Discussion
Started 5 May 2024

【NO.39】Doubts about General Relativity (4) - Who should determine the spacetime metrics of matter itself?

General Relativity field equations [1]:
Gµν = G*Tµν...... (EQ.1).
It is a relation between the matter field (energy-momentum field) Tµν and the spacetime field Gµν, where the gravitational constant G is the conversion factor between the dimensions [2].Einstein constructed this relation without explaining why the spacetime field and the matter field are in such a way, but rather assumed that nine times out of ten, they would be in such a way. He also did not explain why the spacetime field Gµν is described by curvature and not by some other parameter. Obviously, we must find the exact physical relationship between them, i.e., why Tµν must correspond to Gµν, in order to ensure that the field equations are ultimately correct.
We know that matter cannot be a point particle, it must have a scale, and matter cannot be a solid particle, it must be some kind of field. The fact that matter has a scale means that it has to occupy space-time; the fact that matter is a field means that it is mixed with space-time, i.e., matter contains space-time. So, when applying Einstein's field equations, how is matter's own spacetime defined? Does it change its own spacetime? If its own energy-momentum and structure have already determined its own spacetime, should the way it determines its own spacetime be the same as the way it determines the external spacetime? If it is the same, does it mean that the spacetime field is actually a concomitant of the matter field?
If one were to consider a gravitational wave, one could think of it as a fluctuating spacetime field that propagates independently of the material source after it has been disconnected from it. They have decoupled from each other and no longer continue to conform to the field equations (EQ.1). Although gravitational waves are the product of a source, the loss of that source prevents us from finding another specific source for it to match it through the equation (EQ.1). Just as after an electron accelerates, the relationship between the radiated electromagnetic wave and the electron is no longer maintained. Does this indicate the independence of spacetime field energies?
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Related questions
♛ “Does the Energy Tensor Tµν in the Field Equations Contain the Energy-momentum of the Spacetime Field?”:https://www.researchgate.net/post/NO37Doubts_about_General_Relativity_2-Does_the_Energy_Tensor_Tmn_in_the_Field_Equations_Contain_the_Energy-momentum_of_the_Spacetime_Field
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References
[1] Grøn, Ø., & Hervik, S. (2007). Einstein's Field Equations. In Einstein's General Theory of Relativity: With Modern Applications in Cosmology (pp. 179-194). Springer New York. https://doi.org/10.1007/978-0-387-69200-5_8

Most recent answer

Yokesh Kumar S
Central University of Tamil Nadu
Its Bootstrap. System acts collectively , emerging , feedback loop of previous two state. No one is deciding or intervening the process. We as a scientist , having code, research finding must be repeatable , recreateble and universal. So while going through all these hundreds of steps ,we need a database and database manager. Maths served as Database Framework, Equation becomes an identifier, solutions as observable value.
Nature doesnt act as by Equations. We observe and try to fit it in a expression whatever is possible. Mathematical equations gave us solutions and approximations ,coincidently almost exactly similar to actions in Nature.
The fundamental constant 'h', 'c' and Higgs mechanism is responsible for all values of observable ,eigen values , solutions everything, the fine structure constant, coupling strength of field, instable heavy element decaying.
Did 'h' and 'c' and Higgs mechanism were predetermined by Nature ? Nope. Quantum fluctuations create a change ,either increase or decrease in Potential value of other particle/quanta. The Quantum Fluctuation is RANDOM. But isnt Quantum Fluctuation result of present values of Field , Particle , constant ? Yes. That indicate Quantum Fluctuation is pseudo Random.
Fluctuation behave by given Fundamental Values. Fundamental Values determine Fluctuation.
I think we have hit at a Feedback Loop, which never can be answered except in Higher Dimensions similar to our 3 + 1 Dimension.

All replies (29)

Stam Nicolis
University of Tours
The spacetime metric, determined by matter, is the solution of Einstein's equations. That's all, nothing more and nothing less.
Walter Smilga
Independent Researcher
"It is a bad habit of physicists to take their most successful abstractions to be real properties of our world." (N. David Mermin)
If we consider space-time as an abstraction of the trajectories of material objects, there is no difference between "curvature of space-time" and "curvature of matter".
Sergey Shevchenko
Institute of Physics, National Academy of Sciences of Ukraine
The scientific answer to question “what is Gravity” is given in a few SS posts on page 1 in https://www.researchgate.net/post/NO36_Doubts_about_General_Relativity_1-Is_the_Geometry_Interpretation_of_Gravity_a_Paradox/1,
first of all that Gravity fundamentally is only some fundamental Nature force, which, as all other – Weak, Electric, Strong/Nuclear, Forces, exists and acts in the Matter’s fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct),
- by that particles [so further bodies, etc.], again as that happens at actions of all other Forces, radiate Gravity Force real mediators, intensive flows of which compose “gravitational fields” in 3D space, again, as that all other Forces do;
- and at that, again as that happens at actions of all other Forces, at Gravity action fundamentally nothing happens with the space/time/spacetime above. More see the link above and the linked papers in this link, where the Shevchenko-Tokarevsky’s Planck scale informational physical model, including initial Planck scale Gravity model is presented.
So only a note to
“…【NO.39】… - Who should determine the spacetime metrics of matter itself?…..”
Really metrics of the spacetime above indeed “is determined by matter”, as that follows from the rigorous scientific definitions of the absolutely fundamental phenomena/notions “Space”, and “Time”, which can be, and are, given only in framework of the SS&VT philosophical 2007 “The Information as Absolute” conception, the link again see the link above:
- the spacetime has fundamentally unique one time dimension,ct,
- while the number [4+4] and nomenclature of the space dimensions are determined by number and nomenclature of degreases of freedom at changing of states of the Matter’s ultimate base –primary elementary logical structures – (at least) [4+4]4D binary reversible fundamental logical elements [FLE], which compose the (at least) [4+4]4D dense FLE lattice that is placed in the space.
- while everything in Matter/matter is/are only some disturbances in the lattice.
So indeed, metrics of the space is determined by “metric of matter”, though more rigorously scientifically – yet by “FLE metric”, the fundamentally infinite Matter’s spacetime “immediately appeared” in parallel just when first FLE was created,
- while “FLE/matter metric” is determined by the conditions above – FLE must be binary [for this is necessary 3 degreases of freedom and 3XYZ dimensions], reversible [for this is necessary 1 degrease of freedom and one cτ-dimension], and at least 4 logical marks/degreases of freedom [and g,w,e,sdimensions] that determine the at least 4 Forces above action. That’s all.
Though, of course, here the question appears – Who did this “FLE metric” designed/determined? With a well non-zero probability that was done by some Matter’s Creator, etc., but this point is now rather far from physics.
More see the SS first of all April 19, posts, in the linked above thread..
Cheers
Thanks for your answer!
"It is a bad habit of physicists to take their most successful abstractions to be real properties of our world." (N. David Mermin).
Couldn't agree more with that sentiment. But I don't quite understand your sentence:“If we consider space-time as an abstraction of the trajectories of material objects, there is no difference between "curvature of space-time" and "curvature of matter". ”
What does“the trajectories of material objects”means?object self? a good idea.
Best Regards, Chian Fan
1 Recommendation
Thank you for your answer! You said "The spacetime metric, determined by matter, is the solution of Einstein's equations. That's all, nothing more and nothing less."
You mean Einstein's Equations determines all spacetime metrics, Including the space-time of matter itself? Then, in essence, it is the same as saying that all spacetime metrics are part of matter, similar to Walter Smilga 's point above, that a spacetime metric is a "curvature of matter".
For example, who determines the spacetime of an electron? If the electron is a field, even though we can define a radius for it that describes the size, it has no truncated boundaries when viewed as a whole. So does it have the same mechanism of action for its internal and external spacetime metrics? Does the electron field represent all mass/energy and determine all spacetime metrics? Is this the relationship between fields and spacetime?
We know that gravitational fields affect the frequency of photons, so does a photon traveling in free space affect the spacetime around it?
Is it the starting point of quantum gravity theory to consider the effect of photons and electrons on the spacetime metric in this way?
Please, if it's convenient, I look forward to your answering the following two questions together.
Best Regards, Chian Fan
1 Recommendation
Stam Nicolis
University of Tours
The spacetime metric-in the presence of matter-is determined by Einstein's equations, by virtue of the fact that the energy-momentum tensor of matter appears on the RHS of Einstein's equations.
In the absence of matter, Einstein's equations have as solution the flat metric, describing Minkowski spacetime, if the cosmological constant is zero; if it isn't zero, the solution is de Sitter spacetime, if the cosmological constant is positive or anti-de Sitter spacetime, if the cosmological constant is negative.
In the presence of matter, Einstein's equations acquire a non-zero RHS, essentially equal to the product of Newton's constant and the energy-momentum tensor of matter.
The equations of motion for matter, also, depend on the metric; the equations are coupled and are solved together.
However, since Newton's constant is dimensionful, it does matter that the--dimensionless--combination of Newton's constant and the ``typical'' energy of matter is a very small number, unless we're dealing with objects like the Earth (or more massive). That's why ordinary matter affects spacetime to a negligible extent and therefore spacetime can be taken to be flat for non-astronomical situations (the cosmological constant, too, doesn't affect this; that's why its name is appropriate, it is relevant for cosmological siuations), so an electron doesn't contribute to curving spacetime in any meaningful way; its equations of motion can be solved by taking the metric to be the flat metric, which is also a solution of Einstein's equations when the contribution of matter and of the cosmological constant can be neglected-and the appropriate boundary conditions, of course, have been imposed.
Stam Nicolis
University of Tours
There's no particular ``origin'' in any spacetime, due to general coordinate invariance.
``Central objects'' make sense in the Newtonian approximation, not in spacetime.
de Sitter spacetime has a (past) singularity-in spacetime-not an origin. That singularity isn't ``anywhere in particular'', though.
``Origin'' refers to a coordinate system, a spacetime doesn't have a unique coordinate system.
The difference between an origin and a singularity is that the singular behavior of coordinate systems at an origin can be resolved by changing coordinate systems; the existence of spacetime singularities doesn't depend on the coordinate system chosen and is a property of the spacetime, whatever the choice of coordinate system.
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Walter Smilga
Independent Researcher
Dear Chian Fan,
What I mean is simply this: The kinematics of a material body can be described by its position in time or by its trajectory in space-time. This trajectory will generally be curved by the forces acting on the body. Einstein took this curvature as the curvature of spacetime (cf. his paper of 1916). Einstein's spacetime can therefore be seen as an abstraction of all possible trajectories of a material object in a given environment.
The "bad habit" to take "abstractions to be real properties of our world" (Mermin) obscures this connection and opens the door to all kinds of misinterpretations.
Best regards,
Walter Smilga
Chian Fan,
"It isn't about doubts but about lack of knowledge."
The answer to your question is in this short YouTube video with Distinguished Theoretical Physicist and String Theorist Robbert Dijkgraaf.
Stam Nicolis
University of Tours
No metric has any particular origin and that includes the Kottler metric or any solution of Einstein's equations.
It would be useful to understand the difference between objects moving in space and time separately and spacetime.
1 Recommendation
Sergey Shevchenko
Institute of Physics, National Academy of Sciences of Ukraine
The thread question is scientifically answered in SS post on page 1, and more in detail in links in the post; if quite briefly
- Gravity is fundamentally nothing else than some fundamental Nature force, and, as all other fundamental Nature forces, exists and acts in Matter’s fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct),
- and at existence and acting of Gravity Force, again as that happens for all other Forces, fundamentally cannot be, and so isn’t, any interactions between any/everything in Matter, including “masses”, with the spacetime. Including, of course, to spacetime no any “stresses” “energies”, etc. fundamentally cannot be transmitted, etc.
So considering of any other spacetime metrics besides the Cartesian one above really is fundamentally senseless.
[Note also that in mainstream physics only a part of utmost universal “kinematical” spacetime with metrics (cτ,X,Y,Z,ct), i.e. really space with metrics (icτ,X,Y,Z ), “i” is imaginary unit, i.e. Minkowski and pseudo Riemannian spaces is really of course erroneously postulated as the spacetime, where the space -dimension with imaginary unit is postulated as the time dimension]
More see the SS pointed post and links in the post.
Cheers
Are you telling me that my question was already scientifically settled and my questioning it is my ignorance? No matter, we are all ignorant.
The link you provided is forbidden in my area, please summarize the content of the short video for us.
Best Regards, Chian Fan
1 Recommendation
Usually we think of gravity's relative manifestation in the microscopic space as being too small to have any substantial effect. But such an understanding is not without problems.
1) Generally we use the gravitational and electromagnetic force ratio of protons or electrons to assess their magnitude difference, which is roughly 10-36 when r is the macroscopic distance. This is indeed too big a difference. However, we must note that a small gravitational force is not the same as a zero gravitational force. There is a fundamental difference here. If we don't use ratio analysis, but instead consider the gravitational force alone, it is clear that the gravitational force Fg=Gme2/r2 increases dramatically as r decreases. If the electromagnetic force does not similarly increase at this point, or even the charge fails, then gravity undoubtedly becomes the dominant force at the microscopic level.
2) Do the Einstein field equations not apply to microscopic particles? Then we would have to make a change in Einstein's starting point for establishing the field equations, because the field equations are established without any energy level constraints. If the quantum level does not hold, then why does the macroscopic hold? Has mass changed qualitatively in any way from microscopic to macroscopic?
3) As long as we acknowledge the basis of Einstein's ideas in constructing the field equations, that mass generates a spacetime metric, how would it be more reasonable to proceed in the hope that Einstein's field equations would be quantized at both ends and linear at both ends?
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Chian Fan,
If you are a nerd,you should be able (by) yourself to find a workaround to overcome the glitch that prevents you from having access to that YouTube video.
Since you have participated in the discussion and made suggestions, it should not be too much to ask that you generously share your understanding.
Young man, please do not speak rudely.
1 Recommendation
Esa Säkkinen
University of Oulu
From the point of view of GR spacetime buoyancy, the real structure of spacetime develops event by event, and when the particle has passed the event shell, the curvature is updated and the correlation settles over the distance, and the existence of energy density in itself is not a prerequisite for the shape of spacetime. In accordance with the holographic principle, the event shell stores the curvature information in tidal stresses, which are bundled into shape by a continuous light-like waving as a manifold that preserves the momentums of the field parts. Other entangled quantum states can also be conserved as non-local hidden variables over the spacetime structure.
Spacetime geometry and matter content do not need to be separate - they can be modeled as a whole as 4-buoyancy with 4-density, which is mainly based on the motion state in the tangent plane of the local event shell, giving the equilibrium state of geodesics and density equally.
Eugene Prokhorenko
National Academy of Sciences of Armenia
Gµν = G*Tµν...... Can be rewrite as g(mu,nu) = G(mu,nu,a,b)*T(a,b).
For simplicity we use G(mn,nu,a,b) as set of constants. Equations are nonlinear. Lets think if it's possible to split matter and and field like:
1: g(mu,nu)=0
2: T(a,b)=0
Further depends on our understanding of matter and field.
a. Does g depends on on matter (T)
b. Does T depends on field (g)
So in easy case its possible to have solutions for field without matter or for matter without field. And it's hard to see physical sense for such solutions.
Sergey Shevchenko
Institute of Physics, National Academy of Sciences of Ukraine
The thread question is rigorously scientifically answered in SS posts o pages 1, 2. If quite briefly – Gravity fundamentally is nothing else than some fundamental Nature force, and as all other Forces, acts in the Matter’s fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct).
The spacetime, as that rigorously proven in the Shevchenko-Tokarevsky’s really philosophical 2007 “The Information as Absolute” conception, recent version of the basic paper see
- and more concretely in the Shevchenko-Tokarevsky’s Planck scale informational physical model, which is based on the conception, 3 main papers are
- fundamentally cannot be “contacted”, “dilated”, “curved”, etc., by anything in Matter, and so fundamentally cannot have other metrics than the above one.
What concretely really Gravity Force is see the Shevchenko-Tokarevsky’s 2007 Planck scale informational physical Gravity [and Electric Force] model either in section 6. “Mediation of the fundamental forces in complex systems” in 2-nd whole model paper link above, or in https://www.researchgate.net/publication/365437307_The_informational_model_-_Gravity_and_Electric_Forces
In 3-rd link of whole model the 2023 initial Planck scale model of Nuclear Force is presented; where it is rigorously scientifically shown that on Planck scale at least these 3 Forces above act by the same one scheme.
So, say, to that
“…Lets think if it's possible to split matter and and field like: …So in easy case its possible to have solutions for field without matter or for matter without field. And it's hard to see physical sense for such solutions.…..”
- [besides that in the GR there is no Gravity “field”, gravitational interactions are determined by “curved spacetime metrics”, which for/by some completely mystic reasons/ways has some “stress-energy”], note that really Gravity field – as fundamentally all other Forces fields without Forces charges – cannot exist without Gravity charge “gravitational mass”, and in Matter everything that has inertial mass, i.e. practically everything at all [besides the fields at least at statics] has gravitational mass.
More see the SS posts above and links in the posts.
Cheers
A good answer to each of the questions does not require many copies. Please leave the opportunity for others to express different points of view and to see different points of view.
Best Regards, Chian Fan
1 Recommendation
Sergey Shevchenko
Institute of Physics, National Academy of Sciences of Ukraine
Dear Chian Fan,
You write
“…A good answer to each of the questions does not require many copies…”
- that looks as a bit questionable claim. There is nothing bad when good answers to scientific questions are repeated as some copies, besides in RG discussions that is simply convenient for readers, first of all for new in a thread ones.
While that
“… Please leave the opportunity for others to express different points of view and to see different points of view...”
- looks, since is addressed to SS posts, as a too questionable claim. Really in RG threads rather numerous posts contain quite “non-good” answers, and the posters are rather vivid, what essentially interfere with the readers, who really want to know good, i.e. really scientific, answers, to read them; in some cases that looks as some deliberate spamming.
At that I don’t write as a rule more one post/day; and, if the thread’s question is already answered, no more one notification to the readers above about where the answers are, than one post in a page. What evidently don’t disturb opportunity for others to express different points of view and to see different points of view. When, again, rather often it would be better if some strange scientifically points would not appear in threads at all.
Cheers
Yokesh Kumar S
Central University of Tamil Nadu
Its Bootstrap. System acts collectively , emerging , feedback loop of previous two state. No one is deciding or intervening the process. We as a scientist , having code, research finding must be repeatable , recreateble and universal. So while going through all these hundreds of steps ,we need a database and database manager. Maths served as Database Framework, Equation becomes an identifier, solutions as observable value.
Nature doesnt act as by Equations. We observe and try to fit it in a expression whatever is possible. Mathematical equations gave us solutions and approximations ,coincidently almost exactly similar to actions in Nature.
The fundamental constant 'h', 'c' and Higgs mechanism is responsible for all values of observable ,eigen values , solutions everything, the fine structure constant, coupling strength of field, instable heavy element decaying.
Did 'h' and 'c' and Higgs mechanism were predetermined by Nature ? Nope. Quantum fluctuations create a change ,either increase or decrease in Potential value of other particle/quanta. The Quantum Fluctuation is RANDOM. But isnt Quantum Fluctuation result of present values of Field , Particle , constant ? Yes. That indicate Quantum Fluctuation is pseudo Random.
Fluctuation behave by given Fundamental Values. Fundamental Values determine Fluctuation.
I think we have hit at a Feedback Loop, which never can be answered except in Higher Dimensions similar to our 3 + 1 Dimension.

Similar questions and discussions

【NO.36】 Doubts about General Relativity (1) - Is the Geometry Interpretation of Gravity a Paradox?
Discussion
24 replies
  • Chian FanChian Fan
“According to general theory of relativity, gravitation is not a force but a property of spacetime geometry. A test particle and light move in response to the geometry of the spacetime.”[1] Einstein's interpretation of gravity is purely geometrical, where even a free point particle without any properties and any interactions, moves in a curved spacetime along geodesics, but which are generated by the energy tensor Tµν [2]. Why isn't gravity generated directly by Tµν, but must take a circuitous route and be generated by the geometry of spacetime Gµν?
Gµν=G*Tµν
This is Einstein's field equation, and the Einstein tensor Gµν describes the Space-Time Curvature. We know that in classical mechanics and quantum field theory, it is the Hamiltonian, Lagrangian quantities that determine motion. Motion is essentially generated by energy-momentum interactions. Why is it irrelevant to energy-momentum in GR? Einstein had always expected the unification of electromagnetic and gravitational forces to be geometrically realized [3]*. Is such an expectation an exclusion of energy-momentum interactions in motion? Can the ultimate unification of forces be independent of energy-momentum and manifest itself only in motion in pure spacetime? If not, one of these must be wrong.
--------------------------------------
Supplement: Gravity is still a force
Gravity appears to be a ‘spacetime gravity’, i.e., gravity caused by spacetime metric differences, the same as gravitational red shift and violet shift [1]. The current four-dimensional space-time ‘geodesic’ interpretation of gravity is to match the geometric appearance of Space-Time Curvature. Time and space are symmetrical, and geodesic motion is not initiated by the ‘arrow of time’ alone, but must be accompanied by equivalent spatial factors. Any interpretation that destroys the equivalence of space and time should be problematic.
[1] "What is Force, a Field? Where is the Force Field? How does it appear? Is the Force Field a Regulating Effect of the Energy-Momentum Field?"
-----------------------------
Notes
* "After his tremendous success in finding an explanation of gravitation in the geometry of space and time, it was natural that he should try to bring other forces along with gravitation into a “unified field theory” based on geometrical principles."
If one thinks that it holds only at Tµν = 0, see the next question NO.37: Is there a contradiction in the Schwarzschild spacetime metric solution?
-----------------------------
References
[1] Grøn, Ø., & Hervik, S. (2007). Einstein's Field Equations. In Einstein's General Theory of Relativity: With Modern Applications in Cosmology (pp. 179-194). Springer New York. https://doi.org/10.1007/978-0-387-69200-5_8
[2] Earman, J., & Glymour, C. (1978). Einstein and Hilbert: Two months in the history of general relativity. Archive for history of exact sciences, 291-308.
[3] Weinberg, S. (2005). Einstein’s Mistakes. Physics Today, 58(11).
【NO.51】Is a Particle a Circle with Clear Boundaries? If not, on what Basis should its Radius Range be Determined?
Discussion
11 replies
  • Chian FanChian Fan
‘How big is the proton?"[1] We can similarly ask, “How big is the electron?” “How big is the photon?” CODATA gives the answer [2], proton rms charge radius rp=8.41 x10-16m; classical electron radius, re=2.81x10-15m [6]. However, over a century after its discovery, the proton still keeps physicists busy understanding its basic properties, its radius, mass, stability and the origin of its spin [1][4][7]. Physics still believes that there is a ‘proton-radius puzzle’ [3][4], and does not consider that the size of a photon is related to its wavelength.
Geometrically the radius of a circle is clearly defined, and if an elementary particle is regarded as a energy packet, which is unquestionably the case, whether or not it can be described by a wavefunction, can its energy have a clear boundary like a geometrical shape? Obviously the classical electron radius is not a clear boundary conceptually in the field, because its electric field energy is always extending. When physics uses the term ‘charge radius’, what does it mean when mapped to geometry? If there is really a spherical charge [8][9], how is it maintained and formed*?
----------------------------------------
Notes:
*“Now if we have a sphere of charge, the electrical forces are all repulsive and an electron would tend to fly apart. Because the system has unbalanced forces, we can get all kinds of errors in the laws relating energy and momentum.” [Feynman Lecture C28]
----------------------------------------
References:
[2] Tiesinga, E. (2021). CODATA recommended values of the fundamental physical constants: 2018.
[3] Carlson, C. E. (2015). The proton radius puzzle. Progress in Particle and Nuclear Physics, 82, 59-77. https://doi.org/https://doi.org/10.1016/j.ppnp.2015.01.002
[4] Gao, H., Liu, T., Peng, C., Ye, Z., & Zhao, Z. (2015). Proton remains puzzling. The Universe, 3(2).
[5] Karr, J.-P., Marchand, D., & Voutier, E. (2020). The proton size. Nature Reviews Physics, 2(11), 601-614. https://doi.org/10.1038/s42254-020-0229-x
[6] "also called the Compton radius, by equating the electrostatic potential energy of a sphere of charge e and radius with the rest energy of the electron"; https://scienceworld.wolfram.com/physics/ElectronRadius.html
[8] What is an electric charge? Can it exist apart from electrons? Would it be an effect? https://www.researchgate.net/post/NO44_What_is_an_electric_charge_Can_it_exist_apart_from_electrons_Would_it_be_an_effect ;
[9] Phenomena Related to Electric Charge,and Remembering Nobel Laureate T. D. Lee; https://www.researchgate.net/post/NO46Phenomena_Related_to_Electric_Chargeand_Remembering_Nobel_Laureate_T_D_Lee
【NO.43】Doubts about General Relativity (8) - How is Energy-Momentum of Gravitational Field Expressed? How is It Transferred? How is It Exchanged?
Discussion
32 replies
  • Chian FanChian Fan
Free spacetime contains no energy-momentum*, so when objects m are travelling at constant velocity in it, they do not exchange energy-momentum. Non-free spacetime contains energy-momentum. The Einstein field equation of general relativity,
Rµν - (1/2)gµνR = G*Tµν,
expresses the relationship between the energy-momentum (mass) and the structure of spacetime ( metric) at a point (region) in spacetime**. Usually we think that "Gravity couples universally to all forms of energy" [1]. Then, we need to ask three basic questions:
1) What is the best way to express the energy-momentum of the gravitational field? or how are the "long-standing problems about energy-momentum localisation in GR" [2][3][4] addressed? The energy-momentum of the gravitational field is the energy-momentum of the spacetime field, which must be localizable. The energy-momentum of the spacetime field must involve only the spacetime parameter xi(i=0,1,2,3), because the independent spacetime field has no other parameter (or it has some other hidden parameter that does not play an explicit role). But it cannot be expressed directly in terms of spatio-temporal coordinates (t,x,y,z) because they must be background independent, nor can it be expressed in terms of time lengths T and space lengths L because we have no way of determining the measurement boundaries. So what are the remaining covariates? The rates of measure change, curvature, and deflection, etc.. which are the most appropriate? Even if we consider space-time as a "medium", what are the properties of the medium? Density, elasticity? What density? What elasticity?
2) By what means are gravitational fields and other forms of energy-momentum exchanged with each other? Obviously it must be through a common covariate, and then the only option available is the spacetime covariate. Does this qualify that all other forms of energy-momentum must contain spacetime covariates? Includes energy-momentum of dark matter (no dark energy involved). And more critically, the form of these spacetime Attributes and the form in which the spacetime energy-momentum is expressed should be the same, i.e., if the energy-momentum of spacetime is expressed in terms of a change of metric, the other forms of energy-momentum must be related to a change in the spacetime metric; and if it is expressed in terms of a curvature, the other forms must be related to a change in the curvature.
3) Is the energy-momentum of the gravitational field conserved[5]? If the energy-momentum of the gravitational field is not conserved, what will become of the gravitation dominated evolution of galaxies?
-------------------------------------------
Notes
** The concept of a strict "point" interaction does not really exist in physics.
-------------------------------------------
References
[1] Kiefer, C. (2006). Quantum gravity: general introduction and recent developments. Annalen der Physik, 518(1-2), 129-148.
[2] Einstein Ann. d. Phys. 49, 769 (1916).
[3] Hestenes, D. (2021). Energy-Momentum Complex in General Relativity and Gauge Theory. Advances in Applied Clifford Algebras, 31(3), 51.
[4] Møller, C. (1958). On the localization of the energy of a physical system in the general theory of relativity. Annals of Physics, 4(4), 347-371.
[5] Szabados, L. B. (2009). Quasi-local energy-momentum and angular momentum in general relativity. Living Reviews in Relativity, 12(1), 1-163.
【NO.37】Doubts about General Relativity (2) - Does the Energy Tensor Tµν in the Field Equations Contain the Energy-momentum of the Spacetime Field?
Discussion
12 replies
  • Chian FanChian Fan
The external spacetime field produced by an object of mass M, the Schwarzschild spacetime metric solution, is usually obtained as follows [1]:
1) Assumes a spherically symmetric spacetime metric, and is static and time invariant;
2) Assumes a vacuum conditions outside, with Tµν = 0;
3) Solve the Einstein field equation, Rµν - (1/2)gµνR=Tµν...... (EQ.1)
4) Utilize the boundary condition: the Newtonian potential ф = -GM/r, which introduces the mass M. Obtain the result:
ds2 = -(1-2GM/r)dt2 + (1-2GM/r)-1dr2 + r22...... (EQ.2)
Overall, the Schwarzschild metric employs a priori derivation steps. The solution is unique according to Birkhoff's theorem.
Einstein does not explain why M leads to ds2, our questions are:
a) The spacetime metric is containing the energy-momentum Tspacetime , which can only originate from Tµν and is conserved. Why then must spacetime receive, store, and transmit energy-momentum by curvature* ?
b) The implication of condition 2) is that the spacetime field energy-momentum is independent of M or can be regarded as such. Comparing this to the electric field of an electron is equivalent to the fact that the energy contained in the electron's electric field is independent of the electron itself. Since Tspacetime is also bound to M, is it not part of M?
c) For complex scenarios, in the Tµν of Einstein's field equation EQ.1, should one include the spacetime energy momentum at the location? With the above Schwarzschild solution, it seems that there is none, otherwise both sides of the equation (EQ.1) become a deadly circle. So, should there be or should there not be? Does the field equation have a provision or treatment that Tµν can only contain non-spacetime energy momentum?
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Notes
** "Doubts about General Relativity (1) - Is the Geometry Interpretation of Gravity a Paradox?" https://www.researchgate.net/post/NO36_Doubts_about_General_Relativity_1-Is_the_Geometry_Interpretation_of_Gravity_a_Paradox
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References
[1] Grøn, Ø., & Hervik, S. (2007). Einstein's Field Equations. In Einstein's General Theory of Relativity: With Modern Applications in Cosmology (pp. 179-194). Springer New York. https://doi.org/10.1007/978-0-387-69200-5_8
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2024-04-26
Additional information*:
1) In his Karl Schwarzschild Memorial Lecture, Einstein summarized the many scientific contributions of his short life, stating [1], in commenting on Schwarzschild's solution, that “he was the first to succeed in accurately calculating the gravitational field of the new theory”.
(2) Einstein emphasized in his article “Foundations of General Relativity” [1], “We will make a distinction between 'gravitational field' and 'matter', and we will call everything outside the gravitational field matter. Thus the term 'matter' includes not only matter in the usual sense, but also electromagnetic fields.” ; “Gravitational fields and matter together must satisfy the law of conservation of energy (and momentum).”
(3) Einstein, in his article “Description based on the variational principle” [1], “In order to correspond to the fact of the free superposition of the independent existence of matter and gravitational fields in the field theory, we further set up (Hamilton): H=G+M
4) Einstein's choice of Riemannian spacetime as the basis for the fundamental spacetime of the universe, which I have repeatedly searched for in The Collected Papers of Albert Einstein, still leads to the conclusion that he had no arguments, even if only descriptions. In his search for a geometrical description, he emphasized that “This problem was unsolved until 1912, when I hit upon the idea that the surface theory of Karl Friedrich Gauss might be the key to this mystery. I found that Gauss' surface coordinates were very meaningful for understanding this problem.”[2] And, although many physicists also do not understand what Space-Time Curvature is all about, everyone accepted this setup. This concept of `internal curvature', which cannot be mapped to physical reality, is at least a suitable choice from a modeling point of view.
5) Einstein's initial assumptions for the field equations were also very vague, as evidenced by his use of terms such as “nine times out of ten” and “it seems”. He was hoping to obtain the gravitational field equation by analogy with the Poisson equation. Thus, the second-order derivative of the spacetime metric is assumed on the left side of the equation, and the energy-momentum density is assumed on the right side.
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* The citations therein are translated from Chinese and may differ from the original text.
[1] University, P. (1997). The Collected Papers of Albert Einstein. Volume 6: The Berlin Years: Writings, 1914-1917. In. Chinese: 湖南科学技术出版社.
[2] Einstein, A. (1982). How I created the theory of relativity(1922). Physics Today, 35(8), 45-47.
Is spacetime an elastic medium that propagates waves?
Discussion
7920 replies
  • John A. MackenJohn A. Macken
The fallacy of the aether was that its only function was to propagate light waves. This question goes much further and probes whether space (the vacuum) is an elastic medium that propagates waves at the speed of light. For example, do gravitational waves propagate in the elastic fabric of space? If space is assumed to be an elastic wave propagation medium, then gravitational wave equations imply this medium has enormous impedance of c3/G = 4 x 1035 kg/s.
This is a discussion question, and I am going to take the position that spacetime is an elastic medium with “spacetime foam” properties first proposed by John Wheeler. He determined that the uncertainty principle and vacuum zero-point energy implied space has Planck length oscillations at Planck frequency. This would make spacetime a physical medium that propagates waves at the speed of light with impedance of c3/G. This impedance is so enormous that a rotating wave with Planck length amplitude and an electron’s Compton radius would have an electron’s energy.
I am taking the position that the quantum vacuum is a sonic medium that propagates waves at the speed of light. This medium gives the vacuum its “intrinsic” properties such as vacuum permittivity εo, vacuum permeability μo, impedance of free space Zo, virtual particle formation, etc. If spacetime is not a physical medium, why does it have finite values for εo, μo and Zo? The following link has more information about my opinion and model. What is your opinion?

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