Anything-just like the mass of an electric charge can take any value. The Dirac quantization condition relates the electric and the magnetic charge (in non-relativistic quantum mechanics); it doesn't have anything to say about the mass of the sources of the electric and magnetic fields.

The Reissner--Nordstrom black hole spacetime, that's an exact solution to Einstein's equations, and describes an object that has a mass and can carry electric and magnetic charges, does imply relations between the mass and the charges.

Dear Stam,

Thank you very much of your answer, although I don't understand what tries to say. It is well known that the mass of the magnetic monopole is very high, much higher of the known particles (at least by me) and it is about 1016 GeV. My question is about of what mass is used nowadays in the experiments in the particle's accelerator, for instance the one seen in

https://arxiv.org/pdf/1905.10130.pdf

or in

https://arxiv.org/pdf/1705.07052.pdf

which are different. And there are much more different values, what are the more realistic or possible ?

Dear Daniel

I am not underestimate Dirac, but his era atom was not clear as today. Even today we have a lot theories regarding of atom's property. To me an atom is smart, and any smart entity must born, like us. Article Dark­Matter in the Quantum Mechanic Universe

You can try to model electron, muon and tau particles as a self-interacting magnetic monopole coupling as a pair with itself. It's due to the skyrmion-like world line length what determines the mass of elementary lepton particle (three ways to rotate 720 degrees; round one axis [electron], round two axis [muon] and round three axis [tau]). I think the magnetic monopoles are timeless objects, topological defects in space (not in time at all). At least the Koide formula is well motivated by this hypothesis.

Dear Esa,

Thank you very much for your answer but I know the family of leptons are fermions with half-integer spin and therefore they have 720 degrees to do a full round instead of 360. I also know that the skyrmions are topological solutions which take into account the spin configuration but I don't know what is the relation of skyrmion with their mass and less with the mass of a magnitic monopole. Please could you be more explicit? Thanks.

Dear Daniel,

My point was only that there are several points of view to consider the concept of magnetic monopole as something else than massive object - it's like regulation, not like structure.

Dear Esa,

Sorry, I didn't understood you. In any case, the monopole is associated to a to topological solution ( Chern 1) which can be seen within different physical contexts as condensed matter or as in particles. In this thread I tried to know the mass of the magnetic monopole as particle: mainly Dirac, Schwinger or t'Hooft-Polyakov.

Ok, first tell us what's the mass of the magnetic dipole. ;)

Dear Esa,

The magnetic monopole is a particle which would have a well defined mass at difference of what happens with magnetic dipole.

Dear Daniel,

Maybe we have our prejudices, hardly anything else that interferes with our understanding.

about mass: Once upon a time when in cosmos was no mass yet, Instead of energy is m square c should have been set Energy is equal, In other words energy is… ergo E=

Dear Daniel,

Please, could you evaluate the Dirac's situation when he proposed the possibility or even a demand for magnetic monopole - is it only an intuitive guessing that proposing as elementary particle lefting the mass as a free parameter or were there some solid arguments? Why not to model as intercation signalling like photon or gluon and the monopole would be just a spatial knot?

Dear Esa,

I don't know the details of how Dirac create this particle, but what is easy to see is that he tried to explain why the electric charge in all the particles at those times were plus or minus 1.6x10-19 Coulombs. Only with that it would be enough for being interested in such particles and nowadays we know that there are monopoles in gauge theories etc. Thus the strange of this particle is that we haven't it among us. Perhaps the problem is that its huge mass doesn't allow it to be created or being interacting very soon with its antiparticle. But it is very strange that it doesn't exist!

Dear Daniel,

I think charge is timelike by nature and magnetism spacelike. Then all the dynamics seem natural and the monopoly cannot have mass just like dipole (or any multipole structural phenomenom) cannot have mass by itself. Is this any contradictory in your mind?

Dear Esa,

Being timelike or spacelike magnitude, for example the density of charge and the density of current, is not related with the mass. The mass of the electric field is the same that the one of magnetic field, i.e, it is zero. The mass of the magnetic monopole is out of this space-time representation. Nowadays we know that the mass of the monopole for the unified theories is higher than 1016 GeV which is too big if we compare it with the one of the electron or even the proton.

Is the dipole property of particle or field? Is it a carrier or a direction? Why the monopole concept should be different, anything else but a geometrical idea? Look at the symmetry logic in quantum world, global complexification and antipodes in spacetime. Maybe next the same logic can be solved out in nuclear tripoles (yep, there could a tripole be considered in the opposite phased alternately observables of antipodal continuum, I see) or in gravitational oscillative quadrupoles... No mass definable with directional phenomena themselves - no common method for quantity with mass/energy.

Dear Esa,

Perhaps I don't understand you and there is a property behind the classical magnetic dipoles. Please, go ahead and explain how you get a magnetic monopole using a magnetic dipole.

Although it is far of this problem, at the beginning of Quantum Mechanics people thought that it was possible to explain magnetism just with magnetic dipoles. But the Bohr-van Leeuven theorem proves clearly that magnetism needs Quantum Mechanics (in fact the concept of exchange) for explaining how is possible to get a ferromagnetic phase or so on. A parallel thing happens with the magnetic monopole, you need quantum mechanics and also topology, at difference of what happens with the magnetic monopoles.

The magnetic monopole that was the subject of Dirac's work doesn't have anything to do with the ``magnetic monopoles'' in extensions of the Standard Model; that's why the question about bounds on the mass that are relevant for the latter aren't relevant for Dirac magnetic monopoles.

In the same way that it's possible to describe electric multipoles, it's possible to describe magnetic multipoles. And, similarly, their masses aren't constrained by the Dirac quantization condition, that only relates electric and magnetic charges.

Dear Stam,

Thank you very much for your opinion, but you are absolutely wrong. The gauge theories of the Standard Model have SU(N) symmetries and always contain the Abelian subgroup which first homotopy group can be non zero, i.e. they have a magnetic monopole exactly the same as the Dirac's one. This was stablished by Wu-Yang many years before the t'Hooft-Polyakov model. The strong language that you use only can impress people ignorant of this subject. My advice, for instance, is that you work a little bit on the Higgs field non homogeneity and you can see how is the same concept of magnetic monopole for Standard Model than the one of Dirac's from the topological point of view.

Not all U(1) subgroups of extensions of the gauge group of the Standard Model can be identified with electromagnetism (and a very particular subgroup of the group of the Standard Model can). The 't Hooft-Polyakov monopole (that's a classical solution of the field equations of an SO(3) gauge theory coupled to a scalar field) doesn't have anything to do with the Standard Model, nor does it have anything to do with Dirac's monopole, which doesn't have anything to with the a Higgs field, any more than an electric charge does.

Once more: the mass of an electric charge is as much an input to the source terms of Maxell's equations as is the mass of the magnetic monpole.

When studying quantum effects of electric charges and magnetic charges, in interaction with classical electromagnetic fields, the Dirac condition relates the electric and magnetic charges-but the masses in the corresponding Schrödinger equations for the wave functions of the particles, are free parameters.

The work, that's relevant for searching for Dirac monopoles, may be found here: http://cds.cern.ch/record/444509/files/0005041.pdf

when because of using symmetries phisicists cannot explain thing anymore, the begin to consider broken symmetries- in my opinion perfect symmetry does not exist in nature.

Dear Stam,

I'm sorry to say that you don't know what is a magnetic monopole at all and let me to say that Maxwell equations cannot tell anything about this issue as the magnetic (or electric ) dipole. Respect to the different aspects of the magnetic monopole, although is not the best reference let me to recommend you the basic

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

where you have the topological interpretion.

More explicitally(just two simple references )the magnetic monopole in the Standard Model as I have told you

http://cds.cern.ch/record/451154/files/0008098.pdf

https://web.mit.edu/8.286/www/lecn18/ln09-euf18.pdf

One day very soon, we will discover that an atom has no magnetism, and particles are panpsychist. Then we treat an atom as a intelligent element of universe.

Article Dark­Matter in the Quantum Mechanic Universe

There's too much nonsense in this thread already. Topological monopoles, like the t'Hooft Polyakov solution, certainly may exist in our universe. The electroweak physics spontaneously breaks down to a gauge group with the Electromagnetic U(1) factor, and depending on how this phase transition occured, magnetic monopoles may have well been produced.

Alternatively, monopoles may have been produced if a GUT theory broke down to the standard model. These monopoles would be gauged under the Hypercharge U(1), and there's a possibility they gained some small electromagnetic interaction when electroweak symmetry broke.

A typical characteristic of topological solitons is that their mass depends inversely on the coupling strength of the theory. If they were produced at the GUT scale then, and the GUT physics was weakly coupled at this energy, it would be reasonable to expect the monopoles would be orders of magnitude more massive than the GUT scale particles.

So the answer is very massive, as long as they are treated in the context of renormalized perturbation theory.

Dear Daniel,

Thank you very much for your answer but unfortunately you didn't understood the question. The question is not how the magnetic monopole appears in different physical contexts but what is the mass of a magnetic monopole there or what is the mass that reseachers employ. As you know this is one of the limits for producing them in one accelerator of particles. This is the question!

Trying to help in understanding my question, let me to give my theoretical limits for the mass of the magnetic monopole:

Minimum mass of monopole= 4692 mass of the electron

Maximum mass of the monopole= 3. 1044 mass of the electron

Article Magnetic monopole as the shadow side of the electric charge

Monopole is the same election, which is not in the electric state but in the magnetic state. Each section \lambda (the particle's de Broglie wavelength) the charged particle changes its electric state to the magnetic state. Also its mass state changes to a tension state. So, a neutrino / antineutrino is the magnetic monopole with the rest mass equal to zero, but due to the motion it arrives an inertial mass, which is really very small.

All this is easy to understand when develop a mechanics of a canonical particle not in the emptiness, but in a substrate that interacts with the moving particle. Besides, a particle itself is a deformed cell of the cellular space, which was named the tessellattice by late Prof. Michel Bounias in 2001-2002.

In fact there might be some arguments for the "mass energy" of the monopole being alfa^3 × the mass of electron - but as like you can say it is alfa^3 × the mass of muon or tau (alfa = fine structure constant).

Dear Volodymyr,

The concept of magnetic monopole is not for given us a symmetry of the Maxwell equations. In fact even if the monopoles existed asymmetric Maxwell equations would continue to be same, i.e. the

div B=0

and the Ampere-Maxwell too, i.e. without the g that you introduced. These are very well experimental known equations and a change as you introduce is only mathematical.

The main interest of the monopole is for explaining the quantization of the electric charge, i.e. the fact that, for instance, an atom could be perfectly neutral for the electric field, being the nucleus (protons) positive charge and electrons negative. How is this possible for all the known charged particles less for the quarks? The explanation is the magnetic monopole which always has to have a topological character

pi(S1) equal an integer in Z or pi (U(1))

This is very well known and it doesn't need any new theory at Planck scale.

Dear Esa,

You are right that the lepton family has very different masses: the muon is 207 times the one of the electron and 3.552 for the tau particle. It is a little arbitrary to choose the mass of the electron and no the mass of the two others. The problem is that we haven´t got a theory which explains the different masses and the choice of the electron is due to be the used in electrodynamics ( in the same form as you do it in QED). Notice that this is one reason more to do the question of this thread interesting and perhaps people looking for the monopole could tell us something interesting about this issue, which at least for me it is quite interesting.

Dear Daniel Baldomir,

In my theory I show how the electric charge is periodically converted to the magnetic monopole. To show this, one has to elaborate a theory at a submicroscopic level, i.e. Planck's scale. In my approach, a particle appear from a cell of space and the entire space is a lattice of such cells (each cell is a primary topological ball). From the consideration of the motion of a charged particle, it is automatically followed that the charge state of the particle is changed periodically by the monopole state. This process is described by the Maxwell equations. At some fast non-adiabatic processes, the electron /positron can escape from the system studied in the monopole state. Then it is travelled in space staying in this monopole state. This is exactly is an antineutrino/neutrino. The monopole that you have talked about is something artificial and whether it can exist - I do not know.

Dear Volodymyr,

without repeating arguments about the usual magnetic monopole and its associated mass, which is the target of this thread, let me to tell you only that the vacuum cannot be never a "lattice" at Planck scale. The quantum fluctuations forbid it clearly. For a very basic seening of this issue, take a look at

wikipedia.org/wiki/Quantum_fluctuation

Dear Daniel Baldomir,

Thank you for the link on the fluctuations. However, they started from Heisenberg's uncertainty principle. But it never has been observed! Moreover, during the recent years there appeared a number of publications in which researchers showed the this principle does not work at the atom scale.

What is bad in particle physics and nuclear physics? Researchers still consider physical system studied in an emptiness. However, the real physical space is a mathematical lattice of primary topological balls, which is a SUBSTRATE!! Hence, all particles are strongly interact with the ambient space with cells of the mathematical lattice of topologic balls (the tessellattice). Each particle appears as a deformation of a cell and when is moving, it must interact with ongoing cells. This is a submicroscopic approach to physics, which allows one to derive the formalist of quantum mechanics at the atom scale starting from Planck's scale.

Before my works, quantum mechanics was derived starting from a macroscopic scale, say 1 m, which presented a strange behaviour of objects at a length about 10-10 m. But when we derive quantum mechanics starting from 10-35 m, from the lattice of space, then no strangeness appear because we can see that a moving particle is accompanied with a cloud of spatial excitation (I named these excitations inertons). So, a moving particle covered with its inerton cloud is mapped to the conventional formalism of quantum mechanics as the particle's wave \psi-function. Then the overlapping of two \psi-functions means the overlapping of two inerton clouds of two physical objects. Hence, inertons plays the role of quasi-particles of space, which carry out a short range action, they are carriers of the quantum mechanical interaction of particles. Besides, inertons are carriers of the nuclear forces and also carriers of the gravitational interactions. The existence of inertons were demonstrated in various experiments conducted by me and my colleagues. Moreover, we designed a device, a receiver of inerton signals, which measures then intensity and spectrum of inertons from a few Hertz to 100 kHz.

Dear Volodymyr,

There is a clear contradiction in your picture of Quantum Mechanics obtained from a Planck lattice, you start assuming that Heisenberg principle is not followed. If this were true, then you cannot get Quantum Mechanics. What is the experimental support to your idea of Planck scale order? How can you reach so small lengths where the quarks are even giant objects?

Dear Daniel,

In my works I cite papers in which researchers show experimentally that Heisenberg's uncertainty principle does not work at an atom scale. You can find a number of works on this subject in the internet. In QM the researchers explode a couple of important anti commutations, like this one: xp - px = h. This commutation is enough to develop the formalism of QM. This formalism with the communication expression above reflects a pulsation principle of motion of a particle, as follows from my submicroscopic consideration, namely: in the first (odd) section of \lambda the moving particle emits excitations (inertons) and finally stops; in the second (even) section, which is also equal to \lambda, the particle adsorbs those excitations and restores the initial values of its velocity and mass. Here, \lambda is the particle's de Broglie wavelength.

Regarding experimental support to my ideas. First, a theory of real physical space was developed by late mathematician Prof. Michel Bounias (publications in 2002-2004), which is based on set theory, topology an fractal geometry. Our works show that fundamental physics is derived from the pure mathematical knowledge base. Hence, a primordial substrate exists! This means that all physical processes take place not in an abstract emptiness, but in the substrate and any particle must interact with this substrate. This made it possible to develop a submicroscopic mechanics of particles and the quantum mechanical wave \psi-function became the particle surrounded with its inerton cloud. The size of this cloud was calculated. The most important object of the theory is "inertons". They in fact were measured! This means that the theory has been working successfully. Then I decided to investigate particle physics. It was revealed, what is a lepton and what is a quark. A dynamics of quarks was described as a hydrodynamics of bubbles in the primary substrate. The confinement of quarks was explained, the asymptotic freedom of quarks was explained as well. It was shown that a quark possesses only an integer charge +e or -e. Besides, the notion of the electric charge was defined and the Maxwell equation derived. The nuclear forces were complete clarified. Then gravitational physics was studied in detail - I managed to derive Newton's gravitational potential starting from submicroscopic principles, then accounted for 4 experiments predicted / described by general relativity. Dark matter and dark energy were defined. Currently my colleagues and I are starting a project "Inerton radio communication" and in the framework of the project we will design a receiver and transmitter of inerton signals (we will try also to transfer a sound/voice and in the receiver will play the received signal). A machine that produce biodiesel was designed and now 3 our machines produce biodiesel in Singapore. In the machines we use intensification of chemical physical process using an inerton field (it is generated in the interior of the chemical reactor). So, I think the results are plentiful and I can conclude that the theory developed successfully describes the whole fundamental aspects of physics. Here is my book:

http://www.appleacademicpress.com/structure-of-space-and-the-submicroscopic-deterministic-concept-of-physics-/9781771885300

Maybe my co-authored work below would be interested to you:

Article On the Nuclear Coupling of Proton and Electron

Besides, I think the information below would be useful too:

http://inerton.kiev.ua/Studies.of.inerton.field.effects.in.1944-1945.pdf

Best wishes,

V.K.

Dear Volodymyr,

I think that you wanted to write a the non commutation between the position x and linear momentum p as operators`

[x,p]=ih/2pi

That is equivalent to the Heisenberg's uncertainty principle for these two conjugate variables. In this case you are within Quantum Mechanics, and I don't understand the sentence:

"In QM the researchers explode a couple of important anti commutations, like this one: xp - px = h. "

which is wrong and it is not one anticommutator. In fact wrongly written it corresponds to the uncertainty principle of QM. Again, this simple result of QM forbits you to have a lattice at Planck scale if you don't emply new physical interactions that I cannot imagine. For me this is impossible.

Dear Daniel,

Please forget about QM for a while. This will allow you overcome a psychological barrier that you feel reading my comments. So, once again% the formalism of QM was derived started from a macroscopic physics, say 1 m. When approaching an atom scale, researchers observer strange behaviour of matter. To explain this, they invented a peculiar QM. But many notions in this discipline are not defined at all. For me, it was the most important the particle's de Broglie wavelength - what does it mean? No explanation in the framework of QM...

I started from the structure of a real physical space. It was reasonable to suggest that a cell of space has the Planck's size. Then it was necessary to introduce in the lattice of space the notions of a particle (both a lepton and quark), mass, charge, electric and magnetic field. After that a mechanics was considered - since I was a specialist in a small polaron theory, I was able to construct the motion of a particulate cell through the lattice of cells. In such a way inertons have appeared. The de Broglie wavelength aromatically emerged as a spatial period of th moving particle: due to a friction, the particle must stop passing the section \lambda. After that excitations emitted by the particle into the tessellattice, after reflection from distant cells come back and pass on to the particle its initial velocity and mass. Therefore, in the second section of \lambda the particle acquire its parameters again. Note de Broglie mentioned that it his opinion the real way should guide the particle. The is exactly happened in the second (odd) section \lambda of the particle path. Thus, the means that the particle is surrounded with the cloud of its excitations. Then in the Jacobi-Hamilton presentation I derived the de Broglie relationships for the particle:

E = h \nu;

\lambda = h / (m v).

These two relationships allow the derivation of the Schoedinger wave equation (it was demonstrated by Louis de Broglie). So, I really derived QM. But in my approach instead of the along particle I had two subsystems: the particle and its inerton cloud. In such a way, unifying the particle and its inerton cloud in one object, one easily come to a conclusion that the wave \psi-function of conventional QM is the particle with its inerton cloud. The overlapping of two inerton clouds mean an exchange between the two particles by their inertons, which is obviously mean the quantum mechanical interaction between these particles.

How can one turn himself to study all this in detail? I think this is first of all a pure psychological problem. Researchers are not ready to think in the way different from that one presented in manuals, which are the basis of the university education... For me it was also VERY DIFFICULT, because I started practically from ABSOLUTE ZERO. However, today I feel quite comfortable as I understand the languages of QM, quantum field theory, general relativity, particle physics (the so called standard model), and I also know how fundamental physics can be formalised at a much deeper level. The key issue is the existence of inertons. My hands were trembling when my colleagues and carried out first experiments trying record effects caused by inertons. But all of the experiments were successful.

Free inertons (those that release from the particle's inerton cloud) are an actual driving force of antigravity. Hence, many very new areas of studies are opening.

Yours very truly,

Volodymyr

Hello all,

Although I have not addressed that question of magnetic monopole mass, modification of Maxwell's equations that I have addressed can be found at:

MODIFIED MAXWELL EQUATIONS WITH MONOPOLE POINT MAGNETIC SYSTEMSArticleFull-text available

• October 2018
• 📷Rajan Iyer
• ENGINEERINGINC MEDITERRANEAN HELLENIC GLOBAL TEI PLATFORM

Dear Rajan,

the density JM of the magnetic current would be accompanied by a curl of the E field: curl E = -d B / d t - JM, instead of curl B (or curl H) as on page 2 of your paper.

This follows directly from the fact that the energy contained in the magnetic field of a moving monopole has to move with the monopole, and from the properties of the Poynting vector (analogous to a moving electric monopole, electric and magnetic fields exchanged, of course).

Hello Joerg:

Thank you with editing notes about modified Maxwell enhanced adaptable equations.

We will take into account in further analysis.

Sincerely,

Rajan Iyer

ENGINEERINGINC MEDITERRANEAN HELLENIC GLOBAL TEI PLATFORM

Dear Emmanouil Markoulakis,

Thank you for the interesting analysis. It consists very well the picture I described but those ridiculous tachyons... :(

I think the monopole "lives" only in spacelike falling frame with only discret inertia correlations with mirror world and these antipodes together define the interaction world with time and mass and non-orientable cell automaton continuum of quanta in the time-indepedendent submicroscopic level. We in the macroscopic level see mainly the classical on-falling orientable differentiable spacetime.

Under my preparation the model seems to be structured by two klein bottle manifolds mirrored to each other. The challenge is how those two non-orientable surfaces could be piled together as orientable 4-dimensional conformal group with causal time development...

Anyhow, this might be seen as a kind of AdS-CFT correspondence.

Hello Joerg:

Having more analysis about comment that you had about modified M eqns. "....

the density JM of the magnetic current would be accompanied by a curl of the E field: curl E = -d B / d t - JM, instead of curl B (or curl H) as on page 2 of your paper.......This follows directly from the fact that the energy contained in the magnetic field of a moving monopole has to move with the monopole, and from the properties of the Poynting vector (analogous to a moving electric monopole, electric and magnetic fields exchanged, of course)....", there are two main aspects that we will consider:

(1) if you are considering only monopoles, just like what Emmanouil pointed out, they exist everywhere jointly. However, if are just focusing on the monoples, which are necessary per most advanced theories now including GUTs, they don't have time aspect or electric aspects to consider curl E with dB/dt; they may have time-like conditions. So we will have to consider as separately, like point or zero point & then use equations that I have with only magnetic tensor acting. You have pointed out correctly about moving monopole. This we have modeled as Vaccum Energy quagmire ref: Structure of the Vacuum Energy Magnetic QuagmirePreprintFile available

• June 2019
• 📷Rajan Iyer
• 📷Emmanouil Markoulakis
• 📷André Michaud
• [...]
• 📷Emmanuel Antonidakis

we will have to here consider what you are talking about i.e. curl E. This is more complex subject that we are working on. For example we are having paper about Quantum Field Magnetism (QFM) that Emmanouil has proved out of his experimental results & myself I am modeling in the team about theoretical aspects. Additionally there are quantum field aspects that I am having, not yet revealed to anyone, that will eventually connect monopole, electron, & photons, etc. on the lines that Emmanouil has stated above, that electron is a dipole!!

(2) Electric field arises out of electron, that only when jointly dipole configurations. We cannot actually talk having electric field to monopole purely. Hence they almost seem having parallel processes with the monopoles, creating dipole - electron, positron, photon, phonon so forth to which we may then apply standard model particle aspects.

Therefore, it's all better to leave alone equations that I developed as Modified Maxwell equations as a pure magnetic monopole situations without any spatiality.

These we'll eventually address as ongoing modeling of magnetic everything quantum field aspects.

More to with discussions coming........

Sincerely,

Rajan Iyer

ENGINEERINGINC MEDITERRANEAN HELLENIC GLOBAL TEI PLATFORM

Daniel,

I do understand your question perfectly well. If you think you can understand monopole mass without understanding the model in which monopoles as manifest, it is you who has misunderstood physics.