Gravity is the only force with universal manifestation. Gravity's only known theory as universal manifestation consists as a capacity to alter time and spatial metrics.
While it's true that Einstein "picked the best available option" to express this universal manifestation (i.e. by relating it to alternations of the spatial and temporal metric, which are universal), there must exist other formulations of this phenomenon, but scientists are not looking ! Why is this, is beyond my understanding.
Antonios Valamontes,
General Relativity is a successful theory, so they think "we don;t need to solve a problem twice", so scientists undermine its deficits, which are many. So this reason they are not very motivated to create a new theory that portaits Gravity as a universal manifestation. Another reason is that it is very difficult to do so or there is a lack of commitment or ambition for such a project
The problem is not that people are not trying to find something better, they have been doing so for a century now.
The problem is - and that is something about which "alternative physics" people can't wrap their heads around - that if you want to truly replace an existing model by a new one, it isn't enough that it is more convenient in explaining some effects which the old theory explains, it has to explain all of them and at least one more. Otherwise, it isn't an improved or new theory, it's an approximation to the existing one.
That gives everyone who attempts to replace it a mountain to climb and it drives some of them truly mad.
Besides being the most tested theory of gravitation and the widely accepted, General Relativity misses field energy density.
This is an issue known since Gullstrand 100 years ago who pointed it out by saying that with GR is not possible to account for non stationary motion, and Levi Civita as well pointed that out, Einstein resorted to pseudotensors to give energy to gravitational radiation.
Some others raised the same issue in 100 years, including FOCK and Baryshev.
The equivalence principle in Einstein's form forbids a field energy localization, hence field energy density.
GR alone gives a very good accounting for the configuration of the potentials, a very good theory for optics..
Besides that
Newtonian gravitation, being accurate to first-order field potentials, has a negative field energy density, this is a sort of double issue because:
a) GR cannot reduce to Newtonian gravitational dynamics
b) Negative energy density gives backward in time dynamics, so basically it cannot be as Maxwell himself mentioned
A way out is to use GR to calculate the configuration of potentials and then use Post Newtonian approximation using those potentials to account for dynamics.
Maxwell provided a hint to overcome such issues, but when he conceived it, it might have taken as science fiction by his contemporaries ...
Dear Philippos: The knowledge of gravity was satisfactorily extended by Einstein; maybe this closes that concept BUT this GTR still needs to conciliate with QM. I think so many ideas are going on that. so the community only takes a few of them, especially from prestige institutions. This was a good initiative BUT after more than a century, these two core theories of modern physics still need to have a common model. Maybe with this new AI involvement in human activity, this new technology can read and analyze a variety of ideas almost in the waste basket. For example, in 2021 there is a new interpretation of QM that joins with GTR by means of energy. It develops the 4th dimension as C*tau; not any "t" or "Delta t" of Minkowski time event, BUT with Planck´s periodic time tau (tau = h/E). This gives a novel approach because tau is linked with energy (GTR) and tau is linked to STR by time dilation and space contraction. For example see Poincare´s equation with this perspective: (Delta r)^2 + Delta iC*tau)^2 = invariant. This express that when energy is incremented, tau is smaller (time dilation) and space also gets a smaller value (Space contraction). This new 4th D as C*tau can be independent from the other 3D; again a novel idea because all other theories consider that existence involves the 4D or more D´s together. What if... existence is oscillating between 3D and this 4th D (energy´s wavelength)? Then Schrodinger-Born expresión that reveals the probability presence in 3D will be clarified. Entanglement will reveal that this proposal makes sense because at the 4th D particles are "Local" even if they are apart in 3D. Attach are some papers that explain this theory; I hope it will inspire you in your research. Regards
P. P. Afxenti
Because they haven't fully sorted out the existing ones. They've strayed from the truth and are wandering. Dividing the inseparable and uniting the incompatible.
If you realize that the mass of celestial bodies (stars, planets, satellites) is the wrong direction. As is the UNIVERSAL gravitational constant. Similar to the early conclusions that everything revolves around the earth. You will be able to look at the world differently and perceive reality in reality. Newtonian mass and forces that have torn apart the logical meaning of phenomena, like blinkers, close the eyes and mind. In accordance with Kepler's third law, no mass is taken into account to describe the motion of ANY celestial bodies. But this law began to be applied SIMULTANEOUSLY to all gravitating celestial bodies by introducing the universal gravitational constant and the masses of celestial bodies that compensate for it. And we apply Kepler's third law to each of them, but with its INDIVIDUAL coefficient.
The first simplified representation can be made by comparing with the movement of small whirlpools inside one large whirlpool. Each of the small ones is independent and rotates around its center, and at the same time they are all in the flow of one large one. The flow of water moves both around its small centers of rotation, and around one large center. But this does not mean that it is necessary to introduce a common constant that describes all the whirlpools in this example and those not included in this example.
People do not realize the physical meaning of gravity, having become confused, thanks to Newton and Einstein, in three "trees".
P. P. Afxenti Let me add, pay attention once again to the fact that when objects fall on a gravitating celestial body, the mass of these objects is not taken into account. Neither in formulas, nor in practice. We do not observe a difference in time when they fall. Many people know this, but not everyone. Only those who know make erroneous conclusions. And even worse, they transfer Newton's law to all objects in a row. And they also cannot finally admit and realize that simple objects cannot even in space "attract" each other by any laws. We are not attracted to the planet, but are pushed by a non-material substance (ether, dark matter, energy, emptiness or vacuum, as it is convenient for someone) rotating at a great distance and flowing into celestial bodies.
T1²/T2²=a1³/a2³ - E=w²R³
Solar system - 1,3*1020
Earth - 4,0*1014
Mars - 4,3*1013
Jupiter - 1,3*1017
Saturn - 3,8*1016
It is not true that no alternative researchers, which try to propose other physical theories not manifestly geometric
as is the Einstein gravity thdiry.
Anatolij K. Prykarpatski There are many different published versions, but they are not known to the general public and are not recognized by mainstream science - they are ignored.
There is probably a theory that goes beyond Newton and Reinstein's theory of gravity:
Article The existence of the graviton can be proven physically and m...
All you have to do is prove, through a simple experiment, that there is a connection between electromagnetism and gravity. And then what would you say if this could actually be proven?
My opinion is that the experimental proof has been done. There is no narrative that can connect it to existing theories.
The first step towards gravitational waves discovered by LIGO. Unfortunately, they chose the wrong path, because it can easily be proven that the narrative of the discovery is based on false data!
Article A 2017. Fizikai Nobel-díj „gravitációs hullámai”
Regards,
Laszlo
Regards,
Laszlo
The contribution from Maxwell to my understanding was paramount...
his genius was not only devoted to electrodynamics but also to astronomy and gravitation... his humbleness provides us with the impression of the giant he was.
Data From the Maxwell TREATIES concerning "gravitational energy"
the above, contrary to what somebody would think, does not single out GR. On the contrary it determines the limits within GR can work and what actually GR can represent: a good description of the skin (curvature) of the apple (energy density)....
By the way, yesterday my friend Gary Nash put his paper on RG
Preprint Local gravitational energy in cosmology
The mathematical model involves a "Lorentzian" line element field which gives a degree of freedom missing in GR.
Besides the fact that one can agree or not on the opportunity to use that extension, that extension is meant to provide the needed predictions relevant to Dark matter.
It certainly says that a least an important ingredient is missing in GR, whatever is the theory that will be considered more suitable, a FIELD ENERGY DENSITY.
P. P. Afxenti
1. Foundations of a theory of gravity with a constraint and its canonical quantization. https//doi.org/10.1007/s10701-021-00521-1; arxiv:2111.14612v7
2. Foundations of a theory of gravity with a constraint. Gravitational energy of macroscopic bodis. https//doi.org/10.1007/s10773-024-05723-7; arxiv:2312.02217v3
The thread question
“Why aren't scientists trying to come up with alternative theories of Gravity as a universal manifestation beyond Einstein's General Relativity?”
- is really incorrect. First of all there exist – and really is widely applied at/in navigations of Space missions - Newton Gravity theory, which is well adequate to the reality in weak Gravity fields and at small speeds.
More comprehensive the Shevchenko-Tokarevsky’s Planck scale informational physical model of the fundamentally nothing else than some fundamental Nature Gravity force [and at least Electric and Nuclear/Strong Forces], which is considered in 2-nd main model paper
https://www.researchgate.net/publication/383127718_The_Informational_Physical_Model_and_Fundamental_Problems_in_Physics , section 6. “Mediation of the fundamental forces in complex systems”.
In the model it is rigorously scientifically shown that all Forces fundamentally act only 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).; and, say, by no means in the curved 4D pseudo-Riemannian the GR space; that there are so any principal problems with “Gravity quantization”, etc.
More see the link above, to read a series of SS posts in https://www.researchgate.net/post/NO47What_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 - where some points in the model are commented/clarified in detail it is useful as well.
Cheers
Stefano Quattrini "It certainly says that a least an important ingredient is missing in GR, whatever is the theory that will be considered more suitable, a FIELD ENERGY DENSITY."
Yes exactly! Considering the field energy density, (energy per volume= W/V) proportional to the field strength squared that is the general solution, applicable to all kinds of force fields.
For electric fields we have W/V= εₒE²/2. For magnetic fields we have W/V=µₒH²/2, and for gravitational fields we have W/V=Wₒ/Vₒ-g²/(8πG). Wₒ/Vₒ is a cosmic energy density with Wₒ/Vₒ>g²max/(8πG). gmax is the maximal possible gravitational field strength which can occur in nature.
The term Wₒ/Vₒ is needed because a negative definite energy density is physically impossible. In addition, this implies a finite volume Vₒ of the universe.
yes a background anti-energy of that kind would create macro dynamics which are not currently experienced.
After the observations of Maxwell, nobody seem to have realized that Newton's gravitation must have been conceived with that background energy density which is actually so revolutionary because it builds the actual mechansim of gravitation itslef.
Stefano Quattrini "yes a background anti-energy of that kind would create macro dynamics which are not currently experienced."
Yes, but the existence of this kind of anti-energy should actually be obvious, because exactly this kind of energy is emitted as radiation from accelerated masses.
Yes, that "anti-energy" is actually the missing energy which was radiated away.
Stefano Quattrini
With this "anti-energy" we can even explain "dark matter".
In the interior of the stars, a strong acceleration of matter particles takes place. The scattering of photons is also a source of gravitational radiation. Compared to electromagnetic radiation, gravitational radiation is weaker by an extremely large factor.
Apparently, this factor proves that the energy content of gravitational radiation is negligible. But exponential multiplication effects and the fact that gravitational radiation escapes without interaction reverse this assessment.
Inside stars, photons have a very short free pathlength. Every collision of a photon with elementary particles leads to gravitational radiation. All collisions of electrons with each other also contribute to this and are not taken into account at all in our models for calculating nuclear fusion events.
Overall, stars are therefore an intense source of gravitational radiation. This radiation increases the density of this "anti-energy", while gravity decreases the density of the "anti-energy". The gravitational radiation emitted by stars therefore partially shields the gravitational effect of the stellar mass.
The shielding decays like gravity with 1/r². It is therefore indistinguishable from gravity. But there is still a difference. The shielding ends after the increased "anti-energy" density has subsided to the background level. But gravity decay never stops. After the shielding is finished, the gravitational effect of the true stellar mass appears. This phenomenon has so far been interpreted by us as dark matter.
The scientific answer to the thread question see in SS post on page 2.
Besides here - an example how Gravity quantum nature reveals itself in cosmology see short paper “The Informational Physical Model: Detection of Dark Matter Particles”
https://www.researchgate.net/publication/388922029_The_informational_physical_model_detection_of_dark_matter_particles
Cheers
Stefan Bernhard Rüster
to my understanding it can be present also, but it is not localized for sure.
Meaning that a field energy density does not exist at all.
In Newtonian gravitation it exists but it is negative since the choice of 0 potential at infinite distance has such a consequence.
Recent SS posts in
https://www.researchgate.net/post/What_is_the_actual_physical_meaning_of_the_Lorentz_Transformations#view=67a0dfb3529f9bf15a0bde20/311/312/312/313/314/314 , page 315,
- and in
https://www.researchgate.net/post/what_is_the_most_important_problem_in_the_theoretical_physics_now#view=67a90cf5aa74d8fdb80e2244/1804/1805/1805/1803/1804/1805/1804/1804/1804/1806/1805/1806/1807 , page 1807,
- are relevant to this thread discussion.
Cheers
More correctly one may state:
In Newtonian gravitation the density of the potential energy exists. It is negative since the forces are attractive.
Stefan Bernhard Rüster
I am quite convinced that Gullstrand's (the examiner of the Nobel committee who criticized GR), Baryshev's and other remarks about GR are well founded.
GR is a well-structured theory dealing with potentials but it totally misses dynamics, it at least a degree of freedom. It is very well suited for optics and steady state motion. If one wants to make it work in a real world it is necessary to resort to PN approximations and reinstate the force.
the form of the "equivalence principle" invoked in GR forbids the localization of the field energy.
The Pseudotensors have been a way out to provide something which the tensor equations in the given form were not able to give.
The energy density is NEGATIVE DEFINITE in Newtonian gravitational theory, due to the choice of "0" as potential at an infinite distance.
By choosing c2 as that potential (background energy density of deep space ), one would have a positive definite energy density everywhere.
Stefan Bernhard Rüster
,basically yes... there is a non trivial contradiction in the theory
while mass is an invariant which experiments showed to be transformed into available energy (capacity to do work), the kinetic energy which is involved in the free fall of the mass can be simply ignored by choosing the comoving inertial frame.
This simply shows how unsuitable is that use of inertial frames that way.
0. My comment was about classical Newtonian gravity field. Below this is described in a more detailed statements.
==========
1. The potential energy of the classical Newtonian gravity is a scalar valued measure (since energy is a scalar). Hence density of this energy, whenever exists is a scalar (locally integrable) field. Its unit is J/m^3 = kg/(s^2 m).
==========
2. The fundamental formula based on the energy conservation law the density ρ of the energy is a value of the negative definite quadratic form of the intensity of the vectorial force field g (measured in m/s^2) as follows*)
. . . ρ = - g•g /(8 π G) . . . (*)
where G is the gravity constant (in m^3/(kg s^2) ), • stands for the scalar product in the 3D space.
------
*) The formula (*) is a consequence of equality of the work W needed to collect the total mass into such a distribution that the vector field of intensity of the forces equals the given g. A more detailed analysis is based on the Poisson equation.
============
3. For sofomors the following example explains this equality in the case of thin sphere of radius R of mass M.
3.1. The work W needed for collecting this mass piece by piece from infinity equals
W(R) = - 0.5 G M^2 /R . . . . (1)
3.2. According to the Newton law, the g-field is oriented to the center with value 0 for r
c^2 is the potential in free space far from masses which will prevent the energy density from being NEGATIVE DEFINITE.
Data From the Maxwell TREATIES concerning "gravitational energy"
by the way c2 is related directly to the vacuum electromagnetic properties of epsilon0 and mu0.
0. c^2 units are J/kg whereas density unit is J/m^2.
1. if ρ at a point has its value less than the -K where K is the value of the added constant, then the density becomes again negative.
2. Density is positive negative or 0.
3. Quadratic forms may be (positive or negative) definite or indefinite.
4. Definiteness of SCALAR makes no sense.
5. By adding a constant to the density is a very fuzzy operation if not based on PHYSICAL PLAIN REASONING. Single wish to have the result positive is childish. Moreover, only changes of energy counts in ANY theory. Hence the sign of energy does not matter. Even the kinetic energy is assumed positive only therefore that its name is bonded with motion. It is thus convenient to have it =0 for objects at rest.
The thread question is really scientifically clarified in the SS post February 11, page 2, including, as that is rigorously scientifically shown that at least the fundamental Nature Gravity, Electric, and Nuclear/Strong forces fields fundamentally don’t contain energy and so any “energy density”, that evidently violates the energy conservation law; more see the pointed post and links in the post.
To read SS posts on page 3 it is useful as well; recent SS post in https://www.researchgate.net/post/Why_is_it_difficult_to_quantize_gravity/2 is relevant to this thread question.
Cheers
Stefano Quattrini "c^2 is the potential in free space far from masses which will prevent the energy density from being NEGATIVE DEFINITE."
You need a mass density to get from that potential to an energy density. What amount has this mass density?
Joachim Domsta "Single wish to have the result positive is childish."
Yes, but gravitational field sources adapt their field to an acceleration via radiation. This mechanism would not work with a field of a negative definite energy density.
@Wolfgang Konle
I would be grateful for tips about this mechanism.
============
Let me make some remarks:
--------------
A. If ρ_m is the (inertial-/gravitational-) mass density, then
ρ_E := ρ_m c^2
is the Einsteinian energy density.
--------------
B. The mass distribution generates gravity vectorial field g ( via the Poisson equstion). It is responsible for the gravity energy potential density
ρ_gr = - g•g /(8πG).
----------
Thus we have two energy densities. It is hardly to assume that ρ_gr is c^2 times any mass density (due to the negative value of this energy density).
==========
Any comment, please?
Joachim Domsta "ρ_gr = - g•g /(8πG)."
The Poisson equation does not consider the gravitational impact of the mass density equivalent of the energy density of the gravitational field.
At the time, the Poisson equation had been developed, E=mc² was unknown.
@Wolfgang Konle
Obviously I wouldn't ever imagine such relation with the P. equation. I was suggested by your answer given in post #8 p.5, in which you responded to Stefano answer who was certainly talking about the energy of the gravity.
Hope it was a misunderstanding.
However key intention is to discuss the sign of the density of gravity potential energy:
It IS obviously negative (not negative definite, since this notion is an attribute of quadratic forms, not of scalar functions).
Issue 1. I do not understand the reasons why it tequires a correction to make it (according to your some former posts) 'positive definite'.
Issue 2. A quite independent question: Are there models of gravity which assign it the equivalent inertial mass (this would be negative if no correction is made, and positive in models assuming suitable correction).
Wolfgang Konle ,
from the following
ϱEgrav(r)= - (∇φg(r))² /(8Gπ)
it can be found the total energy depleted in radiation from a gravitational field of mass M considering that the components interacted with the Newton interaction
Erad = -1/2 (G M2/R) = -1/2 M (GM/R)
Considering ∆φs = φ( ∞ ) - φ(R) is the difference of potential where
φs = φ(R) = -GM/R
considering the classic case where φ(∞) = 0 and φs=φ (R)
Erad = Egrav = -1/2 M∆φs
that means that to build that mass M from its components, the quantity
E= 1/2 M∆φs was radiated away in form of EM or gravitational radiation.
Egrav= M/2 *∆φs is the missing field energy to the first order approx.
.
Stefano Quattrini
g=GM/r². E=-g²/(8πG)=GM²/(8πr4). W=∫EdV=∫4πr²Edr[R,∞]
=-GM²/2∫dr/r²[R,∞]=> ∫dr/r²[R,∞] =1/R => W=-GM²/(2R)=M∆φs/2
W=Energy content of the gravitational field.
Joachim Domsta "Issue 1. I do not understand the reasons why it tequires a correction to make it (according to your some former posts) 'positive definite'."
The reason is that the field source cannot adapt a field with a negative definite energy density via radiation to the new inertial reference system which the source has reached after an acceleration.
The source only can emit a positive amount of radiation energy.
The field adaptation also can be considered as if the inertial mass of the field is added to the inertial mass of the field source. But the inertial mass of the field must be positive. Otherwise causality problems would occur during an acceleration.
"Issue 2. A quite independent question: Are there models of gravity which assign it the equivalent inertial mass (this would be negative if no correction is made, and positive in models assuming suitable correction)."
Standard mechanics only considers potential energy. Field energy density is not a subject in standard mechanics.
The Lagrange formalism only considers kinetic and potential energy. Field energy does not appear in the Lagrange function or in the Hamilton function.
@Wolfgang Konle
Thanks for your response. The second part is doubtless. I have still problem with the first part due to lack of the formulation of the way the radiation must/should/may be created and transmitted from ... to .... Anyway I do not object your words but the application of the notion 'negative definite': how is it defined?
Joachim Domsta "Anyway I do not object your words but the application of the notion 'negative definite': how is it defined?"
There is no doubt that a stronger gravitational field has a lower energy density than a weaker gravitational field. But does this prove that the energy density is absolutely negative?
No, without any impact on gravitational forces it is possible to assume that an additionally constant energy density exists.
The total energy density E of the gravitational field is then given by
E=Eₒ-g²/(8πG).
This formula gives us a positive definite energy density if g
@Wolfgang Konle
Here is the main question: WHY is it impossible?
But first:
What does it mean that the field source (aka: the masses(?)) carries (carry) the field with an accelerated movement?
Joachim Domsta "What does it mean that the field source (aka: the masses(?)) carries (carry) the field with an accelerated movement?"
A force field contains an energy density. Therefor a force field source (charge or mass) cannot afford to permanently renew their field. The field remains static in the inertial reference system of the field source. It is co-moving with its source and there is absolutely no need for any action from the source to support the co-movement.
But if the source gets accelerated, e.g. by a collision with a particle, the source must adapt its field to the new velocity. The source must carry its field with it into the new inertial reference system.
To do this it emits Larmor radiation. The Larmor radiation generates a kink in the radial field lines which moves outwards with the speed of light.
Before the kink has passed the field is oriented according to the old speed of the field source. After the kink has passed, the field is oriented according to the new speed.
The counter force of the Larmor radiation has the effect to add the inertia of the force field to the inertia of the field source.
"Why is it impossible?"
The force, which accelerates the field source provides kinetic energy to the field source. The energy necessary to also accelerate the field is according to the inertia of the mass equivalent of the field energy.
But if this mass equivalent would be negative, the field source would gain energy by accelerating its field. But this would revert causality and must be excluded.
Therefor a field source would not be able to carry a field, which has a negative inertia, with it if it gets accelerated. We then can compare this field source with a man in a vehicle who loses his hat if the vehicle accelerates.
Wolfgang Konle ,
W=Egrav= M/2 *∆φs is the missing field energy to the first order approx.
you were right about the missing energy as M∆φs/2.
It is the work done by the background energy (through the gravitational force).
W/c2 =M/2 ∆φs/c2 is the equivalent mass.
Given a celestial body of mass M, the field energy missing is the same as if
half of the mass was radiated away from its surface, consider that ∆φs /c2 is the redshift of that radiation from the surface to deep space.
The overall energy of the masses at rest at infinite distance had originally an energy of E= Mc2 + 1/2 Mc2 = 3/2 Mc2 =Mtot c2
where M= 2/3 Mtot
Stefano Quattrini "The overall energy of the masses at rest at infinite distance..."
It is not a priori clear if the concept of infinite distance is applicable at all.
In a universe of a S³ structure with a finite volume an infinite distance does not exist. In such an environment the energy contained in mass is an extremely small fraction of the total energy content of the universe.
It also seems that a too large concentration of mass in that environment is inhibited.
Therefor considering all existing mass in one point and analysing the resulting energy content in the gravitational field is pointless.
Apart from that, the negative energy density of gravitational fields cannot exceed the positive energy density of the cosmic field.
This is another reason why a global consideration with infinite distances is pointless.
Wolfgang Konle ,
>
when the gradient becomes negligibly small or the gravitational field is negligibly small in comparison to the field on the surface (10^-6). This is quite easy to achieve.. it is always a matter of a good approximation.
There is no infinite distance and 0 gravitational field, these are only ideal approximations of what realistically can be found.
Stefano Quattrini "...it is always a matter of a good approximation."
In an Euclidian space this is correct without any doubt.
But in an S³ space the tremendous volume filled with field energy at large but not infinite distances also must be taken into account. The problem is that we must explicitly evaluate integrals in the whole curved S³ space, which leads to complicate differential geometric expressions.
Therefor we cannot simply assume that "infinite" is a good approximation for an integral over 1/r² in the complete S³ space. We explicitly need to prove it.
A rough estimate for the upper integration limit would be the value 1/R with R=radius of geodetic circles in the S³ space.
If this is correct, you are right with your approximation proposal.
But I suppose that in distances close to R the 1/r² law is no longer valid because the connection to the field source is given along a large variety of possible paths of nearly equal length. But this is only an assumption. There is no way to avoid the tedius differential geometric evaluation.
Wolfgang Konle ,
the space is Euclidean till contrary proof (which I don't know what it can be), an Hyperfield is there and has differences in densities, locally (particle) and globally (gravitational field).
Stefano Quattrini "the space is Euclidean till contrary proof (which I don't know what it can be), it is an Hyperfield which is there and has differences in densities, locally (particle) and globally (gravitational field)."
Due to a non-zero Ricci curvature the space is not Euclidean.
Stefan Bernhard Rüster
,the diffeomorphism acts on the space-time not in space only
Stefano Quattrini " space-time not space.
Yes, but with the assumption that all the components of the space-time metric, which are related to time, are equal to the according components of the Minkowski metric, then the non-zero Ricci curvature also applies to the space.
The only thing what we have done with this assumption is to discard the hypothesis of an expanding universe.
Stefan Bernhard Rüster
"The FLRW metric nevertheless describes an expanding universe."Therefor I propose to apply a metric which does not describe an expanding universe. This only is a more general approach to the consequences of a cosmological constant in Einstein's field equations.
"Ricci tensor and Ricci scalar always encompass space and time"
Have a look at differential geometry. Ricci tensor and Ricci scalar also applies to a three dimensional manifold.
"The spatial part of the curvature of the FLRW metric is given by k."
Yes, but if we do not use the FLRW metric, this is irrelevant.
"I already explained this to you in our other discussion."
Yes, but you are always insisting to apply the FLRW metric. This excludes all theories which do not assume an expanding universe in advance.
Wolfgang Konle ,
give me one case where the diffeomorphism of space-time applies only to space then...
Stefano Quattrini "space-time in GR is not euclidean, space is Euclidean.."
No. Space need not be Euclidean. The spatial part of the metric of a Schwarzschild black hole is non-Euclidean, the spatial metric of a rotating disk is non-Euclidean.
There are in general several methods to split space-time into space and time which hence does not produce a unique 3D space. However, there exists a particular splitting (based on Cattaneo's projection technique) that leads to the so-called relative space which is unique and agrees with the proper space, at least for stationary metrics. That is why the non-Euclidean space of a rotating disk (rotating at constant angular velocity) is well-defined (in that case space time is Minkowskian, i.e. flat). In the case of the Schwarzschild metric both space-time and space are not flat.
In the Friedmann-Lemaître cosmological models, which are not stationary but orthogonal, so a unique proper space is still defined, space is curved, i.e. non-Euclidean, for k=1 and k=-1, but Euclidean for k=0. The space-time is curved, i.e. non-Minkowskian for all values of k.
Stefan Bernhard Rüster
: 'This is the reason why I wrote "Ricci tensor and Ricci scalar always encompass space and time."'Which is incorrect. It is correct, if you consider the tensors appearing in Einstein's field equations. But spatial metrics are sometimes discussed in the literature (they are usually denoted by γij, not gij). And of course, the Ricci and Riemann tensors are defined for those 3D metrics as well. In fact, one of the general relativity exercises that I regularly gave to my students in the cosmology course that I taught, is to calculate the number of independent components for the Riemann tensor in an arbitrary number of dimensions, including three. Another exercise requires them to calculate the Ricci scalar for the metric on the surface of a sphere (which gives the Gaussian curvature up to a factor of (-)2).
Stefano Quattrini "give me one case where the diffeomorphism of space-time applies only to space then..."
I don't intend to apply a diffeomorphism, a mapping from one manifold to another. I am only considering a subspace of a four dimensional spacetime under the assumption that all metric coefficients related to time are equal to the according coefficients in the Minkowski spacetime.
Stefan Bernhard Rüster
"since it is observed that the universe is accelerated expanding other theories can be excluded."It is not observed that the universe is accelerated expanding. The observation only includes a certain distribution of red shifted light, emitted by galaxies. Combined with observations about astronomic standard candles this red shift information is interpreted as an accelerated expansion of the universe.
But we also can interprete the cosmic red-shift as the influence of space curvature and of a gravitational interaction of photons with a dark energy background.
With this assumption the universe is static but the spatial subspace of spacetime has a constant positive Ricci curvature proportional to 1/R².
This curvature configures the spatial sub-space to a 3-sphere. In a 3-sphere geometry the pressure equivalent to the dark energy background does not blow up the space because there is no outer rim. Pressure forces cancel out in any location within the finite space volume of 2π²R³.
The same happens with far reaching gravitational forces. They also cancel out in any location.
The only problem which could remain in such a configuration would be building infinitely growing mass clusters.
But the proposed recycling mechanism of star fuel also solves that problem.
However this is another story.
@ Stefan Bernhard Rüster "it makes no sense for me to further comment regarding your statements."
I understand that it does not make sense for you to communicate with somebody who does not exactly share your opinion. Such a communication could damage the reputation of your work. Most scientists show this kind of habit.
Wolfgang Konle ,
I tell you again, if space only is curved (provided that it can be curved alone) in any case it does not affect the Ricci curvature in GR.
Stefano Quattrini "I tell you again, if space only is curved (provided that it can be curved alone) in any case it does not affect the Ricci curvature in GR."
(1) The curved geodesics around massive celestial objects in astronomy show that space can be curved. (Light follows geodesics in space.)
(2) The three dimensional geometrical object "3-sphere", described in differential geometry is characterized by a constant scalar Ricci curvature.
Do you think these two facts are in contradiction to GR?
@ Stefan Bernhard Rüster "your statements are not able to damage the reputation of my work."
It is not my intention to damage the reputation of your work with my statements. Your work is related to general relativity.
My work is about fundamental errors in the basics of physics, which consequently even lead to a new cosmology.
This is quite disjoint.
Wolfgang Konle
it is space-time according to GR that is curved and gives the geodesic motion, with space only curvature no geodesic motion
which is quite interesting, but is not General Relativity though.
Stefano Quattrini
Why shall we think that general relativity gives us all information about the structure of the universe?
Wolfgang Konle ,
I do not think that at all.
Since it is known what GR gives, what it is able to give and do not give, I do not expect it to give more or different things.
As a matter of fact there is NO SPACE TIME other than in math.
There is no warping of space-time, yet another suitable model to explain some interesting features.
All these effects must be the outcome of an HYPERFIELD determined by an HYPERMEDIUM which is omni pervasive.
Stefano Quattrini "All these effects must be the outcome of an HYPERFIELD determined by an HYPERMEDIUM which is omni pervasive."
Yes, that's it.
But do you think it is by accident that the cosmic constant Λ matches to the existence of such a HYPERMEDIUM ?
Wolfgang Konle
to my understanding that is one way to insert some "external energy" in the model. That is very very weak energy density.
The thread question is really scientifically clarified in the SS post February 11, page 2, including, as that in the Shevchenko-Tokarevsky’s Planck scale informational physical model, in this case it is enough to read one of two main papers
https://www.researchgate.net/publication/383127718_The_Informational_Physical_Model_and_Fundamental_Problems_in_Physics [first sections and section “Mediation of the fundamental forces in complex systems”]
- is rigorously scientifically shown that at least the fundamental Nature Gravity, Electric, and Nuclear/Strong forces fields fundamentally don’t contain energy and so any “energy density”,
- while postulates in official physics classical fields theories and QFTs that the fields [in the GR “curved spacetime”] contain energy, and so energy density, evidently violate the energy conservation law.
Etc., more see the pointed post and links in the post, including that really scientific theory of the Gravity Force, which will not so have any problems with “quantization of Gravity”, etc., with a well non-zero probability will be based on the SS&VT model above. including on the postulate that Mater’s spacetime is the 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 absolutely fundamentally is real, since – as that rigorously proven in the S&VT “The Information as Absolute” conception - absolutely for sure any/everything can exist and change only in some concrete spacetime [including so, say, in all mathematical theories obligatorily - though mostly instinctively – without spaces math theories don’t want to be developed - concrete spaces are introduced] and so, say, such claim in the thread as
“…As a matter of fact there is NO SPACE TIME other than in math.….”
- is too strange something. As that most of other claims in the too vivid chatting in the thread that appear after SS posts, are, though.
To read SS posts on page 2, 3, and links in the posts here it is useful; recent SS posts in https://www.researchgate.net/post/Why_is_it_difficult_to_quantize_gravity/2 ,pages 1, 2; and in
https://www.researchgate.net/post/Is_it_true_that_time_and_space_change_inside_a_black_hole_A_conflict_with_the_shell_theorem/1
- are relevant to this thread question as well.
Cheers
@ Stefan Bernhard Rüster "Einstein's field equations with the cosmological constant demonstrate that:
matter-energy plus energy of the gravitational field is equal to total energy. Very simple and also plausible. Hence, the cosmological constant Lambda has absolutely nothing to do with the energy density of the vacuum."
The energy density E of the gravitational field is given by E=Eₒ-g²/(8πG).
The major part of the total energy comes from the energy density Eₒ in the volume of the universe. This is indeed simple and plausible.
With the alternate formula E=-g²/(8πG) the energy density of gravitational fields would be negative definite. In this case a mass would not be able to adapt its gravitational field to an acceleration.
Hence the cosmological constant Lambda is closely related to the energy density Eₒ of the gravitational field.
Wolfgang Konle
The gravitational field energy density according to Newtonian gravitation is rho = -g²/(8πG), hence "negative definite". That is a consequence of assuming that the energy density of deep space far from masse is negligible.
Since no experience in Nature behaves like a "movie going backward", but always goes "forward" using positive definite energy, we must keep any energy as "POSITIVE DEFINITE" everywhere (see MAXWELL).
For that, it is necessary to assume that there is a background energy density as an "HYPERFIELD" , omnipervasive in euclidean space whose energy density fully compensates any possible "gravitational energy density".(see MAXWELL), may call it VACUUM energy density.
The background energy density which is a form of "potential energy" is not a property of gravitation but is the cause of gravitational phenomena, making gravitation an emergent phenomenon from Vacuum energy.
so as a first-order approximation
rho E = rhoE0- g²/(8πG)
where rhoE0 is the maximum background energy density available in the universe.
I would say no, although they are energy densities.
GR describes only the SKIN of this hyperfield, which is the differences in space between the local and maximum value
rho E - rhoE0= - g²/(8πG)
the diffeomorphism of the space-time is able to take into account the effects of such difference. That is like representing a "surface" on a 3D space.
The famous curvature is only relevant to the "local DIFFERERENCES" of the energy densities. According to that light travels in curved trajectories (in euclidean space).
GR Cannnot take into account the energy density as an absolute value...
Only a unified theory with electromagnetism (hence also quantum mechanics) will be able to do it.
Stefan Bernhard Rüster,
As I recall, both Straumann and Hooft tried to convince you that you are wrong but you never listened, and the same goes for China Nash and his kung fi theory.
Dear Stefan Bernhard Rüster
,the only way to solve this conundrum is to admit that GR is the description of how a very energetic background behaves in presence of masses. Then all the energy topics are solved.
Dear Stefan Bernhard Rüster
,The gravitational field energy density according to Newtonian gravitation is rho = -g²/(8πG), hence "negative definite". That is a consequence of assuming that the energy density of deep space far from masse is negligible.
Since no experience in Nature behaves like a "movie going backward", but always goes "forward" using positive definite energy, we must keep any energy as "POSITIVE DEFINITE" everywhere (see MAXWELL).
For that, it is necessary to assume that there is a background energy density as an "HYPERFIELD" , omnipervasive in euclidean space whose energy density fully compensates any possible "gravitational energy density".(see MAXWELL), may call it VACUUM energy density.
The background energy density which is a form of "potential energy" is not a property of gravitation but is the cause of gravitational phenomena, making gravitation an emergent phenomenon from Vacuum energy.
so as a first-order approximation
rho E = rhoE0- g²/(8πG)
where rhoE0 is the maximum background energy density available in the universe.
GR describes only the SKIN of this hyperfield, which is the differences in space between the local and maximum value
rho E - rhoE0= - g²/(8πG) (first order)
the diffeomorphism of the space-time is able to take into account the effects of such difference. That is like representing a "surface" on a 3D space.
The famous curvature is only relevant to the "local DIFFERERENCES" of the energy densities. According to that light travels in curved trajectories (in euclidean space).
GR Cannnot take into account the energy density as an absolute value...
Only a unified theory with electromagnetism (hence also quantum mechanics) will be able to do it.
Dear Stefan Bernhard Rüster
,Never seen that paper before and I do not agree either on the Minkowski flat space-time at infinity. At large distances from masses (except in DM regions) the energy content of space is 10^110 J/cm3...that does not enter directly in GR because it just takes account of differences, curvature is determined by differences of energy densities.
Stefano Quattrini , Stefan Bernhard Rüster
Let us consider a space filled with that hypermedium and that accelerated masses just emit that hypermedium, which consists of the same energy as contained in gravitational waves.
It is an undeniable fact that accelerated masses emit energy. We cannot ignore this fact. We then also must consider that this kind of energy accumulates in a finite volume.
It also is obvious that stars emit quite a bit of that energy and that this emission must have gravitational impact because it leads to a gradient in the density of the hypermedium.
How can we ignore this kind of gravitational impact and instead halluzinate about dark matter or even MOND theories?
Stefan Bernhard Rüster
"the energy of gravitational waves is nothing else than a part of the energy of the gravitational field."No, the energy of gravitational waves is the energy needed to accelerate the mass equivalent of gravitational field energy.
When a field source is accelerated, the source must carry its field with its movement. It can't leave its field behind.
But since the field has an energy density, it also has a mass equivalent.
This mass equivalent must be accelerated with the acceleration of the field source. However, this costs energy, which must be provided by the field source.
However, the only option that the field source has is to provide this energy via radiation. The opposing force of this energy emission through the field source simply adds the mass equivalent of the field energy to the inertial mass of the field source.
Standard physics' ignorance of the energy content of force fields leads to a fatal misconception about the radiation exerted by accelerated field sources.
Are these connections comprehensible or would you see it differently?
Stefan Bernhard Rüster
"I am speaking about general relativity where this what you mentioned in your last comment does not apply. When you want to consider something else than general relativity, then this other theory must compete with it to obtain all the highly accurate results from general relativity which are also observed. I do not want to discuss with you about new ideas or theories. I have no interest in doing this, because it leads to nothing meaningful."OK, general relativity does not consider or explain the emission of gravitational waves from an accelerated mass. But considering something else as general relativity leads to nothing.
Is it that what you want to tell me?