This is a good start and finallyasks the important question about the fine structure of space itself once youthrow away the mathematical assumption of smoothness. An inevitable consequence of applying my metric(Pub. June 2010, Phy. Essays) to particle physics is that concepts such assmoothness and continuity are way more tricky than has been assumed. Enough in fact to revisit the whole ofcalculus to establish an empirical version of calculus.
At present, I expect the electronto be formed far more complexly than presently suggested but that is a lot ofsimulation away.
Otherwise I am pleased to seewhere we are at now and see the value of my ideas emerging from this cloud ofwork. It looks like we will be able to measurefine structure through the manipulation of graphene which is exciting.
Is space like a chessboard?
March 18, 2011 ByJennifer Marcus
Electrons are thought to spin, even though they are pure pointparticles with no surface that can possibly rotate. Recent work on grapheneshows that the electron's spin might arise because space at very smalldistances is not smooth, but rather segmented like a chessboard with triangulartiles. (Image: UCLA CNSI)
(PhysOrg.com) -- Physicists at UCLA set out to design a bettertransistor and ended up discovering a new way to think about the structure ofspace.
Space is usually considered infinitely divisible — given any twopositions, there is always a position halfway between. But in a recent studyaimed at developing ultra-fast transistors using graphene, researchers from theUCLA Department of Physics and Astronomy and the California NanoSystemsInstitute show that dividing space into discrete locations, like a chessboard,may explain how point-like electrons, which have no finite radius, manage tocarry their intrinsic angular momentum, or "spin."
While studying graphene's electronic properties, professor Chris Reganand graduate student Matthew Mecklenburg found that a particle can acquire spinby living in a space with two types of positions — dark tiles and light tiles.The particle seems to spin if the tiles are so close together that theirseparation cannot be detected.
"An electron's spin might arise because space at very smalldistances is not smooth, but rather segmented, like a chessboard," Regansaid.
Their findings are published in the March 18 edition of the journal Physical ReviewLetters.
In quantummechanics, "spin up" and "spin down" refer to the twotypes of states that can be assigned to an electron. That the electron's spincan have only two values — not one, three or an infinite number — helps explainthe stability of matter, the nature of the chemical bond and many otherfundamental phenomena.
However, it is not clear how the electron manages the rotational motionimplied by its spin. If the electron had a radius, the implied surface wouldhave to be moving faster than the speed of light, violating the theory ofrelativity. And experiments show that the electron does not have a radius; itis thought to be a pure point particle with no surface or substructure thatcould possibly spin.
Electrons are thought to spin, even though they are pure pointparticles with no surface that can possibly rotate. Recent work on grapheneshows that the electron’s spin might arise because space at very smalldistances is not smooth, but rather segmented like a chessboard. The standardcartoon of an electron shows a spinning sphere with positive or negativeangular momentum, as illustrated in blue or gold above. However, such cartoonsare fundamentally misleading: compelling experimental evidence indicates thatelectrons are ideal point particles, with no finite radius or internalstructure that could possibly “spin”. A quantum mechanical model of electrontransport in graphene, a single layer of graphite (shown as a black honeycomb),presents a possible resolution to this puzzle. An electron in graphene hopsfrom carbon atom to carbon atom as if moving on a chessboard with triangulartiles. At low energies the individual tiles are unresolved, but the electron acquiresan “internal” spin quantum number which reflects whether it is on the blue orthe gold tiles. Thus the electron’s spin could arise not from rotational motionof its substructure, but rather from the discrete, chessboard-like structure ofspace. (Image: Chris Regan/CNSI)
In 1928, British physicist Paul Dirac showed that the spin of theelectron is intimately related to the structure of space-time. His elegantargument combined quantum mechanics with special relativity, Einstein's theoryof space-time (famously represented by the equation E=mc2).
Dirac's equation, far from merely accommodating spin, actually demandsit. But while showing that relativistic quantum mechanics requires spin, theequation does not give a mechanical picture explaining how a point particlemanages to carry angular momentum, nor why this spin is two-valued.
Unveiling a concept that is at once novel and deceptively simple, Reganand Mecklenburg found that electrons' two-valued spin can arise from having twotypes of tiles — light and dark — in a chessboard-like space. And theydeveloped this quantum mechanical model while working on the surprisinglypractical problem of how to make better transistors out of a new materialcalled graphene.
Graphene, a single sheet of graphite, is an atomically-thin layer ofcarbon atoms arranged in a honeycomb structure. First isolated in 2004 by AndreGeim and Kostya Novoselov, graphene has a wealth of extraordinary electronicproperties, such as high electron mobility and current capacity. In fact, theseproperties hold such promise for revolutionary advances that Geim and Novoselovwere awarded the 2010 Nobel Prize a mere six years after their achievement.
Regan and Mecklenburg are part of aUCLA effort to develop extremely fast transistors using thisnew material.
"We wanted to calculate the amplification of a graphenetransistor," Mecklenburg said. "Ourcollaboration was building them and needed to know how well they were going towork."
This calculation involved understanding how light interacts with theelectrons in graphene.
The electrons in graphene move by hopping from carbon atom to carbonatom, as if hopping on a chessboard. The graphene chessboard tiles aretriangular, with the dark tiles pointing "up" and light ones pointing"down." When an electron in graphene absorbs a photon, it hops fromlight tiles to dark ones. Mecklenburg andRegan showed that this transition is equivalent to flipping a spin from"up" to "down."
In other words, confining the electrons in graphene tospecific, discrete positions in space gives them spin. This spin, which derivesfrom the special geometry of graphene's honeycomb lattice, is in addition toand distinct from the usual spin carried by the electron. In graphene theadditional spin reflects the unresolved chessboard-like structure to the spacethat the electron occupies.
"My adviser [Regan] spent his Ph.D. studying the structure of theelectron," Mecklenburg said. "So hewas very excited to see that spin can emerge from a lattice. It makes youwonder if the usual electron spin could be generated in the same way."
"It's not yet clear if this work will be more useful in particleor condensed matter physics," Regan said, "but it would be odd ifgraphene's honeycomb structure was the only lattice capable of generating spin."
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