness fundamentally cannot be impacted by, and fundamentally cannot impact on, any material object. As well as the emptiness fundamentally hasn’t some intrinsic measure, and so, say, any attempt experimentally to observe some “spacetime curvature” are fundamentally impossible – and, of course, any experiments, where some just “curvature” really fundamentally could not, and so never, were made.

Though in this case it looks as more clear to tell about other spacetime transformations, which are, of course also fundamentally impossible, however are postulated in the SR in 1908, that in this case doesn’t principally differ from the GR curvature, i.e., say, “space contraction” and “time dilation”

- nobody and never observed/observes these effects, if hadn’t/hasn’t some mental problems, nonetheless the true SR believers soon 100 years quite frankly believe that muons that are created in Earth atmosphere with Lorentz factors large enough really reach the surface because of that they “contract space” and “dilate” time;

- in spite of such belief is possible only at a childish look on environment, when the believer knows only that about muons above, and quite natural for any normal adult human thoughts that muons in full accordance with the SR contract and dilate not only “Earth atmosphere”, they also contract and dilate everything in Matter, including Earth, and everything on Earth, including all/every believers, are blocked in the believers seems on subconscious level,

- whereas, if the SR is correct, than, since billons of muons in Earth atmosphere are created in 4π directions, and so the believers must be constantly rather bizarrely contracted up, sometimes to atoms sizes, etc.

However really, thank heavens, everything on Earth, including the believers’ bodies, take completely no attention to what happens in the space/time/spacetime when some muon, electron, etc., moves in space.

And, say, when a “matter-curvature” in the quote above, say, “a boxer” in a ring, hits the jaw of an other curvature “other boxer”, he curves well usually only the jaw; and nothing becomes be curved in the ring, stadium, viewers, on Moon, etc.

Again, the development of the really scientific Gravity theory can be made only basing on the postulate that Gravity is nothing else than the fundamental Nature force, which is similar to fundamental Electric/EM Force,

- and basing on the Shevchenko-Tokarevsky’s informational physical model, see https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics ; https://arxiv.org/abs/0707.4657, section 2.9 “Mediation of the forces in complex systems”;

- and on experiments, where really non-observable in official physics Gravity traits can be studied, first of all

- the quantum nature of Gravity in https://www.researchgate.net/publication/215526868_The_informational_model_-_possible_tests ; http://arxiv.org/abs/0706.3979 ; at least the section 2.1.2. “Monochromatic photon beam distortion”;

- and that confirm that everything in Matter has gravitational charges in https://www.researchgate.net/publication/277710038_The_informational_model_-_gravity_a_next_experiment DOI: http://dx.doi.org/10.13140/RG.2.1.4502.8008

Cheers