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Classical spin of an electron?

  1. Jan 7, 2009 #1
    Listening to Susskind's online QM lectures, he has mentioned the "classical spin" of an electron a few times (with an associated magnetic moment), but I didn't think the electron really has a classical spin.

    Specifically, in Maxwell's equations we only get magnetic fields for moving charges, so I don't see how a point particle like an electron would have a magnetic moment in a classical context if it is at a fixed position in space.

    The only way I can think of a electron with spin in a classical context would be if you modelled it as some specific charge distribution in a volume and then set that charge distribution spinning. Then add up the magnetic field contributions from all the individual bits of that moving distribution, to achieve a classically model of a spinning electron with Maxwell's equations. But if you did this it would radiate (like a classical electron in the Bohr model should), and I presume would eventually loose its angular momentum and spin to that radiation.

    Can anybody guess what Susskind may be talking about here?
  2. jcsd
  3. Jan 7, 2009 #2
    Actually In the early twenties before Pauli, there were models of the electron being a spinning particle, and these were made by well known physicists, like Kronig (the same guy from the Kramers-Kronig relation), but after doing calculations, In this model the "edge" of the electron should have had greater speed than that of light and there were many other discrepencies.
    So later building on the stern-gerlach experiment, Pauli built his theory of this so called "spin" which was as I wrote above considered earlier as the "true" angular momentum of the electron itself. In this he introduced the famous Pauli-matrices. And concluded that this was a purely quantum mechanical effect. But this was a phenomenological description, which even Pauli himself dubbed mysterious.
    But 2-3 years later, Dirac formulated his equation for the relativistic electron, and from there the spin arose naturally as a quantum mechanical effect.
  4. Jan 8, 2009 #3
    I dont believe that the electron really spins but why would it radiate? the field isnt changing.
  5. Jan 8, 2009 #4
    I was imagining a sphere of spinning charge. None of that is moving linearly, so there would be radiation associated with the acceleration.

    I should go back and relisten to the lectures in question and note down exactly what Susskind said.
  6. May 11, 2009 #5
  7. May 11, 2009 #6
    There are two critical problems in the electron spinning model.

    The size of the electron is too small. So by equating the angular momentum of the spinning sphere of the electron to 1/2 h-bar, the sphere speed leads to about one hundred times the speed of light.

    And the spin g factor is about 2. This means the unequally distribution of the charge and mass of the electron.
    (If the charge and mass are equally distributed, the g-factor is usually 1. So the spin g-gactor 2 is remarkably different.)

    Considering the electron size, If we suppose that the whole electron cloud is spinning,
    we can not explain about the spin g-factor 2.
    ( The mass and charge of an electron are separated !?).
  8. May 11, 2009 #7
    separate charge and mass could conceivably explain why the electron (seems) to fill atomic orbitals out of order (filling higher orbitals before lower ones)
  9. May 11, 2009 #8
    So what is this electron size you talk of. Are you referring to the classical electron radius? This size is based on the assumption that the electron mass is entirely due to it's electrostatic potential energy. This assumption is not necessarily true, therefore you can not rely on this as a solid basis to eliminate the spinning electron model.

    As grandpa has mentioned repeatedly, although an accelerated point particle radiates, an extended distribution of charge can accelerate without radiating.
  10. May 11, 2009 #9
    Ok. Then how do you explain about the spin g-factor 2 ?
    The mass and charge of one electron are separated !?

    And if the whole electron cloud is spinning, what state is the center of the cloud ?
    The orbital angular momentum in the ground state in the hydrogen atom is zero.
    Why is not the electron scatterd by the nucleus.
  11. May 11, 2009 #10


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    The actual radius of the electron is actually smaller than the radius you speak of, which only makes things worse...
  12. May 12, 2009 #11
    An electron HAS an actual radius?
    This is news to me...
  13. May 12, 2009 #12


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    I meant the upper bound to the actual radius, sorry, slip of the tongue.
  14. May 12, 2009 #13
    We can not measure the correct size of an electron.
    Because an electron is too small to find a proper smaller particle in the scattering experiment.

    If one electron is as big as the electron cloud, we can measure the size of an electron using a proton or something in the scattering experiment.
  15. May 12, 2009 #14


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    Yea, what an electron ACTUALLY is is unknown. Is it a 1-D loop of string vibrating at some mode? Or is it a point? Or some other? Who knows. In many of these cases, a "radius" is not even well defined. The point I was making is that IF you view the electron as a really small ball that's spinning, the upper bound to that radius is smaller than the classical electron radius (more pedantically, the mass/energy of the electron is confined to a smaller region of space).

    My semantics may have been wrong, or overly misleading, and I apologize for that, but the point I was making still stands. But do forgive me because it would take forever (and be rather annoying) if I typed every post in a completely pedantic sort of way...
  16. May 12, 2009 #15
    most of the experiments 'measuring' the size of the electron just measure g (gyromagnetic ratio). its agreement with the calculated value is taken as proof that the electron is a point particle.

    if the electron is a spinning sphere of charge then it is quite trivial to determine what radius it must have. we know that the frequency at which an electron in the ground state of hydrogen rotates is R (Rydberg constant). we know the magnetic moment and so from the definition of magnetic moment the required radius can easily be determined. (not forgeting that g is not equal to 1)

    the equation for determining magnetic moment is the same as for determining angular momentum. just replace mass with charge.

    is the idea that the mass and charge occupy different orbitals any more strange than any other quantum phenomena (like superposition or entanglement)?
    Last edited: May 12, 2009
  17. May 12, 2009 #16


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    Maybe he is just refering to the fact that much of the physics can be modelled as if the electron had a "classical" spin with angular momentum [itex]\hbar L [/itex].

    If you look in a book about e.g. NMR you will find a LOT of classical physics, this does not mean that anyone believes that this is an accurate description of what is really going on(for that you need QM), but in many cases we can "pretend" that we are dealing with classical systems since the formalism is much simpler; it also tends to be quite accurate if we are for example dealing with large ensembles at elevated temperatures (where the "quantumness" of the individual systems tends to be washed out anyway).
  18. May 13, 2009 #17
    Granpa: I think there are actually high energy scattering experiments which place an upper bound on the actual physical size of the electron as 10 ^-18 m. What do you mean by "mass and charge occupuying separate orbitals"? And when does an electron fill higher-energy orbitals in preference to lower ones?
  19. May 13, 2009 #18
    I thought so too until I started looking into it. the experiments I read about arent as impressive as they are made to sound. I have become rather skeptical of experiments that people toss out as 'proof' of some idea without ever bothering to explain exactly how the experiment works and exactly what the raw data from the experiment was.

    separate mass and charge is explained elsewhere in this thread. no point in me repeating myself endlessly.

    higher as in further from the nucleus. that should have been obvious.
    Last edited: May 14, 2009
  20. May 13, 2009 #19
    Well you could write down the dirac lagrangian and not quantize it. The field would then be a classical spinor field. In this sense the electron field could still be said to have spin. This would also correspond to doing a calculation at tree level so with no quantum corrections. this i think gives g=2. The loop corrections then add the decimal corrections to the 2. Both classically and after quantization spin is still defined at a point. An electron is a point particle so it doesn't have a size.
  21. May 16, 2009 #20
    As it stands the statement "mass and charge occupying separate orbitals" doesn't seem to make much sense to me. As properties of the electron, they're parameters that partly determine the solution to the Schroedinger equation, from which one can extract the probabilistic distribution of the position of the electron, i.e. the orbitals. They don't have a position, or a momentum, or any similar dynamical variable. Only the electron itself does. How would you describe such an idea mathematically?

    Whilst I understood what you meant by a higher orbital, I've never heard of a higher orbital being filled in preference to a lower one. Anywhere I could read an account of this being measured? And does the system decay to the ground state in fairly short order?
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