"The point where you created your fallacy is equation 12. That is when you put together three divergent integrals into a single integral and postulate 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, including the combined mass 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.

see Preprint What gravitation really is

"Self-Energy of Coulomb or Gravitational forces are infinite (cannot be calculated)."

Ok, this Self-Energy obviously is an undefined term we should avoid in further discussions. I did not use this term in any context.

"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."

Sorry, the physical process is exactly defined. There is given a closed systems of two masses M and m. We consider two states of that system. First, the gravitational fields of m and M do nearly not overlap. Second, the two masses have approached each other to distance r0.

Changing the mass to M+m simply means that both masses have been combined in the moment of the collision. The larger mass does not change its radius if the small mass is added.

Why are you using the term "Self-Energy" in the capacitor example, after it has been obvious that this term is undefined and even undefinable.

Based on this term your critics is absurd.

Wolfgang Konle

If Gravitational Field Energy is a real Physics construct, it should be well-defined irrespective of the interacting masses. For example, Newton's Gravitational force is GMm/r^2 irrespective of the interacting masses. This means that one should be able to define it for each mass (M, m, and M+m). So, one should be able to calculate them independently and then calculate the difference.

Separate the integral into three integrals. One for M, another for m, and another for M+m. This should be done because U_g(M) is a concept that is defined for a mass M, so it shouldn't be dependent upon the other masses.

Call the smallest radii r_0, r_1, and r_2.

Now explain to us why r_0 should be equal to r_1, and r_2?

This is important because only when they are identical, is that one recover Newtonian Dynamics. Would would the radius used to calculate the Field Energy of a hydrogen atom be the same as the radius used to calculate the Gravitational Field Energy of TON618?

The point here is that you forced them to be equal to recover the value of Potential Energy and that is where you sleight of hand took place.

There is no justification for it.

My work is done!

"Gedanken Experiment" is not an explanation since another "Gedanken Experiment" where the two masses join without just touching each other would give a distinct result. In other words, the Gravitational Energy Field definition should not dependent upon how the masses joined.

Marco Pereira "Now explain us why r_0 should be equal to r_1, and r_2?"

Sorry, what question is that? The equality of the radii is the assumption in the gedankenexperiment. Questioning the setup does not make sense. You simply should respect the results achieved with exactly this gedankenexperiment.

Permanently proposing another setup, which then does not lead to definitve results, is a strange strategy and inappropriate to falsify the results of a specific gedankenexperiment. With other words, your question is irrelevant.

But you can see that real conditions lead to the same result up to an extremely high accuracy:

We can assume that M is the mass of earth and m is 1000kg and r0 is the earth radius.

Then the radius of M+m is of course equal to the radius of M. The radius of m then does not really matter because M²>>m².

I answered your counterarguments in my original answer. I don't want this to be a long debate between the two of us. Instead I would like others to read our arguments and opine. If you cannot see your failures, perhaps others can see it through.

I made a mistake. I created a question instead of a discussion. Mea culpa.

Let's create a discussion and invite everyone to debate.

It is a good idea to create an open discussion. I only hope you do not try to charge the discussion a priori with some of your dogmas.

But you also should keep out names from that discussion. I would prefer a purely factual discussion about potential energy or field energy.

Exactly what do you mean to keep out names from that discussion?

By the way, I still don't know where the discussion is taking place. I created it, but I don't see how to search for a discussion, so, if you don't hear from it, maybe I failed to create it or maybe nobody responded to it.

Marco Pereira "Exactly what do you mean to keep out names from that discussion?"

Do not mention Marco Pereira and Wolfgang Konle! Mention only the subject of the discussion and the controversal assumptions about the subject!

Dear Wolfgang Konle

Wouldn't you want to get the benefit of being shown correctly?

Let me help you here. I spent my whole life with this kind of problem in the back of my mind. I've never opened my big mouth because I wasn't sure about what was really happening.

The reason I did that is because I don't like to look stupid.

That said, even when I was totally sure about the theory, I still made a stupid mistake (my data analysis of the SDSS data) and looked pretty stupid for a second or so. I did so in Quora and wrote many answers with the incorrect analysis. Later, I had to correct all of them and write an ERRATA on each answer (I also sent messages to people who read it and upvoted the answer containing the wrong analysis), telling the readers why the analysis was wrong.

That said, that analysis didn't affect my theory's level of support.

If you are wrong, you should want to make sure everyone on the planet knows that to be the case. I am sure you have many followers who would benefit from knowing of any problem in your reasonings and model.

What is important is to be intellectually honest and honest.

Nobody will blame you for pushing an incorrect analysis or model in bad faith.

In other words, being wrong might force you to change your plans to receive the Nobel Prize in Stockholm next year, but if you are intellectually honest, you will feel good about yourself.

There is no shame in being wrong. In addition, solving the theory of everything is a thankless job. Don't expect anyone (certainly, anyone from academia or your crackpot competitors..>:) ) to thank you for anything.

Every day I write something, I hope that someone will show me wrong so that I can go out and do something else.

That said, I am still waiting for your answer to that simple question.

Marco Pereira "That said, I am still waiting for your answer to that simple question."

What question do you want to be answered?

Dear Wolfgang Konle

The pdfs are 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

Before you irreversibly get worked up with your potential energy concept you should consider the following:

The force on an object which contributes to a force field is given by the dependency of the energy contained in the field overlay on the distance between the object and the field source. This law applies to all kinds of force fields and explains the common cause of the force.

The next point finally kills your potential energy concept:

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.