Thanks for that, 

I am actually in favour of the pure spherical model.

By the way I have it on good authority that the g factor is due to the structure of the electron and its interaction with space-time

Spin does seem to be intrinsic, especially if you have a particle that originates from a moving photon.

    Dear Andrew,

    The g-factor or gyromagnetic factor is the relation between the dipole magnetic moment (for an electric charged particle) and the angular momentum. If you have one free this relation is between the magnetic moment of the electron and the spin. This had to be two using quantum mechanics but if you go to QED, due to the anomalous magnetic moment of the electron, it a little bit more.

    You can consider the electron in one orbital L of one atom (s, p, d,...) and in such a case the value of g depends strongly of this orbital and also its electronic occupation. The atomic g orbital for one electron must be the sum of both J=L+S, which in the case of spheric symmetry you can use the Hund's rules to do it as simple as possible this complex calculation.

    Thus this gyromagnetic factor g is without any kind of conceptual difficulty and only relates the magnetism (in Bohr magneton for the spin of one free spin electron is the unit of measurement) with the mechanical angular momenta (spin, orbit)

Dear Andrew and all,  

The Bohr magneton is the unit of a magnetic moment measured with a precision generally of the order of 1%. Bohr has given the first step of the interpretation of the magnetism. Uhlenbeck and Goudsmit introduce the notion of own rotation to explain the half integer unit of angular momentum h. The Runge’s law (1902) has  already put in view a factor to express the anomalous Zeeeman effect in Lorentz unit. The factor is in fact the same that given by Dirac in the second part of its: “Quantum Theory of the electron that is g = k/(k+1/2), in the study of the Zeeman effect. The use of this expression give theoretical result in good agreement with experiment see “Total angular momentum and atomic magnetic moments” on my site with G. Lochak. The g factor appears as the ratio between the magnetic moment and the angular momentum.

According to Dirac the doublet structure of the shell np, nd and nf is the result of the two value of k, k=l and k=-l-1, giving the same product for k(k+1). It is not clear if this corresponds to the own rotation of the electron call spin.

The theoretical and experimental results seems indicate that each electron behave as belonging to a hydrogen like atom, allowing a simple understanding of the periodic table.  

And that dear Xavier is the key to understanding the free electron - it is also a cloud

    I suppose that the last sentence of Xavier's post :

   "The theoretical and experimental results seems indicate that each electron behave as belonging to a hydrogen like atom, allowing a simple understanding of the periodic table."

    is related with which in the Dirac vacuum where the electron has always associated one positron and both form a kind hydrogen atom. The g-factor of this pair is zero.

    The g-factor is useful when you need to add different spins using Clebsch-Gordn coefficients (even using the Wigner-Ekart theorem) which very difficult and it is better to reduce all the sum to only a factor.

Hi Andrew,

  Regarding your statement  "a magnet is just something that hangs on the fridge door - or is it."  

 There are a lot of magnetic materials that are not magnetic in the sense of being practical for hanging things on the fridge. I wrote something years ago that illustrates the simple classical picture for various forms of magnetism. The article was in the "Connecticut Journal of Science Education: with the title "Physics of Magnetism", but ResearchGate insists on calling the journal the Connecticut Journal of Physics of Magnetism.  In any case, antiferromagnetism, ferromagnetism, ferrimagnetism, and rare earth magnetism are described with the distinction made between contributions from the spin versus the orbital motion of the electron. In rare earth magnetism you have both spin and orbital contributions contributing a significant effect.

 You can access the article here by going through the following steps: 1. Look at my article publication list under "contributions". 2. On the third page of the list of publications click the article square on the left. This will show only the magazine cover. 3. On "linked data" click "+ 2 more resources" 4. You should then see page 1, page 2, page 3 and "last page"

Then read these in that order; Each is an archive image, which is probably why ResearchGate makes one jump through all these hoops.

Hope this helps,

Doug Pease

Dear Daniel Baldomir your post suggest me to recall a part of the introduction of my work with Georges Lochak:

“In our opinion it would be wrong to restrict the role of the Dirac equation to the relativistic field of high energies and to reduce its usefulness in the atomic field to small corrections in optical spectra. Dirac's theory is able indeed to provide such corrections, but moreover, it is also the only one which describes correctly the angular momentum of an atom and which gives an exact nomenclature of the magnetic states. More precisely it is the only one which establishes the essential physical point that neither orbital momentum nor spin are constants of motion and that only the total angular momentum is a constant. This is not simply a relativistic correction which could be accounted for by the introduction of a spin-orbit coupling in the Schrödinger equation: it is another statement of the law of conservation of the angular momentum which leads, for the shel1s np, nd and nf to a structure in subshells which is different from those obtained by associating spin-up and spin-down states with each state described by the Schrodinger equation. This structure is also different from the one suggested by the Pauli equation, in which the orbital momentum and spin are separately constants of motion, supporting the spin-up and -down structure.

Strictly speaking, the properties of the e1ectron angular momentum invoked above are proved only for an isolated atom and even in the hydrogen case and it seems obvious at a first glance that such an individual property of the electron cannot be conserved in a many electron atom and a forti-ori in a crystal field. But precisely, our basic assumption will be that something remains of this indi-vidual property of the electron even in the many electron cases, despite the strength of the perturba-tion. The fact that this is admissible will be suggested by the periodic classification as will be shown and, for a crystal, it will be supported by some curious and even striking results in the domain of magnetism, which will be given below”.

You will see that the classical approach are not sufficient.

     Dear Xavier,

     Nowadays there are several examples of Dirac equation in condensed matter as can be the graphene, where the electron-hole plays the role of the electron-positron for QED. The same happens in the Topological Insulators where the semiconductor superfice is with a linear diffusion equation which leads to a Dirac's cone (or several Dirac's cones).

Hi Andrew,

If you consider the energy levels involved, you will observe that the Bohr magneton is not a property of the electron proper, but of its adiabatically induced carrying energy (27.2 eV) or in joules: 4.35974377E-18 J, and is supposed to apply to the electron when captive of the hydrogen ground rest orbital.

I analyzed this case a few years back and found that the Bohr magneton at the standard value pertains in fact by very definition to an electron moving in straight line with this amount of energy.

The g factor is a measure of how the magnetic field of this carrying energy is increased due to the gyroradius corresponding to the mean rest orbital in a hydrogen atom, where the electron is induced with the same amount of carrying energy, which is what experiments measure, and would classically correspond to the increased magnetic field of this carrying energy if the electron was moving on a closed orbit of this radius.

If interested, you can find my calculations here:

http://ijerd.com/paper/vol7-issue3/E0703021025.pdf

      Dear André,    

     Thus the magnetization of the electron is about

               M=4,77 x 105T

     Fantastic! You have in one only electron the best magnet that never was created or seen in a laboratory which cannot reach less than 3 orders of magnitude. Sorry but something is very wrong or you must go to patent it inmediatally.

Hi Daniel,

At least, I am in line with Schwinger.

Actually, equation 10 gives alpha as calculated from first principles

If you check equation 12, you will see that the result is identical to Schwinger's conclusion that g must theoretically be equal to alpha/2pi

I think that agreeing with Schwinger is not that bad. The only difference is that I arrived at this result from the electromagnetism perspective.

Hi Daniel,

I don't know where you take this value of M=4.77 E5 T for what you call "the magnetization of the electron"

Do you mean the electron magnetic field? If so, this is impossible, because this is only twice the magnetic field of its carrying energy at the Bohr radius. The energy making up the rest mass of the electron is 0.522 MeV so its intrinsic magnetic field is way higher. from my calculations: B = 8.289E13 T.

You can calculate it with equation (3) if you replace Lambda_Bohr with the electron Compton wavelength.

    Dear André,

    The g factor is calculated in QED with great accuracy and Schwinger has made it. The agreement with the experiment is to more than tenth digit. That is not wrong. What is wrong is the sentence:

    you will observe that the Bohr magneton is not a property of the electron proper, but of its adiabatically induced carrying energy (27.2 eV) 

Hi Daniel,

As you can see, the g factor can also be calculated to the same great accuracy from electromagnetism, by using the electron Compton wavelength and the wavelength of the electron carrying energy adiabatically induced on the hydrogen ground state orbital.

Your option to disagree, but since this can be calculated only from the wavelength of the energy induced at the mean ground state hydrogen orbital, and is in full agreement with QED and Schwinger's results, that you say you agree with, there is no way it can be wrong.

Or do you think that the energy induced a the ground state orbital is part of the electron rest mass? Or is it something else you are disagreeing with?

     The magnetic moment has not wavelength.

Certainly not, but the energy that allows calculating it has one.

Just like the mass of a particle has no wavelength, but the energy that makes it up and that allows calculating it has one.

If you consider the verified fact (it seems to me) that the rest mass (in kg) of the electron can be found by dividing its energy value by the square of the speed of light: m0= E/c2  that you get from the famous equation E=m0c2, where m0 is its rest mass, it is obvious that the value of E has to be in joules (8.18710414E-14 J) for the equation to work out and give the correct mass in kg.

Now, if you consider that the value of E for the rest mass of the electron actually is electromagnetic energy, you also know that the wavelength of this amount of energy is equal to the electron Compton wavelength, which is the exact wavelength of this particular amount of electromagnetic energy

If you divide the speed of light by this wavelenth, you obtain the frequency of this amount of electromagnetic energy.

Also, knowing that 1 joule of energy has a frequency of 1,50919E+33 Hz, simple calculation can tell you the frequency of any amount of energy from its joules value.

You can also obtain the wavelength by dividing the speed of light by the frequency.

It is basically just a matter of becoming familiar with the units and decomposing the complex units into their basics sub-units, For example, kg is basically only (joules x m2)/s2, and so on.

Basic physics.

@ andre

And  by that token the frequency of the electron is approx 1.23 X 10^20 Hz. But how does that explain magnetism.?

Hi Andrew,

Indeed, it does not. It only explains why the magnetic field of an electron carrying energy is stronger when the electron is captive on an atomic orbital than when it is moving in straight line with the same amount of carrying energy.

What explains magnetism is the interaction between the magnetic fields of elementary particles, as a function of the inverse cube of the distance between them, in attraction when in anti-parallel "spin" alignment and in repulsion when in parallel "spin" alignment.

"Spin" is quite a misnomer actually, since the word seems to imply that some spinning or rotating is involved. The mix up that caused it to be named "spin" is that any cyclic motion can be mathematically described the same way.

When electrons are paired on orbitals, they pair only in antiparallel spin alignment, which makes their magnetic fields sort of cancel out as seen from our macroscopic level, but when unpaired in the immediately inner orbital of some atoms, the ambient electromagnetic equilibrium states in these materials can allow these unpaired electron to be forced to remain in mutual parallel spin alignment, which is what we measure as magnetism at our macroscopic level.

The fields of these individual electrons then add up to make up the macroscopic field that we can observe.

The Einstein-de Haas and Barnett effects allow better understanding of ferromagnetic materials and magnetism.

Thank you

Can you also define the ratio of the magnetic field strength to the electric charge of the electron

    The neutron has spin but no magnetic field at all.

     Only a Zeeman coupling between spin (it is a fermion) with one external magnetic field.

Hi Andrew,

Paul Marmet published a paper in 2003 where he did a mathematical derivation from the Biot-Savart equation that seemed to relate the electron magnetic field to only part of the mass of an electron in motion.

His demo also showed that its magnetic field increased as a direct function of the square of its velocity, all the while with its electric charge remaining invariant.

This intrigued me quite a bit, so I followed the trail and ended up being able to separate the contribution to this total magnetic field of the electron proper from the contribution of its carrying energy.

The end result is that it can be established that both electric and magnetic fields of the electron proper are of equal strength and each are attached to a separate half of the electron invariant rest mass, and that the part of the magnetic field that varies when the electron is in motion belongs to its carrying energy, which varies with velocity.

This further allowed establishing a clear internal electromagnetic structure for the electron and other electromagnetic particles, but this is another story.

If you wish to see my reasoning and math that stem from Marmet's conclusions, they are available in this paper:

Article Field Equations for Localized Photons and Relativistic Field...

Daniel,

Quite the contrary. Neutrons have a very strong magnetic moment. In fact magnetic fields are the only means at our disposal to control their motion. Magnetic neutron scattering is a quite useful tool.

You can find all about it in this reference:

http://neutrons.phy.bnl.gov/presentations/MagneticNeutronScattering_proofed_indexed_unlinked.pdf

   Sure! And by the way the magnetic moment of the neutros is much smaller than the one of the electrons, The question is that the Compton wavelength hasn't anything to do with those values as you claim.

    Dear André,

   Just by curiosity, if the electron's magnetic moment has an associated energy of 27,2 eV (which is quite a lot), what is the energy related the neutron magnetic moment?

Hi Daniel,

This amount of associated energy (27.2 eV) is its carrying energy when at mean rest orbital distance from the proton in a hydrogen atom.

This is the unreleasable (because adiabatically induced) energy induced by the Coulomb force in the electron at this stabilized electromagnetic equilibrium distance between the electron and proton in a hydrogen atom between the negatively charged electron and the positively charged proton.

If the electron is chased away from the proton, this energy will progressively fall to zero as the distance increases.

If you can locate the Coulomb equation in any basic textbook, you can do the calculation yourself.

Regarding Compton wavelengths, they apply to the energy of any elementary particle depending on the amount of energy making up its rest mass. That's the definition of "Compton wavelength".

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

     Magnetic moment of:

    electron        −9284.764

    proton                14.106

    neutron              −9.662

     in units of 10−27 J·T−1. As you can see the neutron is about thousand of times less and smaller than the one of the proton. By the way, this proton doesn't need to be in an hydrogen atom to calculate its value.

    Frankly speaking,if I were you, I didn't show the paper that you present for the question that Edward's has put. You introduce more confusion and than clear answers of what is the g-factor.

   Good sunday for everybody and I am going to stop here.

Well Daniel,

You obviously are free not to look at the data and disagree.

I have no idea who this Edward is that you mention. I first gave an answer right on topic to Andrew's question and provided an answer to further questions by him.

You addressed me then with more questions to which I answered. As I said, feel totally free to disagree. Anybody can read the papers I appended and make up their own mind.

Hi Xavier.

Re-reading the various contributions to this thread, I observed that you worked directly with George Lochak.

I had the privilege of receiving a very helpful direct answer from this lifelong colleague of Louis de Broglie to a question I had addressed to Fondation Louis de Broglie in 2003 about Louis de Broglie's double particle photon hypothesis. As I was preparing my question to the Foundation, I was not aware that he was the director of the Foundation, so I was very surprised and honored to receive a direct answer from him.

His answer helped me prepare this possible solution to de Broglie's hypothesis that was peer-reviewed and published last year:

http://www.omicsonline.com/open-access/on-de-broglies-doubleparticle-photon-hypothesis-2090-0902-1000153.pdf

From par. 3.2 of Article The Electron and Occam's Razor

[in the proposed model] the electron has an "intrinsic" angular momentum = h/2 π.

"We can interpret the spin value ±1/2 as the component of the intrinsic angular momentum Ω = h/2 π aligned with the external flux density

field B. In this case the angle between the B vector and the angular momentum have only two possible values, namely π/3 and 2π/3 while the electron is subjected to a Larmor precession."