Johan K. Fremerey ,

how did you find that relation, which implies that the vacuum potential is

c2 /2.

Stefano Quattrini: "how did you find that relation"

It just results from Schwarzschild radius Rs = 2GM/c2.

Johan K. Fremerey

Ah yes...

Johan K. Fremerey ,

c2 = 2GMu/Ru

what is the Mass of the universe and Radius which you considered?

Stefano Quattrini

In a first approximation I took data from Wikipedia for the visible universe, even though I'm aware of the dark matter issue. In fact, I'm satisfied with Mu/Ru = c2/2G.

Right.

Dear Gary Nash ,

shouldn't the background have a positive definite energy?

Dear Stefano. From the connection-independent tensor that represents the energy-momentum of the gravitational field (Einstein's missing tensor) Phi_ab constructed with the Lie derivative, the gravitational energy density is

W =−c4Φ00/8πG =−μ GM2/4πr4 −μ c4a20 16πG

where μ = 1+2u0u0. In an orthonormal basis (eα) with respect to gαβ such that e0 = u, uα = δα0 and u0 = −1. In that comoving frame, the gravitational energy density is positive and twice both of the Newtonian gravitational energy density and that calculated in GR from the weak field approximation.

Gary

Dear Johan K. Fremerey ,

it is infact like that...Shapiro relies on the VSL in euclidean space..

Preprint SHAPIRO TIME-DELAY, Curved 4D space-time or Variable speed of light

it is beautifully calculated with GR but physically it is accountable only by assuming a slower speed of light in presence of masses and yes the potentials can be referred directly to the squared SOL.

Excuse me: ¿What deceleration of rapidly spinning rotors indicates a possible interaction with distant masses? ¿Could you explain this?

Jose Gaite "¿What deceleration of rapidly spinning rotors ... ?"

The spinning rotor experiment devised by James C. Keith, see reference in previous post, was performed in the early 1970s indicating characteristic deceleration as expected, see references below.

Article Significant Deviation of Rotational Decay from Theory at a R...

Research A second look at experimental data suggesting gravity speed ...

Dear Johan K. Fremerey ,

Thank you for the references. However, you are studying en effect unlike the one that I expected; namely, I expected an effect due to the "gravitational potential originating from distant masses". That would be a Machian effect, but you seem to have considered in those papers "the effect of gravitational radiation". Am I misunderstanding something?

Dear Johan K. Fremerey ,

that spinning rotor problem reminds me a lot of the spinning experiment of Kunding to test the blueshift of radiation according to the tangential speed of the disk at diameter distance.

Preprint AN INDUCED NUCLEAR SPIN A TOY MODEL TO ACCOUNT FOR THE MOSSB...

Jose Gaite

You will probably find an answer to your question on page 11 of above cited paper.

Johan K. Fremerey ,

to my understanding the cumulative contribution to gravitational potential of distant masses is quite negligible. For how large a mass can be, the distance is so large that the gravitational potential is virtually 0.

The interesting fact is that you have found a reasonable way to estimate the actual absolute potential of the vacuum as c2 .

That potential corresponds to a vacuum energy density close to the Planck energy density. Such value is quite significative since it is the cut off energy necessary to make quantities converge to a finite number in QED. The result of such process are very close to experimental results.

Stefano Quattrini

"to my understanding the cumulative contribution to gravitational potential of distant masses is quite negligible. For how large a mass can be, the distance is so large that the gravitational potential is virtually 0."

This certainly applies to the gravitational potential gradient which falls off by 1/r2 while gravitational potential accumulates to immense values, ie about 108 times the Sun's gravitational potential at Earth's distance, throughout the universe as it goes by 1/r.

Edit: You just state: "The interesting fact is that you have found a reasonable way to estimate the actual absolute potential of the vacuum as c2." That's it - ie not "virtually 0".

Stefano Quattrini

Please note that I have withdrawn my above calculations and related posts as they start from erroneous assumptions.

The absolute magnitude of a gravitational potential is (locally) meaningless. The crucial point here should be that due to the average isotropy of the mass distribution in the universe around the solar system (if you take into account all masses till the particle horizon) the resulting gravitational potential in the solar system will be constant to very good approximation. But that means that the gravitational field is about zero. And there are no observable effects within our solar system.

What might be observable is a red shift between ourselves and light from distant masses. The total red shift including all gravitational effects (i.e., not just the effect from a single gravitational potential) is calculable within cosmological models, using Einstein's equations or rather the Friedmann-Lemaître equations resulting from them.

Dear Johan K. Fremerey ,

It would be worth taking a close look at Einstein's original pre-test prediction of how light is deflected by the Sun's gravity. I am also interested in this original, first officially documented prediction. If you know that paper (title and publication date), please share it... It would be worth comparing with the current official narrative.

Regards,

Laszlo

László Attila Horváth

I think it's this one:

http://myweb.rz.uni-augsburg.de/~eckern/adp/history/einstein-papers/1911_35_898-908.pdf

Dear Johan K. Fremerey ,

Thank you for writing. I think this is an important article from the point of view of your discussion.

I don't know German, it's an old text, so it's difficult to translate it with a translator... (I have often observed traces of circular argumentation in the Hungarian or English translations of Einstein's text.)

That's why I would like your opinion.

Look over the writing carefully, but not mathematically, but rhetorically.

The end may be enough see my copy.

There must be a clear answer to the question In Einstein work , does the light of a distant star, when it passes near the Sun, bend away from it or towards the center of gravity of the central celestial body?

Regards,

Laszlo

László Attila Horváth

"does the light of a distant star, when it passes near the Sun, bend away from it or towards the center of gravity of the central celestial body?"

It is clearly stated that the light bends towards the center of gravity of the celestial body. The distant stars thereby appear displaced away from the celestial body.

Preston Guynn: "The proofs that the Milky Way galaxy is a predominant effect are the strongest of any proofs in physics."

This may at least apply to the phenomena you are dealing with in your cited articles. On the other hand, shouldn't the contribution of distant galaxies to the local gravitational potential be much larger than the contribution from our local galaxy, as the potential falls off by 1/r while the sum of distant masses increases with r3 ?

Johan K. Fremerey ,

to support the conclusions that the background potential in deep space should be close to c2 I restored an old paper of mine...

Article Radiation power invariance across gravitational potentials

I have recalled a problem that is related to this discussion. It has been estimated here the magnitude of the gravitational potential originating from distant masses of the universe, as being very large. The absolute value of the potential has no physical effect and the potential inside a cavity surrounded by a spherical mass (or charge) distribution is constant. That is why only the inhomogeneities matter.

I worked, with a collaborator, on the question if the large-scale cosmological expansion has a local effect:Article Influence of the cosmological expansion on small systems

That is to say, if the motion and not just the potential can be felt locally (a question amply considered in the literature). Our answer is that hardly.

Jose Gaite: "That is why only the inhomogeneities matter."

In case of extreme outdoor temperatures I imagine inhomogeneities are less important than the absolute level.

Dear Johan K. Fremerey ,

Sorry, I don't understand your remark. Are we not discussing the gravitational effect of distant masses?

Jose Gaite: "Are we not discussing the gravitational effect of distant masses?"

When you justify your assumption that gravitational potential has no effect by the absence of local gradients then I think this may justify my analogy with the effect of outdoor temperature level irrespective of local gradients.

The question is missing something. If bodies are only gravitational wells, then the gravitational ambient around a body should be zero (0). But both Newton and GR have the gravitational potential (a medium ?) rarer near and higher away. So, where does this higher value originate?

Dear Johan K. Fremerey ,

I am saying that the absolute value of the gravitational potential has no effect and only the potential differences matter. This is "mainstream science" to such an extent that it is usually taught in high school (I also teach it to freshmen).

Jose Gaite: "it is usually taught in high school"

I imagine that it's in high school where the human potential exists to investigate phenomena that mainstream science teaches as being meaningless.

Dear Jose Gaite ,

yes, it had so far no major difference. The main fact is that assuming 0 potential energy at infinite distance you get negative energy density close to masses which does not make sense in general, unless it is a missing part from a huge quantity intrinsic in the Space.

Dear Stefano Quattrini ,

Thanks for the remark, bringing the problem of boundary conditions to the disscussion. Indeed, going far enough in a homogeneous and isotropic universe, one is not going to find the conditions for the usual definition of the gravitational potential. There are problems with the boundary conditions, some of which were already Newton's concern (https://en.wikipedia.org/wiki/Bentley's_paradox).

At any rate, it should not be said that these questions "are not considered by mainstream science".

Dear Jose Gaite ,

by applying Newtonian gravitation on a basically 0 energy density background one gets an energy density of

rhoE = -K*grad(phi)^2

which is negative...

Maxwell from that considered that in order to avoid a negative energy density had to request a huge background energy...to compensate such effect of gravitation in such cases.

Dear Stefano Quattrini ,

Sorry, I do not understand your comment or Maxwell's consideration. Where did Maxwell consider that?

Dear Jose Gaite ,

Dear Stefano Quattrini ,

Interesting quotation. I have downloaded THE SCIENTIFIC PAPERS OFJAMES CLERK MAXWELL. Thank you for the link, for it is a bulky file but surely worthwhile.

As to the quotation itself, it makes little sense to me. This being said, I shall add that I have the greatest respect for Maxwell. Obviously, a gravitationally bound system has negative energy, because work is necessary to take it apart, so that the component bodies are far from one another and have vanishing energy. Perhaps, Maxwell meant something else, but I am not able to interpret it.

At any rate, I do not see its bearing on the cosmological problem we are (or were) discussing.

Dear Jose Gaite ,

Yes, or the other way, it lost energy by radiation when its pieces came together...

Just a question then close to the experience of Cavendish

Two masses M1 and M2 are (in deep space) separated by a certain distance left at rest.

They begin to approach according to Newton's law.

They will accelerate till they will collide in the system M1 and M2 center of mass.

The energy of the relevant inelastic collision will be radiated away.

What "agent" do you think gave them the necessary energy measured from the COM, to come together?

By the way, the energy of the emerging radiation will be masured the same from any surface surrounding the two bodies.

Good! But what do you make of Maxwell's comments?

Dear Jose Gaite ,

I was asking before...

after this sentence it can be understood how Maxwell starts...

Dear Stefano Quattrini ,

The energy to start is not as relevant as the gravitational forces, in my opinion. The average energy density of the universe can be positive, null, or negative, but the process of cosmological structure formation proceeds in very much the same way, due to the gravitational instability. I do not think that Maxwell had a clear notion of this, because it has been established later.

Preprint The system of gravitational field equations

Dear Jose Gaite ,

to my understanding it is not the chicken and egg problem.

It is accepted that gravitational forces depend on "something" which gets curved according to GR.

GR can be described also by Stokes Navier equations.

From Navier-Stokes To Einstein  https://arxiv.org/abs/1101.2451

to accept a perfect Hyperfluid is in line with current tested theories.. then this "agent" should be characterized by a positive definite energy density

Isn't it worth at least a thought that the potential energy of a mass m at the potential 2GMu/Ru originating from remote masses of the universe is equivalent to its relativistic energy content Em = mc2 ??

Em = mc2 in particular applies to protons which enabled me to estimate their diameter and magnetic moment ...

Research Proposal Triple-gyro model for deduction of proton radius and magnetic moment

It really appears strange that we are living inside a huge universe, and physicists deny any effects related to the gravitational potential of clearly observable masses except for the secondary effects due to gravitational potential gradients.

Dear Johan K. Fremerey

I argue that the source of dark energy is Gravitational Potential Energy. I would appreciate it if you could read my thesis.

We need to look at the logical structure of standard cosmology.

1.The first result of Friedmann equation for accelerated expansion was negative mass density

Nobel lecture by Adam Riess : The official website of the Nobel Prize

Refer to time 11m : 35s ~

https://www.nobelprize.org/mediaplayer/?id=1729

=====

Negative Mass?

Actually the first indication of the discovery!

=====

HSS(The High-z Supernova Search) team : if Λ=0, Ω_m = - 0.38(±0.22) : negative mass density

SCP(Supernova Cosmology Project) team : if Λ=0, Ω_m = - 0.4(±0.1) : negative mass density

*This value is included in a paper awarded the Nobel Prize for the discovery of the accelerated expansion of the universe.

They had negative thoughts about negative mass (negative energy). So, they discarded the negative mass (density) without sufficient scientific review. They corrected the equation and argued that the accelerated expansion of the universe was evidence of the existence of a cosmological constant. However, the vacuum energy model has not succeeded in explaining the value of dark energy density, and the source of dark energy has not yet been determined.

They introduce negative pressure, which hides the negative mass density in the negative pressure, but this does not mean that the negative mass density has disappeared.

ρ_Λ + 3P_Λ = ρ_Λ + 3(-ρ_Λ) = - 2ρ_Λ

If we rearrange the dark energy term, the final result is a negative mass density of -2ρ_Λ.

2. Logical structure of the standard cosmology

Let's look at the equation expressing (ρ+3P) as the critical density of the universe.

In the second Friedmann equation,

(1/R)(d^2R/dt^2) = -(4πG/3)(ρ+3P)

Matter + Dark Matter (approximately 31.7%) = ρ_m ~ (1/3)ρ_c

Dark energy density (approximately 68.3%) = ρ_Λ ~ (2/3)ρ_c

(Matter + Dark Matter)'s pressure = 3P_m ~ 0

Dark energy’s pressure = 3P_Λ = 3(-(2/3)ρ_c ) = -2ρ_c

ρ+3P≃ ρ_m +ρ_Λ +3(P_m +P_Λ)= (1/3)ρ_c +(2/3)ρ_c +3(−2/3)ρ_c= (+1)ρ_c + (-2)ρ_c = (−1)ρ_c

ρ+3P ≃ (+1)ρ_c + (-2)ρ_c = (−1)ρ_c

The logic behind the success of the ΛCDM model is a universe with a positive mass density of (+1)ρ_c and a negative mass density of (-2)ρ_c. So, finally, the universe has a negative mass density of “(-1)ρ_c”, so accelerated expansion is taking place.

The current universe is similar to a state where the negative mass density is twice the positive mass density. And the total mass of the observable universe is the negative mass state. It is the same as the negative mass density situation, which was the first interpretation of the observation.

In January 2024, the Dark Energy Survey team, an international collaborative research team of more than 400 scientists, announced the results of an analysis of 1,499 supernovae. This figure is approximately 30 times more than the 52 supernovae used by the team that reported the accelerated expansion of the universe in 1998.

https://noirlab.edu/public/news/noirlab2401/?lang

If we look at the key phrases in the text,

The standard cosmological model is known as ΛCDM, or ‘Lambda cold dark matter’. This mathematical model describes how the Universe evolves using just a few features such as the density of matter, the type of matter and the behavior of dark energy. While ΛCDM assumes the density of dark energy in the Universe is constant over cosmic time and doesn’t dilute as the Universe expands, the DES Supernova Survey results hint that this may not be true.

they also hint that dark energy might possibly be varying. “There are tantalizing hints that dark energy changes with time,” said Davis, “We find that the simplest model of dark energy — ΛCDM — is not the best fit.

Dear Johan K. Fremerey

3. So, what can correspond to this negative mass density?

When mass-energy is present, the negative gravitational potential energy produced by that mass-energy distribution can play a role. The gravitational potential energy model is a model in which +ρ and -ρ_gp exist, and shows that |-ρ_gp| can be larger than +ρ.

● ----- r ----- ●

m ------------ m

When two masses m are separated by r, the total energy of the system is

E_T=2mc^2−Gmm/r

In the dimensional analysis of energy, E has kg(m/s)^2, so all energy can be expressed in the form of (mass) X (velocity)^2. So, E=Mc^2 holds true for all kinds of energy. Here, M is the equivalent mass. If we introduce the negative equivalent mass "-m_gp" for the negative gravitational potential energy,

−Gmm/r=(−m_gp)c^2

E_T=2mc^2−Gmm/r=(2m−m_gp)c^2=(m^∗)c^2

The gravitational force acting on a relatively distant third mass m_3 is

F=−G(m^∗)(m_3)/R^2=−G(2m−m_gp)(m_3)/R^2=−G(2m)(m_3)/R^2 + G(m_gp)(m_3)/R^2

That is, when considering the gravitational action of a bound system, not only the mass in its free state but also the binding energy term (-m_gp) should be considered.

In the general case, the value of gravitational potential energy(gravitational self-energy) is small enough to be negligible, compared to mass energy Mc^2. However, as more mass is collected, the ratio of (negative) gravitational potential energy to (positive) mass energy increases.

In the case of Moon, U_{gp - Moon} = ( - 1.89 x 10^ -11)M_{Moon}(c^2)

In the case of Earth, U_{gp - Earth} = ( - 4.17 x 10^ -10)M_{Earth}(c^2)

In the case of the Sun, U_{gp - Sun} = ( - 1.27 x 10^ -4)M_{Sun}(c^2)

In case of a Black hole, U_{gp - Black - hole} = ( - 3.0 x 10^-1)M_{Black - hole}(c^2)

At R=2GM/c^2,

U_gp-Black-hole = -(3/5)(GM^2/R) = -(3/5)(GM^2/(2GM/c^2)) = -(3/10)Mc^2

In the case of a black hole, the negative gravitational potential energy is 30% of the positive mass energy (mass energy when the masses forming a black hole are free state). It can be seen that the magnitude of the gravitational potential energy is not negligible compared to the mass energy.

What would happen in a universe with more mass?

4. For the observable universe, calculating mass energy and gravitational potential energy

Use a critical density ρ_c=8.50x10^-27[kgm^-3]

[Result summary]

At R=16.7Gly, (-M_gp)c^2 = (-0.39)Mc^2

|(-M_gp)c^2| < (Mc^2) : Decelerating expansion period

At R=26.2Gly, (-M_gp)c^2 = (-1.00)Mc^2

|(-M_gp)c^2| = (Mc^2) : Inflection point (About 5-7 billion years ago,

consistent with standard cosmology.)

At R=46.5Gly, (-M_gp)c^2 = (-3.04)Mc^2

|(-M_gp)c^2| > (Mc^2) : Accelerating expansion period

Even in the universe, gravitational potential energy (or gravitational action of the gravitational field) must be considered. And, in fact, if we calculate the value, since gravitational potential energy is larger than mass energy, so the universe has accelerated expansion. Gravitational potential energy model accounts for decelerated expansion, inflection point, and accelerated expansion.

As the universe ages, the range of gravitational interactions increases, and thus accelerated expansion appears to have occurred because the negative gravitational potential energy increased faster than the positive mass energy.

As the universe grows older, the range R of gravitational interaction increases. As a result, mass energy increases in proportion to M, but gravitational potential energy increases in proportion to -M^2/R. Therefore, gravitational potential energy increases faster.

Therefore, as the universe ages and the particle horizon expands, the phenomenon of changing from decelerated expansion to accelerated expansion occurs.

ρ+3P ≃ (+1)ρ_c + (-2)ρ_c = (−1)ρ_c

If there is a positive mass density +ρ, there is an equivalent mass density -ρ_gp of the gravitational potential energy created by this positive mass, so the gravitational potential energy model conforms to the logic above equation.

In addition, through numerical calculations on the observable universe, it is proved that the negative gravitational potential energy is greater than the positive mass energy, and it suggests the time at which the universe transforms from decelerated expansion to accelerated expansion. Therefore, it is worth reviewing.

Λ(t)= (6πGR(t)ρ(t)/5c^2)^2

Dark energy is a function of time.

Preprint Dark Energy is Gravitational Potential Energy or Energy of t...

Birkhoff's theorem

~

As a corollary, the acceleration of an expanding shell in our fluid universe is determined solely by the fluid lying within the shell.