This discussion has been great. I am finally considering I have an explanation of this obscure part of my theory.

Like in any force field, the force on an object in a gravitational field is given by the derivative of the total field energy in respect to the position of the object.

This relation does not allow different dependencies of inertial and gravitational mass.

Dear Wolfgang Konle

What you just said is "correct" within the paradigm you decided to use: "Field".

I showed that this is not the correct paradigm. As you know, a field decays in intensity with the inverse "area" of the hyperspherical hypersurface it covers.

In other words, in a 4D spatial manifold, the concept of Field would require that Gravitation decays with the inverse cubic distance. We know that is not true and yet, there are many models that use a 4D spatial manifold. Here is one example:

Banerjee, S., Danielsson, U., Dibitetto, G., Giri, S., & Schillo, M. (2018). Emergent de Sitter Cosmology from Decaying Anti-de Sitter Space. Physical Review Letters, 121(26).

https://www.mendeley.com/reference-manager/reader/7a341458-1762-3501-94b1-bdf854ffcbfe/698b49e8-2e75-52a1-25ee-2614978f2d30

This article is incorrect since it adopts L-CDM, that is, despite copycatting my hyperspherical hypersuperficial Universe, the radius refect the "observed" SN1a distances. It fakes Dark Energy and Dark Matter by introducing a negative surface tension consistent with whatever is observed.

In other words, it is a fake, contrived model, with no prediction capability.

So, Field is not the only paradigm that will result in a force. My theory derives the laws of Nature using the Quantum Lagrangian Principle (QLP).

Read my answer to understand the rest. In creating this question, I think I understood the problem better. That said, I need to create some figures to explain it to you in a simple way.

Dear Marco Pereira

Fields among other items, explain the interaction between charged particles or bodies. In this view matter is a monoclonal charge. The field view does not require leaving our spacetime. Fields are mathematically defined, and we know them as scalar-, vector-, and tensor-fields. Describing physical interactions with fields is standard and not a special paradigm. Stokes’ and Gauss’ theorems apply to vector fields. We do not need an excursion to higher dimensions in order to understand what is going on with fields in nature.

I have no qualified answer, but a question: In this theory, what is the gravitational mass of neutral particles (neutron, neutrino), if a neutron can be considered to first order as a proton bound with an electron? If it is twice the gravitational mass of a proton, one could measure the gravitational force of a neutron rich set of atoms, to be compared to another set of neutron poor atoms of same total inertial mass. I think the equivalence principle as been tested long ago for such cases without showing any discrepancy.

Wolfgang Konle

You said: We do not need an excursion to higher dimensions in order to understand what is going on with fields in nature.

Implicit in this statement is that there are fields in nature (where fields would be a static property of a point in space, given that the source of the field is not moving or being somehow modulated).

If you start with the conclusion, you will never be able to investigate the concept of field.

My point is that my theory explains gravition with waves (propagating metric waves in a 4D spatial manifold, where propagation is constrained by the motion of the elements capable of creating these waves or dephasing them). In other words, the polarizable medium (the Matter in the Universe) defines the path of the wave.

This is new to you and it allowed me to derive this epoch-dependent law of Gravitation. You can see that G is inversely proportional to the 4D radius of the Universe.

You might ask: What does an extra spatial dimension buys me? Well, it eliminates the need for Dark Matter and Dark Energy. The proof is in these two plots (predictions of the SN1a distances from their redshifts using this simple equation d(z)=R_0*z/(1+z)

Most people would think that that is amazing that you can explain the Universe without acceleration, inflation, Dark Matter, Dark Energy.

Hubble observations are explained just with inertial motion in 4D

You might conclude that the Universe does not obey Einstein's equations and you would be correct. LEHU (Lightspeed Expanding Hyperspherical Universe topology) is not a solution to Einstein's equations.

Does HU Laws of Nature satify GR and SR tests? Yes

https://www.quora.com/Does-the-hypergeometrical-universe-satisfy-Einsteins-GR-and-SR-tests/answer/Marco-Pereira-1

So, consider not use the conclusion as the basis for your reasoning.

Dear Daniel Pfenniger

If you read what I wrote, I started not knowing if an individual charge particle sensed gravitation, where Gravitation is a van der Waals electromagnetic force with a 1E-24 relaxation rate.

The article seems to nail the gravitational mass as being the actual inertial mass of the particle.

At that point one might disagree with how the gravitational force was added to the model, which has to be based mostly in the interraction of charges with magnetic fields or review my model.

I decided to accept the analysis (even though I didn't follow it through) and reconsider how my model could make sense under those circumstances.

In my model I introduced the 4D mass, which basically maps to charge. The 4D mass of an electron is equal to the 4D mass of a proton (or antiproton or positron). They are just phases of the Fundamental Dilator Coherence.

So, their fields are created in the same way as any other field.

So, the problem reduced to having the interaction with that field to be proportional to the footprint of the Fundamental Dilator in our 3D hypersurface. That footprint is the 3D volume of the particle, which is proportional to the particle inertial mass.

It turned out that that was always my understanding. The 4D mass is used to derive forces. The dynamics was always meant to be calculated using Newton's laws (with HU forces) in a 4D Spacetime (right-panel in the cross-section below).

This means that I had the information required to understand and accept the article's observations. I've just needed an experimental or observational reassurance.

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

I have no qualified answer, but a question: In this theory, what is the gravitational mass of neutral particles (neutron, neutrino), if a neutron can be considered to first order as a proton bound with an electron?

Below I showed the model of a neutron and the difference between a neutron and a hydrogen atom. The redlines are transmutation chords and they correspond to rotations inside our hypersurface (3D rotations). They change the relationship between tunneling and spinning.

Notice that in my theory matter is a shapeshifting deformation of space that also spins in 4D. That creates a stroboscopic Universe and time quantization. I said time quantization because some stupid theoretician will copycat my ideas and proposed that. It is actually not time quantization, it is ABSOLUTE TIME quantization, at best. I normaly describe it just as intermittent interaction.

Interaction only happens when there is a footprint (0, pi, 2pi, 3pi...).

If it is twice the gravitational mass of a proton, one could measure the gravitational force of a neutron rich set of atoms, to be compared to another set of neutron poor atoms of same total inertial mass.

Just consider a neutron and a hydrogen atom. I wrote my laws of nature in 4D. That means that the 4D mass is twice. That will also mean that G will be half. It is arbitrary how you distribute the effects on the model. That is used to derive the force.

A neutron has the red lines (transmutation chords) and it is a dimer due to the quantum uncertainty in which phase is in phase with our Universe. So, it rotates and obey the Quantum Lagrangian Principle (QLP). QLP describes ALL interactions (all forces are the result of QLP).

Rotation in 3D will change the inertial mass by the amount consistent with the extra two half-electron-antineutrinos (each red line is half of an electron antineutrino). That is due to the trwisting of the fabric of space with absolute velocity. The footprint doesn't need to change as long as any force interacting with the moiety becomes weaker.

HU explains time dilation or relativistic mass in terms of the weakening of forces (slowing down of dynamics). That is implicit in HU Laws of Nature themselves.

The dynamics will be consistent with the 3D footprints (inertial mass).

I think the equivalence principle as been tested long ago for such cases without showing any discrepancy.

As you can see, there can be much more to the equivalence principle than just the standard confirmation biases of scientists.

Dear Daniel Pfenniger

Please read my answer to Wolfgang Konle and you will see that my theory provides a replacement to SR and GR and debunks them.

https://www.quora.com/How-much-support-from-astronomy-does-the-Hypergeometrical-Universe-Theory-HU-have/answer/Marco-Pereira-1

Dear Daniel Pfenniger

We only need to look at the atomic mass of the chemical elements and their isotopes to verify that neutrons and protons have about the same mass. Concerning the electron mass, cyclotrons verify the electron rest mass and their relativistic mass, dependent on their speed.

Dear Marco Pereira "If you start with the conclusion, you will never be able to investigate the concept of field."

I do not exactly know what you want to tell with this statement. But I think the mathematical / physical concept of fields is obvious. A field assigns or maps physical parameter (scalars, vectors, tensors) to points in our spacetime. Apart from gravitational, electrical, and magnetic fields, even distributions of matter and the movement of fluids, plasmas and gases can be described with them.

We know important equations named by Navier/Stokes, Boltzmann, Vlasov, Einstein, to only mention some, which describe field relations.

What you are telling, denies the usefulness of fields to describe physical phenomena.

However, concerning the gravitational field there is a significant tendency in physics to consider gravity as a capability of mass to store potential energy. But in fact, the energy is stored in the gravitational field. An elementary particle only can store kinetic energy. There is no degree of freedom available to store potential energy. Sets of elementary particles can store energy in their confinement. But the confinement energy is nothing else as the energy stored in microscopic fields which surround them. Every confinement minimises the field energy.

Dear Wolfgang Konle

You said: Dear Marco Pereira "If you start with the conclusion, you will never be able to investigate the concept of field."

I do not exactly know what you want to tell with this statement.

Some of the examples of fields you provided me come from phenomenological models (Navier Stokes, Boltzmann, Vlasov). The fields they describe are not properties of space. They are properties of points in space where the phenomenon is taking place.

I am obviosly speaking of Fundamental Physics and Fundamental Fields. The current view has a few: Electric, Magnetic, Gravitational fields, Higgs Field, Inflaton Field.

Those fields assign to positions in SPACE, a vector or scalar value which is time independent if the source is also time independent..

I proposed the existence of a field made from traveling metric waves. In other words, the field at any given point is time-dependent. The wave has wavelength of 0.19 femtometers.

Matter, on the other hand, is composed of shapeshifting, spinning in 4D deformations of space. Interaction occurs every 6.33E-25 seconds, thus interaction is intermittent.

So, I was able to derive the laws of Nature (the ones one normally describe using fields) using this paradigm.

Hence, I am trying to convey a different interpretation of field, which you are not familiar with.

What you are telling, denies the usefulness of fields to describe physical phenomena.

This is obviously wrong. What I wrote doesn't deny the usefulness of fields in phenomenological models. It denies the usefulness of fields in Fundamental Physics.

You said: An elementary particle only can store kinetic energy. There is no degree of freedom available to store potential energy.

This is clearly a postulate without any experimental or observational support. It is clear that the concept of "gravity as a capability of mass to store potential energy." is nonsense. Just because one say that, it doesn't mean it is true.

Marco Pereira

In some respects, we agree. But I do not understand at all:

“Matter, on the other hand, is composed of shapeshifting, spinning in 4D deformations of space. Interaction occurs every 6.33E-25 seconds, thus interaction is intermittent."

What shape is shifted from where to where? What kind of intermittent interaction occurs, and which entities are interacting?

Wolfgang Konle

In my theory, I introduced the concept of the Fundamental Dilator (FD).

The Fundamental dilator is a coherence between stationary states of deformation of SPACE. I emphasize SPACE because my theory debunks General Relativity and Spacetime.

So, your next question should be: Which States of Deformation?

My answer: The proton and Electron States.

So, in my theory, protons convert into electrons and vice versa as they spin in a 4D spatial manifold. Mor e complex particles and isotopes are easily constructed from this monomer (they are polymers of FD).

As you can see the four fundamental particles (electron, proton, antiproton, and positron) are justs different phases of the Fundamental Dilator.

As they shapeshift, they create a dilaton field (traveling metric waves). They interact through these metric waves (all forces of nature with the exception of the Hypergeometrical Acceleration) are driven by these metric waves or dilaton field.

At this point you should be able to see how frugal (a la Occam's Razor) my theory is. All particles and isotopes depend upon just two states of a potential which I don't need to know anything about other than these two states volumes (mass).

My theory add the Lightspeed Expanding Hyperspherical Universe (LEHU) topology and from that I derived these laws of Nature:

I also replace Newton's Laws of Dynamics with the Quantum Lagrangian Principle QLP). QLP states that FDs will move into positions where they are in phase with the local dilaton field.

This is the simplest and most fundamental principle possible. It is supported by the fact that particles don't dissipate just by existing.

So, to derive HU laws of Nature, I used FD, LEHU, and QLP and nothing else.

The final form of the macroscopic law is in flux as I review everything to a new polished publicatoin of the papers.

That said, the current form already passes all GR and SR tests.

You asked: What kind of intermittent interaction occurs, and which entities are interacting?

FDs and polymers of FDs interact through the dilaton field. The interaction is proportional to the 3D volume. In other words, I separated the ability to generate a field (4D mass) from the ability to sense the field (3D mass or FD footprint).

If you call the ability to produce gravitational field, the Gravitational Mass, then WEP is wrong, despite of the experimental result tell you otherwise.

The interaction is intermittent because the cross-section (3D footprint) of particles is much smaller when the FD phase is perpendicular to the 3D hypersurface.

QLP and the intermittent interaction is the reason for Quantum Mechanical Nature of Material Systems.

In other words, QLP is the reason for the uncertainty described in wavefunctions.

HU rejects the Copenhagen Interpretation and recast the wavefunction as the locus of those 3D footprints of the 4D construct (Fundamental Dilator).

Dear Marco Pereira,

As you imply, they cannot accurately measure the mass of a single particle because of the interference of the background field virtual particles, particle charge influences, etc. etc. The background field at the quantum scale is full of local unobservable and unmeasurable variables. But also as you may know, by measuring quantities of these entities they can come very close to knowing their individual masses.

Dear Wolfgang Konle,

The equivalence principle for neutrons vs. protons has been tested much more accurately than their rest mass difference (an account was presented already in the 1970's in the textbook "Gravitation" by Misner, Thorne & Wheeler).

In the meanwhile individual particles or atoms of matter or antimatter (for example at CERN) , in quantum superposition states ot not, have been tested as falling in an external gravity field as predicted by Einstein theory. But measuring the minuscule gravitational force between pair of particles is very hard and not achieved, as far as I know.

So the point of Pereira is to ask essentially whether the equivalence principle has been tested at the atomic scale between pairs of particles. This provides to Pereira the opportunity to expose his theory, from which I just did not get the basic assumptions, and going further seems to imply spending hours of study. In comparison, Einstein papers are limpid, and worth to read already just to learn how to write good scientific papers.

Dear Forrest Noble

It is never a good idea to try to second-guess your young self. In 2005, when I wrote my theory, I proposed also the solution to this problem.

At the time, I didn't have the focus to solve it properly (there was so many bigger fish to fry). Now, I came back and it is clear.

The Gravitational Mass is distinct. The Force is proportional to the observed mass (3D mass).

In other words, the Gravitational Mass of an electron in a Hydrogen Mass is equal to 2 hydrogen masses (2 protons plus 2 electrons).

The force a single electron sense when interacting with a mass M is GMm/r^2

That is the force an electron sense is proportional to its inertial mass.

The Gravitational force a hydrogen atom creates is proportional to four of that atom mass since the electron contributes with two hydrogen gravitational masses and the proton also does the same.

So, things are not what they seem to be.

Never mind the uncertainty in the measurement.

My answer above really addressed a different question: can we accurately measure the mass of a single particle, hence my answer. Your question instead was: Do we really know the Gravitational Mass of single particles? Yes, we have accurate knowledge concerning the mass of single particles via different means. I find no fault with your answer :)

Marco, - I can prove we know the gravitational mass of an electron. The preprint article linked below presents a wave-based model of an electron. This model generates an electron’s energy, inertia, and de Broglie waves. However, the model unexpectantly also generates an electron’s gravitational and electromagnetic forces. This model predicts that these two forces are related through a square incorporating an electron’s wave amplitude. This unification of an electron’s forces is proven correct. The model also predicts that the electron’s gravitational radius rg is derived from a combination of an electron's wavelength and wave amplitude. The electron's Compton angular wavelength is: (ƛc = ħ/mc). This wave has an undetectable amplitude equal to Planck length Lp. The derived equation for the electron's gravitational radius is:

rg= Lp2/ƛc = 6.77 x 10-58 m.

This gravitational radius is half an electron's Schwarzschild radius. The article proves the electron’s gravitational mass corresponds to the mass obtained from its energy (511 KeV).

www.researchgate.net/publication/353049276

Marco Pereira Your statement: "protons convert into electrons and vice versa"

How do you explain that in the Large Hadron Collider protons can be accelerated and the proton beam can be controlled. Controlling this beam needs a perfect knowledge of the relativistic mass of the particles. This is the same with cyclotrons which control electron beams or even with Brown's tubes, which control non-relativistic electron beams.

In none of these devices a conversion between electrons and protons has been observed. Electrons remain electrons. By the way, charge conservation forbids such a strange conversion.

Wolfgang Konle

Obviously, when they change nature (3D footprint or 3D volume), the offending phase is perpendicular to the Universe and had a negligible cross-section or interaction.

The drawing shows that.

Thanks for asking. That is one of the most important aspects of the Fundamental Dilator Paradigm.

Marco Pereira

Dear John A. Macken

I will take a look at your work. The problem I believe is that you didn't understand my answer. In other words, Gravitational Mass, in my theory, is a proxy to the ability to create metric waves. This maps to the 4D volume of the particle.

Once those metrics waves are created the Force sensed by a probe particle is proportional to its 3D volume or 3D mass.

This last sentence makes the common reasoning fail because the Gravitational Mass of the Electron appears both in the creation of Gravitational Force and in the sensing of that force.

I am in my paper writing phase and cannot stop right now to investigate your detailed paper.

As soon as I get the papers done, I will check it out.

Thanks,

Marco

Marco Pereira "...the offending phase is perpendicular to the Universe"

What is an offending phase? What means perpendicular to the Universe?

Dear Wolfgang Konle

You asked: What is an offending phase? What means perpendicular to the Universe?

What means perpendicular to the Universe?

In my theory, our 3D Universe is a lightspeed expanding hyperspherical hypersurface. In other words, our Universe as we see it is a hypersurface embedded within a 4D SPATIAL manifold. I emphasized SPATIAL because you might think 4D spacetime when someone mentions 4D.

The Fundamental Dilator is a 4D shape-shifting deformation of space, so it has 4 lengths to describe its volume. One of the lengths is small. This means that when the Fundamental Dilator phase is perpendicular to the hypersurface (our Universe), its cross-section is small, and no or negligible interaction occurs.

What is an offending phase?

The offending phase is the perpendicular phase. If the phase in-phase with the Universe is the electron phase, the perpendicular phases will be proton and antiproton. Proton and antiproton have the same 3D volume, but they differ by being a dilation and a contraction.

You have to understand volumes as displacement volumes (in an analogy to displacement current in Alternate Currents or electronics).

Since the flushed 3D volume is what defines the inertial mass of a particle, the Fundamental Dilator paradigm allows for particles to always keep the same inertial mass and charge (charge is dilation or contraction).

Marco Pereira

"The Fundamental Dilator is a 4D shape-shifting deformation of space, ..."

Your explanation uses more undefined terms as questioned. Your theory is structured like eastern mythology. It contains many interrelated terms of minimal overlap with standard physical terms.

The introduction of a fourth dimension allows claiming abstruse properties of everything.

Instead of overloading your reader with unknown terms, you should specify a concrete difference of your theory and the standard theory and provide a proof or observation which underlines your theory.

Dear Wolfgang Konle

Don't mistake your lack of understanding (inability to learn) with my inability to explain.

If you don't understand the meaning of a hypersurface or hypersphere, take a course on Mathematics. It is embarrassing you spouting ignorance on a public site.

If you want to understand the meaning of something, just ask.

Here is the hypersphere:

https://en.wikipedia.org/wiki/N-sphere

Here is hypersurface:

https://en.wikipedia.org/wiki/Hypersurface

Stop being ignorant and ask questions or read Wikipedia.

Best of luck in finding knowledge "with NO unknown terms only". Don't you sense that it is wrong for you to try to impose on the world to say only things that you can understand?

You said: you should specify a concrete difference between your theory and the standard theory and provide proof or observation which underlines your theory.

You should ask that as a question instead of writing it as if I was supposed to add that to the many things you couldn't understand (in prior answers).

A concrete difference between my theory and the standard theory (whatever that means - I will consider Cosmology/Physics):

My theory used the Fundamental Dilator Paradigm and the Lightspeed Expanding Hyperspherical Universe topology to derive this law of Gravitation that is epoch-dependent.

I propagated the epoch-dependent G to derive the G-dependence of the Absolute Luminosity of Supernova to be G^{-3.33}. That is, the stronger G is, the weaker the Supernova explosion is.

This refutes the Stellar Candles Hypothesis and corrects the Supernova Cosmology Project SN1a distances.

Once these SN1a distances are corrected, I parameterless predicted them just using this law: d(z)= R_0* z/(1+z)

where R_0 is 14 billion light-years.

This debunks L-CDM. The lightspeed expanding hyperspherical Universe topology is not. a solution to Einstein's equations and thus, the prediction debunks General Relativity.

SO, my theory has concrete differences when compared with the standard theory.

The Fundamental Dilator is distinct from the model that you get in Quantum Field Theory.

By the way, if you felt offended by me calling you ignorant it was because you complained about not knowing the meaning of hypersphere and hypersurface.

That is way too much ignorance to go together with your sense of entitlement (entitled to criticize my work).

So, learn something and ask real questions.

Marco Pereira

Marco Pereira "If you don't understand the meaning of a hypersurface or hypersphere"

I had specified the non-understandable term. It was the Fundamental Dilator and not the hypersphere surface.

Considering the spatial geometry of the universe topologically equivalent to the surface of a 4D-hypersphere is comprehensible.

But the existence of an allegedly tiny fourth dimension is unclear. The tiny dimension obviously shall be a limited small spatial interval with a minimum and a maximum coordinate value. Eventually oriented perpendicular to all three spatial directions.

But this raises questions:

Which circumstance proves the existence of this dimension? What is the width of this limited dimension? How are physical quantities distributed along this dimension?

How is this dimension oriented in respect to oriented physical quantities (vector or tensor fields)?

How does this dimension contribute to a volume?

I am not criticizing your work. I am criticizing that it is presented in a non-understandable way.

(I cannot criticize what I don’t understand)

Wolfgang Konle

You complained about 4D space. Here is a paper that uses 4D space:

https://pubmed.ncbi.nlm.nih.gov/30636156/

IN other words, contrary to what you claimed, there is nothing special in introducing an extra spatial dimension.

The Fundamental Dilator was explained in detail. If you had more questions, you should have asked.

You said: But the existence of an allegedly tiny fourth dimension is unclear

I never said about the "tiny fourth dimension". There isn't any compact dimension in my theory!!!

Please, point us towards the sentence where that was said.

I can understand that you clearly didn't understand what I wrote. You should have said what you said about "allegedly tiny fourth dimension" and you shouldn't have said:

Your theory is structured like eastern mythology. It contains many interrelated terms of minimal overlap with standard physical terms.

The introduction of a fourth dimension allows claiming abstruse properties of everything.

It is not my fault that you didn't understand and decided not to ask a question to clarify it.

Since there is a lot of confusion in your head, let's clear them before I answer the questions you asked. They might be misguided or you might not be ready to understand my answer.

So, let's clear the confusion about small 4D spaces...

I will go on a limb and guess that you are confusing the Fundamental Dilator (which is a model for electron, proton, antiproton, and positron - each phase corresponds to one of them) and curved spaces.

The Fundamental Dilator is a coherence between LOCALIZED stationary states of deformation of space. This is more complex than just calling them shapeshifting deformations of space. I used that not to complicate your mind with unnecessary detail.

Does that clear the confusion? Feel free to ask questions.

Marco

https://youtu.be/jsUFpz1iU9Q

This explanation is model-based and not fundamental. You can see that it is model-based because it starts from the end: it starts from Relativity, Minkowski spacetime, and time dilation. It is not fundamental because it uses the concept of energy. In other words, the better explanation uses just space, time, and velocity.