In a parallel thread under the headline „Does formation of elementary particles confirm Mach's principle?“ (see reference below) we are meanwhile discussing the internal structure of protons and electrons. Special attention is devoted there to the Compton wavelength λC = h/mc which, in fact, represents the „experimental“ radius rCom of the respective particle. By multiplying with the respective rest mass mrest we obtain the simple relation mrestrCom = h/c which obviously applies to both, the proton (subscript p) and the electron (subscript e). So we can write:
mprp = mere = h/c
The above relation became essential to the development of a semi-classical „triple-gyro“ model of the proton (see reference below). Modeling was inspired by the idea that energy should generally occur in two distinct states of existence, a propagating and a localized one, with the latter being established by rotation. This, in fact, reflects the well known wave-particle duality as also suggested by Planck's constant h on the right hand side of the above relation.
Now we might raise the question whether or not it will make sense to define some elementary quanta of mass and length. Wolfgang Finkelnburg in his textbook „Einführung in die Atomphysik“ (see reference below) already in the 1940s proposed the Compton wavelength of the proton, besides the so called „classical“ electron radius (!), as a candidate for the shortest, i.e., elementary length. In view of mere = h/c, shouldn't we assume me to be a candidate for the smallest, i.e., elementary mass, as recently suggested by Sofia Wechsler in the parallel discussion mentioned above?
https://www.researchgate.net/post/Does_formation_of_elementary_particles_confirm_Machs_principle
Research Proposal Triple-gyro model for deduction of proton radius and magnetic moment
https://books.google.de/books/about/Einf%C3%BChrung_in_die_Atomphysik.html?id=nwQsAAAAIAAJ&redir_esc=y
Our current understanding of the Universe and all matter around us is based on the Standard Model, which in spite of its unassuming name is the best theory of elementary particles we have, and which has been tested in truly staggering detail through numerous experiments, all the way up to the LHC. Within this framework, the electron is indeed an elementary particle, and its mass could be considered elementary but it certainly is not a fundamental UNIT (such that other masses are simple multiples of it). Protons are emphatically NOT elementary (they are composed of quarks and gluons) and their masses are the consequence of complicated interaction effects. Neutrinos indeed have mass as well, much less than that of an electron, and the evidence for that is multifaceted and unassailable if you understand the physics underlying the relevant experiments. So this is not some random "theorizing".
One more point: the Compton wavelength of any particle is not considered elementary in any way - it is just a combination of constants that appears in Compton's formula for scattering of light off elementary particles. In particular, it has nothing to do with the "physical size" of an object - more appropriately it refers to an intrinsic limit on the resolution of any MEASUREMENT of the size of an elementary particle. (Again, the proton "size" is not elementary or point like, but just as that of an atom due to complicated structure and interactions. It is about 10^(-15) m or about 5 times larger than its Compton wavelength.)
As a general comment: Don't expect that an "armchair physicist" can (easily) upend decades of research of thousands of highly trained (and very smart) people and come up with a new theory that is correct - it's a nice fantasy but nearly never is true.
@Johan,
what are you writing here? Where from do you take the formula λC = h/mc? I am sorry but the de Broglie wavelength of a quantum object is λ=1/k = h/(mv). The quantity v is the velocity of the object, and it is defined ONLY when the position is UNdefined.
You can't build models on re-inventing the physics! I advise you to check your formulas!
(Sorry for my taugh answer!)
"Where from do you take the formula λC = h/mc?"
Dear Sofia,
the above formula is nothing else but the Compton wavelength as determined by Compton scattering (see reference below), which is taken for the experimental radius of the respective particle.
https://en.wikipedia.org/wiki/Compton_wavelength
(I like tough answers)
@Johan,
"I like tough answers"
You are a lovely person.
Well, I will look in the reference. Now, I would advise you something. Won't you mention in your question, also my question about the mass-gap? I ask this not for myself, but for you. You see, it is desirable to connect the users with as many aspects of the problem as you can.
Fot instance, if the mass-gap truely exists (it is not known today, there is a high prize for whom would be able to solve this theoretical issue) then, there exists a bottom limit to the complexity of the particles. In other words, there exist particles which are truely elementary and no matter how much energy one would invest, one won't split them.
Well, if the mass-gap exists, the electron may be such a particle.
With kind regards!
"Indeed, the visible and detectable smallest stable mass is the electron, but calculus from gravity shows that smaller particles are possible to exist."
Dear Thierry,
thanks for providing further interesting aspects. In view of the above formalism, mrestrCom = h/c, particles with rest mass much smaller than me should have much larger size. I don't know whether or not this would make sense with "elementary" particles.
Johan, the mass of a neutrino is much smaller than that of an electron, but not zero.
Dear Thierry, I first got into contact with h by photon energy hν.
Dear Johan, read
Shulman, M. (2017) On the Structure of Electrons and Other Charged Leptons. Journal of High Energy Physics, Gravitation and Cosmology, 3, 503-521. doi: 10.4236/jhepgc.2017.33039.
@George: The rest-mass of the "neutrino" is a question of belive and nothing else. If those particles exist actual with its great spectrum of energy then they would have also a great spectrum of speed.
Have the so-called theoretical "strings" at least even a smaller rest mass than the "neutrinos"? Where is the pure theorize all going to end?
To define the rest mass of electron/positron as an elementary quantity is totally meaningful because this dual particles are the fundamental building blocks of all material matter. There do not exist particles below!
Dear Mikhail, great stuff - thanks a lot!
P.S. - I've never seen before such a clear, comprehensive and convincing analysis of subatomic particle physics, congratulations!
HGH: The rest-mass of the "neutrino" is a question of belive and nothing else. If those particles exist actual with its great spectrum of energy then they would have also a great spectrum of speed
The mass is less than 1eV, see the various limits set by a range of experiments listed here:
https://en.wikipedia.org/wiki/Neutrino#Mass
Energies for most neutrinos are in the keV to GeV range so all modern sources produce neutrinos moving at virtually the speed of light. Relic neutrinos from the Big Bang would have significantly lower speeds but their energy is so low, there is no practical way to detect them at present. Here is the spectrum:
https://inspirehep.net/record/944151/plots
In the following I'll refer to the above cited paper „On the Structure of Electrons and Other Charged Leptons“ by Mikhail Shulman which, for ease of viewing, I allow me to append in PDF form.
Mikhail after starting from the Compton wavelength λce= h/mec (1) of the electron comes to a series of quite remarkable conclusions. I just take out the following one as this appears relevant in view of our current search for an elementary mass:
Ee = Eel + Em + Ek = mec2/2 + 2(mec2/4) = mec2 (43)
where Ee denotes total energy of the electron, while Eel, Em and Ek stand for "Coulomb mass" related, magnetic and kinetic, respectively, subcomponents thereof.
This result, in fact, indicates some specific substructure of the electron, as earlier suggested on the basis of our triple-gyro model. It further suggests, at a first glance, that me shouldn't be regarded as an elementary mass. On the other hand, as the electron subcomponents apparently won't survive as single particles in a similar manner as quarks of a proton won't do, we may state me to represent the minimum stable aggregation of matter.
Our current understanding of the Universe and all matter around us is based on the Standard Model, which in spite of its unassuming name is the best theory of elementary particles we have, and which has been tested in truly staggering detail through numerous experiments, all the way up to the LHC. Within this framework, the electron is indeed an elementary particle, and its mass could be considered elementary but it certainly is not a fundamental UNIT (such that other masses are simple multiples of it). Protons are emphatically NOT elementary (they are composed of quarks and gluons) and their masses are the consequence of complicated interaction effects. Neutrinos indeed have mass as well, much less than that of an electron, and the evidence for that is multifaceted and unassailable if you understand the physics underlying the relevant experiments. So this is not some random "theorizing".
One more point: the Compton wavelength of any particle is not considered elementary in any way - it is just a combination of constants that appears in Compton's formula for scattering of light off elementary particles. In particular, it has nothing to do with the "physical size" of an object - more appropriately it refers to an intrinsic limit on the resolution of any MEASUREMENT of the size of an elementary particle. (Again, the proton "size" is not elementary or point like, but just as that of an atom due to complicated structure and interactions. It is about 10^(-15) m or about 5 times larger than its Compton wavelength.)
As a general comment: Don't expect that an "armchair physicist" can (easily) upend decades of research of thousands of highly trained (and very smart) people and come up with a new theory that is correct - it's a nice fantasy but nearly never is true.
"Don't expect that an "armchair physicist" can (easily) upend decades of research"
Dear Sebastian,
I really don't expect this way but, on the other hand, I'm quite aware as well that "thousands of highly trained (and very smart) people" will be able to erect solid walls against breaking ideas. Maybe you will enjoy reading and comment on above cited paper by Mikhail Shulman. It doesn't only appear advantageous that "armchair physicists" have widely been replaced with high-budget collaborations.
The paper you refer to is a nice toy model that combines some aspects of classical and quantum physics, but it has little relevance to reality. Trained physicists are not erecting walls against truly groundbreaking ideas (the history of physics is full of them, including the most famous example, Einstein). However, there are some stringent tests that any such ideas must survive to select the ones that are truly new insights - most importantly, experimental confirmation. An electron that is made up of a rotating "protoelectron" as posited in this paper would immediately have a multitude of observable consequences - mostly ruled out by existing data. That's why I'm advocating that one should first learn all there is to know about a particular field (eg., elementary particle physics) before one picks some random fact and tries to "explain" it with an idea based on limited knowledge - it's a nice pastime, but does not contribute to the advancement of scientific knowledge...
"Again, the proton "size" is not elementary or point like, but just as that of an atom due to complicated structure and interactions. It is about 10^(-15) m or about 5 times larger than its Compton wavelength."
Dear Sebastian,
I won't oppose against your general statements, but please let me know what you mean by the above special one. When it is about 5 times the Compton wavelength then the proton radius should be about 6x10^(-15) m. From the triple-gyro model cited earlier we get, by explicitly considering internal structure, about 1x10^(-15) m that you refer to, and which is not "point like".
Dear Sofia,
while Sebastian Kuhn apparently is still unclear about proton radius and associated Compton wavelength but, nevertheless, clearly declines suitability of the latter as a basis for discussion of subatomic phenomena, I would like to refer to your earlier remark on the De-Broglie wavelength λB = h/mv. When replacing particle speed v with speed of light c, λB immediately reduces to Compton wavelength λC = h/mc.** This apparently emphasizes the significance of λC for discussion of the wave-particle duality and obviously justifies Mikhail Shulman's approach on the basis of λC, in particular, as he was able to approve interdependence of well established elementary particles and relation between natural constants with amazing precision.
** While the De-Broglie wavelength (λB)e = h/(mv)e in case of the electron with limited "orbital" speed ve quantitatively decribes the Bohr radii in its bound state within the central field of a positively charged atomic nucleus, the Compton wavelength (λC)e = h/mec apparently describes the minimum possible radius of a free, i.e., unbound electron at maximum "rotational" speed c.
Some additional remarks:
I still didn't answer something you asked earlier in the current thread:
„Won't you mention in your question, also my question about the mass-gap?“ (see reference below)
The mass-gap issue according to my understanding is rather a mathematical problem, so I would leave it with mathematicians and theoretical physicists that I don't belong to.
On occasion of a parallel discussion, referring to the triple-gyro model you asked:
"And why the experts considered your idea irrelevant? What wasn't correct?"
I remember the response was quite similar to what Sebastian Kuhn just stated in the present discussion in view of Mikhail Shulman's paper:
„The paper you refer to is a nice toy model that combines some aspects of classical and quantum physics, but it has little relevance to reality.“
http://theconversation.com/millennium-prize-the-yang-mills-existence-and-mass-gap-problem-3848
Dear Johan,
I don't see an answer to the journal's claim of "little relevance to reality". I also had a doubt on your model, because most of the proton internal energy is due to the gluons, which have no rest mass. Whithout the gluons, which provide the potential energy that keeps the quarks - ellectrically charged - together, the proton would explode. So, the proton internal structure does not seem to be three orbiting masses.
I understand that your idea is dear to you - it happens to us all. A lovely fellow wrote to me asking to read an article, but when I began to ask questions confronting his hypotheses with facts experimentally proved, he withdrew.
I don't intend to try to convince you to quote my question, but I just want to tell you that it's not a technical (mathematical) issue. It's a deep physical issue. If there indeed exists a mass gap, then the matter in the universe is discrete. Radiation is not continuous matter - photons - matter possessing rest mass is not continuous - there is a minimal particle which cannot be further split. Next, in between these particle exists vacuum = zero amount of on-shelf particles.
With kind regards!
SDW: I understand that your idea is dear to you - it happens to us all
I remember a post in a forum a few years ago in this light from a professional scientist. He was attending an international conference on string theory and the Integral probe had measured the signal from a distant supernova which showed that any quantisation of space was at least 13 orders of magnitude below the Planck length. That confirmed an earlier similar result from Fermi.
The poster said the loud noise at the meeting was the sound of hundreds of presentation papers being shredded. There were plenty of papers on hypotheses that put the quantisation so low it was unaffected but those at the Planck length went straight in the bin. Just two results wiped out man years of work for hundreds of people.
http://www.esa.int/Our_Activities/Space_Science/Integral_challenges_physics_beyond_Einstein
Dear Sofia,
thanks for your comments! Here are a few answers along with your related questions:
> I don't see an answer to the journal's claim of "little relevance to reality"
The "little relevance" wasn't a journal's answer but a statement by Sebastian Kuhn out of his latest post here.
> So, the proton internal structure does not seem to be three orbiting masses.
Of course, we shouldn't imagine point charges to orbit in small circles since, as we know from Bohr orbits, these would get unstable as well, even though not by "explosion", but rather by "implosion" due to radiation loss. The triple-gyro model, in fact, doesn't tell of orbiting masses but rather of cycling fields that in form of standing waves or orbitals by their localized field energy are suggested to constitute an equivalent amount of gravitating matter.** Energetic substructures may be attributed to special particles like, in particular, gluons or just be categorized as presented by Mikhail Shulman for the electron, see his above cited paper and my earlier comment thereon.
"Mass gap": > It's a deep physical issue.
Such is also the existence of gravitational waves, black holes and mergers thereof, big bang, dark matter and energy, etc., up to now nothing else but theoretical models.
** https://www.researchgate.net/post/Does_formation_of_elementary_particles_confirm_Machs_principle
"most of the proton internal energy is due to the gluons, which have no rest mass."
Dear Sofia,
when gluons don't have rest mass, and rest mass of quarks is of the order 1% of the proton rest mass, doesn't this mean that the latter is to be looked at as mainly the mass equivalent of field energy? Similar should apply to the electron and its energetic subcomponents.
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