Gravity has puzzled modern researchers in its inability to be incorporated into the unification models and in its lack of microscipic origin. I proposed a way to call this aim complete by discrediting gravity.
A solution might be to disgard it as force, a path taken by Einstein in GR in 4D.
However, few advanced this path. My idea is that gravity should be seem as a force by convetion, a pragmatically labeled as a force one because systems described by thevpresence of this phenomrnon or effect are equivalent to systems with real forces. This unification of forces is complete.
The New problem is to give rational or justification of this convention. If we stand with GR, we must give reasons the spacetime in presence of mass gives geodesic motion that resembles force-mediated motion in 3D.
There must be a category of phenomena that share many aspects of common force dynamic phenomena but are not genuine.
Also, there must be something unique with spacetime that generates these. Maybe at its macroscipic level some phenomena lead to this behavior, which is pseudodynamics.
Gravity is described by a force in the Newtonian approximation and by the dynamics of the metric of spacetime more generally. And it’s possible to recover the Newtonian description from general relativity by a well-defined limiting procedure. So that’s understood. It’s a fundamental force in the sense that it describes the dynamics of spacetime itself and is similar to the other forces in that it, also, expresses a ``gauge principle", namely invariance under general coordinate transformations. It is different from the other forces in that its gauge group is noncompact and infinite-dimensional, whereas the gauge groups of the other known forces are compact and finite-dimensional. These differences imply that it’s not possible to count the configurations of spacetime geometries in the same way that it’s possible to count the configurations of the fields of the other interactions and is one way of understanding how spacetime singularities can arise. How to resolve them and count spacetime configurations in general is an open problem.
Dear Philippos Afxentiou
One of our mistake is, we do not consider our universe as a complete entity, as Mr. Einstein calculate everything is mechanical. when you study GR, it is all about one sun, three planets, and one moon...When you investigate earth's gravity, it is working under Pressure, Temperature, and mass of object, not Newtonian 9.81 weight. This unprecedented article proves it.
Article Earth Gravity is not Newtonian
Article Why Einstein's Theory of Gravity is wrong!
Good question
General relativity can and does consider the universe as a whole and it’s not limited to the study of single particles. It would be useful to actually learn it. Mathematically it is consistent and it does provide results consistent with experiments, so it isn’t wrong. It is incomplete, since, while it does provide a framework for describing spacetime singularities, it doesn’t provide a way for resolving them. How to do so requires going beyond classical gravity. Incompleteness≠inconsistency.
It's, also, not obvious, whether fields, beyond the metric of spacetime, are necessary to describe it; examples are ``scalar-tensor theories'' (that include a scalar field, that can't be identified as a matter field), first introduced by Brans and Dicke in the late 1950s, early 1960s and supergravity, that was introduced in the 1970s. For the moment, though, it appears that general relativity, i.e. a description of spacetime that involves just the metric, is both necessary and sufficient. (Incidentally, the cosmological constant is part of general relativity; that its numerical value was measured in 1998 doesn't mean that its presence isn't consistent with the properties of general relatvity, namely general coordinate invariance.)
Incidentally, nobody cares whether some theory is wrong; what matters is what theory is correct. That’s why the statement that ``Einstein’s theory of gravity is wrong" isn’t interesting... One doesn't become famous, by poining out that someone else is wrong, but by showing what the right way of doing things is. Once general relativity was invented-by Einstein, as regards the equations and Hilbert as regards the variational principle, it became part of physics and everybody who studied it could and many did contribute and still are doing so.
Mathematic is the greatest tool for our innovation, but it is wrong tool for nature that Mr. Einstein used it. Mathematic equation is a flat, one dimension that does not consider Temp & pressure, and wrote in past, while nature is constantly change in three dimensions.
Science must be easy to understand not esoteric that Mr. Einstein himself could not explain it. Reading new things is good.
Evrything is easy to understand, one must, however, learn it, first. It would be good to actually learn general relativity and mathematics is the language that's necessary to actually understand anything and compute anything that makes sense to compute. This: Article Lecture Notes on General Relativity
might be a good place to start.Once more, focusing on any particular person (like Einstein) doesn't make sense.
“…Is gravity a force by convention only? If so, what makes it so similar to fundamental forces &how spacetime creates a "force effect" ?…..”
Really Gravity is fundamentally real – the “fourth”, non-existent in mainstream physics, since the GR is standard theory in physics, fundamental Nature force, as that Weak, Electric and Strong forces are;
- whereas spacetime fundamentally cannot create any “force effect”. Matter’s spacetime is the fundamentally absolute, fundamentally flat, and fundamentally “Cartesian”, at least [7]4D spacetime with metrics (cτ,X,Y,Z,ct), which is fundamentally nothing else than some infinite “empty container”, where Matter exists and always, because of energy conservation law, evolves. Emptiness fundamentally canot be affected by anything in Matter, i.e. cannot be “contracted”, “dilated”, “curved”, etc.; and fundamentally cannot impact on anything in Matter.
More about what is Gravity [and Electric] forces see the Shevchenko-Tokarevsky’s 2007 initial model of Gravity and Electric Forces in
https://www.researchgate.net/publication/365437307_The_informational_model_-_Gravity_and_Electric_Forces
Cheers
The flip side of the solution presented in the original post could be that the other forces are derived from gravity. For example: (7) How can gravity be seamlessly combined with the other three forces? (quantum gravity) | LinkedIn
Gravity is Space-Curvature-Geometry in GR. So GR completed with Thermodynamics should come up with Quantum Gravity should come up with inertial force. A first step to understand this concept might be the following: Conclusions from the Principles of Thermodynamics
Gravity should not be considered a force because it affects all matter and fields the same way. We recognize the electromagnetic force because it acts only on charged particles, for instance. We recognize forces in general because they act on some things and not on others. Gravity affects everything In the same way, and thus is a property of spacetime itself. Read my arXiv paper with title The Structure of Local Gravity Theories.
"Gravity should not be considered a force because it affects all matter and fields the same way." (you can not shield gravity (mass) but electromagnetic fields (charge).)
Yes that of course (Einsteins interpretation only to use field as the base camp of all) is and remains correct.
I only said: if GR is based on the principle: "inertial force (say Newton) and gravitational force (say Newton and Einstein) cannot be distinguished" then I believe that in the future Quantum Gravity is based on inertial mass (not zero (rest) mass quants, so no Gravitons!). So only inertial mass exists in quantum G-field approach! In this sense Quantum Gravity is from Momentum Exchange and Conversation-Law applied as well. (Local Gravity Theory from my point of view.) And the structures is based on the FSC alpha from GR combined with Thermodynamics to be derived only this way! QED fails since 1916 to solve this question about alpha)
And than we can use inertial force for that ( old gravitational force from Newton). In Quantum Space only dynamics exist! (Static does not exist in Nature, see Einsteins "my greatest blunder") But in macro space it is (than possible to use) an approximation: To use Einsteins Geometry as an equivalent field-interpretation being geometry.
By the way mass-quants (non zero restmass) are the field-particles of the G-Field while photons are the mass-quants (zero restmass) of electromagnetic field and so on....
See: manfred geilhaupt john wilcoxen "Universe and large numbers in between" from 2000 internet 2005. Or Derivation of the FSC from GR+TD or Conclusions from Thermodynamics. Research square.)
“……Gravity should not be considered a force because it affects all matter and fields the same way. We recognize the electromagnetic force because it acts only on charged particles, for instance. We recognize forces in general because they act on some things and not on others…”
- that is rather strange claim, from that indeed, 3 existent in the mainstream physics fundamental Nature forces, i.e. Weak, E/EM and Strong Forces, act specifically by no means it follows that there cannot be some universal Force that acts on any/every particle, i.e. that any/every particle has the Gravity charge – “gravitational mass” , and just that is really observed in Matter.
Correspondingly that
“….Gravity affects everything In the same way, and thus is a property of spacetime itself..”
- looks as some questionable claim, from that all/every particles interact gravitationally by no means it follows that Gravity is some property of spacetime itself; though this really strange - and fundamentally incorrect - claim is postulated in the GR; and is used in innumerous published versions of the GR applications in concrete cases,
- when, say, at applications the GR such strange fantastic for any normal human physical objects as “black” , “white”, “worm”, etc., “holes in spacetime”, etc., are “discovered”.
That happens in the mainstream physics because of in the mainstream – and for the authors of the GR, etc., the really fundamental phenomena/notions, first of all in this case “Matter”– and so everything in Matter, i.e. “particles”, “fields”, etc., “Consciousness”, “Space”, “Time”, “Energy”, are fundamentally completely transcendent/uncertain/irrational,
- and so all theories, including the GR, really are based now on only some really transcendent ad hoc, by no means grounded really scientifically, in the SR/GR fundamentally transcendent illusory, postulates; in the GR that has too indirect relation to what exists and happens in Matter at all, and so from the GR the fantasies above are really quite legitimate.
Really scientific physics is possible only if the phenomena/notions above are scientifically defined, what is possible and done only in framework of the 2007 Shevchenko-Tokarevsky’s “The Information as Absolute” conception, recent version of the basic paper see
https://www.researchgate.net/publication/363645560_The_Information_as_Absolute_-_2022_ed
- and more concretely in the informational physical model, which is based on the conceptions, two main papers are
https://www.researchgate.net/publication/367397025_The_Informational_Physical_Model_and_Fundamental_Problems_in_Physics ; and
https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics
More, including about what really Gravity and Electric Forces are, see the SS post on page 1, 3 days ago now.
Cheers
Gravity is a force *for sure*.
This can be - easily - seen and understood by analyzing the recent confirmation of the Quantum of gravitstional force as predicted by my Wolfram IMS-2015 conference paper (pls. see and download from my RG home) claiming to be a force of simplified 3/c^4 in SI system (exactly 3/(299792458*10^3)^4 Newton or VAm/s to be precise).
Recent research of mine to be published imminent now confirmed my 2015 hypothesis to be *physically correct* by giving iSpace exact (symbolic - not only somehow numerically approximated to some order!) same value when multiplying undoubrly physical Planck-force by the finestructure constant of gravitation (alphaG) *squared* (!!) using:
Planck-force = c^4/G
alphaG = (me)^2/(Planck-mass)^2
with me being just the electron mass. Do your homework, get the values and check for yourself! When a force is multiplied by a unitless other primary constant of nature, it naturally remains a force. If said force is equal to totally different way derived iFg (the ddrives iSpace quantum of gravitational force) than that is never just coincidental.
Instead of doing your homework you might however just read my papers as published on RG about the geometry, exact value and inner geometric relations of constants of nature themselves, or you watch the 2h+ Youtube video of TEGS group online since yesterday where all this is both revealed, summarized and fully explained by me at the same time:
https://www.youtube.com/watch?v=EhGeANkwUME&t=8035s
Gravity, in my opinion is somehow a force, but a different one than electromagnetism (Balance of forces, Energy conservation)
While in Quantum Physics (Electromagnetism 1=1), Gravity is the input of "Life". So it is a force, but not balanced. No energy conservation for all universe applies to it.
Gravitation is a force at a first order approximation(Newtonian), it is not a vector at higher orders. General relativity is a model which considers higher orders in gravitation, only the Newtonian potential is representable, not the force since space time diffeomorfism cannot produce work.
Bottom line, gravity is not a force. Gravity affects everything the same way but forces do not.
Or … all of current physics is plain outright disastrous wrong.
Because this is the logical fair valid alternative nobody does dear or even think to consider.
Well - i bet on iSpace.
Watch my video - and *learn*.
bottom line, General Relativity is a limited model of Gravitation which is not able to contemplate gravitation as a force
Naturally, gravity, i.e., the value of the gravitational force depends on the properties of our reference space. Meanwhile the "basic value" of the force depends only on the mass that created it (the source of the field), and not on our agreement (our choice of the reference space). Gravity can be zero only in a point that is the origin of the gravitating massive island of substance.
Without being an expert on the subject, this is my reservation regarding the R.G.
Questions :
- Is it the same to say: "gravity affects time" than to say: "gravity physically affects atomic clocks"?
- Are the periods of pendulum clocks longer because the acceleration due to gravity changes with height or because time lengthens?
- When a ray of light leaves a planet, its wavelength lengthens, because time runs slower or because it loses energy?
My personal answer to all three questions is: gravity affects clocks and wavelengths because they lose energy, not because time changes.
In summary, I think that the relativistic effect of time is NOT because time changes with gravity but that the change in gravitational energy affects the frequencies of clocks and light rays.
We know that the energy density E of force fields (g, E, H) (gravitational, electric, magnetic) is given as E = (-g²/(8πG), ε0E²/2, μ0H²/2).
We also know:
The force on an object, which contributes to a force field, is given by the derivative of the energy in the field overlay in respect to the distance of the object to the source of the field.
The gravitational force is no exception. The only remarkable fact is that the energy density of the gravitational field is negative.
“…We know that the energy density E of force fields (g, E, H) (gravitational, electric, magnetic) is given as E = (-g²/(8πG), ε0E²/2, μ0H²/2).…..”
- really that is rather strange knowledge.
More see https://www.researchgate.net/publication/365437307_The_informational_model_-_Gravity_and_Electric_Forces
- to read recent SS post in https://www.researchgate.net/post/Which_particles_mediate_the_electric_force_of_a_constant_electric_field#view=63db766c87e32b969a0498bc/3 it is useful as well.
Cheers
Sergey Shevchenko “…We know that the energy density E of force fields (g, E, H) (gravitational, electric, magnetic) is given as E = (-g²/(8πG), ε0E²/2, μ0H²/2).…..”
- really that is rather strange knowledge.
What exactly do you consider as being strange? All energy density expressions or a specific one? Or is it the fact, that the energy density of force fields is proportional to the field strength squared?
Gravitation is no vectorial/tensorial distortion of HIGHER-ORDER magic TEXTURES ...............
Occam razor rule tells us (as scientists) to remain loyal to the principle of "Parsimony" and bring in as few mathematical/logical statements and formulae as possible .
Gravity is a Force . A force has the capability to procreate Field around itself . We have gravitational field the same way as we observe , say , magnetic Fields ;;;;;;;;;;;;
I remember once My Mentor , Freeman Dyson , told me some people have the tendency to put up things as much more complicated than they truly are..... to which statement I replied :
" Yes , , , that is so , , I guess it is for show-off purposes . . . ."
I would add one should consider the force definition of variation in potential energy as one for force, and less the Newtonian paradigm notions (primitives) based ones to make safer analysis and safer/valid assaults to its presense in gravity effects and type of phenomena.
This def applies best to effects like Casimir and others.
Philippos Afxentiou With respect to the only required base units for iSpace-SI (a fully MKS/A SI compatible) and more so iSpace-IQ integer quantum geometric unit system (the first of its kind to get away without any human artifacts (!) whatsoever) - the Volt (electric *potential*), the Ampere (multiples of Golden-Ratio base unit), the Meter (integer multiples of 1) and the Second (time is quantized in 1/6961 integer steps) in iSpace-IQ unit system I can fully second and support what you have written above.
Of course (and as a matter of published easy to verify fact) the Newtonian force equation gives exact quantum of gravitation in iSpace-SI when feeding with proper mass (me) and proper radius squared (root of a0 and re) but this does not at all mean,some much deeper physical model (or thinking) like you commented above about the potential energy to consider is surely helpful and in the right direction. However, Casimir force being a small distance experimental and theoretical verified quantum effect of vacuum (spacetime!) can be in turn perfectly verified just by a primary geometrically quantized model of a theory like iSpace (as has been done by me some years ago, but never published).
“…SS quote “…We know that the energy density E of force fields (g, E, H) (gravitational, electric, magnetic) is given as E = (-g²/(8πG), ε0E²/2, μ0H²/2).…..”
- really that is rather strange knowledge.[end quote]
What exactly do you consider as being strange? All energy density expressions or a specific one? Or is it the fact, that the energy density of force fields is proportional to the field strength squared?….”
- everything in the SS quote above is rather strange, because of that is based on the mainstream physics postulates that the fundamental Nature Electric and [Newton] Gravity forces fields , in quantum ED – flows of “virtual photons”, in the GR theory of gravity the “curved spacetime”, that are produced by the Forces charges, contain some energy,
- while this energy in the fields, virtual photons, and the curvature, constantly flows and really transmit to electric and gravitational charges real non-zero momentums – and corresponding energy.
What is possible only if the charges, i.e. electric charge in Electric Force, gravitational mass in Newton Gravity, and “mass” in the GR, have some sources of infinite energy, and the sources constantly in infinitely long time radiate flows of some energy;
- what is evidently strange, since evidently violate the energy conservation law.
Really the charges interact not by some really mystic “fields” above that have some own mystic “strengths”. The Forces act as that the charges constantly radiate the Forces’ mediators, which aren’t particles – as that the virtual photons in QED are, and carry only momentums, having at that no energy, but when a mediator hits in another charge that results in that the irradiated charge obtain momentum, in statics directed to the first charge; if a charged body is free, it obtains a portion of corresponding kinetic energy – however in accordance with the energy conservation law the body’s intrinsic energy decreases on this portion.
Again - see the SS posts above – there is no some “potential energy of some fields”, which by some mystic gradients creates some forces that act on the charges in the fields, producing some work, and so changing energies of the charges,
- really only in concretecoupled by some Force systems of charges – and corresponding bodies – the charges and bodies have concrete potential energies; more see links in the yesterday SS post.
Cheers
Sergey Shevchenko "Really the charges interact not by some really mystic “fields” above that have some own mystic “strengths”."
Charges interact via forces. This is an obvious fact. The forces are exerted by force fields. This is a definition. The force fields are an inseparable part of charges. There is no flow of energy. The relation between charge and force field is constant, without any flow.
Why is there energy contained in a force field? In the electric or magnetic case, we only have to consider a capacitor or a magnetic coil. The energy stored in that electric components is field energy. This also is a proven fact. In the gravitational case, the relation between field energy and force is the same as in the electric or magnetic case.
By the way, we cannot explain the energy content in capacitors or coils with potential energy.
Wolfgang Konie,
Εnergy flow, according to the numerical ontology endorsed by most academics in unificational theoretical framework (description of broad range of phenomena), abstract ontology, has aspects such as it is transfer able, storable& conservable.
This transmision is done via paths, either heat or work-but work conveys or is inseparable from force concept.
So force concept is doningrsined i standard Newtonian paradigm that it is a keystone and possible removsl needs a big plan to prevent destructive implications.
On another note of interest, seen in the energy framework definition, it cannot be seen as redundant unless heat is identified. There is indeed one gravitational theory with realist predictions with thermodynamics roots, proposed by a Dutch Scientist that gravity' cause is entropy, along with the above lines (i have not read the article but it must be close).
But reducing gravitational phenomena to heat flow phenomena has not been well received.
Wolfgang Konle
“…Charges interact via forces. This is an obvious fact. The forces are exerted by force fields. This is a definition. The force fields are an inseparable part of charges…”
- yeah, that is postulated in classical electrodynamics, however CED by no means clarifies what are these “fields”, and by what mystic way these fields “exert forces”
“… There is no flow of energy. The relation between charge and force field is constant, without any flow.….”
- yeah that is also postulated in CED, but in CED the flows of “forces' strengths”, i.e. E and H, are postulated, which, at that, constantly and always in billions of years “exert forces”, and, say if a charge in a field is free, the forces make corresponding physical works, i.e. transmit some portion of energy to the charges. In QED the virtual photon constantly and always in billions of years flow, directly carrying energy.
“…Why is there energy contained in a force field? In the electric or magnetic case, we only have to consider a capacitor or a magnetic coil. The energy stored in that electric components is field energy. This also is a proven fact. …..”
- the fact that the energy is stored in capacitor or a magnetic coil, and is at that the field energy, is “proven” only in CED, what is really wrong. The energy in such cases is stored in systems of static charges in first case, and systems of moving charges in the other one.
Again, energy isn’t stored in the CED fields [and QED virtual photons flows], and forces that act on charges in the fields aren’t really mystically “exerted” by the fields. Again – see example the SS posts above and links in the posts – if a charged having small mass m body moves with zero angular momentum in a field of other having large mass body – in CED textbooks that is usually considered as “motion in stationary field with 1/r potential” ,
- the mass m - because of in CED “fields exert forces” – if r is small can obtain from “field” any, including infinite, energy, in the GR infinite energy in some “hole in the spacetime”.
Really in any real systems of – either electric or gravitational, charges fundamentally no any infinities can exist. Again, if a system of charges was on infinite distances, the potentialenergy U, that could be spend in any, including when the charges [and corresponding bodies] interact in a coupled by some Force system, is equal U=sum(m0+M0+…)c2=E0, and at anything that happens in the system the energy of the system, E=sum(m0γ+M0γ+…)c2 by no means can be more than it had before the coupling, including at any rat any motion of charges/bodies at any coupled system any evolution.
While if the fields are as are defined in CED [and in the GR], i.e. for some mystic reason and by some mystic way, using Newton’s wording “of itself, and from its own nature” “exert forces”, the sum(m0γ+M0γ+…)c2 can exceed E0 in any times. What is evident physical absurdity.
Again, the initial model of what happen in Matter really when Gravity and Electric Forces act see https://www.researchgate.net/publication/365437307_The_informational_model_-_Gravity_and_Electric_Forces
That is initial model, however any real development of the Gravity and Electric Forces theories must be based on this model.
Cheers
Sergey Shevchenko "Again, energy isn’t stored in the CED fields"
Sorry, but we know that the energy density E of force fields (g, E, H) (gravitational, electric, magnetic) is given as E = (-g²/(8πG), ε0E²/2, μ0H²/2).
The energy in such cases is stored in systems of static charges in first case, and systems of moving charges in the other one.
Yes, the energy is contained within the fields, this systems contain.
We can prove that the mechanical work done, if we move point charged objects from infinity to zero distance, is equal to the change in field energy. Line and volume integrals show this equality. This proof works for all three kinds of force fields.
Problen is just … *nothing* is of zero length (point charge objects like electrons DO HAVE FINITE small size but never zero, this is just mathematical algebraic higher math nonsense which yes - works with more such mathematical nonsense combined to give physically proper measurable values - but hence being an effective theory only and hence by no argument means it’s also proper actual physics).
One also can’t move anything to infinity as this is just a causal consequential error of the invention of the concept of zero.
We ALL really start getting rid of this intrinsically flawed geometric models implicitly or explicitely making use of zero and infinity.
iSpace theory (able to derive constants of nature from first principles up to precise level of CODATA by a „simple“ finite LEGO style integer geometric model using the key ingredient of a so called changed distance definition) does away with all such unphysical „tand“ and was hence able to solve a decade old physical problem where all the great minds failed on while I am just an ambitioned hobbyist - but use both the proper geometric model and tools, like Wolfram Mathematica and - job DONE.
Philippos Afxentiou "So force concept is doningrsined i standard Newtonian paradigm that it is a keystone and possible removsl needs a big plan to prevent destructive implications."
This is not understandable, please reformulate.
Wolfgang Konle
“…[SS quote]"Again, energy isn’t stored in the CED fields"[end quote]
Sorry, but we know that the energy density E of force fields (g, E, H) (gravitational, electric, magnetic) is given as E = (-g²/(8πG), ε0E²/2, μ0H²/2)….”
- yeah, those “we” indeed seems quite frankly “know” that italicabove; and so quite inevitably logically frankly, and quite seriously, believe that, say, really a particle “electron” doesn’t exist, but that is some, for some mystic reason appeared and always existent EM field’s region, where integrals of the “energy density” above have the energy of electron, etc.
What for any normal human looks as rather strange, so there exist a number of “EM masses” and “EM radiuses” of electron; while, say, besides electron there exist neutral particles that have masses, etc.; and besides the inertial mass of electron – as that was firstly in the first integrals – there exist gravitational – and equivalently - mass of electron, which seems even for the “we” doesn’t follow from the EM integrals.
And, besides, there exist very numerous “we”, who state that, as that is postulated in the GR, some fundamental Nature force “Gravity” – and corresponding the Force’s filed – don’t exist at all, and the energy is stored in the “spacetime curvature”. So in this case quite logically would be derived by some integrals, say, some electron’s “spacetime mass”, which should be the same as “EM mass”, but the author of the GR in more 30 years didn’t develop corresponding “unification” of CED and GR – what means, though, that he really scientifically attempted to do that, since really that is fundamentally impossible, Gravity and Electric are fundamentally different Forces, and if he would “unite” the Forces, that would be rather strange mental construction.
[SS quote]"The energy in such cases is stored in systems of static charges in first case, and systems of moving charges in the other one. "[end quote]
Yes, the energy is contained within the fields, this systems contain.
We can prove that the mechanical work done, if we move point charged objects from infinity to zero distance, is equal to the change in field energy. Line and volume integrals show this equality. This proof works for all three kinds of force fields...”
Again, that the mechanical work done, if we move point charged objects from infinity to zero distance, is equal to the change in field energy by no means proves that the energy is contained within the fields. That in the mainstream physics means only the fact that the integrals, for some mystic in the mainstream reason and by some mystic way adequately to the reality describe what happens if some mystic “body/charge” moves in some mystic “field” – as, say, the theory that Sun rotates around Earth was adequate to the reality;
- and so, as some continuation of the comment to the first quote, say, if after the motion of, say, two charged particles [Gravity or ± Electric] the particles compose a coupled system, then at least the sum of inertial and gravitational masses of the particles, after the kinetic energy is dissipated from this system, is lesser than the sum of masses when the particles were on infinite distance on the Forces’ mass defects that are exactly equal to the corresponding “change in field energy”,
- from what so in the mainstream at least the strange “EM mass” of any charged particle follows.
And, again, in this case in full accordance with the CED in QED, where the evidently strange always constantly radiating flows “virtual photons” also compose EM fields, these fields also have “energy densities”, etc. – and, at that these fields in QED for some mystic reason quite non-virtually exist in Matter always, and particles are some “excitations” of these non-virtual fields
- what is rather evidently a next, strangeness in mainstream physics “we” truly believe in which.
Again, these strangenesses can be avoid in physics only if the fundamentally transcendent/mystic in the mainstream physics phenomena/notions “Matter” ”– and so everything in Matter, i.e. “particles”, “fields”, etc., “Consciousness”, “Space”, “Time”, “Energy”, “Information”, are really scientifically defined, what is possible, and is done, only in framework of the 2007 Shevchenko-Tokarevsky’s “The Information as Absolute” conception; more concretely in Matter case, in the informational physical model that is based on the conception, and, more concretely in this case, in the 2007 initial model of Gravity and Electric Forces, the links see in SS posts above, at least on the page 3.
More see the SS posts above and links in the posts.
Cheers
Sergey Shevchenko "Again, that the mechanical work done, if we move point charged objects from infinity to zero distance, is equal to the change in field energy by no means proves that the energy is contained within the fields. That in the mainstream physics means only the fact that the integrals, for some mystic in the mainstream reason and by some mystic way adequately to the reality describe what happens if some mystic “body/charge” moves in some mystic “field”.
This is a mystic rejection of a fact. A mystic rejection does not make sense. You could assume that it is by accident, that the change in field energy is exactly the same as the change in kinetic energy. But assuming something mystic is not acceptable. An accidental match is also not acceptable because this match is too fundamental. It also works with electric point charges.
The proof of the fact that falling from infinity to a small distance r0 in a two body system, exactly converts gravitational field energy into kinetic energy, is as follows:
-------------------------------------------------------------------
Given is a closed system with two equal far distant point masses. The energy content of the gravitational field is 2X.
Via gravitational attraction the two masses have approached each other to an infinitesimal small distance r0. The gravitational energy then is 4X. (The field strength has doubled, because the mass also has doubled, and the energy density is proportional to the field strength squared.)
The kinetic energy the two masses have gained is Y. The gain in field energy is 2X because the system already started with 2X.
Energy conservation says Y+2X=0. Because kinetic energy always is positive, we get X=-Y/2. This shows that the energy content of the gravitational field is negative.
Now we calculate this energy quantitatively:
We know: g=GM/r², F=Mg, F=GM²/r². F is the accelerating force and G is the gravitational constant, g is the gravitational acceleration, r is the distance.
The kinetic energy is given with the integral force times pathway:
Ekin=∫[r0, ∞]Fdr = GM²/r0.
We get the field energy if we consider E=-g²/(8πG) and g=GM/r² and insert it in
Efield=∫4πr²Edr for the combined masses.
We get Efield=-∫[ r0,∞]4πr²G²(2M)²/r4/(8πG)dr = -2GM²/r0
This value is the kinetic energy gain duplicated. But because the system only has gained half of the field energy it exactly corresponds to the gain of kinetic energy.
If we consider two different masses, we get GMm/r0 in the line integral instead of GM²/r0.
In the volume integral we get ((m+M)²-m²-M²) instead of 2M² for the mass term difference between initial and final state. Which again exactly corresponds to the gain in kinetic energy.
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If you do not understand details of this proof, you can ask. But please do not declare the basic mathematic in this proof as "mystic". If this would be mystic, then everything in our world would be mystic.
Gravity is of TOTALLY differing nature than both electric and magnetic fields . Otherwise , stars and planets would not have formed .
Early high-school physics :
A field is the area around an object where it can exert a force on another object, usually without there being any contact between the objects. We can represent a field as lines showing the direction of the force experienced by another object in the field. For example a gravitational field exists around a planet and causes there to be a force of weight on any mass placed in the field.
As for Plasmas :
The coupling constant of a plasma is given by the ratio of its average Coulomb-interaction energy to its average kinetic energy—or how strongly the electric force of each atom holds the plasma together. Plasmas can therefore be categorized into weakly- and strongly-coupled plasmas depending upon the value of this ratio.
Reza Sanaye
Your early high-school physics does not tell the full story. The concept is missing, which allows fields to exert forces. The fields do not only exert forces on objects in a fixed position, they also maintain forces along paths the objects follow. Maintaining forces along paths requires energy. Therefor it is obvious that the energy density contained in force fields drives the force exerted by the force field.
In my work "Mass as the geometry of space" all this has an explanation.
Wolfgang Konle
- sorry, but now in Kiev rather serious problems with electricity and so internet are, and, besides, what is in the SS posts already is enough as the answer to the thread question, so here only one point.
“…[SS quote] "Again, that the mechanical work done, if we move point charged objects from infinity to zero distance, is equal to the change in field energy by no means proves that the energy is contained within the fields. That in the mainstream physics means only the fact that the integrals, for some mystic in the mainstream reason and by some mystic way adequately to the reality describe what happens if some mystic “body/charge” moves in some mystic “field”.[end quote]
This is a mystic rejection of a fact. A mystic rejection does not make sense. You could assume that it is by accident, that the change in field energy is exactly the same as the change in kinetic energy. But assuming something mystic is not acceptable. An accidental match is also not acceptable because this match is too fundamental. It also works with electric point charges.…..”
- italic in the quote it looks as rather strange, since in the SS posts already a few times it is explained that in mainstream physics all/every theoretical objects/events/processes/properties/variables/values are fundamentally transcendent/uncertain/irrational ones, which really in the mainstream – and for mainstream physicists, including you, only for some by some mystic ways are logically connected in some theories only aimed at consistence with experiments.
Including that happens in the properties/variables “ Forces’ fields” and “energy”.
Again, consistence with experiments by no means proves truth of any theory, while really all/every mainstream theory is based on some really mystic postulates, which all really are wrong.
Again, the theory that Sun rotates around Earth, when for humans “Sun” and “Earth” were completely transcendent/mystic objects, was, nonetheless well consistent with experiments;
- and, if we say about Gravity, from, say, experiment that some ball moves from a height h down on a inclined plane quite consistent theory follows: the ball moves because of on the plain there is the gradient of l(h), and this gradient forces the ball to move as that is observed,
- and this theory would explain all gravitational events/processes on Earth, despite that the theory’s gradient is quite transcendent and mystic.
But in some times it turned out to be that Gravity is observed not only on Earth, and so the Newton theory appeared, which again really without any rational grounds, i.e. completely mystically, postulated the Newton’ law of Gravity, etc.,
- where, instead the mystic gradient of l, the quite equally mystic gradient of mystic “gravitational filed” forces the ball to move. Again, both gradients really are mystic quite equally.
Further, because of real transcendence of Newton’s theory, even more transcendent GR appeared, which now as the standard physical theory explains why the ball moves; etc.
Again, what are Gravity and Electric Forces it is completely non- transcendently explained in the 2007 initial model of Gravity and Electric Forces https://www.researchgate.net/publication/365437307_The_informational_model_-_Gravity_and_Electric_Forces
- where, including, it is rigorously shown, that the ball moves by no means being impacted by some mystic “gradient” of some mystic mainstream gravitational “field”. The ball moves because of the mass “Earth” radiates the Gravity Force mediators, which compose some media so, that if some other mass occurs in the media, it’s particles’ algorithms’ FLEs spend their “energy” to exist in the media, and, at that, because of the energy conservation law the mass mobtains momentums toward Earth;
- i.e. – see the linked paper – masses move toward each other in each other media, which are real gravitational fields, as, say, a human swims in water, spending own energy, while the field has no energy, so “density of energy”, and other really mystic things that are in the men stream physics.
Cheers
Ilya Boldov
" In my work "Mass as the geometry of space" all this has an explanation. "
What is , plzz , the link to this piece of your writing on internet ??
Sergey Shevchenko "The ball moves because of the mass “Earth” radiates the Gravity Force mediators, which compose some media so, that if some other mass occurs in the media, it’s particles’ algorithms’ FLEs spend their “energy” to exist in the media, and, at that, because of the energy conservation law the mass mobtains momentums toward Earth;" (1)
The ball moves downwards because this movement reduces the energy content of the gravitational field overlay of ball and earth. (2)
Now let us compare the alternative explanations (1), (2) above. Be honest, which one is more comprehensible?
Force impact is always the same. An expanded spring exerts a force and moves an object fixed at the end of the spring, because moving the object, reduces the elastic energy, stored in the expansion of the spring.
Force and energy are linked together because energy is force times displacement. Physically exact, energy is given by the line integral over the scalar product of force vector and line element vector. This fact is behind all force effects, without any mystic or trancendency.
You also should notice that all the technical achievments have been made with mainstream science. If that would be wrong, technic would not work.
Philippos Afxentiou and others:
GR is not a complete theory of gravity because it lacks a tensor that describes the energy-momentum of the gravitational field. Modified General Relativity (MGR) corrects that deficiency by introducing a connection independent tensor Φαβ that preserves the equivalence principle. The Orthogonal Decomposition theorem and Lovelock's theorem generates the complete Einstein equation in one line: Λgαβ +Gαβ +Φαβ = 8πG/c4˜ Tαβ where ˜ Tαβ is the matter energy-momentum tensor. Gravitational energy-momentum is invariant under free-fall and can be localized.
The gravitational force in a metric theory of gravity is entirely determined by the connection on the Lorentzian manifold. The symmetric Levi-Civita connection is constructed from the Lorentzian metric and its first derivatives. The metric is a solution to the Einstein equation, which depends on the line element covectors in Φαβ and the matter energy-momentum tensor.
Hence, gravitational forces in MGR are completely determined by the curvature of spacetime resulting from all sources of matter and energy. Whereas GR geometrically determines the force of gravity from ordinary matter, it cannot describe the gravitational force from dark matter without introducing a dark matter profile that represents the invisible matter.
Ilya Boldov
I studied two of the three links you had sent me . You are a TRUE thinker .
Sincerely
reza
Gary Nash "GR is not a complete theory of gravity because it lacks a tensor that describes the energy-momentum of the gravitational field."
This is an excellent base of looking beyond the current horizon. But now let us actually extend this horizon.
Let us assume that a cosmic homogenous field of gravitational nature and positive energy density exists. This field everywhere overcompensates the negative energy density of gravitational fields. Now let us assume that the geometric shape of this field is a 3-sphere.
Let us further assume, that the gravitational medium of that field everywhere in the 3-sphere flows without divergence.
Then this field with its positive gravitational energy density also will warp the space to a 3-sphere geometry. (The flow is necessary to rotate the Ricci tensor of the space curvature.)
My view is now that we can assign this cosmic field with an additional component of your tensor Φαβ.
Dear Wolfgagn !
Before talking about a three-dimensional universe, try to understand how gravity and inertia will act in one-dimensional space. This is in my work - Mass as the geometry of space, laid out on this site.
Dear Wolfgang: Your conception of a positive energy density in addition to MGR is actually already in MGR and is called dark energy. The trace of Φαβ with respect to the metric is Φ, and dark energy is defined by the condition Φ>-2Φ00. The integral of Φ over all spacetime vanishes. That keeps the Universe in balance; preventing a collapse to oblivion or an uncontrolled expansion to rip it apart. The static spherically symmetric energy density is twice the Newtonian gravitational density since gravity gravitates; both are negative. Φαβ is not divergenceless unless the matter energy-momentum tensor vanishes.
In general, spacetime is defined with a smooth Lorentzian metric on a manifold where a line element field (X,-X) exists. In fact, a Lorentzian metric exists if and only if a line element field exists. So we definitely do not want to define spacetime as a 3-sphere; that is far too "restricting".
Dear Gary "So we definitely do not want to define spacetime as a 3-sphere; that is far too "restricting"."
Only the spatial part is supposed to have the structure of a 3-sphere. Or do you have another structure in mind?
Dear Gary, even without applying a deep formalism, we can see that a curved space geometry leads to a red shift.
If we compare a light path along a circular geodesic in a 3-sphere geometry with a straight light path, we see that the path along the arc becomes more and more extended. Compared with the straight path of twice the radius, the relative extension reaches the factor pi/2.
This geometrical red shift shows that we do not need an expanding universe to explain the red shift, we observe. Something like that also occurs in a static spacetime with a curved spatial component.
(pi/2 is not a large red shift factor, but with a cosmic field, which curves space, we have some more arguments to explain larger factors.)
Dear Wolfgang: Yes, curved spacetime leads to gravitational lensing. To show that, one needs to do a more general calculation than that restricted to a 3-sphere. I leave you to pursue that notion of spacetime, but I know that spacetime is much more general based on a study of Lorentzian spacetimes in MGR.
GR has failed to unite the forces. So, First, start from experiments, then consider there is only 1 force, then model this force. GR and interference experiment should be derived from the model application.
John Hodge "GR has failed to unite the forces. So, First, start from experiments, then consider there is only 1 force, then model this force."
Unification of forces is not the task or intention behind general relativity. Apart from that, forces are already united:
A force on an object, which contributes to a force field, is given by the derivative of the energy contained in the force field, in respect to the distance between the object and the source of the force field.
This energetic definition applies to all kinds of force fields (gravitational, electric, magnetic, atomic(mechanic), nuclear), and unites all forces exerted by fields in respect to a common origin. The only type of force, which is not included in this field consideration is inertia. But we know that inertia is the capability of mass to contain kinetic energy.
Gary Nash "Yes, curved spacetime leads to gravitational lensing. To show that, one needs to do a more general calculation than that restricted to a 3-sphere."
Yes, curvature caused by matter leads to gravitational lensing. It is also true, that the curvature caused by matter and the curvature which causes a 3-sphere are different things without a direct relation.
If we say, that the universal structure of the universe is a 3-sphere, we do not restrict space curvature to a 3-sphere shape. The 3-sphere curvature is a homogenous global positive scalar curvature. But it is overlaid by various inhomogenous negative scalar curvatures caused by matter. But the convention is, that the amount of negative curvature nowhere exceeds the positive curvature.
Convention is all we have to analyze transference of force lines as tensorials or vectorials to be satisfactory to present mood of exact sciences , , ,, However : As of force lines as tensorials or vectorials to be satisfactory to present mood of exact sciences is apparently merely given by the derivative of the energy density contained in the force field, in respect to the distance between the object and the source of the force field. This energetic flux applies to all kinds of force fields ; Again, that the mechanical work done, if we move point charged objects from infinity to zero distance, are the purview of equality to the change in field energy ,which by no means proves that the energy is contained within the fields. Gravitation not excluded .
Gary Nash
You are a giant Genius !
Period ...................................
Respectable Sir-Gary-with-Detailed-Mathematix !
Do you know I am not your teacher , deary dear dearest pupil ??
1 Gravity is not a moving force
2 Gravity is not spooky action at a distance
There is a third option:
3 Gravity is ether-based action at a distance, since gravity emerges inside matter due to effects from the ether. Gravity is an effect from the values of m and M in 2 different positions. So, the cause of gravity must have information about the values of both masses. The only concept with this property is the ether. Gravity demands the ether.
Reza, I didn't ask you as a student, which I am not, but as a relativist to explain what a Lorentzian spacetime actually is. Apparently you don't know the answer; otherwise you would have addressed the question in a logical manner instead of the bogus manner in which you responded.
Gary Nash
You must , one day , learn two things :
1--Not be so scared as to hide your face on ALL forums you attend...........
2--Not expecting people to write a booklet or so for you to simply prove they are not frightened by your "Bluffs" .
This is actually a debate thread . This is no elementary school nor a college . You have , of course , the right to pinpoint exactly where in that stuff you do not understand , in order to receive some level of clarification .
The sources for a backwarded character like you is out there in paper print and also in digital form (WITH ALL THE FULL MATHEMATICAL DETAILS YOU ARE BOLDLY DEMANDING) on internet so that you learn a tiny little bit about your beloved Lorentzian spacetime.
Have nice dreams !
Reza Sanaye
Reza, it is unfortunate that you are so ignorant that you cannot participate in an intelligent conversation. If you think you can google 'Lorentzian spacetime" and learn all the specific details that I am hinting at, that only exposes your ignorance. You will have a hard time to find something on the structure of a Lorentzian metric from your search. I will certainly not waste any further time responding to you so say anything you want; I could care less.
Gary Nash "Spacetime, as of today, is described by a Lorentzian metric. Period."
Two parts of this statement are questionable. It is "today" because spacetime is defined as it is. And "Period." is wrong because the Lorentzian metric only describes the conversion between inertial systems with a relative velocity.
Within the spatial part various metrics are possible.
Dear Gary, Gary Nash ,
if you remember we talked several times about how gravitation is supposed to work and I illustrated my view...
I recently discovered by reading a famous treaty of Maxwell, that my conception is very similar to Maxwell's...
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THE SCIENTIFIC PAPERS OF JAMES CLERK MAXWELL
https://ia800908.us.archive.org/24/items/scientificpapers01maxw/scientificpapers01maxw.pdf
"The intrinsic energy of the field of gravitation must therefore be less where ever there is a resultant gravitating force.
As energy is essentially positive, it is impossible for any part of space to have negative intrinsic energy.
Hence those parts of space in which there is no resultant force, such as the points of equilibrium in the space between the different bodies of a system, and within the substance of each body, must have an intrinsic energy per unit of volume greater than
R2/8π
where R is the greatest possible value of the intensity of gravitating force in any part of the universe.
The assumption, therefore, that gravitation arises from the action of the surrounding medium in the way pointed out, leads to the conclusion that every part of this medium possesses, when undisturbed, enormous intrinsic energy, and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction.
As I am unable to understand in what way a medium can possess such properties, I cannot go any further in this direction in searching for the cause of gravitation."
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So Maxwell speaks clearly about energy density. The relation he referred to is the same as ϱEgrav(r)= - (∇φg(r))² /(8πG)
where R = max[∇φg(r)]
the sign can be negative since that is a missing energy density in the background.
The background, on the other hand, should have an energy density that can withstand the depletion created by the deepest of the black holes. The maximum conceivable is the Plank "force" max[∇φg(r)] = c4/G
ϱEgrav(r)= (∇φg(r))² /(8πG) =c8/8πG2 which is 1093 grams per cubic centimeter
Dear Stefano: As we have discussed many times, the line element field is ignored in GR. Gravity gravitates; thus the static spherically symmetric gravitational energy density is twice that obtained from GR and twice the Newtonian value.
You talk about a medium of enormous background energy; that is described by the line element field because it satisfies the spin-1 Klein-Gordon equation in curved spacetime and therefore Maxwell's equation for the mass k=0. The geometry of spacetime and the quantum nature of matter are linked together by the unit line element covectors that belong to both the Lorentzian metric gαβ = g+αβ − 2uαuβ, and the spin-1 Klein Gordon equation ∇α∇αuβ = k2uβ where g+αβ is a Riemannian metric that always exists.
The regular line element vector field describes dark matter, which GR cannot do without the introduction of a matter profile to represent it. Each point of a Lorentzian spacetime contains a myriad of quantum-metric covectors from which Φαβ and Φ, the trace of Φαβ, are constructed. Spacetime is filled with dark matter, gravitational energy-momentum, and dark energy.
Wolfgang Konle
That GR does not suggest a unification of forces IS the problem - it cannot be out goal. Indeed, Einstein and many others have sought and failed to obey Mach's Principle. Some have sought and failed to show how inertia derives from all the universe. The ``energy'' definition doesn't work because there are so many different types of energy fields, each with different sources and behavior. Don't forget dissipation as an energy not included in LaGrangian and Hamiltonian.
What I suggest is 1 field with 1 force (the gradient) which is sourced from all the universe - the close components predominate. It is a Kuhnian paradigm shift which means it is incommensurable with current models. But it does reduce to current models and explain many problems current models have.
The geometry of spacetime and the quantum nature of matter are linked together by the unit line element covectors that belong to both the Lorentzian metric gαβ = g+αβ − 2uαuβ, and the spin-1 Klein Gordon equation ∇α∇αuβ = k2uβ where g+αβ is a Riemannian metric that always exists.
In the thread after a couple of SS posts on page 4, February 6 and 7, where the thread question “Is gravity a force by convention only? If so, what makes it so similar to fundamental forces &how spacetime creates a "force effect" ?” was really and clearly answered, again rather strange series of rather strange posts appeared. Most of the posts cannot be scientifically commented, besides that they are tooo strange ones, so only to one that at least references to what Maxwell wrote:
“…I recently discovered by reading a famous treaty of Maxwell, that my conception is very similar to Maxwell's
….So Maxwell speaks clearly about energy density. The relation he referred to is the same as ϱEgrav(r)= - (∇φg(r))² /(8πG) where R = max[∇φg(r)] the sign can be negative since that is a missing energy density in the background. The background, on the other hand, should have an energy density that can withstand the depletion created by the deepest of the black holes. The maximum conceivable is the Plank "force" max[∇φg(r)] = c4/G
ϱEgrav(r)= (∇φg(r))² /(8πG) =c8/8πG2 which is 1093 grams per cubic centimeter….”
- yeah, Maxwell soon 200 years ago wrote clearly about Gravity field energy density – analogously as that is in Maxwell ED, and yeah, the EM field’s energy density remains in mainstream physics till now. However Maxwell was really a physicist, and understood at that that he writes about something that is completely transcendent for him, and so finally writes
“…As I am unable to understand in what way a medium can possess such properties, I cannot go any further in this direction in searching for the cause of gravitation."…”
- unlike the poster in the quote above, who writes, say, about evidently fantastic energy density of some fantastic field that is equivalent “1093 grams per cubic centimeter”.
Again, the answer to the thread question was done in SS posts above, here briefly:
– as that rigorously scientifically shown in the Shevchenko-Tokarevsky’s 2007 initial model of Gravity and Electric Forces in
https://www.researchgate.net/publication/365437307_The_informational_model_-_Gravity_and_Electric_Forces, Gravity Force fundamentally is some fundamental Nature force, and fundamentally nothing else; so it exists and acts in Matter and in the Matter’s fundamentally absolute, fundamentally flat, and fundamentally “Cartesian”, at least [4+1+1]4D spacetime with, in this case, metrics (cτ,X,Y,Z,g,ct),
- where the ultimate base of Matter, i.e. the Matter’s aether – the at least [4+1+1]4D dense lattice of at least [4+1+1]4D binary reversible fundamental logical elements [FLE] is placed, whereas everything in Matter, including particles and fields of fundamental Nature forces, exists, changes its positions and interacts, and
- where 4 dimensions cτ,X,Y,Z, are utmost fundamental and universal “kinematical” space dimensions, ct is absolutely fundamental and universal time dimension, and the g-dimension relates just to actualization of the [4+1+1]4D FLE’s corresponding to Gravity Force degrease of freedom changing of its state.
Correspondingly Gravity exists and acts fundamentally really and objectively, by no means as by some convention, and fundamentally Gravity by no means is created by some “spacetime force effect”.
Besides, in the model a few fundamental problem in Newton Gravity theory and classical and quantum electrodynamics – from where and how real forces, and at motion real energies, appear in gravitationally/EM coupled systems of the corresponding charges – “gravitational mass” and “electric charge" – at all what happens in concrete systems only real “potential energy” - the energy of the system’s elements is used and re-distributed,
- while there exist no, really fundamentally transcendent/mystic “energies of the fields”, which are fundamentally ad hoc postulated in the mainstream because of in the mainstream the fundamental phenomenon/notion Matter – and so everything in Matter, i.e. particles, fields, energy, etc., really are fundamentally transcendent,
- and the postulates, including, really are not only mystic, but also simply wrong.
Again, the thread question is essentially answered in the SS posts above, nonetheless after these posts a series of rather strange posts appeared, which have really only some strange relations to physics and to the thread’s question; what looks as is rather strange for any really scientific discussion.
More see the SS posts above and links in the posts.
Cheers
So the comment now arises from Sergey-Shevchenko "a series of rather strange posts appeared, which have really only some strange relations to physics and to the thread’s question; what looks as is rather strange for any really scientific discussion." The threads question is "...what makes it so similar to fundamental forces &how spacetime creates a "force effect" ?"
The answer to the question follows from the fact that the gravitational force in a metric theory of gravity is entirely determined by the connection on the Lorentzian manifold. The symmetric Levi-Civita connection is constructed from the Lorentzian metric and its first derivatives. The metric is a solution to the Einstein equation. The metric is fundamental to the curvature of spacetime; matter tells spacetime how to curve, and curved spacetime tells matter how to move. Few people seem to understand this.
When a background field is invoked, the word "ether" appears or some convolution of it. That is where the missing tensor in GR that represents the energy-momentum tensor of the gravitational field becomes fundamental. Only Modified General Relativity has provided the missing tensor that must have the property of being connection independent, which preserves the equivalence principle. Gravitational energy-momentum is invariant under free-fall and can be localized. Moreover, the line element fields link the Lorentzian metric of spacetime to the spin-1 Klein-Gordon equation; the unit line element covectors belong to both the metric and the spin-1 KG wave equation. So all of this is related to the question as stated and the curvature of spacetime.
The concept of a force (actually a force field) originates from classic physics in macroscopic reality. So it is not easy to imagine the existence of a “bare” force field because of the complexity of macroscopic reality.
The “connection” between gravity and spacetime originates from Einstein’s idea that matter – rest mass carrying particles – force space to curve. That idea is quite troublesome because in the early universe there was a period without matter, although space existed. Like Einstein confirmed in his lectures at Leiden University in 1920. But the most troubling issue is the equivalence of matter and free energy (E = m c2). Einstein had the idea that a local concentration of energy – matter – can curve space. Although energy is a variable of surface area (c2). The latter is easy to understand because if we accelerate a particle its volume doesn’t increase. There is a constant flow of high energy particles from everywhere in the universe with velocities near the speed of light and none of these particles have macroscopic proportions.
The search for the Higgs boson was a way to show the existence of a universal scalar field everywhere in the universe (Higgs field). The confirmation of the existence of a universal scalar field was really important because the theory predicted that the energy of rest mass of particles like the proton was transferred from a local decreased scalar to the electric part of the electromagnetic field around the decreased scalar. Because the amount of transferred energy has a scalar signature.
Unfortunately the transfer of energy from the local decreased scalar to the universal electric field around wasn’t a magic creation of energy out of nothing (“pushing” space around), it was a transformation of the configuration of energy between 2 basic quantum fields. In line with the law of conservation of energy.
So there is a lot to discuss about the nature of the force of gravitation. Like Newton's use of Christiaan Huygen's centripetal force (another huge theoretical problem).
With kind regards, Sydney
With respect to imho VERY interesting ratios of Planck force to iSpace-SI Quantum of Gravitational force you might have a look on attached PNG!
The origin of all forces simply is the distance dependency of the energy content of force fields.
Sydney Ernest Grimm ,
In a good way, we should first start by understanding the space itself. And the only option is a discrete-continuous space. Only this eliminates Zeno's paradoxes.
Energy is always associated with movement. Simply put, the motion of a particle/photon is a discrete transfer of the bulk state of a plankton to a neighboring plankton.
A noticeable increase in the mass of an elementary particle occurs when the excited (volumetric) state of the previous plankeon has not had time to return to the zero dimension. And for some time, two or more plankeons exist in the form of a certain volume of three-dimensional space. The sum of their masses \ volumes turns out to be greater than that of a stationary particle. In fact, relativistic motion "smears" a particle across space.
The boiling of the vacuum constantly unfolds 0-dimensional plankeons into 1,2,3-dimensional objects.
These one-dimensional samples are carriers of the electric field. !!!!!!
I do not know how it is formed. But the fact that elementary particles\quarks-polyhedra with the ratio of the number of edges to vertices 3/2 have this is a fact. Naturally, one-dimensional electric field samples can have only 2 directions, these are two types of charge + and -. The Coulomb charge of a particle forms a sphere of these vectors around itself in three-dimensional space. The polarization of discrete vectors causes the polarization of neighboring discrete ones, and the velocity again remains the same constant as the speed of light.
The number of samples increases quadratically with increasing radius, and, naturally, the length of the vectors also decreases quadratically with respect to the radius.
When a charged particle moves, the surrounding discrete vectors begin to rotate "after" it.
This rotation is the magnetic field. Energy is spent on unwinding the samples. And this causes the effects of induction and self-induction. When several charges are applied to the torsion disk, it will resist and slow down if the rotation is counter, and resist less if the rotation is co-directional. That's why parallel currents attract or repel.
And that's why the electrons don't fall on the nucleus.
Because the electron, flying up to the proton, begins to deploy discrete elements that are already deployed to the proton. And they resist this, first slowing down the speed of the electron, and then forcing it to rotate in a circle. And when an electron orbits around a proton, it experiences the same thing as parallel currents.
The discretes between the electron and proton are deployed in a co-directional manner and do not interfere with movement, and the discretes behind the electronic counter interfere with movement, so the electron deviates in their direction without falling on the proton.
It's something like that.
Dear Ilya Boldov
I agree that space as a continuum with discrete properties (quantized space) is the concept that fits physical reality the best. By the way Zeno tried to explain to other philosophers that the concept of Parmenides of Elea (the existence of an underlying “creating reality”) needs a structure of elementary spatial units – “atoms” in the Greek language – that cannot be divided ad infinitum.
I don’t know the term “plan(c)kton” in relation to theoretical physics but I suppose that you use this term to identify a single unit of quantized/discrete space. If I interpret it right you are describing the units of the structure of the dynamical part of our universe, the electromagnetic field. Thus the exchange of energy (pass on of surface area in E = m c2) by and between these units is the fixed amount of energy, Planck’s constant. Although we have to keep in mind that Planck’s constant is a mutual relation with a continuous nature (only the interaction is quantized).
The following text is difficult for me to underscore (although parts are more or less familiar). For me the term “electromagnetic field” indicates 2 corresponding fields, the universal electric field (3D topological field) and the corresponding magnetic field (1 dimensional vector field). Both fields are detectable because of local differences in the properties of both fields. So if I want to make a connection between the existence of quantized space and the observable/detectable mutual relations between the phenomena in physical reality I have to construct a geometrical model that shows the universal properties that we know in physics. Like the conservation of energy and momentum, the universal constants and universal principles (like Heisenberg’s uncertainty principle). I don’t think that we must try to transform all kinds of known “phenomena” in one theory. But that is only my opinion, maybe you or someone else will prove that I am wrong.
Anyway, the discussion is about the gravitational force field. That means that the possibilities to understand gravitation with the help of the properties of primary quantum fields are limited. There is the Higgs field, the universal electric field and the corresponding magnetic field. Newtonian gravity shows to be an emergent force field (Eric Verlinde 2011), in line with Einstein’s opinion about curved spacetime in 1920.
With kind regards, Sydney
Dear Sydney,
If you accept that space is discrete, then take the second step - accept that the electric field in space is also discrete. And this discreteness is possible only in the form of 1-dimensional discrete vectors. Their number will grow with the square of the distance from the charge, and the length (the magnitude of the field) is inversely proportional. When the charge moves through space, the surrounding vectors rotate after it. This rotation is a magnetic field. The Dirac monopole is impossible, i.e. the rotation of the vector has no material carrier.
Dear Ilya Boldov
A couple of years ago they did an experiment at an technical university with electromagnetic waves that were forced to exceed the speed of light. If I remember well it was with the help of a fast rotating emittter.
At the velocity of the speed of light the sensor registered the electric field and the corresponding magnetic field. Above the speed of light the electric field broke down but the magnetic field still influenced the sensor. The experiment made the headlines in the news papers but unfortunately I forgot to get the paper so I have no link.
Anyway, the experiment didn't violate the text books in relation to the properties of the universal electric field because this is known physics. So if you have the opinion that the electric field is a 1D vector field like the magnetic field and not a 3D topological field it is difficult to understand the description of your concept. Because your concept has the consequence that the velocity of electromagnetic waves is not restricted by the speed of light. Nevertheless, why don't you focus on gravitation? Newtonian gravity is thought to act instantaneously, like the magnetic field. That means that the vectors of the magnetic field and the vectors of Newtonian gravity are superpositioned "in discrete space".
With kind regards, Sydney
Dear Ilya Boldov
Maybe I was a bit too vague in my previous comments, so I will try to do it better. :)
The image above (enclosed) shows a schematic representation of discrete/quantized space. That means that the image only represents the mathematical (geometrical) properties “volume”, “tessellation” and “equality”. Of course the image shows a metric. The schematic image is well known by researchers in the field of quantized space (mathematical physics).
If we want to know how discrete space can “create” physical reality we have to know the basic properties of the units of the spatial structure. Unfortunately all the physics is about the mutual relations between the observable/detectable phenomena. Thus “our daily reality” represents the mutual dynamical differences between these units, not “the stuff” (the structure of) our universe is made of.
In physics we have all kinds of descriptions about phenomena (e.g. particles) and their mutual interactions. All these phenomena must have a size that is larger than the size of 1 unit. So if we fantasize how our universe actually “functions” with the help of all these phenomena we don’t know if our created concept is correct. Because other types of phenomena will result in other concepts.
The solution to this problem is the choice of those “phenomena” that exist everywhere in the universe (thus are caused by the basic properties of every unit of discrete/quatized space). That means that we have to create a mathematical model of the structure of discrete space with the help of the known universal properties:
- the conservation of energy and momentum
- the universal constants (speed of light; Planck’s constant)
- the universal principles (e.g. Heisenberg’s uncertainty principle; the principle of non-locality)
If your model is correct the dynamical mutual relations between the units must show what we know in modern physics (QFT) about physical reality at the smallest scale size. In other words, your model will show the existence of the Higgs field, the electric field and the magnetic field and the mathematical origin behind the properties of each quantum field. The gravitational field is not a basic quantum field (gravity is an emergent force field) so your model will not show the properties of the force of gravitation. Because you have to implement matter in the model to get the effect of the gravitational force.
I hope that this is a better description than my comments before.
With kind regards, Sydney
Dear Sydney !
My understanding of mass as the geometry of space and the geometry of elementary particles, where each elementary particle has one (or several) volumes of regular polyhedra, has already been written and posted on this site. They are not the main thing for me. I plan to get a Nobel Prize for a Geometric model of atomic nuclei. The article is also on this site. I am attaching an archive with a computer program for modeling kernel structures. It should be unzipped into a separate folder and run ANV.exe
Wolfgang Konle,
Force concept is a binding glue in Newtonian paradigm. If gravity is proved to be a non standard force type then paradigmatic problems, not just single theory problems would arise. The "big plan" needed is a conceptual entity as a substitute to the theoretical role done by force
Gravity is not a force itself, nor is inertia. These are the properties of mass as the geometry of space. The figure shows two masses L1,L2 located in one-dimensional space, but also in a conjugate two-dimensional one, which distorts one-dimensional space, spreading it apart. The inhabitants of the one-dimensional universe cannot feel this distortion, but it manifests itself as the forces of gravity (Fg) and the forces of Inertia (Fi). Replace one-dimensional space with three-dimensional space and bodies with V1, V2, get the forces of gravity and inertia.
Here is a simple drawing with a one-dimensional space and a conjugate two-dimensional space.
Ilya Boldov "Energy is always associated with movement."
Kinetic energy only is one half of the story. The other half is the energy density of force fields.
We know that the energy density E of force fields (g, E, H) (gravitational, electric, magnetic) is given as E = (-g²/(8πG), ε0E²/2, μ0H²/2).
Dear Wolfgang !
There is no density of fields, there is an absolute value.
The magnitude of the so-called gravitational field is the angle of inclination of the curvature of three-dimensional space in 3+ dimension. See the picture above. If the body rolls into someone else's curvature of space - gravity. If they try to push the body out of its own curvature of space - inertia. The magnitude of a discrete one-dimensional vector that distributes an electric charge around itself is an electric field. The rotation of this vector is a magnetic field.
“…The threads question is "...what makes it so similar to fundamental forces &how spacetime creates a "force effect" ?"…”
- yeah, that is so. And that
“…The answer to the question follows from the fact that the gravitational force in a metric theory of gravity is entirely determined by the connection on the Lorentzian manifold. …. The metric is fundamental to the curvature of spacetime; matter tells spacetime how to curve, and curved spacetime tells matter how to move. Few people seem to understand this ….”
- in mainstream physics is so. Indeed in the mainstream “matter tells spacetime how to curve, and curved spacetime tells matter how to move”; though that “Few people seem to understand this” looks, in certain sense, though, as rather questionable claim. The “metric theory of gravity” , i.e. the GR, is the standard theory in mainstream physics, and that matter tells spacetime to curve, etc., rather numerous people know.
Though the words “know” and “understand” indeed, are really different, including in this case the word “understand” simply evidently isn’t applicable – it is fundamentally impossible really to understand the fundamentally impossible, and so unscientific, wording “matter tells spacetime how to curve, and curved spacetime tells matter how to move”.
That can be really understood by some people evidently only if they can really scientifically explain – so how some “mass” impact on the “spacetime”?, for what evidently is necessary before to understand – what are “mass”?, “space”?, and “time”?
Since in the mainstream philosophy and sciences all really fundamental phenomena/notions, , first of all in this case “Matter”– and so everything in Matter, i.e. “particles”, “fields”, etc., “Consciousness”, “Space”, “Time”, “Energy”, “Information”, are fundamentally completely transcendent/uncertain/irrational, any scientific answer in framework of the mainstream is fundamentally impossible,
- including, correspondingly, in the case above any explanation doesn’t exist in the GR, and really this GR postulate is completely nothing else than some ad-hoc claim of the author, for whom the phenomena/notions above, and so “mass”, “space”, and “time”, were – and for recent people in the mainstream, which “understand” this really transcendent, and really scientifically fundamentally incorrect, assertion really only in some strange sense.
What really the fundamental phenomena/notions above are can be, and is, really scientifically explained only in framework of the 2007 Shevchenko-Tokarevsky’s “The Information as Absolute” conception, recent version of the basic paper see
https://www.researchgate.net/publication/363645560_The_Information_as_Absolute_-_2022_ed
- and more concretely in physics in the Shevchenko-Tokarevsky’s informational physical model , the two main papers, where the model is presented are
https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics, and
https://www.researchgate.net/publication/355361749_The_informational_physical_model_and_fundamental_problems_in_physics
Including in the model it is scientifically explained what is the Gravity, which is, of course, nothing else than some fundamental Nature force, which in a few traits is similar to fundamental Nature Electric force, more see https://www.researchgate.net/publication/365437307_The_informational_model_-_Gravity_and_Electric_Forces
- and that is the really scientific answer to the thread question, though to understand why and how Gravity acts as it acts is necessary to read, and really to understand, what is written in the papers
- while in this case that is possible, since the conception and the models are completely scientific and fundamentally don’t contain any transcendence and mystic.
So more see the links above, recent SS posts in https://www.researchgate.net/post/Can_we_think_that_general_relativity_rather_predicted_that_the_universe_is_a_black_hole, and
https://www.researchgate.net/post/Why-there-is-a-force-on-a-charge-within-the-electric-field/3 , though, are relevant to this thread question.
Cheers
If we want to use a simple example of a force we can imagine an enormous spherical magnet and some iron powder. It is obvious that the iron powder is “attracted” by the enormous magnet so without further experiments it is like the magnetic force has the same nature as the gravitational force.
But further experiments show that the magnetic force field has the signature of a loop. So the question raises if every force is a loop. The consequence of the main law of physics – the law of conservation of energy – is that there must be some kind of a loop (reversal motion) to keep the total amount of energy transfer in the universe invariant. The argument that the whole loop is situated within the volume of the universe has no sense because if the laws of nature have the same origin everywhere in the universe the whole universe is “filled” with all kinds of loops.
The force of gravity seems to be “loop-less” and that is worrying. The solution is the concept that gravity isn’t a pull force but it is a push force from vacuum space around. Like the experiments of Louis Rancourt and Philip Tattersall showed (shielding the force of gravity with a “sheet” of light: http://dx.doi.org/10.5539/apr.v7n4p4).
The cause behind the “creation” of gravity is the existence of matter, local concentrations of energy. Thus to create a proton (matter) we have to concentrate energy – quanta – from vacuum space around (E = m c2). Unfortunately, matter is not only a concentration of energy within and by the electromagnetic field, above a certain threshold the concentrated energy forces one of more enclosed scalars of the Higgs field to decrease their magnitude. The mathematical consequence is that the electromagnetic field can concentrate more quanta from around. This surplus of energy was termed “rest mass” but the quark/gluon hypothesis has displaced the term. Although it is still valid and it is thought that the Higgs boson “intermediate” between the local Higgs field and the local electromagnetic field to create this surplus of energy. In general the present hypothesis is that matter is an excited state of the underlying basic quantum fields (QFT). The origin of the energy of the mass is mysterious because there is no description of the mechanism of the electromagnetic field that is responsible for the concentration of energy (that is the prize we pay if we transform physical reality into a fall of equations).
The electromagnetic field shows to be a rest frame (https://iopscience.iop.org/article/10.3847/2041-8213/ac6f08) and the velocity of the solar system in relation to the rest frame is ≈ 370 km/s. That means that the orbit of our planet isn’t a nearly circular motion around the sun. The motion is like a swirl. Thus the curvature of space itself in the theory of General relativity is a hypothetical model that can be qualified as an “illusion” because the curvature shows to be a swirl… I am really curious to read all the arguments of physicists who claim that the foundation of our universe – space itself – is forced to swirl by the existence of matter.
However, Isaac Newton used the centripetal force of Christiaan Huygens to prove that the orbits of the planets of the solar system are caused by the force of gravitation. But the centripetal force is derived from true circular motion and it simply doesn’t exist in relation to the rest frame of the electromagnetic field (the basic quantum fields create physical reality).
The conclusion must be that all the concepts we have constructed with the help of observations and measurements are only “true” in relation to a certain relative point of reference. That means that forces are only forces by convention. Like proposed by Philippos Afxentiou in the title of the question.
With kind regards, Sydney
Ilya Boldov "There is no density of fields, there is an absolute value."
The correct term is: "Energy density of force fields". This energy density is proportional to the field strength squared.
Sydney Ernest Grimm "So the question raises if every force is a loop."
A nice in-depth treatise about the origin of forces. However, there is a profound short explanation:
Any force F on an object, which contributes to a background force field, is given by the derivative (differential quotient) of the energy contained in the overlay of the object field O and the background field B, in respect to the distance S of the object from the source of the background field. (Bold entities are vectors.)
F=d/dS (k ∫ (B+O)²dV). d/dS=(d/dx, d/dy, d/dz); k is a proportionality constant, which can be equal to (-1/(8πG), ε0/2, μ0/2) in the cases (gravitational, electric, magnetic); The volume integral ∫dV is over the significant volume filled with field O.
The field energy density is proportional to the field strength squared. We know that the energy density E of force fields (g, E, H) (gravitational, electric, magnetic) is given as E = (-g²/(8πG), ε0E²/2, μ0H²/2). (bold entities are vectors)
It is so amazing how people continue to deviate from the facts that I must repeat the answer to the question of this thread: the gravitational force in a metric theory of gravity is entirely determined by the connection on the Lorentzian manifold. The symmetric Levi-Civita connection is constructed from the Lorentzian metric and its first derivatives. The metric is a solution to the Einstein equation. The metric is fundamental to the curvature of spacetime; matter tells spacetime how to curve, and curved spacetime tells matter how to move. Few people seem to understand this. It should be added that GR cannot describe the complete curvature of spacetime without the addition of a matter profile to represent dark matter. MGR does not suffer from that deficiency because it contains Einstein's missing symmetric tensor representing gravitational energy-momentum.
A comment then arises concerning a metric theory of gravity "That idea is quite troublesome because in the early universe there was a period without matter, although space existed" whereas spacetime is filled with dark matter, gravitational energy-momentum, and dark energy. That follows from: 1) the structure of MGR where Einstein's equation is completed with the missing energy-momentum tensor that is constructed from the line element vector field, and 2) from the curvature of spacetime on a Lorentzian metric.
A positive definite Riemannian metric g+αβ exists on any paracompact manifold. It describes the fundamental curvature of spacetime that is attributed to gravitational attraction: g+αβ = gαβ + 2XαXβ/|gαβXαXβ| involves a pair of line element covectors. Since they describe dark matter particles, the pair of covectors in g+αβ is gravitationally attractive, as is each particle in the pair. Dark matter persists when ordinary matter is absent because the line element covectors always exist. Each point of a Lorentzian spacetime contains a myriad of quantum-metric covectors from which Φαβ and Φ are constructed. Spacetime is filled with dark matter, gravitational energy-momentum, and dark energy. Immediately after the Big Bang, intense radiation prevented ordinary matter from forming. Spacetime was maximally symmetric and the associated Killing vectors rendered Φ= 0. The intense radiation did not interact with dark matter. It gravitationally clumped and formed dense pockets or wells, which broke the symmetry of spacetime. Ordinary matter accumulated in the wells by gravity.
The interaction of dark matter with ordinary matter follows from the discussion: LXoXodm = −λ0Xαo Xβo ∇αXβ, which describes an interaction (with a coupling constant λ0) of ordinary matter (denoted by the subscript o) with dark matter. It follows that LXoXodm = λ0f2o uα∇αf = λ0f2o uαuαΦ =−λ0f2o Φ. Provided Xβ is not a Killing vector, Φ does not vanish, and dark matter can locally couple to ordinary matter.
Thus, In the absence of ordinary matter, dark matter is still present and curves spacetime. GR cannot describe dark matter because the line element field has been ignored.
Gary Nash "the gravitational force in a metric theory of gravity is entirely determined by the connection on the Lorentzian manifold"
Yes, but this is no contradiction to the energy dependency in the classic theory of gravity.
You write: "determined". What is the exact mathematical expression for a force on an object, which contributes to the space curvature?
The (per) Metric density of gravitation field lines relies on the topology you choose for demonstrating it . Since the limit of the attractive gravitational effect decreases inversely to the 3rd power with increasing atomic weight in almost any topology , supernova explosions could be explained by the process that the gravitational boundary shrinks below the surface of a star.
gravitational boundary shrinks below the surface of a star, when in the star interior nuclei with large atomic weights would be distorted even further .
With increasing field mass the reality boundary drops according to
Heim's law of gravitation decreases. For the smallest possible ponderable
mass results , a largest possible distance Dmax- which is a
maximum distance D'= 2 Dmax in the R3 somes out . Heim substituted
with the electron mass explicitly expressed by general natural constants and replaced it by curvature coefficients - He thence obtained spherical Distances (Maximum) and substituted in this cosmological relation for the time zero of the universe. The algebraic equation of determination of 7th degree for mereological derivation yielded 3 real solutions, which after their time update, i.e. the initial triggering of the R3-expansion in a later lying R4-region, 3 DIFFERENT TENSORIAL "STRUCTURAL UNITS" WERE FORMED.
A spherical surface with a diameter of about 3.6 m, the "protosphere
encloses a "Mesosphere" of approx. 1 m diameter . This sphere trinity is not a contradiction to the metron condition, because only the protosphere lies completely in the R3, while the two smaller svären lie only partially in the R3, i.e. merely their projections lie on that topology .
Wolfgang, as stated above and in any textbook on GR, the gravitational force in a metric theory of gravity is entirely determined by the connection on the Lorentzian manifold. The connection is given by \Gamma^\alpha_\alpha\beta, which depends on the metric and its first derivatives.
Gary Nash "The connection is given by \Gamma^\alpha_\alpha\beta, which depends on the metric and its first derivatives."
Yes, but the connection is a tensor field which describes the differential modification of the curvature on an arbitrary infinitesimal path. The question is about the force on an object, which contributes to the spacetime curvature. How do you determine this force? Or more precise, how can you calculate this force from the connection?
The problem with the connection dependency is, that the connection only depends on the given spacetime curvature and does not take into account the influence of the object on the spacetime curvature.
The energy formula considers both, the mass which causes the spacetime curvature and the influence of the object.
Wolfgang, in a metric theory of gravity, the notion of a force is replaced by the curvature of spacetime. Your statement "The problem with the connection dependency is, that the connection only depends on the given spacetime curvature and does not take into account the influence of the object on the spacetime curvature" is completely wrong since the metric, and therefore the curvature of spacetime, is a solution of the Einstein equation. That depends on the total of the energy-momentum of matter and that of the gravitational field. There is no "influence of the object on the spacetime curvature" that is not taken care of by the Einstein equation; all matter and associated energy from any source curves spacetime.
the gist of Gary Nash statement is that :
The connection of matter dependency is wrong, as the curvature of spacetime is a solution of the Einstein equation.
Wolfgang Konle is ALMOST opposite to this , thinking that :
Quote :
" the connection is a tensor field which describes the differential modification of the curvature on an arbitrary infinitesimal path. "
Truth of the matter is that as on Pseudo-Riemannian Manifolds , Spacetime is a manifold that is continuous and differentiable. This means that we can define scalars, vectors, 1-forms and in general tensor fields and are able to take derivatives at any point. A differential manifold is an primitive amorphous collection of points (events in the case of spacetime). Locally, these points are ordered as points in a Euclidian space. Next, we specify a distance concept by adding a metric g, which contains information about how fast clocks proceed and what are the distances between points. Einstein’s theory of gravitation is a geometric theory, in the sense that gravitational forces exerted by masses are mediated by a nontrivial structure of space and time. In particular, in the presence of matter, physical distances between bodies change, and time lapses at a different rate. All information about the effects of a matter distribution on space and time are elegantly encoded in a symmetric metric tensor gµν with a Lorentzian signature, which means that a local Minkowski metric around the observer has the signature.
Gary Nash
How do you calculate the motion of an object in curved spacetime?
Reza Sanaye "The connection of matter dependency is wrong, as the curvature of spacetime is a solution of the Einstein equation."
There seems to be a misunderstanding of the term "connection". My remarks are addressed to the mathematical term "connection" as defined by Levi Civita in differential geometry.
My understanding is not almost opposite to the understanding of Gary Nash. The main difference is that I think that the universe has the global shape of a 3-sphere, which locally is deformed by the influence of matter.
This shape is generated by a cosmic field of a high energy density and of gravitational nature, which overcompensates the negative energy density of gravitational fields. The cosmic field also has a divergence-less flow, which is aligned with the direction vector field of the Ricci tensor of the 3-sphere.
The main difference between my view and the MGR theory, as proposed by Gary, only is that I think MGR is not complete. Just the cosmic field is missing, which overcompensates the negative energy density of gravitational fields.
Apart from that I consider MGR as a substantial progress in theoretical physics.
Wolfgang you can calculate its geodesic curve if you know the solution of the Einstein equation for the metric.
I hope you can fully appreciate the line element field and how it defines the symmetric connection independent tensor that represents the energy-momentum of the gravitational field. From that we get a natural description of dark matter and dark energy that GR cannot provide without introducing a matter profile.
Gary Nash
Another point: Is it possible that a medium exists, which has the consistence of a gravitational field, but has a positive energy density?
Let us consider dark energy as an energy density of gravitational nature. This would mean that an overlay of an equal amount of dark energy density and of gravitational field energy density would lead to a zero-energy density. A gradient of dark energy density then would have the opposite gravitational impact as a gradient of gravitational field energy density.
But how could we consider such a dark energy density in Einstein's field equations? There is no negative mass present, which has a gravitational field consisting of dark energy. Dark energy could not be represented in the energy-momentum tensor, because this would not lead to the direct gravitational impact.
Could it be represented in the field equations at the position of the cosmological constant?
Can we exclude that dark energy is of gravitational nature with all the implications of directly causing space curvature?
Dear Gary, Gary Nash ,
we can say that the effects attributed to "Dark matter" are phenomenologies of something which goes beyond any kind of "matter"....
Dark matter, in the way it was conjectured to let GR continue to be valid, is a sort of ad "hoc intangible, transparent material stuff" like it was supposed to be the aether conceived by somebody more than a century ago to drive light, with the difference that it is localized in some volumes.
As a (dark) matter of fact the phenomenology of lensing and gravitational pulling which those volumes of sidereal space show, is due to a much deeper "essence" which normally pervades everything, which shoud be the quantum vacuum energy density.
Let's say that the whole universe is deeply made by something unknown with incredible energy density, so far modeled up to a certain extent, whose bizarre phenomenologies are the "dark matter" and "dark energy" .
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