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March 24, 2011

Physics Nobelist, Richard Feynman, was a fount of interesting ideas. One of his earlier conjectures was on the reason why all electrons have the same properties. Leave it to a master to invert nomenclature to reveal a deeper idea. We casually look at particles, note how they match a prototype, and drop them into their labeled bucket. Why are there such prototypes? Shouldn't all particles be different? Quantization, of course, limits your choices, but that just leads to the deeper problem of why everything is quantized? All our theories just explain how they are quantized.

Feynman's idea was that all electrons have the same properties because they are all the same electron. It's a particle that zips forwards and backwards through time so it can be in all the right places at all the right times. When the mathematics of time-reversed electrons was developed, what was found, instead, was the positron. This probably rules out the idea of electronic solipsism.

One property of the electron is spin, which is mysterious on two counts. First, spin cannot be a rotational property, since the surface of an object of the supposed very small dimension of an electron would need to spin faster than the speed of light to give the observed magnetic moment. Second, experiments show that electrons are point-like, so there's really nothing to spin.

Two UCLA physicists got an interesting idea about electron spin while studying graphene, and this idea was developed and published in the recent issue of Physical Review Letters.[1-2] While modeling electrons as they hopped between atoms on graphene, they found that their low-energy excitations obeyed an equation that was identical to a (2 + 1)-dimensional Dirac equation.

Along with showing that a property of graphene electrons called pseudospin is a real angular momentum, their equations seemed to indicate that the spin property, in general, can arise from a hidden substructure; that is, it wouldn't be a property of the particles, themselves, but rather a property of space. This result would hold for all half-integer spin particles, such as quarks and leptons, as well as electrons.

Figure caption

As a graphene electron moves from one carbon atom to another, its pseudospin state changes depending on whether it's in a blue or gold region. The electron pseudospin depends on its location, rather than a rotational motion of its substructure.

(Image: Chris Regan/UCLA)

This conjecture alludes to the idea that space is quantized. General relativity supposes that spacetime is continuous; simply speaking, for any two positions, you can always find a position halfway between them. On the other hand, quantum mechanics seems to requires a granularity of space of the order of the Planck scale.

The Dirac equation combines relativity and quantum mechanics to explain the half-integer spin particles. This equation, formulated by Paul Dirac in 1928, shows that relativistic quantum mechanics requires spin; but there's still no explanation of how point-like particles like the electron can have an angular momentum, or why spin should be two-valued.

The UCLA equation describes a state called pseudospin, not spin itself.[3] Shining light on graphene will cause electrons to hop between carbon atoms, and this transition changes the electron pseudospin, a spin-like state that's different from the electron's inherent spin. The pseudospin arises just from the geometry of the graphene lattice and the confinement of electrons to just the carbon atoms in that geometry.

Chris Regan, an assistant professor in the UCLA Department of Physics and Astronomy, a member of the California NanoSystems Institute, and an author of the paper, had this to say:[2]
"It's not yet clear if this work will be more useful in particle or condensed matter physics, but it would be odd if graphene's honeycomb structure was the only lattice capable of generating spin."
I'm attuned to the graphene part of the research, not the quantum/spacetime part; so, interested readers should consult the original article for a better explanation.[1] This paper is likely another example where it's good to work in a place that employs people with a lot of different specialties with whom you can vet your ideas. Many people think that this type of environment is what made places like Bell Labs the innovation centers that they once were.

Paul Dirac

Paul Dirac with some simpler equations than his accustomed milieu. Note how theoretical physics and experimental physics share adjoining wall sections. (Photograph via Wikimedia Commons)


  1. Matthew Mecklenburg and B. C. Regan, "Spin and the Honeycomb Lattice: Lessons from Graphene," Phys. Rev. Lett., vol. 106, no. 11 (March 16, 2011), Article No. 116803.
  2. Jennifer Marcus, "Is space like a chessboard?" UCLA Press Release, March 18, 2011
  3. Hongki Min, Giovanni Borghi, Marco Polini and A.H. MacDonald, "Pseudospin Magnetism in Graphene," Physical Review B, vol. 77, no. 4 (January 15, 2008), Document No. 041407; a summary presentation is available here.

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Linked Keywords: Nobel Prize in Physics; Richard Feynman; electron; nomenclature; elementary particle; prototype; quantization; mathematics; positron; solipsism; Spin-1/2; rotation; speed of light; magnetic moment; point-like; University of California, Los_Angeles; UCLA; physicist; graphene; Physical Review Letters; Dirac equation; space; quark; lepton; quantum spacetime; general relativity; spacetime; quantum mechanics; Planck scale; Paul Dirac; angular momentum; carbon; geometry; Chris Regan; UCLA Department of Physics and Astronomy; California NanoSystems Institute; Bell Labs; Wikimedia Commons.