I apologize for erroneously having inserted angular momentum Iω instead of torque I*dω/dt in the original text version.

"the dimensional equivalence of torque I*dω/dt and energy"

In fact, we don't need this aspect for linking local elementary mass to remote masses of the universe as in view of Mach's principle this already follows from linking inertia I to elementary spin via Iω = ℏ/2.

Johan,

maybe I don't understand what you drive at, but the relativity tells us that a body in muvement with velocity v has a "movement mass", m = m0/sqrt(1 - v2/c2). The mass depends on the movement. But why mass should be rotational? It doesn't have to. Linear translation is also a motion with respect to distant stars. In general, we have in physics the parallelism

Mass m - inertial momentum I,

Linear momentum p - angular momentum p x r,

General kinetic energy mv2/2 - rotation energy Iω2/2.

Then, what's the point in your question? Can you explain a bit deaper? And what do you infer about formation of elementary particles? I don't see the relationship between the title of your question, and the text. Can you explain?

Best regards!

“…according to Mach, inertia I is a phenomenon resulting from reference to remote masses of the universe, then this should also apply to related energy. Consequently, mass as a rotational, i.e. localized form of energy might be similarly regarded as resulting from interaction with the universe…. ”

So called “Mach principle”, which postulates that some properties of material bodies, including the inertia, are formed by all masses in Universe [more correct – in Matter] is nothing more then a fantastic suggestion, which has no any scientific grounds. Though in physics there is no some rational explanations what is the inertia/mass also; the explanation as that the inertia is a result of interactions of bodies with some “Higgs field” seems as not too much lesser questionable then the Mach principle, besides form that by any means doesn’t follow the existence of the gravitational mass and  the equivalence of the masses. The existence of the masses in physics is simply experimental fact.

However the existence of the inertia and corresponding  measure of the inertia, “mass”, indeed with great probability is caused “by a rotation”, what seems rather rationally follows from the “The Information as Absolute” conception, where it is rigorously proven that there is nothing besides some informational patterns/objects, including all/every material objects in Matter are some informational patterns also.

At that every material object, including every particle, uninterruptedly changes its internal states and spatial positions  in 4D sub-spacetime of Matter’s absolute Euclidian [5]4D spacetime because of the  energy conservation law; when the phenomenon/ absolutely fundamental Quantity “Energy” is the quantity that is necessary to overcome the self-inconsistence of the absolutely fundamental notion/phenomenon “Change” [besides, because of this self-inconsistence at some level the changes become be uncertain].

Since the uninterruptedly changing particles have, nonetheless,  stable parameters, from that follows that informational patterns “particles” are some closed-loop algorithms, which run cyclically with very high operation rate; these close-loop chains are in  the spacetime some 4D gyroscopes, which “resist” to changing of their 4D vector rotation rates [i.e. to change fixed informational states is necessary to spend additional energy] in many aspects analogously to usual 3D gyroscopes, what realizes as the inertia/mass of the particles and, since every body consists of the particles, of bodies also . Besides from  this suggestion follows the existence and the equivalence of the inertial and gravitational masses.

More see https://www.researchgate.net/publication/273777630_The_Informational_Conception_and_Basic_Physics

Cheers

Article The Informational Conception and Basic Physics

"But why mass should be rotational?"

Dear Sofia,

thanks for your kind response and quite understandable questions. Maybe I should have explained what idea motivated me to develop the above cited "triple-gyro" model of the proton. The idea was simply that energy may exist in two states, a propagating and a localized one. Next consideration was that something moving straight, like a car, may get localized by turning in a circle. Next question was about the circle diameter when taking into account energies typical of elementary particles. Surprisingly, the circle diameter turned out as nearly equal to the proton diameter, provided the proton is made of three subcomponents as described in the above paper. Astonishingly, not only the proton diameter but also its magnetic moment turns out right.

Mach's principle comes in via inertial momentum I, which he suggests to be a phenomenon due to interaction with remote masses of the universe.

"So called “Mach principle”, which postulates that some properties of material bodies, including the inertia, are formed by all masses in Universe [more correct – in Matter] is nothing more then a fantastic suggestion, which has no any scientific grounds."

Dear Sergey,

A gravitational drag experiment as proposed by James C. Keith, see annexed paper, might be looked at as a means for proving Mach's suggestion.

@Johan,

it's very interesting what you say. Indeed, if you get the magnetic moment correctly, this is an achievement. I will read your proposal. But, for economizing time, let me ask you, what you did with the internal structure of the proton, all those quarks and gluons? In my modest opinion, people would ask you this question.

Look what I found in Wikipedia: https://en.wikipedia.org/wiki/Proton

"The rest masses of quarks contribute only about 1% of a proton's mass . . . The remainder of a proton's mass is due to quantum chromodynamics binding energy, which includes the kinetic energy of the quarks and the energy of the gluon fields that bind the quarks together. Because protons are not fundamental particles, they possess a physical size, though not a definite one; the root mean square charge radius of a proton is about 0.84–0.87 fm . . . "

Good luck!

Dear Sofia,

thanks for providing further details on protons. Of course, the model is nothing but a crude estimate, on basis of simple analogy, yet with surprising fit in magnitudes. Due to the model, mass is interpreted just as equivalent of rotational energy, m = (Iω2/2)/c2, of something spinning at about speed of light, so it won't make sense to consider "rest masses" in a way as specified on Wikipedia.

The simple model in no way is intended to compete with advanced theories on subnuclear structures even though it already suggests the proton to be made up of three subcomponents, which in turn leads to a reasonable value of the magnetic moment. On the other hand, via inertial moment I, it apparently provides sort of link to Mach's principle as suggested by the leading question.

    Dear Johan,

    It seems that this explanation only works on the protons, what about the rest of particles?

Johan,

You considered inside the proton three objects. As you see in Wikipedia, indeed, three there are. Also, it's their kinetic energy, and potential energy, and also the gluon field, that provides the mass of the photon. The rest mass is only 1%.

Why shouldn't you in your analyses refer to this? The kinetic energy of the quarks may by rotational. I understood that you declared a project about your research. Well you did.

Next, wouldn't you try your model on mesons too? Thay also consist in quarks?

Good luck!

"Why shouldn't you in your analyses refer to this?"

Dear Sofia,

I agree and will consider doing this in an update to my current project. You should know that I've put down the original proposal as an internal note back in about 1990 when there still was no reference to Wikipedia. I didn't publish it before now as it was far outside my professional activities and was rated insignificant by expert particle physicists at that time. I honestly doubt the model to be suitable for further extension into particle physics as you suggest. I presently was motivated just by the idea that the model might provide a link between particle physics and cosmology, in particular in view of above cited gravitational drag experiment proposed by James C. Keith, see attachments.

Thanks and regards!

"It seems that this explanation only works on the protons, what about the rest of particles?"

Dear Daniel,

maybe you are right. As mentioned before, I didn't consider other particles and should prefer to leave this to expert particle physicists which I certainly don't belong to.

Dear @Johan,

And why the experts considered your idea irrelevant? What wasn't correct?

I am no expert in particle physics, but, if your model predicts with such precision the proton properties, maybe there is some truth in this model.

A problem I see with your model is that most of the energy of a proton, therefore most of its mass (m = E/c2) is due to gluons. They have no rest mass they just carry the strong interaction field. So, the proton mass is due not only to the kinetic energy of the quarks - which may be rotational indeed - but also to the gluons.

As to other particles, as Daniel correctly says, one cannot build the roof before building the basement. So, let's take it easy, first of all the proton should be clarified.

    Dear Johan,

   It is true that the angular momentum of the electromagnetic field does not depend of the distance and therefore it would be a good candidate to overcome the difficulties that Sofia has shown with the Lorentz transformations. In fact this could help to apply the Match's principle as a topological contribution from my humble point of view. But what is very difficult to believe is that the protons are the only antennas to catch such topological fields. For instance, notice that inmediatally the neutrons would be (udd) while the protons (uud) both with three quarks, which makes fundamentally change the electric charge 2/3 +2/3 - 1/3 =1 for proton and -1/3-1/3 +2/3 =0 for the neutron. Thus in spite of these "electromagnetic" differences their mass is quite similar, why if the source of the mass is the topological field associated to the "electromagnetic" angular momentum?

   How the leptons are without an experimental radius in spite of having mass and therefore provided with classical angular momentum zero? Obviously they have spin but this is not directly related with an angular momentum related with the electromagnetic field rotation. Thus, as Sofia is telling you, even for a non speciallist in fundamental particles as me, it is quite difficult to see where the mass can have a cosmological origin.

"And why the experts considered your idea irrelevant? What wasn't correct?"

Dear Sofia,

as far as I remember, they didn't really rate it wrong but rather unsuited for extension of particle models at that time. In fact, I didn't dare to oppose in view of the more developed gluon model as compared to my simpleminded "car-running-in-a-circle" model. I'm quite aware that on subnuclear scales certain properties well known from macroscopic physics, such as in particular mass, are attributed to specific particles, and I have no reason to doubt this as a useful means for describing processes on that scale.

As mentioned before the "car" model by introducing inertial moment I as a macroscopic entity in view of Mach's principle seems to additionally allow linking subnuclear with cosmological physics.

@Daniel,

where did I say that mass cannot have cosmological origin? I said other things, please read again. I am not a specialist in the Big-Bang theory, but one can admit that the mass of elementary particles is not something at hazard, but resulted from some constraints.

Now, I see from your profile page that QFT is not one of your skills. Neither is mine. But there are many people here who yes are specialized in it. I hope that such people would get into this thread and this project, and help.

Again, I don't believe that the good fit that Johan found, can be just a coincidence. So, I think it's a good idea to get deaper in this issue.

With kind regards!

Oh, @Johan,

It seems to me that Mach would remain somewhere in the background. Probably, in the foreground, the gluons have to be brought, i.e. how to incorporate their energy in your model. Agter all, the gluons are also particles and also have a movement. What I understood though, is that their energy is regarded as POTENTIAL ENERGY, i.e. the energy of the field in which move the quarks.

With kind regards!

"the gluons have to be brought, i.e. how to incorporate their energy in your model ... their energy is regarded as POTENTIAL ENERGY"

Sofia,

I don't feel a real need to incorporate advanced achievements of modern particle physics into my rather crude mechanistic model, in particular, as state-of-the-art particle models obviously have proven consistent to a high degree. Do you have reason to doubt upon that, or do you really expect my model to provide some extended view in the field of subnuclear physics?

    Dear Sofia,

    I wrote with respect to you:

   " it would be a good candidate to overcome the difficulties that Sofia has shown with the Lorentz transformations"

     and you wrote:

    but the relativity tells us that a body in muvement with velocity v has a "movement mass", m = m0/sqrt(1 - v2/c2). The mass depends on the movement. But why mass should be rotational? 

    This is the difficulty that you have put and with a topological idea could be overcome. I apologize if you have understood that I was speaking on cosmology.

"it is quite difficult to see where the mass can have a cosmological origin"

Dear Daniel,

Unfortunately, I have been missing your comment until now.

What I learn from Mach's principle is that inertia might have a cosmological origin, and we know that inertia is an intrinsic property of matter. (edit: Should we even state that inertia substantiates the existence of matter?) Anyway, it is the inertia underlying the inertial moment I that enters my proton model when deliberately relating classic mechanical to elementary entities via Iω = ℏ/2. So we may state that mass itself according to the model seems to depend on the existence of cosmological sources. I think Mach himself a century ago has argued similarly.

    Dear Johan,

    I cannot see it and the expression Iω = ℏ/2 is just the lowest state of a spinor identifying a classical angular momentum with the spin of one fermion 1/2 as could be one electron, your proton or a neutron. Frankly that equality is valid for many different particles having a I quite different.

    From my humble point of view, if the origen of the mass were cosmologican, then almost all the particles would have the same mass and that is not the case. But that is just common sense and very far of a serious analysis of the issue.

"Iω = ℏ/2 ... is valid for many different particles having a I quite different."

Dear Daniel,

shouldn't then their masses be different as well? I ask this in view of your later statement: "if the origen of the mass were cosmologican, then almost all the particles would have the same mass". When Iω is constant this doesn't necessarily mean that I and ω be constant.

@Daniel,

You are not the only user here. You comment things as if Johan would discuss only with you, and it is impossible to see what you refer to. For instance, in your last comment you say:

==> "I cannot see it . . ."

Tell us what you cannot see. How do you expect people to understand?

Now, I just make a guess that you don't see what Johan said "inertia might have a cosmological origin, and we know that inertia is an intrinsic property of matter." Of course, I am not sure whether my guess is good.

Anyway, I agree with Johan, and his idea is beautiful and worth of deep examination. The values of the masses of the particles can't be arbitrary. I think that they may even vary with the evolution of the universe, and if so it is, the implications are far going. Probably they are solutions of some equations that we should still dicover.

By the way Daniel, your statement

==> "the expression Iω = ℏ/2 is just the lowest state of a spinor identifying a classical angular momentum with the spin of one fermion 1/2"

is not a counter-argument to Johan's idea. The fact that a proton is a quantum system and his nature is fermionic as resulting from its internal structure (the quarks) then the angular momentum is quantifies due to the properties at a rotation by 2π. What Johan explains has nothing to do with this quantification.

With kindest regards!

   Dear Johan,

   When I have spoken about the formula Iω = ℏ/2, I have said clearly that my opinion is without a full analysis of this issue. Let me put the immediate difficulties associated to such formula:

   1. As I said, this is the minimal angular momentum of a fermion of spin 1/2. This means that bosons and even fermions of other spins are out of receiving a mass by this mechanism.

   2. The inertia moment is inverse of the angular frequency for all fermions spin 1/2. I didn't examined it but I suppose that this is not true.

   3. To have a cosmological origin means the universe is able to create energy ( or mass) locally from very far sources. This can be against of the relativity if you do not introduce a mechanism which allowed it.

   Dear Sofia,

   You comment things as if Johan would discuss only with you, and it is impossible to see what you refer to

    I try to follow the ideas of each one, but obviously my answer can be shared with everybody.

  Johan wrote in his post:

What I learn from Mach's principle is that inertia might have a cosmological origin, and we know that inertia is an intrinsic property of matter.

  I answered:

I cannot see it and the expression Iω = ℏ/2 is just the lowest state of a spinor identifying a classical angular momentum with the spin of one fermion 1/2 as could be one electron, your proton or a neutron

  And now Johan, has argued another post on this issue and I have just tried to answered him, but obviously I hope that you also can follow it.

  Your guess is good (in general) and your believe in his model is only your choice.

  Finally you wrote:

What Johan explains has nothing to do with this quantification.

  If this equation has not relation with the quantum angular momentum then I am wrong and all my answers were missunderstood and clearly I didn't understood anything of his model. Sorry.

Dear Daniel,

@ 1. and 2.: The proton model discussed here is to be looked at as completely independent of alternative models in particle physics that you are referring to.

@ 3.: My understanding in view of Ernst Mach and James C. Keith is that the remote universe provides local conditions enabling phenomena like inertia and mass to come into being. This issue is currently being considered in a parallel discussion, see link below.

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

@Daniel,

You say,

==> "If this equation has not relation with the quantum angular momentum then I am wrong and all my answers were missunderstood and clearly I didn't understood anything of his model. Sorry."

Oh, Daniel! Do you punish me in a polite way? Your answers are wise, there is no doubt on that.

But let me explain myself. Assume you have an equation depending on two independent parameters, f(x, y, z, . . . ; a, b) = 0. The parameter a decides whether the function f depends on the neighbor masses and distances to them. The parameter b allows quantization. What's the problem?

I repeat, doesn't your intuition tell you that masses and other properties of elementary particles cannot be randomal, but defined by some general constraints? My intuition yes tells me this.

By the way, I don't see, if we are going to speak of particles with other spin, why the formula Iω = ℏ/2 couldn't be generalized to Iω = nℏ/2 where n in an integer suitable for the respective particle. You see, Johan's research is in a very early stage, he tested his assumptions for the moment on the proton.

With kind regards, and, please don't doubt my appreciation for you!

"You see, Johan's research is in a very early stage, he tested his assumptions for the moment on the proton."

Dear Sofia,

in fact, when applying similar modelling procedure to the electron on the basis of respective Compton wavelength λe = 2πℏ/mec, radius r = ℏ/mec, in a first step, also turns out low by a factor 2π.* This can be resolved again, as in case of the proton, by assuming a corresponding volume expansion due to internal structure. Although rather speculative, this approach at least appears interesting in view of other, much more refined studies, see e.g. reference below.

*Note added September 29, 2017:

In fact, the procedure should read as follows: Combining Iω = ℏ/2, I = mr2/2 and ω = mc2/ℏ, according to my proposal, we get to r = ℏ/mc, which is low also in case of the electron by a factor 2π as compared to the experimental radius re , respectively Compton wavelength λe = 2πℏ/mec.

As procedures are similar, misfit by factor 2π, as obviously due to the Iω = ℏ/2 approach, should apply to all spin 1/2 particles.

http://www.ccaesar.com/eng_structure_of_the_electron.html

   Dear Johan,

   The electron has not structure as a fundamental particle and it works as if it where a pointlike in QED within the scattering, which is the form to see the size of the particles. Although this works quite well experimentally, giving that we cannot do scattering experiments at infinite energies, we have a limit where we don't know its size. Therefore, the resolution with which we can observe the electron is limited by the largest energy that we can produce in collider experiments. The cross-section that we observe from a pointlike particle is therefore determined by the resolution with which we observe it. With current experiments one sees that the scattering cross-section of the electron follows a scale invariant curve. Hence, no scale where the electron is resolved has yet been seen. An important observation though is that the energies with which the scattering has been done, far exceeds the mass of the electron. So if there does exist an energy scale where the electron would be resolved, such a scale would be very high above the scale set by the mass of the electron.

   Therefore I do not know in what kind of review is published the paper but what I can say is that it is outside of the accepted mean stream in nowadays physics.

"... it is outside of the accepted mean stream in nowadays physics."

Dear Daniel,

... all the more should we read the paper and try to follow the valuable ideas conveyed.

@Johan,

you say

==> "also turns out low by a factor 2π."

I don't know of what you speak, you said this in some context I guess. Where is that context?

Now, I am reading someone's proposal about electron structure, s.t. I will be able to read the article you recommend, only after that. And probably i"ll compare the two proposals.

@Johan and @Daniel,

The electron is the most stable particle known at present. Quarks for instance are unstable in the sense that they immediate combine with other particles around.

I have the feeling that there is no bottom limit to the structure of particles. The question is only how much money we can invest for building accelerators of higher and higher energies. No doubt that for breaking an electron we need by far higher energies than for breaking a proton.

You know, when going deeper and deeper into the structure of the particles, who can tell us whether by breaking a particle we don't find a structure that WE CREATED, by the very investment of high energy? A structure that didn't exist before our intervention.

Kind regards! 

"I don't know of what you speak, you said this in some context I guess. Where is that context?"

Dear Sofia,

you are completely right that my above explanation was quite confusing, I'm sorry about that. In fact, the procedure should read as follows: Combining Iω = ℏ/2, I = mr2/2 and ω = mc2/ℏ, according to my proposal, we get to r = ℏ/mc, which is low also in case of the electron by a factor 2π as compared to the experimental radius re , respectively Compton wavelength λe = 2πℏ/mec.

As procedures are similar, misfit by factor 2π, as obviously due to the Iω = ℏ/2 approach, should apply to all spin 1/2 particles.

"who can tell us whether by breaking a particle we don't find a structure that WE CREATED, by the very investment of high energy?"

Dear Sofia,

I fully agree with what you say. When trying to explain quantum and particle physics to my children and friends I sometimes do this by comparing with a bell: The stronger you hit, the more harmonics of the base resonance will appear.

Dear @Johan and @Daniel,

Doesn't seem strange to you that the electron, which is so stable, contains a unit electrical charge, not 1/3, and is a fermion, not a boson? To my understanding it cannot be an elementary particle, it should also have 3 quarks in it. But what binds the quarks together in the electron shouldn't be gluons, but something else with terribly stronger energy.

I am also going to place this question, let's see what say people with better knowledge than mine, about the standard model.

"To my understanding is cannot be an elementary particle, but should also have 3 quarks in it."

Dear Sofia,

so you would say that only quarks should be looked at as "elementary" particles?

This morning I contacted Christoph Caesar, the author of above cited paper on electron substructure, in order to draw his attention to our present discussion. He just replied (translated from German): "I'll take a look at your approach - at first glance a model of triple magnetic moments and rotors would be compatible with my lepton and quark models."

I am working that the brick box of CERN (called standard model) can be seen in a picture; I hope you can find it better than a mathe formula

Dear Johan,

What you know about the "mass-gap"? Please take a look at these

1) https://en.wikipedia.org/wiki/Mass_gap

2) https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_existence_and_mass_gap

There are hints in all sort of theories in which I don't understand much, that there should exist a minimal rest-mass. If that is true, then maybe the electron is the candidate for that minimal rest-mass. You see, fractionary charges cannot live independently, they react immediately with the environment and complete the total charge to an integer number of elementary charges.

Though, the existence of fractionary charges seems to me as hinting that the electron should have a structure and an extraordinary high binding energy.

Anyway, if you contacted an expert, can you ask him to indicate a material about the mass gap? I understand that it is not bsolutely sure that this gap exists.

> What you know about the "mass-gap"? the existence of fractionary charges seems to me as hinting that the electron should have a structure

Local physical laws are probably determined by the large-scale structure of the universe, but there is no proof of it.

Mach's Principle was not stated by Mach. Other people deduced it from his writing. Mach was one of the first to challenge absolute space and absolute time, opening the way for others to follow. Now some researchers seem to believe enough has been learned and the book should be closed to new entries.

One is reminded of the Renaissance in which chemistry was being developed. The old guard had only four elements - earth, air, fire, and water. Erasmus noted in his "Praise of Folly" that many researchers wasted their lives and resources looking for a fifth element. Then later some people discovered a different chemistry.

Now physics has four forces, and many people are wasting their lives and resources looking for a fifth force. Most recent claim is a new force connecting the Higgs to other particles. Maybe someone will write a new page in physics, most likely at high speed in deep space.

> Local physical laws are probably determined by the large-scale structure of the universe, but there is no proof of it.

@Paul Riggs,

I almost each comment in this thread and in most of the comments on physics in RG, you can see "this my article", or "read these articles".

It is impossible! Therefore, usually, the articles AREN'T read, unless the user who indicated the article explained in a few lines what is the main thing that the article proves.

So, maybe you'd tell us in general what is that novel approach.

Also, one more thing. As I found Johan's idea appealing, I looked in the literature for articles connecting the masses of the elementary particles (those in the Standard Model table) and universal constants. I found no such things. I would like to see predictions for the masses of those basic particles. I found nothing. Well, in fact, a user indicated me an article, however his theory totally disregarded the facts in the Standard Model, and when I asked him questions and showed him contradictions, he withdrew from the dialogue. So, if you can tell us numerical predictions for these masses, and if the calculi respect the Standard Model, it would be interesting.

With best regards!

> I looked in the literature for articles connecting the masses of the elementary particles (those in the Standard Model table) and universal constants.

Dear Johan,

Where from do you take (mr)e = ℏ/c? What is light-velocity doing in this formula? By the way, the formula is not correct, I checked it. In invite you to check it too - the proton radius is 1.2fm. Also, what is the index "e"? We use this index for electron.

For the electron the formula (mr)e = ℏ/c? is totally incorrect, you can check it as the electron radius is cca. 1.8fm.

==> "The latter representation also implies that matter relates to some circular, i.e., accelerated motion, respectively localization or "condensation" by rotation. Have you been looking for something like that?"

I happen to have encountered some material of this kind, but it wasn't convincing.

But, wait a bit. When we say that a particle has spin, does that mean that it rotates? According to which axis? A free electron, or proton, has no particular axis of rotation, it has spherical symmetry.

The Earth rotates around itself having a well-defined axis of rotation. This rotation is necessary for opposing the gravitational self-attraction that would collapse it. But those particles why do need to rotate? Protons are held from splitting due to the electrostatic repulsion, by the gluons. Why do they need rotation? The proton spin means rotation?

Best regards!

> If the distance between atoms is reduced by an external force, there is an imbalance between the electromagnetic forces, which tries to re-obtain a balance by the displacement of all the consequent atoms of the whole object. This is requiring energy.

Dear Thierry,

according to my understanding, s = v t means force-free linear movement, while s = a t2/2 implies steady acceleration with "internal" imbalancing forces being compensated by counteracting forces, in particular those resulting from mutually deviated electric charges, thus establishing a net overall internal equilibrium.

> Where from do you take (mr)e = ℏ/c?

Dear Sofia,

thank you very much for carefully reviewing my latest posts. I apologize for not having been as carefully when preparing my posts, thus running into confusion and ending up at some misleading conclusions. After having withdrawn two posts in reply to your above question, I'll now try it once more.

The above relation is derived from r = ℏ/mc which, as explained earlier, came out from a „first-step approximation“ of the proton radius within the triple-gyro model. For both, proton and electron, r is small by a factor 2π as compared to the „experimental“ radius.

When looking for numerical results we should better discuss the experimental radii. For the electron it is re = 2πℏ/mec = h/mec, or, after multiplying with me, mere = h/c. This, except for the factor 2π, looks quite similar to the questionable relation you cited above.

We should be aware of the fact that the revised relation also applies for the proton, mprp = h/c, and is completely independent of the models described as it is simply the Compton wavelength multiplied by the rest mass of the respective particle:

mere = mprp = h/c = 2.21E-42 kgm

Your further questions:

> When we say that a particle has spin, does that mean that it rotates?

In some or the other way I think it should do so.

> For the electron the formula (mr)e = ℏ/c? is totally incorrect, you can check it as the electron radius is cca. 1.8fm.

You obviously refer to the so called "classical" electron radius as theoretically deduced from elementary charge, while I refer to the experimental Compton wavelength (λC)e = 2.4 pm which is larger by three orders of magnitude.

I would like to find out some reasonable meaning of the "classical" electron radius. But, anyway, this won't work with the above formula. On the other hand, it matches quite well with the proton radius rp, as already pointed out by Wolfgang Finkelnburg in his textbook "Einführung in die Atomphysik", 5. - 6. edition, p. 247, Springer-Verlag 1958. Finkelnburg by still using cgs units suggested the classical electron radius "re = e2/2mec2 = 1,41 . 10-13 cm" and also the Compton wavelength of the proton "l0 = h/mpc = 1,32 . 10-13 cm" as possible candidates for what was generally expected as a „shortest length“ and further natural constant back in early 1940s. This idea in fact inspired me later on to develop the triple-gyro model of the proton.

> When we say that a particle has spin, does that mean that it rotates?

Dear Sofia,

such idea I think, in particular, will help avoiding singularities.

"instead of forces, I spoke of the Coriolis effect"

Dear Thierry,

I'm quite aware of Coriolis forces since having tried, as a young boy, to walk on a merry-go-round platform, but also in view of weather spirals and Coriolis drag involved with Keith's spinning rotor experiment.

Nevertheless, I'm still not clear about your idea of an "equilibrium obtained by the Coriolis effect", nor for what reason gravitational reaction forces should lag behind electric ones. Maybe I'm blocked by the speculative idea that matter establishes by rotational localization (condensation) of electromagnetic fields that otherwise may propagate as well in linear motion.

„The Coriolis force also amazingly and unexpectingly coincides with Newton's gravity law for the Sun's parameters M, R and rotation (spin), as explained in the annexed paper.“

Dear Thierry,

thank you very much for referring to your amazing paper from 2010 that I haven't been aware of before. I think the paper should be regarded highly significant as it unveals unexpected correlations and thus provides deeper understanding of some really basic physical phenomena. What, in particular, appears convincing is that your conclusions match with observations of our sun. While after so many years of intensive work you are well accommodated to your concepts it will take me some time to get into details. But let me just comment on one of your conclusions:

„I would say that inertia is not caused by the action of the whole universe.“

Gravitomagnetism and electromagnetism may be interpreted as due to limited propagation speed which is typical to media of whatever kind. Is there any reason to exclude 1/R fiels originating from remote masses of the universe (see reference below) to be interpreted as a local medium responsible for phenomena like limited speed, formation of waves and related ones?

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