What is Intrinsic Quantum Spin?

In a sci.physics.foundations post, Jay Yablon has brought to light an obscure article by Hans C. Ohanian on the nature of the intrinsic spin of quantum objects and kindly loaded it onto the web: What is Spin? Am J. Phys. 54 (6) June 1986. The abstract is:

According to the prevailing belief, the spin of the electron or some other particle is a mysterious internal angular momentum for which no concrete physical picture is available, and for which there is no classical analog. However, on the basis of an old calculation by Belinfante [Physica 6 887 (1939)], it can be shown that the spin may be regarded as an angular momentum generated by a circulating flow of energy in the wave field of the electron. Likewise, the magnetic moment may be regarded as generated by a circulating flow of charge in the wave field. This provides an intuitivelyl appealing picture and establishes that neither the spin nor the magnetic moment are “internal” — they are not associated with the internal structure of the electron, but rather with the structure of the field. Furthermore, a comparison between calculations of angular momentum in the Dirac and electromagnetic fields shows that the spin of the electrons is entirely analogous to the angular momentum carried by a classical circularly polarized wave.

If you’re interested in the foundations of physics, the above is well worth reading. My efforts on quantum mechanics has been to look at things at a qubit level, where one reduces the number of degrees of freedom down to an absolute minimum. The calculations in the above are of momentum density, and energy density and the like. It’s nice to see them done explicitly.


Filed under physics

13 responses to “What is Intrinsic Quantum Spin?

  1. Hi Carl,

    Thanks to you and Jay Yablon for turning me on to this paper! There is an interesting similarity to optical vortices, which also carry angular momentum, as described by Michael Berry here:

    Click to access BERRY382.pdf

    You might also enjoy this 20-minute audio interview with Berry. Near the end he describes how circularly polarized light can transfer angular momentum to a refracting crystal:

    [audio src="http://cdn1.libsyn.com/iop/berry.mp3" /]

    Maybe you remember I’ve been working with a space-time not unlike the Euclidean one you use, with a “hidden dimension.” Following de Broglie’s idea that particles represent singularities in real quantum-mechanical waves, particles in my model resemble optical vortices, stretched out in the extra dimension.

    For the time being, I’m still neglecting particles to work on gravity, since that’s where I know I have testable predictions. A previous post mentioned you’re in the opposite position: focusing on elementary particle masses for empirical support there. Hope we end up meeting in the middle somewhere!

  2. carlbrannen

    That’s an interesting paper. Reminds me a little of catastrophe theory. It should have applications to Bohmian mechanics.

    And whoa, that’s the Berry of “Berry phase.” I didn’t know that he was still doing stuff!

    The only article I could find on arXiv with his byname is quant-ph/0508117, Reflectionless Potentials and PT Symmetry, 2005, which is about non Hermitian Hamiltonians that nevertheless have only real eigenvalues.

    The reason I find the non Hermitian Hamiltonians interesting is that what I’m doing is done without Hamiltonians, but instead just uses the machinery of QFT. It should be possible to back track to get a Hamiltonian from the Feynman rules but I’ve not done it. However, my suspicion is that when you do this, you will end up with something that either violates Lorentz symmetry or is otherwise strange, perhaps non Hermitian.

  3. Hi Carl,

    You’re exactly right, it is related to catastrophe theory. Berry has some fascinating papers on that too. You can find most of his publications here:


    It’s a gold mine. You’re also correct that his work has applications to Bohmian mechanics. (I believe he is a fellow traveler there.) Would like to make his acquaintance. Like John Bell (a strong Bohm advocate), he’s one of those whose work is so good, he can’t be ignored — even if it doesn’t follow fashion.

    This is from Berry’s introduction of Yakir Aharanov when the latter won the Wolf prize:

    “I am a quantum mechanic. So is Yakir Aharonov. A technical term in our subject is the entangled state. Anyone who has a conversation with Yakir gets into an entangled state, with contradictions, digressions and interruptions all mixed up – Talmudic, I suppose. But now, here, Yakir can’t interrupt me, as I declare what an honour and delight it is to share this occasion with such a quick, deep and subtle man. There is only one sadness that I’m sure he shares with me: that David Bohm, with whom he did some of his seminal research, is no longer living; if he were, he would surely be here tonight.”

    I think Berry got “quantum mechanic” from Bell, who called himself that.

    My main route to understanding the world is through optics. Relativity, group transformations are in there. Quantum mechanics is in there. Hamilton’s optical-mechanical analogy shows how one gets from relativistic wave mechanics to classical mechanics. I’m amazed how few physicists notice something deeply profound there. Berry does.

  4. Oops. Bell was a “quantum engineer” who designed accelerators. But both guys are quantum mechanical realists, driven by connections with the real, hands-on world. Looking at your backhoe and hard hat, would you like call yourself a quantum-mechanical equipment operator?

  5. carlbrannen

    Thanks for the Berry links.

    Calling me a QMEO would be putting too nice a spin on it. Maybe “trash mechanic” would be too far down. “Scrap mechanic” is about right.

  6. I always thought that there was a confusion regarding the concept of spin in physics and this article explains why. The same kind of ambigiuity or duality of a physical concept without a “physical basis” also exists in the concept of electron itself when physicists attribute structure to a concept that must exist only as a mathematical point. Maybe similar computations can be done for the other properties of the electron to remove the mathematical point/physical entity duality.

  7. Hi Carl,

    Thanks for bringing this to folks’ attention. The Ohanian article should be more widely known, as it uses classical theory to explain the “non-classical, two-valued” spin and so reclaims a subject widely thought to be accessable only with quantum theory. Even more fundamentally, it redraws the line between classical and quantum theory in a way that actually is redeeming of classical theory.

    Based on the Ohanian paper (and I note that Ohanian was my relativity teacher in the 1980s), I am in the midst of working with a decomposition of the intrinsic spin operator into terms which include the canonical commutation relationship between the position and momentum operators. I am sure you have seen it; your readers can view a rough draft at http://jayryablon.files.wordpress.com/2008/04/intrinsic-spin-decomposition-11.pdf. (The sigma are the helicity operators, not the Pauli matrices as misstated in the draft, and x is the position operator in the sense of [x,p]=i hbar and not a position from center of mass as also misstated.)

    I believe that this decomposition may provide a basis for explaining the anomolous magnetic moment on the basis of the Heisenberg inequality delta x delta p >= hbar/2 , which in this context, leads to g>=2 for the gyromagnetic ratio of a “point” particle. I will write this up more formally in the next few days, but for now, I have outline the approach in a recent post at sci.physics. research, see http://groups.google.com/group/sci.physics.research/browse_frm/thread/ce7515f259ad0ea3/c44ac63578b941fd#c44ac63578b941fd.

    Best regards,


  8. carlbrannen

    Also see Jay’s interesting biographical comment on Ohanian.

  9. Hi Carl and all:

    I just posted an update on my hypothesized connection between Heisenberg Uncertainty and Schwinger anomaly, at http://jayryablon.wordpress.com/2008/05/08/how-precisely-can-we-measure-an-electrons-heisenberg-uncertainty-or-how-certain-is-uncertainty/.

    I would be very much interested in receiving comments from you and others. I am presently trying to put the “new” extrinsic g-factor I have derived in section 10 into the right physical context, and would especially appreciate any thoughts on that, as this is most certainly the trail to experimental validation or falsification.

    I believe this paper also picks up on pioneer1’s comment about spin, 4 up from here, that “The same kind of ambigiuity or duality of a physical concept without a “physical basis” also exists in the concept of electron itself when physicists attribute structure to a concept that must exist only as a mathematical point. Maybe similar computations can be done for the other properties of the electron to remove the mathematical point/physical entity duality.”

    Specifically, in essence, I have come around to what in some respects is the obvious viewpoint, that the main point of quantum thoery is that the cassical idea of measuring an electron’s position and momentum with precision, is to be replaced instead with the idea of meauring the electron’s *uncertainty* with precision. The problem to date is that Heisenberg is generally formulated as an inequality. This paper summarized (and linked) at http://jayryablon.wordpress.com/2008/05/08/how-precisely-can-we-measure-an-electrons-heisenberg-uncertainty-or-how-certain-is-uncertainty/ shows why one should really be asking, for any given electrion wavefunction, “what is the *exact* value of that electron’s uncertainty?”


  10. 3zy

    Thx for this paper. This external wave field is the Dirac sea, again.
    The wave field is not a simple plane wave, but also rotates. The wave coming from all directions into moving particle . This create a wave packet, which determines the particle position in the vacuum. Vacuum is a solid lattice. So particle is not moving, but jumping over vertices of lattice.
    The particle is only one grid point.

  11. Vladimir Kalitvianski

    Interesting concept! I have to read it carefully. In my electronium model the charge and the field variables (degrees of freedom) are naturally joined in one compound system. So the electron spin may be attributed to the field degrees of freedom. Can’t wait to read!

  12. Vladimir Kalitvianski

    Ah, no, I was too quick to judge. H. Ohanian shows that a vector field has spin 1 and a spinor field has spin 1/2. What is interesting is the corresponding “derivation” as if it is due to energy flow around z in a wave packet of a finite size. By the way, the size is not involved explicitly so it is a size-independent feature.

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