See:

Preprint What gravitation really is

Wolfgang Konle

This is a question about my work, which somehow you didn't refer to. It is prior art in the 3-sphere context, just in case you don't know it.

In other words, my work is public since 2006:

For a paper that claims to tell us WHAT GRAVITY REALLY IS, it lacks the most basic support. In other words, any work that claims to tell you something about Gravity, has to explain the Supernova Cosmology Project. That is basic.

I don't see your plot of the SN1a data. This is the paragraph you provided in lieu of a real analysis:

Redshift in the 3-sphereIn the 3-sphere, two points are geodesically connected to each other by a great circle arc. If a beam oflight propagates along such a great-circle arc, then the relative path of light grows into a rectilinearpropagation with distance. This results in a geometric redshift that increases from antipode toantipode to a factor of π/2. However, this would be far too little for observed redshifts. However,since the 3-sphere is spanned by a cosmic field, the gravitational interaction between photons andthe cosmic field is added. This means that with the theory of the cosmic field, the redshift can be explained and the to antipode rectilinear propagation of light explained even without expansion of space.

Here is prior art. Make sure to refer to it since it was done before your article.

Pereira, M. (2019). The Optical Path of Ancient Photons and the Supernova Project. World Scientific News, 130, 195–215.

http://www.worldscientificnews.com/wp-content/uploads/2019/04/WSN-130-2019-195-215.pdf

In other words, for an article that claims to tell you WHAT GRAVITY REALLY IS, it lacks a simple explanation for gravity.

I derived the law of gravitation and showed that it explained the Supernova Data.

I made is even easier by providing a simple Excel spreadsheet and posting it in Quora for you to copy:

https://www.quora.com/Could-cosmological-redshift-be-caused-by-some-unrecognized-quantum-effect-giving-rise-to-emittance-of-tiny-gravitational-waves-from-photons-Could-such-a-mechanism-replace-the-hypothesis-that-space-is-expanding-due/answer/Marco-Pereira-1it

Here is the spreadsheet:

https://1drv.ms/x/s!AiskZuFLk1-ZgdUmq72bujVPQL39fQ?e=TfmmbV

Feel free to ask questions.

Marco Pereira

REFERENCES

Smarandache, F. (2007). Hadron Models and related New Energy issues. "Hadron models and related New Energy issues" by Florentin Smarandache

https://digitalrepository.unm.edu/math_fsp/283/

Smarandache, F., & Christianto, V. (2007). Quantization in Astrophysics, Brownian Motion, and Quantization in Astrophysics, Brownian Motion, and Supersymmetry Supersymmetry. "Quantization in Astrophysics, Brownian Motion, and Supersymmetry" by Florentin Smarandache and Victor Christianto

https://digitalrepository.unm.edu/math_fsp/76/

Pereira, M. (2017). The Hypergeometrical Universe: Cosmogenesis, Cosmology and Standard Model. World Scientific News, 82, 1–96.

http://www.worldscientificnews.com/wp-content/uploads/2017/07/WSN-82-2017-1-90.pdf

Pereira, M. (2018). The Case for a Fourth Spatial Dimension and the Hyperspherical Force. World Scientific News, 98, 127–139.

http://www.worldscientificnews.com/wp-content/uploads/2018/02/WSN-98-2018-127-139.pdf

Pereira, M. (2018). The Hypergeometrical Force: The Coma Cluster without Dark Matter. World Scientific News, 101, 222–228.

http://www.worldscientificnews.com/wp-content/uploads/2018/04/WSN-101-2018-222-228.pdf

Pereira, M. (2019). The Optical Path of Ancient Photons and the Supernova Project. World Scientific News, 130, 195–215.

http://www.worldscientificnews.com/wp-content/uploads/2019/04/WSN-130-2019-195-215.pdf

Pereira, M. (2017). The Hypergeometrical Universe: Cosmogenesis, Cosmology and Standard Model. Global Journal of Science Frontier Research, 17(5).

https://globaljournals.org/GJSFR_Volume17/3-The-Hypergeometrical-Universe.pdf

Pereira, M. A. (2010). The Hypergeometrical Universe: Cosmology and Standard Model. AIP Conference Proceedings, 1316(1).

https://doi.org/10.1063/1.3536448

Marco Pereira. The Big Pop Cosmogenesis - Equation of State, this article.

https://www.preprints.org/manuscript/202201.0106/v1

Wolfgang Konle

By the way, I explained what Gravitation is in my theory. I explained that Gravitation is the null response from Gravitational Fundamental Dilator (hydrogen atoms) to the Dilaton Field under the ruling of the Quantum Lagrangian Principle.

This made Gravitation to be inversely proportional to the 4D radius of the Universe.

That is covered here in the Basics:

HU Basics

https://www.youtube.com/watch?v=wuGlDECvifc

Without his G-dependence, no 3-sphere model can replicate the Supernova Data.

The reason is simple: a Lightspeed Expanding 3-sphere is not a solution to Einstein's GR and thus cannot use FLRW.

Without that, it cannot explain the SN1a data.

So, if you didn't copy my work completely, you will not be able to explain the SN1a data, and your model will be horrendously flawed. No model for gravity can be considered if it cannot explain the Supernova Data (The Cosmic Distance Ladder), which is the basis for all Cosmology.

Light is an undulation on the top of the metric field, with a wavelength equal to the Compton Wavelength of a Hydrogen atom and corresponding frequency.

In other words, in my theory, there are metric waves with frequency at 1E24 Hertz coming out from each and every particle (neutrinos have a different frequency).

WHAT IS GRAVITATION?

I mentioned the Gravitational Fundamental Dilator as a Hydrogen Atom because it is the simplest atom where Gravitation appears. In my theory, all protons and electrons (FDs) of matter will try to do zero work.

This means that they will move from position to position every 1E-14 seconds. This will create a shielding that will be almost perfect. That said, almost perfect is not perfect. The residual interaction is what we call gravitation that, and the moving sidewise within the hypersurface in accordance with QLP.

In the attached picture, you can see that one can move x within the hypersurface with a full rotation (in 4D spatial manifold) of the 3D volume of particles by arctan(v/c) or just move sideways by x without that full rotation, rotating only by an angle x/R_0, where R_0 is the 4D radius of the Universe.

Gravitation is the latter response (rotating just by x/R_0). That is the reason why Gravitation is inversely proportional to the 4D radius R_0.

If your model doesn't have that G dependence, your model will fail to explain SN1a data. That is a good reason why a paper would be rejected by peer review.

Wolfgang Konle

You said: After my professional retirement, I switched from working in the subject “radar data processing” to “cosmology”. I consider that the energy density of the gravitational field is negative. However, the existence of an absolute negative energy density violates physical laws. Consequently, the negative energy density of the gravitational field must be compensated by a cosmic positive energy density. The cosmologic implications of this compensation is the kernel of my contribution.

The first statement: I consider that the energy density of the gravitational field is negative

Why would that be? The potential energy is defined minus a constant, which can be anything and doesn't affect dynamics (that is, it cannot be detected).

So, this statement is arbitrary and there is no law of physics that defines an Absolute Reference for Energy.

In fact, the current view assigns energy to mc^2. When the Universe matter decayed into Hydrogen and the hydrogen is spread out over distances, that energy will still be here.

In other words, the Universe has positive energy.

My theory assigns the negative energy to an Inner Dilation Layer, or a metric dilation layer that travels at the speed of light and that is just behind us in our travel along the radial direction.

This is different from postulating a zero energy reference and forcing the existence of a negative energy density (somehow, you proposed a positive energy density).

In other words, the reasoning is not accurate, and you got the wrong sign for the missing energy density.

IN SUMMARY

Nobody questions that the end of the Universe will be diluted matter (as opposed to everything inside a single black hole).

If you dilute matter, the Gravitational Potential vanishes and you are left with E=mc^2, a positive energy density.

So, off the bat, the assumptions are wrong and thus are the Cosmological Implications.

Marco Pereira "The first statement: I consider that the energy density of the gravitational field is negative. Why would that be?

The answer to that question is simple. Gravitation increases if it provides energy. You see this if you consider two objects in free space, which attract each other. The attraction provides kinetic energy and the common gravitational field becomes stronger.

If you cannot see why this implies a negative energy content, look at the following example:

If the absolute amount of your bank account increases after you have redrawn some money, it must have been in the red.

Marco Pereira "In other words, for an article that claims to tell you WHAT GRAVITY REALLY IS, it lacks a simple explanation for gravity.

I derived the law of gravitation and showed that it explained the Supernova Data."

The following law of nature explains what gravity really is:

The force on an object, which contributes to a force field, is given by the dependency of the energy content in the field overlay on the distance between the object and the field source.

This law holds for all kinds of force fields including gravitational fields.

Don't you think that referring to supernovae is a bit too far fetched? Apart from that I miss a reference to the energetic reason of the gravitational force in your article.

If I would cite your ideas about the nature of gravitation I only could cite it as another example of a misconception. But I think you would not like that.

Dear Wolfgang Konle ,

You said: Gravitation increases if it provides energy. You see this if you consider two objects in free space, which attract each other. The attraction provides kinetic energy and the common gravitational field becomes stronger.

The language is imprecise, and so it is the reasoning.

For a system composed of a large body with mass M (e.g., sun) and a probe mass m in orbit, with velocity v_1, the total energy of the system will be:

GravitationalEnergy1 = -GMm/R_1,

KineticEnergy1 = mv_1^2/2

The Angular Momentum is L = m*v_1*R_1

or m*v_1 = L/R_1

So the TotalEnergy can be written as:

TotalEnergy = -GMm/R_1,+ L^2/mR_1^2/2= -L^2/(2mR^2)

In other words, conservation of angular momentum and energy only allows for a single value of R_1.

There is no interplay between Gravitational Energy and any other degree of freedom that would preserve energy and angular momentum conservation.

In other words, your Gedanken Experiment, where "attraction provides kinetic energy and that leads to gravitational field becomes stronger" would disobey those conservation laws.

Gravitational Energy is only sensitive to changing the radius of the orbit. If you change the value of R_1 while keeping angular momentum, you are changing the system's energy.

That would not happen spontaneously.

In other words, the proposed statement is flawed. It is not Physics.

If you cannot see it, look at the following example:

The Universe expands... (that is an observation) for another trillion years. During this time, all isotopes decayed into hydrogen (protons and electrons).

All galaxies fell into the Central Black Holes.

All black holes decayed into Hawkin Radiation, and their mass spread out across the universe.

So the final configuration is mass distributed across cosmological distance uniformly.

Under those conditions, the Gravitational Energy goes towards zero, and the kinetic energy goes to zero (zero temperature). The total energy remains positive since the energy of each particle is equal to mc^2.

This means that the total energy of the Universe is positive. If you want the Universe to be Energy Neutral (not depend upon someone giving it Energy), then you should postulate a negative energy source.

Gravitational Energy is negative, but that is not enough to make the Universe Gravitationally Energy-Neutral. That is easy to see just by realizing that the Hubble Law exists. The Hubble Law works well for short distances. This means that galaxies close to us are already gravitationally decoupled (they are receding). Under those conditions, their energy is just the energy contained in their masses.

Somehow your model states that there is a missing "POSITIVE ENERGY SOURCE".

"Properties of the cosmic fieldThe cosmic field, with its high positive energy density, first ensures that gravity does not lead to anabsolute negative energy density. (6) (PDF) What gravitation really is. Available from: https://www.researchgate.net/publication/372952071_What_gravitation_really_is [accessed Sep 08 2023]."

In other words, you are POSTULATING the existence of an imaginary Cosmic Field with positive energy. That wouldn't make the Universe Energy-Neutral.

So, the basic postulate disobeys the law of energy conservation.

That occurs again inside the model:

Recycling mechanism for star fuelIn the previous chapter, we addressed a mechanism that causes the energy density of the cosmic field to increase continuously. (6) (PDF) What gravitation really is. Available from: https://www.researchgate.net/publication/372952071_What_gravitation_really_is [accessed Sep 08 2023].

Dear Wolfgang Konle

The following law of nature explains what gravity really is:

The force on an object, which contributes to a force field, is given by the dependency of the energy content in the field overlay on the distance between the object and the field source.

If this were a law, you could write it down as a formula. Please do it. Words are cheap... Write it down some equations because the words are Mumble-Jumble.

You said: Don't you think that referring to supernovae is a bit too far fetched?

Of course not. The Supernova Data was used to calibrate the Cosmic Distance Ladder and thus it is basic for anything related to Gravitation and Cosmology.

The Supernova Data Analysis is where crackpots discover they don't have a theory. It separates self-delusionists from real scientists.

You said: Apart from that, I missed a reference to the energetic reason for the gravitational force in your article.

It seems you missed everything in my ARTICLES.

You said: If I would cite your ideas about the nature of gravitation I only could cite it as another example of a misconception. But I think you would not like that.

Of course, I would. If I were wrong, I would like to be corrected and the sooner, the better.

That is what I am doing for you. Time is your best asset. If you waste your time in a self-delusional crackpot model, you will regret it later.

Dear Wolfgang Konle

Am I wrong to conclude that your article does not have a single prediction of an observation, or the derivation of a law, or anything that can be used to test your idea?

In other words, you don't predict Mercury Perihelion Precession Rate, Gravitational Lensing, Time Dilation, Supernova Data, particle masses, spiral galaxy formation, the spiral galaxy rotation curve, particles' structures, the CMB, a prediction of the Galaxy Density Across the whole observable universe... etc...

All these are predicted/explained in my theory.

If I am wrong, please tell me the equation number, page...etc... and I will check it out.

Marco Pereira "If this were a law, you could write it down as a formula. Please do it. Words are cheap... Write it down some equations because the words are Mumble-Jumble."

The force F on an object of mass m at location P that contributes to a force field K is given by the directional derivative of the energy W(K,m) contained in the field superposition with respect to the distance D(P,Q) of the object at position P from the source of the force field at position Q.

F=dW(K,m)/dD(P,Q); dW/dD= (∂W/∂Dx, ∂W/∂Dy, ∂W/∂Dz)

The force field K is defined as vector gK=GMR/R³. R is the distance to position Q. R is the distance vector. The force field vector exerted by mass m is gm=GMr/r³. r is the distance to position P. r is the distance vektor

The gravitational field strength g is given as g=gm+gK. The energy density in the overlay is: W(K,m)=-(ᶴg²/(8πG)-ᶴgK²/(8πG)). The integration is over the relevant Volume around mass m. Because the increased energy density in the overlay drops with the forth power of r, the integration volume is not very large.

Dear Marco Pereira Our universe with several billions of galaxies where each galaxy host billions of solar systems like our, and in addition everything in nature is presenting three dimension that it is changing constantly through temperature and pressure, cannot be described by one dimension static our equation and math that does not recognize temperature and pressure. Unfortunately, the idea to mix our physical science, and apply it to nature is belong to Newtonian-Einsteinian era; We must observe the nature, not assume, predict, postulate and model it.

Article Why Einstein's Theory of Gravity is wrong!

And read more of my articles for real fact.

regards

Marco Pereira "Am I wrong to conclude that your article does not have a single prediction of an observation, or the derivation of a law, or anything that can be used to test your idea?"

Yes you are blantantly wrong. This is the short list of predictions or the derivation of natural laws as described in my article:

(1) The physical effect of the radiation exerted by an accelerated force field source is to restore the field as co-moving with the new velocity of its source.

(2) Gravitation has an upper strength limit given by the energy density of the cosmic field.

(3) The gravitational impact of dark matter is given by the gravitational impact of a gradient of the cosmic field. The cosmic field is excited in the interior of stars. The outflow of those excitations cause the field gradient. Gravitation is nothing else as a reduction of the cosmic field. An increased intensity of the cosmic field partially shields the gravitational impact of star matter. If the enhanced intensity has decayed to the background intensity, the shielding effect vanishes. The sudden appearance of the actual star mass gravity is misinterpreted as dark matter.

(4) Gravitational waves are predicted to be longitudinal waves propagating as energy density oscillations of the cosmic field.

(5) Black holes are predicted to be subject of an energy recycling process. The energy recycling reverts a state transition from neutron star matter to black hole matter.

There are some more predictions. But I stop here to avoid an overload.

All those predictions have an influence on the dynamics and statistics of galaxies. This predictions can be compared with simulation results. But of course it is necessary to consider all new paradigms in those simulations. The most important paradigm is the recycling process which dissolves all black holes to neutron clouds. This recycling event is predicted to occur about all twenty billion years.

Marco Pereira "In other words, your Gedanken Experiment, where "attraction provides kinetic energy and that leads to gravitational field becomes stronger" would disobey those conservation laws."

Sorry, but your example of an object in a circular orbit does not show any conversion of gravitational field energy and kinetic energy.

But if you instead consider two objects at rest in space, which attract each other, you can find the conversion between field energy and kinetic energy.

Javad Fardaei

I saw your article and realize that it didn't have a single equation. The first thing that comes to mind is that a Physics theory without a single equation cannot make a single prediction and thus cannot explain anything.

I asked ChatGPT to summarize it:

Synopsis of the Article: "Why Einstein’s Theory of Gravity is Wrong!"

Traditional View on Gravity:

Einstein's Take on Gravity:

Challenges to Einstein’s Gravity:

Reevaluation of Einstein’s Predictions:

Conclusion:

Anything with "Cosmic Consciousness" is a nonsensical concept.

Saying something like "It is unproven to say that a massive object has a gravitational field" is wrong because one defines the Gravitational Field from the observed gravitational force. Hence, a massive object has a gravitational field "BY DEFINITION OF GRAVITATIONAL FIELD"." It is a definition and thus one cannot challenge that.

It is like saying that the color of Napoleon's White Horse is Black.

To say that scientists haven't detected light-bending by gravitation is akin to negating History or saying that we shouldn't believe our lying eyes.

Yep. Your article is pure, undistilled nonsense, Javad. Congratulations.

This level of detachment from reality can only be found in Cults, Religious Sects...:) and Internet Scam Artists...

Dear Wolfgang Konle

Irrespective of the initial conditions, the total energy remains the same, and eventually, the two bodies will collide or reach an equilibrium with elliptical orbits around a center of mass.

I am still waiting for your predictions (of anything), and specifically of the Supernova Data.

As I mentioned, any theory that claims to speak about Gravitation has to do the basics: Gravitation + Mercury, Gravitation + Light, Gravitation + Supernovae.

That is the bare minimum that one has to do to make sure one is not deluding oneself and wasting other people's time. I did it.

If you place two bodies in space, without any other acting force, energy will be converted from kinetic to potential and vice versa (this is not a one-way conversion) while the bodies perform elliptical orbits.

You cannot use this to claim the existence of an "extra field of positive energy" unaccounted for.

In a two-body problem, everything is accounted for.

As I mentioned, adding positive energy to an already positive-energy Universe makes it not Energy-Neutral. In other words, it goes in the wrong direction.

You can learn from me that your model doesn't make sense or go on your merry way.

It is your choice.

Cheers,

Marco Pereira

Marco Pereira "If you place two bodies in space, without any other acting force, energy will be converted from kinetic to potential and vice versa (this is not a one-way conversion) while the bodies perform elliptical orbits."

If you place two nearly pointlike objects at rest in space, then they will attract each other and finally collide. Just before the collision, they have increased the common gravitational field and they have gained kinetic energy. Energy conversion requires that the sum of the modified field energy and kinetic energy is zero. Only the gravitational field and the kinetic energy had changed in this example. Therefor, the energy conservation only involves field energy and kinetic energy. Potential energy is a chimera. Elementary particles have a fixed rest mass without any possibility to additionally carry potential energy. In fact, the field energy density W is given by W=W0-g²/(8πG).

W0 is the energy density of the cosmic field which prevents the absolute value of the energy density to become negative. G is the gravitational constant and g is the gravitational acceleration.

Dear Wolfgang Konle

Just before collision they have DECREASED (there is a minus sign in the Gravitational Potential Energy). The closer the particles are, the MORE NEGATIVE and thus decreased the energy is.

They gained kinetic energy (it is more positive).

So, your error is not paying attention to signs.

Your mistake comes from interjecting nonsensical concepts (ill-defined) like a common gravitational field. Gravitational Field is not relevant. What is relevant is Gravitational Potential Energy. That is the one that goes into the Hamiltonian.

That kind of imprecise wording is what allowed you to think that particles coming together would "INCREASE THE COMMON GRAVITATIONAL FIELD", when in reality, the field became more negative and thus decreased.

You conflate the intensity of the attractive force with ENERGY. Those are two different constructs. In other words, the FORCE is higher but the Gravitational Potential Energy is lower (because of the negative sign).

Marco Pereira "Just before collision they have DECREASED (there is a minus sign in the Gravitational Potential Energy)."

You are talking about potential energy. I am talking about field energy. The field energy has decreased, but the field has got stronger if the objects came closer. This confirms the negative energy density of the gravitational field.

I only can advice to forget about potential energy, because potential energy cannot have a mass equivalent. Therefor it is not existing in reality.

Wolfgang Konle

Potential Energy is Energy, and thus, it has an equivalent in mass through E= mc^2

Gravitational Potential Field is energy divided by the mass of the probe. This means that the Units for the Gravitational Potential field are not Energy and thus they cannot be converted to mass by any stretch of the imagination.

So, just units analysis will tell you that reality is the opposite of what you are saying.

There isn't such a thing called "potential field energy". If you think there is, please write down its formula for a two-body problem (the simplest possible problem).

Marco Pereira "There isn't such a thing called "potential field energy". If you think there is, please write down its formula for a two-body problem (the simplest possible problem)."

No there is. But we do not call it "potential field energy", we call it field energy because it is real and not "potential".

To proof it, we look at two masses M,m in airless space. First of all, the masses are so far apart that their gravitational fields practically do not overlap and therefore attract each other almost imperceptibly. We also consider the two masses to be approximately point-like with a very small radius and use that the field energy depends quadratically on the field strength. In the separated state, the field energy W is given by

Wfield= ∫[ r0,∞]4πr²(gm²+gM²) X dr. X is a constant, we want to determine.

The change in field energy is given by the volume integral

∆Wfield= ∫[ r0,∞]4πr²(g(m+M)²-gm²-gM²) X dr=X*4πG²*2Mm/r0

The mechanical energy ∆Wkin, which is released when the two masses coincide is given by

∆Wkin= ∫[r0,∞]Fdr. F is the attraction. It applies, F=mg. With g=MG/r² we get

∆Wkin=MmG/r0

From the conservation of energy ∆Wkin+∆Wfield=0 we get

X= -(MmG/r0)/ (4πG²*2Mm/r0)=-1/(8πG) which has to be proven.

Wolfgang Konle

There are fields in Gravitostatics (or Electrostatic). The energy in the field is the ability to do work. One can neglect the "field energy" of the probe mass and only consider the work done from moving the mass from r0 to infinity.

The Energy contained in the Gravitational Field is the Gravitational Potential Energy, and it is given by:

V(r) = -GM/r

That is called potential energy, and it is an energy. It is negative because it opposes the motion from r to infinity and thus one has to do work to escape it.

You could have done the same and considered gm=0. That would lead you into Physics.

Since you didn't define r0, I will choose it to be the closest distance between M and m, starting from an infinite distance.

We know the energy difference between the two configurations and the difference in energy is:

∆Wfield= ∫[ r0,∞]4πr²(g(m+M)²-gm²-gM²) X dr=-GMm/r0

It is known.

Of course, minus that energy variation is the increase in Kinetic Energy.

This means that your analysis does not pay attention to energy conservation.

Your "Fiedl Energy Conservation" is not a law of Physics. The Field Energy does not conserve as masses move around

In other words, this "From the conservation of energy ∆Wkin+∆Wfield=0" is WRONG.

You don't need to choose the point-masses to coincide. The equation should be valid for all distances so, one can choose when they don't coincide because coinciding the two masses means a collision and that energy is not accounted for in your equation.

Below is the plain reading of your poor explanation and following you into the Rabbit Hole.

####################################################

You forgot to give us the formula for gm and gM for the two-body problem. Without them you cannot do the integral

∆Wfield= ∫[ r0,∞]4πr²(g(m+M)²-gm²-gM²) X dr=X*4πG²*2Mm/r0

There is no reason for this dependence.

There is no definition for G, nor explanation for r0 (the geometry of the problem).

From the last equation, it becomes clear that G is also a constant.

There is no justification for "use that the field energy depends quadratically on the field strength."

Could you please, rewrite this such that everything is properly defined? Stop using coincidence for the final position of the masses.

So, my conclusions are that G is a constant and equal to -1/(8piX)

OF COURSE, IF YOU LOOK CLOSE ENOUGH, YOU CAN FIND THE MOMENTS WHERE YOU INTRODUCE YOUR FALLACIES. THE MOST SALIENT IS THE FIELD ENERGY CONSERVATION.

OTHERS HAVE TO DO WITH POSTULATING INTEGRALS, ETC.

OF COURSE, IF YOU CHOOSE TO SAY THAT YOUR FIELD IS NOT THE SAME AS THE FIELD DEFINED IN PHYSICS, THEN YOUR FIELD CANNOT BE EASILY CONNECTED WITH REAL ENERGY CONSERVATION AND KINETIC ENERGY. ALSO A VARIATION OF YOUR "FIELD ENERGY' CANNOT BE CONVERTED INTO A VARIATION IN ENERGY.

Wolfgang Konle

Energy Conservation tells you that

∆Wkin+∆Wfield = -GMm/r0

where r0 is the closest and final distance between the point-like masses

so, your formula is incorrect.

Marco Pereira "Energy Conservation tells you that

∆Wkin+∆Wfield = -GMm/r0 where r0 is the closest and final distance between the point-like masses so, your formula is incorrect."

No, energy conservation says ∆Wkin+∆Wfield=0. ∆ indicates modification. Energy conservation means that all energy modifications add up to zero.

Marco Pereira "∆Wfield= ∫[ r0,∞]4πr²(g(m+M)²-gm²-gM²) X dr=-GMm/r0"

No, this is the final consequence of energy conservation. It tells us:

∆Wfield= ∫[ r0,∞]4πr²(g(m+M)²-gm²-gM²) X dr=X*4πG²*2Mm/r0 = -GMm/r0 and leads to X= -(GMm/r0)/(4πG²*2Mm/r0)

How could you let vanish the variable X, we are looking for, in the expression above? This is not mathematics, it instead is hocus pocus.

g=GM/r² and the small radius r0 also have been mentioned in my description.

It seems that you try to use predistigation to keep right.

Wolfgang Konle

Well... You are wrong.

You forget that you are moving masses around. That requires energy.

In other words, when you change the distance between M and m, your energy balance is not just some adjustment on a field.

You might want to say that the change was adiabatic...and the velocity was always zero, so, zero change in the kinetic energy. That would leave you in the change in the potential energy.

That is the -GMm/r0 that I wrote.

That said, you have a different equation for gm and gM, which means that gM and gm are not what Physics defines as Fields.

So, in subsequent statements, you cannot directly relate whatever you find about these constructs to Energy. That said, this equation ∆Wkin+∆Wfield=0 is never correct.

You can accept what I wrote or ask ChatGPT. He will teach you High School Physics and straight you up.

Marco Pereira "In other words, when you change the distance between M and m, your energy balance is not just some adjustment on a field."

The energy balance is between kinetic energy and field energy, just the two items which change.

"That said, you have a different equation for gm and gM, which means that gM and gm are not what Physics defines as Fields."

We just have gm=Gm/r², gM=GM/r², g(m+M)=(M+m)G/r².

"So, in subsequent statements, you cannot directly relate whatever you find about these constructs to Energy. That said, this equation ∆Wkin+∆Wfield=0 is never correct."

No, I can exactly determine the field energy by integration. After comparison of the field energy difference between the separated and the combined state with the kinetic energy gain, based on energy conservation we can exactly verify the formula for the field energy density.

With other words, ∆Wkin+∆Wfield=0 holds for sure and proofs that there is energy contained in the gravitational field.

All your potential energy considerations are not based on facts.

You ignore that elementary particles cannot contain a mass equivalent of their potential energy, because the rest masses are exactly defined.

Apart from that, mentioning something to be adiabatic or not in this context, is completely off-track.

Have a look at the formula of the energy density W contained in the electric field with fied strength E. W=E²/(8πkC). kC is the Coulomb constant. This energy density is positive. You easily can derive this formula from the energy content W of a plate capacitor, given by W=CU²/2 and C=εA/d; ε=ε0εr , A= plate Area, d=plate distance, kC=1/(4πε0).

Do you think considering the potential energy concept for charges also compromises the electric field energy formula?

Wolfgang Konle

This problem was solved hundreds of years ago (the two-body gravitational problem).

gm and gM are vectors and should be treated as such when you add them together. You are not doing that here, g=gm+gK for example. Why did you change the problem? There was no gK before, there was only gm and gM

Could you just talk about the problem at hand (two-body gravitational problem)?

By the way, ChatGPT already told you that Potential Energy is not conserved.

There is no reason given for this equation (quadratic form):

"∆Wfield= ∫[ r0,∞]4πr²(g(m+M)²-gm²-gM²) X dr=-GMm/r0"

Just by inspection, g is proportional to r^-2 (it is an acceleration). g^2 in the integrand is proportional to r^-2, hence the integral will have a r^-3 dependence, your formula has r^-1 instead, hence it is wrong.

Marco Pereira "gm and gM are vectors and should be treated as such when you add them together. You are not doing that here, g=gm+gK for example. Why did you change the problem? There was no gK before, there was only gm and gM"

Sorry, but you misunderstood the preconditions. We consider the two body problem at two states. In state 1 the masses m and M are separated in a way that the overlap of the fields around m and M can be neglected. We therefor can do the integrations over the vectors gm and gM independently.

In state 2 the two masses are nearly co-located. The sum of gm and gM is equal to g(m+M).

Therefor we can do the calculation in just the way it has been done.

Wolfgang Konle

It is not a "precondition". I am just requesting you not to drag me through as many Rabbits Holes as you can. It is a request of a consistent and logical description of your model.

In fact, it is simpler than that. You just have to answer the questions around the new interpretation of Gravitational Field Energy, which you claim to be distinct from the good old Gravitational Potential Energy.

For example, when you say :"way that the overlap of the fields around m and M can be neglected", the old derivation of Potential Energy would use "start with the masses at infinite distance and then move them adiabatically (keeping zero velocity and thus zero kinetic energy."

Under those conditions, there would be a force or acceleration due to their interaction.

That force would do work (change in energy) and that work would result in the Potential Energy being = - GMm/r

Your field is just a scalar acceleration (g=GM/r²). Why would you change its name????

Am I wrong?

Marco Pereira

You can describe the two body model as you want. Your model can be based upon potential energy and can include an external influence, which prevents the two bodies from gaining kinetic energy. But the purpose of your model is unclear. It does not lead to any new finding.

The purpose of the model I am using is to confirm the energy density of the gravitational field, given by -g²/(8πG). My model does not allow any intervention from outside and therefor assumes energy conservation. The energy conservation is strictly given in terms of the items which have changed in the two states we consider. This leads to ∆Wkin+∆Wfield=0.

The volume integral over the field energy density in the two states and the line integral over the attractive force along the attraction path leads to the confirmation of the energy density contained in the gravitational field.

This derivation is correct and conclusive.

You may have a completely different view, how a two body problem shall be handled. But this does not falsify anything. Your alternate view simply leads to nothing new.

Wolfgang Konle

I redid your calculation at ChatGPT:

Wolfgang Konle

From that result one can calculate the value of X as:

X =

Wolfgang Konle

I recovered a value that is not zero and you cannot assume Gravitations Energy "Density" Conservation.

The definition of r_0 can only make sense if r_0 is the final separation between M and m

That would make the U_g(M+m, r_0) to mean the energy to bring about two masses to r_0 distance from each other.

That said, the other two U_g(M, r_0) and U_g(m, r_0) have no meaningful description in the context.

Marco Pereira

Ok, with your calculation you come to the same result about the energy density of the gravitational field, as I derived.

But you still seem to have some objections about energy conservation and the minor radius r0 of the considered masses.

Of course we cannot assume conservation of the energy content of gravitational fields, if the field configuration is changed. But as we can see, the modification of the field energy leads to forces on the objects, which cause the field. We then have "force times displacement of the objects" to be equal to the "change of the energy content in the field".

Concerning r0 it is simple. We do not want to consider extended objects because this leads to complex calculations. We also cannot consider point objects, because then the integrals would diverge. Selecting a small radius r0 which allows to approximate the two mass geometry as co-located is a good compromise. In the calculation this radius cancels out.

As a summary we retain that we can explain gravitational forces with the energy content of gravitational fields. The only thing, which remains to be discussed, are the consequences of the fact that this energy density is negative.

Wolfgang Konle

The real problem is that the energy calculated in "Gravitational Field Energy" is not a suitable construct for building a model. This is not different from self-energy (electrostatic self-energy) as the path to calculate the mass of a particle.

It is just the wrong model. In other words, the mass of a particle cannot be derived from its self-energy.

You said that "Conservation of Energy" would be zero.

The calculation yields a diverging value that is anything but zero.

Just consider the Physics of the problem. Having two masses M and m separated by an infinite distance is different from having them in the same place. The difference in energy (to bring them close to each other by r_0) is the potential energy difference GMm/r_0.

You cannot overlap two bodies... The physics of the problem you proposed is poor and the construct is a useless one.

IN SUMMARY

The problem is poorly attacked... Energy Conservation does not go to zero, by any stretch of imagination.

The reason the Field Energy difference does not go to zero is the quadratic nature of the Field Energy.

Did I properly show you that you cannot use energy conservation just for the Gravitational Field Energy?

Marco Pereira "The real problem is that the energy calculated in "Gravitational Field Energy" is not a suitable construct for building a model. This is not different from self-energy (electrostatic self-energy) as the path to calculate the mass of a particle."

No, force field energy density is a perfect model, because it allows to identify the cause of forces exerted by force fields.

The law is: The force on an object, which contributes to a force field is given by the dependency of the energy content in the field overlay on the distance between the object and the field source.

"It is just the wrong model. In other words, the mass of a particle cannot be derived from its self-energy."

It may be the wrong mode to define particle masses, but it is a perfect model to identify the cause of forces.

"You said that "Conservation of Energy" would be zero."

No, I say "Conservation of Energy" leads to a zero sum of the energy modifications of all varying components of the closed system.

The concept of potential energy has causality problems.

Where do the two masses M and m know what potential energy they would need to explain the kinetic energy gain, they will get if they attract each other? If the masses M and m are different, their individual potential energies are also different.

If mass m would be a rocket, which changes its mass, this would have an influence on the potential energy of mass M. How could mass M get the according information that it now has another potential energy?

If mass M is a black hole, the potential energy of mass m is in the range of the rest mass of m. Does this mean a duplication of mass m?

Wolfgang Konle

You asked: Where do the two masses M and m know what potential energy they would need to explain the kinetic energy gain, they will get if they attract each other?

The definition of Potential Energy is: "The work to bring the interacting bodies (or charges) from infinity to a distance r_0."

In other words, the kinetic energy of the two bodies would be perfectly defined if they didn't have a history of other interactions with other bodies in the universe or if GOD hadn't placed them at rest with respect to each other at that distance.

There are no "causal" problems because Potential Energy is not defined by a dynamics process. It is potential (the maximum available energy to kinetic energy).

You gave the example of a rocket: If mass m would be a rocket, which changes its mass, this would have an influence on the potential energy of mass M. How could mass M get the according information that it now has another potential energy?

Obviously, in a rocket, you are not talking about just gravitational interaction. You have to write down the problem and solve it with initial conditions, the description of the dynamical process etc.

Your approach, which is solely based on mass, would fail since a rocket with the same mass will behave differently if the propulsion system is based on nuclear energy, oxygen-hydrogen, oxygen-methane, etc...

You said: If mass M is a black hole, the potential energy of mass m is in the range of the rest mass of m. Does this mean a duplication of mass m?

Does this even make sense?

You have a Black Hole of mass M and a body of mass m. The potential energy has the same definition. Consider their distance infinite and then adiabatically bring them to distance r_0, adiabatically. Calculate the work done by the force. That is the potential energy.

It doesn't matter if the masses are Black Holes or cups of coffee.

Don't ask how a mass "knows something." The energy available for kinetic energy (in a system driven just by gravitation) is the difference in potential energy. Here, Energy Conservation is properly applied.

AGAIN, look at the attached picture. Field Energy does not conserve as your wishful thinking wished for.

I didn't debate the rest of your claims because they were just populations.

PS- You said: It may be the wrong mode to define particle masses, but it is a perfect model to identify the cause of forces.

This is a tautology or circular reasoning. You are saying that you are identifying the cause of forces. To do so, you started with g, which is an acceleration (if you multiply m*g, you get the force acting upon m).

In other words, if you start with the definition of force and construct another concept (Gravitational Field Energy), that will be consistent. That is circular reasoning.

It will not shed any light on why there are forces.

If you want to create a model where you actually create an explanation for what a force is, you have NOT TO USE the force you want to explain.

That is what I did in my theory. I actually derive natural laws from first principles, and those first principles don't start with Newton's Law of Gravitation.

Wolfgang Konle

Is this equation relevant to your model?

If it is, and you are equating it to zero, then your model is wrong.

Marco Pereira "The definition of Potential Energy is: "The work to bring the interacting bodies (or charges) from infinity to a distance r_0."

In other words, the kinetic energy of the two bodies would be perfectly defined if they didn't have a history of other interactions with other bodies in the universe or if GOD hadn't placed them at rest with respect to each other at that distance.

There are no "causal" problems because Potential Energy is not defined by a dynamics process. It is potential (the maximum available energy to kinetic energy)."

Don't you see that with this definition potential energy cannot have a mass equivalent?

Potential energy is not defined "a priory", but a mass equivalent must be defined absolutely, because any object must have a definite mass. Mass depending on a history is impossible.

This shows that potential energy does not exist as something real. "It simply is the work to bring interacting bodies from infinity to a distance r_0." But this holds for any interacting bodies at the same time.

A space vehicle has a potential energy in respect to earth, to the moon, and in respect to the sun at the same time. But its potential energy only can have one mass equivalent.

Without a concrete mass equivalent, potential energy only is a mathematical construct without a real meaning.

Marco Pereira "Ug(M+m)-Ug(m) -Ug(M)=8πXG²Mm/r0

Is this equation relevant to your model?"

If Ug indicates a potential energy this equation is not relevant.

If Ug indicates a volume integral over g²X from r0 to infinity it is relevant.

The expression is not equated to zero. It is equated to the line integral of the attractive force along the path of the attraction.

Sorry but I do not understand why you are so desperately looking for an error in the model, which quantizes the energy density of gravitational fields. Do you think that this obvious model is somehow in contradiction to your work?

Marco Pereira "To do so, you started with g, which is an acceleration (if you multiply m*g, you get the force acting upon m). In other words, if you start with the definition of force and construct another concept (Gravitational Field Energy), that will be consistent. That is circular reasoning."

No, by using the gravitational field strength g, in the expression for the field energy, the force mg is not involved.

Wolfgang Konle

The gravitational field strength g for a problem with spherical symmetry is the same as the acceleration. You didn't have to create a new word for field strength. Changing the name does not change the nature of acceleration.

I suppose your Gravitational Field Energy is only defined for systems with spherical symmetry. Am I wrong?

Have you written equations of motion based on that concept? If so, could you please write them here (or upload a picture of the equations)?

I am asking because Newton's equations of motion are based on Gravitational Potential Energy.

Wolfgang Konle

It is impolite to spam your work on someone else's question unless you have a claim that your work is better than the work associated with the question.

If that were the case, I would welcome your challenge and would tackle it as I am doing it right now.

Since you bothered to bring your work into my field of vision, I am determined to find out where did you screwed up.

As far as I can tell, it seems that your error is very close to the beginning of the paper... right on your claim that Gravitational Field Energy is conserved.

You said so and equated the U_g(M+m)-U_g(M) - U_g(m) =0

That is wrong.

You also claim that the Gravitational Field Energy concept brings insight into the nature of forces. It doesn't, despite your claims.

If you don't like scrutiny, you shouldn't go around posting your work. I do like scrutiny and want people to read my work and say something intelligent about it.

I worked hard and presented this criticism:

U_g(M+m)-U_g(M) - U_g(m) 0

So, am I wrong to conclude that you were wrong in your statement that

U_g(M+m)-U_g(M) - U_g(m) = 0

Wolfgang Konle

Isn't g the same as acceleration? In other words, if I multiply it by mass I get a force, in the same way as m*g (mass times acceleration)?

Marco Pereira

Your claim: "As far as I can tell, it seems that your error is very close to the beginning of the paper... right on your claim that Gravitational Field Energy is conserved.

You said so and equated the U_g(M+m)-U_g(M) - U_g(m) =0"

My statement: The expression is not equated to zero. It is equated to the line integral of the attractive force along the path of the attraction.

Why do you insist on your false claim "equated to zero" though I had repeatedly stated that this is not the case?

I never claimed that the gravitational field energy is conserved.

The claim simply is that the sum of the modification of the gravitational field energy and the work done by the field to the objects which generate the field, is zero.

Marco Pereira "Isn't g the same as acceleration? In other words, if I multiply it by mass I get a force, in the same way as m*g (mass times acceleration)?"

Yes the gravitational field strength g is an acceleration. But just this acceleration is used in the formula for the energy density and not the force.

The force is caused by the distance dependency of an energy content based upon this energy density. The force has not been used in the definition of the energy density.

Therefor your allegation of a circular conclusion is unsubstantiated.

Marco Pereira "It is impolite to spam your work on someone else's question unless you have a claim that your work is better than the work associated with the question."

It is impolite to call the work of others "spam". Your reaction shows that your work and my work must have a certain relation.

If there is a contradiction we should clarify this by fair means. But requesting an assessment which work might be better is strange. Every author thinks his work is correct.

You asked a question about the universe based on your work. My answer to that question has been a reference to the answers about the universe given in my article.

My key answer is that the gravitational force is caused by the energy density of the gravitational field, and that the negative energy density has cosmologic consequences. One consequence is a proposed 3-sphere structure of the universe.

Your answer is that the universe is hypergeometrical. My initial thought was about a comparison of "hypergeometry" and 3-sphere structure. I did not expect that you would deny the energy content of force fields with such an intensity.

Wolfgang Konle

Yep... Your work offend me in the same way a Flat Earth article would do.

The fact that you posted it in my question means that you either wanted your work to be criticized or that you wanted to get exposure in the shadow of my success...:)

It might sound like a joke, but among the crackpots (you included), I am quite successful.

You spoiled my question because now that you presented your work and I got engaged in debunking it, no real scientist showed up to say anything.

WHY WOLFGANG KONLE IS WRONG?

Later, I will create this question so that I can present this argument properly.

If you substitute equation 13 into your equation 12, you recover that:

W = -GMm/r0 or W is the value of the potential energy.

It is called potential because it corresponds to the potential of doing work. If a body of mass m comes all the way from infinity to the surface of Earth (radius r_0 and mass M), then that would be the energy that the body would acquire.

Obviously, that energy decreases inversely with distance, and thus, your subtraction from a "Cosmic Field." is meaningless.

The reason is simple: the potential energy is the work produced by forces, and they are vectors. In a homogeneous universe, the gravitational forces add themselves to zero (average out over long distances).

So, there is no work done by bringing a body from infinity. In other words, the Gravitational Fluctuations are local and localized, and so it is the potential energy. Since your Field Energy Density is the same as the potential energy, the argument applies to it too.

I think taht is being wrong enough. I will stop here. I am sure you made other mistakes.

Marco Pereira "It is called potential because it corresponds to the potential of doing work. If a body of mass m comes all the way from infinity to the surface of Earth (radius r_0 and mass M), then that would be the energy that the body would acquire."

Yes, and the gravitational field of earth gets slightly stronger. Do you think that it is by accident that the integral (12) ∆Wfield just has the same value if you insert -1/(8πG) for alpha?

Your potential energy is not real, it is only potential. If m is an elementary particle, it does not have the possibility to store the mass equivalent of its alleged potential energy.

The whole concept of potential energy is a nice trick to simplify calculations. But Einstein's mass/energy equivalence revealed this trick as a chimera.

Therefor, you are wrong and Wolfgang Konle is right.

Dear Wolfgang Konle

You asked: Do you think that it is by accident that the integral (12) ∆Wfield just has the same value if you insert -1/(8πG) for alpha?

YES. It is a Fallacy.

The point where you created your fallacy is equation 12. That is when you put together three divergent integrals into a single integral and postulated a single r_0, later to be conflated with the r in the Potential Energy calculation.

Self-Energy of Coulomb or Gravitational forces are infinite (cannot be calculated). The example of a "Gravitational Capacitor" is contrived and can only be calculated in the case of electrostatics where the field goes to zero on the conducting plates and considered constant between the plates. The energy in the electrostatic capacitor is not being mapped to the self-energy of the EXTRA electrons in the plate, but they should. What you calculate there is the energy of the setup. That always fails when you consider a Coulomb potential.

Even there, if you allow for the existence of charges, the self-energy would become infinite.

So, by accident and carelessness, the difference in "Gravitational Field Energy" becomes "similar" to the Potential Energy.

Of course, in the case of potential energy the value of r is defined by the distance between the centers of mass of the two bodies.

In your case, r_0 has no meaning since in your case, you are changing the mass of one of the bodies to become M+m. There is no physical process of moving masses or anything defining a geometry.

That is when the Fallacy was born.

From that you started believing in the existence of a Gravitational Field Energy that is pervasive and not connected to the capacity of producing work (as it is in the definition of Potential Energy).

Since you started believing in your mistake, you conjured up a POSITIVE COSMIC GRAVITATIONAL FIELD ENERGY...

Since the positive energy nature of our Universe is already an unsurmountable problem in Physics (for the garden-variety scientists), adding more positive energy makes NO SENSE.

I will move this discussion to its own question such that we don't have to take space on mine.

Cheers,

Marco Pereira

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

I started a discussion there... Feel free to answer my critique.

Marco Pereira "The point where you created your fallacy is equation 12. That is when you put together three divergent integrals into a single integral and postulated a single r_0, later to be conflated with the r in the Potential Energy calculation."

Your fault is the assumption of point masses. But point masses do not exist. Therefor it is correct to assume a finite small radius r_0 for any mass. With the assumption of r_0 the integrals you mention are not divergent.

If the masses M and m are not too different, assuming the same r_0 for both masses is acceptable. In the other case if M is the mass of the earth an m is the mass of something small falling down, a too big r_0 for the small mass m does not lead to a significant error in the calculation. m² is much too small compared to M² to make a difference.

Therefor the alleged fallacy in my calculations is a pure phantasm.

Apart from that, I consider it as being a honour that you dedicate a new question on the correctness of my article:

Preprint What gravitation really is

But if you do not find better substantiated arguments than the allegedly divergent integrals, I do not fear that you eventuall could falsify parts of my work. Up to now all your falsification trials failed depressingly.

Dear Wolfgang Konle

I created a discussion but lost it before I could get a link to it to pass to you. I don't know how to find the discussion in this site.

Anyway, just consider that the definition of r_0 should be valid in a context of two masses M and m... and also valid when considering a single mass in the universe m. Of course, the r_0 would be defined by the value of the larger mass M (perhaps the radius of the Black Hole, star or planet).

How could this concept (Gravitational Energy) be independent upon the mass m if it is ok to use the radius of a Black Hole, or star...etc from the other Gedanken Experiment?

In other words, by serendipity, when you use the same radius in your common integration (eq.12), you recovered the garden-variety Gravitational Potential Energy, and that makes eq.12 consistent with Newtonian Dynamics.

That is the problem. The value of r_0 cannot be defined depending upon the "Gedanken Experiment mass of the other body".

If you cannot have a definition for r_0 for mass m that is independent of "Gedanken Experiments", then the concept is useless and conclusions are part of the Fallacy.

It doesn't help that the construct diverges.

So serendipity in recovering the standard Gravitational Potential Energy is what doomed your model.

Serendipity happens all the time. It happened to me in the past, it happened to others.

Your job is not to believe what it too good to be true and to understand what can be calculated from a construct and what cannot.

Your definition of Gravitational Field Energy is the same that everyone else used to calculate Self-Energy. In other words, people tried to calculate the mass of particles using the energy in the electrostatic field (forever) and failed.

Of course, nobody ever said that the energy in the field would define dynamics (you equated change in kinetic energy to change in the Gravitational Field Energy, which only worked because of your sleight of hand).

I am only correcting it because it is wrong.

If there is a way to make sense of your model, I will be happy to correct myself.

Otherwise, consider it a careful peer review.

Marco Pereira

Instead of discussing the definitive result "energy content of the gravitational field", derived and quantitatively confirmed with the two mass gedankenexperiment, you mention arguments like serendity.

No, the energy content of force fields is not a serendity, it is an immutable law of nature and applies to electric, magnetic, and gravitational fields.

We can show that the modification of the specific energy contained in the field overlay, leads to a force on the objects, which cause the field overlay.

The mechanical energy involved in moving the objects under the influence of that force, corresponds to the modification of the energy content in the field overlay.

The fact that this immutable law of nature applies to all kinds of force fields excludes something like a serendity. We have to deal with that real cause for forces exerted by force fields. That also means that we must abandon all "potential energy based trials" to explain forces. Potential energy is not real because it cannot have a mass equivalent.

Wolfgang Konle

Follow this Gedanken Experiment. I give you a bag of 1 kg of Coffee and ask you to calculate the Gravitational Field Energy for it.

Can you do it? What is the value? This is a very simple question!

Below is Claude's explanation after I explained the problem to him.

In the article "What gravitation really is" [1], there appears to be an unjustified assumption in the derivation of the energy density of gravitational fields in equations (11) - (13). Specifically, in equation (12) the gravitational field energy of each mass (ΔW_Feld) is calculated by integrating over all space out to some threshold radius r_0.

However, r_0 is defined based on the particular masses M and m that are interacting, rather than being an intrinsic property of each mass independent of any interaction.

Introducing r_0 in this manner makes the gravitational field energy depend on the specific interaction, rather than being a general property of the mass itself. The potential energy between M and m can only be recovered by adjusting r_0 to those particular values. Using a fixed radius threshold based on the interacting masses to calculate the field energies is an arbitrary parameter that undermines the analysis.

The gravitational field energy should be derived in a way that is independent of any particular interaction.

Furthermore, equating ΔW_Feld to the kinetic energy ΔW_kin is only valid if ΔW_Feld represents the change in potential energy between the masses. However, the recovery of the potential energy from ΔW_Feld appears to be serendipitous, resulting from forcing the same r_0 value for the two different masses. This r_0 would need to be re-adjusted for each different set of interacting bodies to recover the potential energy. The fact that r_0 must be redefined depending on the interaction means W_Field is not an intrinsic property of the masses themselves, making the model internally inconsistent.

In summary, equating the global integral for ΔW_Feld to the local interaction energy ΔW_kin is inconsistent, and the use of r_0 based on the interacting masses makes the field energy definition invalid. A consistent derivation of the gravitational field energy density should avoid these issues.

[1] Wolfgang Konle, "What gravitation really is", Physics Essays Vol. 22, No. 4, 2009

Marco Pereira "Follow this Gedanken Experiment. I give you a bag of 1 kg of Coffee and ask you to calculate the Gravitational Field Energy for it."

Sorry, but you did not understand the principle.

The bag adds its own gravitational field to the field of earth. Therefor the field strength in the field overlay increases. This increased field strength leads to a reduction of the energy content in the overlay region because the energy density of gravitational fields is negative.

The field of earth is very strong and the energy content in the field overlay quadratically depends on the field strength. In upward direction the field strength of earth becomes weaker. Moving upwards then enhances the energy content in the field overlay. The negative energy contained in the gravitational field of the bag is neglectably small.

If we raise the bag by 1m we add 9,81J to the energy content of the field overlay.

Wolfgang Konle

"Follow this Gedanken Experiment. Please consider that there is only a single bag of 1 kg of Coffee in the Universe. I am asking you to calculate the Gravitational Field Energy for it. Show the calculation, that is, the integral"

Marco Pereira

Ok, let us assume the bag has the form of a bowl with radius r0.

Outside the bowl the field energy is -Gm²/(2r0).

Inside the bowl the field linearly increases from zero to Gm/r0²

We have there gi=rGm/r0³. -gi²/(8πG)=-r²Gm²/(8πr06).

The integral from zero to r0 leads to -1/10(Gm²/r0) [The integrand r4 evaluates to 1/5 r5]

We then get for the enenergy of the gravitational field of the 1kg coffee:

W=-(6/10)*Gm²/r0. With r0=8cm we get: W=-5,006E-9J.

What is the justification for the 8 cm? Why not 1 cm or 1 mm?

What is the justification for the 8 cm? Why not 1 cm or 1 mm?

You said its coffee isn't it? 1kg coffee would not fit into a bowl of 1cm or 1mm.

@Wolfgang Konle

What is the error bar on that estimate? What is the rationale?

That is important since that is supposed to make dynamic predictions consistent with Newtonian Dynamics.

What is the Gravitational Potential Energy of two bags of 1kg of coffee, alone in the Universe and separated by 10 meters distance?

Marco Pereira "What is the Gravitational Potential Energy of two bags of 1kg of coffee, alone in the Universe and separated by 10 meters distance?"

There is no potential energy. Only field energy exists.

The field energy is about -2*5.0E-9J. If the to bags get combined, the gravitational field energy is reduced to about -4*5.0E-9 because a duplicated mass leads to a factor 4 in the field energy. But we must reduce this amount of energy by the factor 21/3 due to the increased radius of the doubled volume.

If you want it expressed that way, the potential energy is the difference between the field energy in the separated and in the combined state.

It is about -(2E-8*2-1/3 -1E-8)J.

[The calculation is based upon:

W=-(6/10)*Gm²/r0. With r0=8cm we get: W=-5,006E-9J.

The error bar is determined by the unknown density of the coffee. The field energy contained in the field overlay at a distance of 10m is negligible because the energy is proportional to distance-4. ]

Dear Wolfgang Konle

Please read my comments in the attached pdf file.

Marco Pereira "Why did you use the definition of Potential Energy as your Kinetic Energy?"

Sorry, but why does your question contain a strange allegation? Your allegation is based upon the fact that the term Gm²/r0 partially occurs in the calculation. But the calculation only uses -g²/(8πG) and a volume integral over this expression.

In your assessment you continue with the next false accusation:

"Your mistake in the calculation of the Change in Gravitational Field Energy made it equal to the Potential Energy."

There is no mistake in the calculation. If you think the evaluation of the volume integral is not correct, then present your calculation.

With "stopping at 10m" you revert the scenario I am assuming. My interpretation was "starting at 10m" and ending at 8cm*21/3.

The calculation of the field energy in a non-spherical geometry is an unnecessary algebraic challenge. Therefor we should restrict our considerations on scenarios with a spherical symmetry.

Your conclusion ∆Wfield=0 results from your confusion between start and end point of the scenario. As already said, it does not make any sense to stop in a non-symmetric situation which is algebraically inappropriate to show obvious relations.

You again try to plant something inappropriate into my argumentation for field energy. But the only way with a real chance to falsify my approach, would be to find a valid counter argument.

Wolfgang Konle

The pdf is self-explanatory and it shows that your definition of W_Kin is identical in value and in nature to Gravitational Potential Energy.

I am and always will be talking to you under the premise that you are misunderstanding Physics in good faith.

You claim that you can describe the Universe using the concept you crafted called Gravitational Field Energy.

The first challenge for this new concept is to show it can replace Gravitational Potential Energy. Physics uses potential energy to describe ALL DYNAMICAL PROCESSES.

That is the first challenge any theory should pass, especially if you are introducing a new reservoir of energy to the universe.

In other words, you have no say in the conditions I impose to test your ideas.

That explains why this sentence expresses a lack of understanding of the scientific method and the scope of your proposed model:

With "stopping at 10m" you revert the scenario I am assuming. My interpretation was "starting at 10m" and ending at 8cm*21/3.

Or

The calculation of the field energy in a non-spherical geometry is an unnecessary algebraic challenge.

If your model only works for the conditions you derive and uses the same derivation you used, then nobody can say anything about your model or use it.

This was my question: "What is the Gravitational Potential Energy of two bags of 1kg of coffee, alone in the Universe and separated by 10 meters distance?"

That is clearly the final configuration. If you understood something else, that is not my fault.

I explained through this example that your concept of Gravitational Field Energy cannot explain dynamics (Energy does not conserve or the change in Gravitational Field Energy does not equate to the change in kinetic energy, a.k.a. Potential Energy).

In Conclusion

• Gravitational Field Energy is not a Physical Concept.
• Your model uses as Kinetic Energy, Gravitational Potential Energy, thus restricting the applicability of the model to only a single impossible process.
• A model has to satisfy Physics. In other words, you cannot claim to change the whole Physics and fail to explain the dynamics of two bags of coffee separated by 10 meters.
• You said that the "Calculation of Field Energy in a non-spherical geometry is an unnecessary algebraic challenge". Does physics require an explanation for processes where the final configuration is non-spherical? Of course, the answer is yes, so the challenge is necessary.
• You said: "∆Wfield=0 results from your confusion between start and end point of the scenario." No. I didn't. The initial state (to comply with your definition of Kinetic Energy, as potential energy) is the two bodies separated by infinite distance and thus zero overlap. You said:"The field energy contained in the field overlay at a distance of 10m is negligible because the energy is proportional to distance-4. ]" and thus the final state has the same Gravitational Field Energy as the initial state and the difference is zero.
• That said, I showed that even if one calculates everything, the Kinetic Energy change only depends upon d0 (the 10 meters) and not on r0 (the 8 cm). This means that Energy Cannot be conserved using your definition of Gravitational Field Energy.

I hoped you would understand the flaws in your model. It seems you can't.

Best wishes,

Marco Pereira

Marco Pereira There are some remarks to your conclusions:

You simply claim that gravitational field energy is not a physical concept. But you do not justify your claim.

My model does not use gravitational potential energy. It considers the energy density in the gravitational field.

Your stationary example of two bags in 10m distance does not tell anything about the energy density in gravitational fields.

The gravitational force relates from the interaction of a background field with the weak field of an object. You simply ignore that mechanism and then you tell strange stories about an inappropriate concept you have in mind.

I had explained that considering the field energy in a more complicated geometry is not necessary to proof anything. You then claim that the theory only works in simple geometries. But this is nonsense.

Sorry, but your argumentation is not serious. You only try to show that the concept of field energy is inappropriate by applying it to inappropriate scenarios. I only can repeat this criticism.

The fact is that gravitational fields change if the objects, which make the field, move under the influence of gravitational forces. The mechanical work resulting from that movement corresponds to the modification of the energy content in the gravitational field exerted by the moving objects.

In order to state something serious you must find a way to disprove this fact. Describing ridiculous static scenarios in which nothing happens is not sufficient to convince anybody.

Wolfgang Konle

I said it was not a physical concept because it does not conserve energy. In other words, moving from one configuration to another, energy is not conserved.

In other words, you are trying to assign the change in kinetic energy to a change in Gravitational Field Energy, but the change in Gravitational Field Energy is not the same as the change in Kinetic Energy (a.k.a. Potential Energy).

Your definition of Kinetic Energy is the same as Potential Energy, hence your model uses potential energy.

You said: In order to state something serious you must find a way to disprove this fact. Describing ridiculous static scenarios in which nothing happens is not sufficient to convince anybody.

You mentioned static scenarios. Your model is just based on static scenarios.

Let me know where you published your work and I will be happy to write a critique (basically what I already wrote) to try to convince somebody that your work is nonsensical.

It seems that you are more interested in Vox Populi than Physics.

Cheers,

Marco Pereira

Marco Pereira "I said it was not a physical concept because it does not conserve energy. In other words, moving from one configuration to another, energy is not conserved."

Your claim is wrong. The movement of objects under the forces their gravitational fields exert, conserves energy because the mechanical energy "gravitational force times movement path" is exactly equal to the change of the energy content in their gravitational field.

You simply claim that this is not the case. But I have proven mathematically that the energy density -g²/(8πG) leads to the equality between the mechanical energy and the field energy.

But simply repeating pure claims without the faintest proof only is an imposition.

Wolfgang Konle

Is your work published somewhere?

I ask because I don't want the author of the model to be the judge of my critique.

Marco Pereira "I don't want the author of the model to be the judge of my critique."

Now I understand. You are not interested in an open factual discussion. The concept of force field energy density seems to be in contradiction to your work. Therefor you see this concept as something which sheds a bad light on your work.

But look, it is a concept, a way to understand nature. You cannot enforce that a concept must be abandoned. Your only option is to refute it by factual arguments. There is no legal way to prohibit publishing that concept.

You better should find a way correcting your own work and make it compatible to the concept of energy density in force fields.

Following such a way could be painful and enforce rethinking about claims you might already had considered of being sure. But this is the only way to avoid the loss of reputation.

Wolfgang Konle

We already had the factual discussion. I showed the definition of Wkin and the definition of potential energy, and they are identical, and yet, you refuse to acknowledge that.

I told you that your "new concept" does not obey Energy Conservation if one just changes the final configuration of the involved bodies, and you complained that "asymmetric configuration is unnecessary complication". The Universe disagrees with that. Bodies interact under all kinds of configurations, and any model will have to conserve energy in the analysis. Yours does not.

The concept is not in contradiction with my work. It is in contradiction with Physics and all observations.

I hoped you would be intellectually honest and understand basic arguments. I was wrong. I asked where you published your work to rebut something that I consider detrimental to Science (a.k.a. fake science) and to the populace. I did so because I consider that Science should be protected, and protection is done through scientific arguments. I would never arbitrarily attack your ideas. I think that thinking is a good thing.

I guess you either know that you have no hope to publish your articles or you already published in some vanity journal and hope to hide them from criticism.

Either way, that is ok. I will just make a write-up of our conversation and place it here in researchgate and on preprint.com.

Behaving as you are behaving gives crackpots a bad name. Since my theory competes for visibility with crackpots' models (unfortunately, I am one among the ones like yourself), it is only fair to correct the worst examples of crackpottery, especially since you pushed it in front of my face by putting this nonsense as an answer to my question.

Cheers,

Marco Pereira

Marco Pereira "I showed the definition of Wkin and the definition of potential energy, and they are identical, and yet, you refuse to acknowledge that."

Yes, I refuse that the definition of potential energy proofs anything about the energy content of force fields.

It is sufficient to look at a plate capacitor. It is obvious that the energy 1/2CU² is contained in the electric field between the plates. If we increase the distance between the plates, the electric field strength does not change. Only the volume filled with the electric field growths. This simple fact proofs that the energy is contained in the field. The charges in the plates could not find out that the plate distance has been enlarged. So they could not increase their potential energy if the distance between the plates gets enlarged.

If we look at the gravitational field between those plates we find the same conditions. But in this case, the field is outside, but also without any change of the field strength, if the distance between the plates is changed.

The Atoms in the plate have no chance to get information about the modified distance. Causality again disproofs the potential energy concept.

A short summary:

The plate capacitor geometry incontrovertibly proofs that the energy is contained in the force field around the plates. This is because moving the plates modifies the energy content, but leaves the field strength. The only thing, which is modified by changing the plate distance, is the energy content and the volume filled with the homogenous field.

By repeating irrelevant details of your misconceptions you have no chance disproving the facts about the energy content of force fields. Your complete ranting and raving about the energy content in force fields is ridiculous and useless.

Wolfgang Konle

In the past, you refused to accept that your model was using Potential Energy instead of Kinetic Energy...now you want to refuse something else.

We never talked about capacitors because there is never a gravitational capacitor, and your model is about Gravitation, so this is a silly misdirection.

THE ANALYSIS OF THE CAPACITOR AND ENERGY CONTAINED IN IT IS CORRECT - IT WASN'T DONE BY YOU. THAT SAID, THAT ANALYSIS DOES NOT CONTAIN ANY KINETIC ENERGY. THERE IS NO MECHANISM IN THE CAPACITOR MODEL TO CONVERT THE ELECTRIC ENERGY TO KINETIC MOTION OF THE CAPACITOR PLATES. YOU DON'T SEE THE MASSES OF THE PLATES, THE RATE OF CHARGE LOADING OR THE VOLTAGE APPLIED TO THE ELECTRODES, THE INITIAL DISTANCE BETWEEN ELECTRODES, THE ELECTRODES INITIAL VELOCITIES... ETC.

SO, THAT MODEL IS NOT A MODEL THAT EXPLAINS DYNAMICS (IT ALSO CONSTRAINS THE PLATE MOTION TOignore MOTION ALONG A SINGLE AXIS), AND CERTAINLY, IT IS NOT A MODEL THAT CAN EXPLAIN THE DYNAMICS OF GENERAL BODIES UNDER GRAVITATIONAL INTERACTION.

IN OTHER WORDS, YOU JUST ADOPTED A CAPACITOR MODEL WITHOUT THINKING.

You seem you cannot understand how wrong you are. Why do you bother replying nonsense to me?

Just go on your merry way, and I will do whatever I decide to do.

You are free to defend your idea where it is needed to be defended.

Here is just the comment section of my question about the achievements of my theory...:)

I know you disregard courtesy and don't pay attention to science; that said, it would be good form just to go away...:)

Do you think you can save face after writing the stuff you wrote? Don't be so vain. As I said, being wrong happens to the best among us...

Unfortunately, I cannot just block you from writing where I write or seeing your postings...:) Researchgate leaves a lot to desire...:)

I discovered I can block you, so you are now blocked.

Cheers,

Marco Pereira

Marco Pereira

It seems that you do not understand the consequences of the homogenous field structure in the capacitor plate geometry.

Nothing in the plates can detect the modification of the plate distance, because viewed from the plate nothing changes in the homogenous field. There is no causal connection between something in the plates and the distance of the plates.

This simply means that there is no chance to change potential energy according to the modification of the plate distance.

But it does not matter if you understand this causality argument or not. You definitively cannot deny facts.

I told you, that simple examples allow to illustrate the facts. A homogenous field structure is the most simple structure possible.

I am sorry that I did not mention this example before. Presenting it earlier could have helped to avoid some misunderstandings.

The capacitor plate geometry reveals a causality problem for potential energy. Modifying the distance between the plates modifies the field volume and nothing else. There is no causal relation ship between the distance and ingredients of the plates. Therefor no information is available which could adapt potential energy to this distance.

This causality problem in the capacitor plate geometry concerns the homogenous electric and gravitational fields in the same way.

Consequently the energy content is localized in the field and not in a potential.