This is the sort of theoretical work I was thinking of when I said
everything is discrete. That space is not continuous but discontinuous and
has a fundamental resolution.

I wasn't aware of this specific work but there has been other work
undertaken over the past few years that is very similar. Here at Edinburgh
we are lucky to have a pretty smart physicist (Higgs, as in the Higgs Boson)
with a lot of people round him doing this kind of work. Their focus is the
Hadron Collider at CERN and they talk about this at research seminars, how
there is a smallest particle, a shortest period, etc. That's what they are
looking for. They are convinced they will find it.

Best

Simon


On 19/03/2011 06:13, "Alan Sondheim" <[log in to unmask]> wrote:

> Perhaps I'm just completely wrong!
> 
> 
> UCLA Newsroom > All Stories > News Releases
> Is space like a chessboard?
> By Jennifer Marcus March 18, 2011
> 
> (Click image for description)
> Physicists at UCLA set out to design a better transistor and ended up
> discovering a new way to think about the structure of space.
> 
> Space is usually considered infinitely divisible  given any two positions,
> there is always a position halfway between. But in a recent study aimed at
> developing ultra-fast transistors using graphene, researchers from the
> UCLA Department of Physics and Astronomy and the California NanoSystems
> Institute show that dividing space into discrete locations, like a
> chessboard, may explain how point-like electrons, which have no finite
> radius, manage to carry their intrinsic angular momentum, or "spin."
> 
> While studying graphene's electronic properties, professor Chris Regan and
> graduate student Matthew Mecklenburg found that a particle can acquire
> spin by 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 their separation cannot be detected.
> 
> "An electron's spin might arise because space at very small distances is
> not smooth, but rather segmented, like a chessboard," Regan said.
> 
> Their findings are published in the March 18 edition of the journal
> Physical Review Letters.
> 
> In quantum mechanics, "spin up" and "spin down" refer to the two types of
> states that can be assigned to an electron. That the electron's spin can
> have only two values  not one, three or an infinite number  helps explain
> the stability of matter, the nature of the chemical bond and many other
> fundamental phenomena.
> 
> However, it is not clear how the electron manages the rotational motion
> implied by its spin. If the electron had a radius, the implied surface
> would have to be moving faster than the speed of light, violating the
> theory of relativity. And experiments show that the electron does not have
> a radius; it is thought to be a pure point particle with no surface or
> substructure that could possibly spin.
> 
> In 1928, British physicist Paul Dirac showed that the spin of the electron
> is intimately related to the structure of space-time. His elegant argument
> combined quantum mechanics with special relativity, Einstein's theory of
> space-time (famously represented by the equation E=mc2).
> 
> Dirac's equation, far from merely accommodating spin, actually demands it.
> But while showing that relativistic quantum mechanics requires spin, the
> equation does not give a mechanical picture explaining how a point
> particle manages to carry angular momentum, nor why this spin is
> two-valued.
> 
> Unveiling a concept that is at once novel and deceptively simple, Regan
> and Mecklenburg found that electrons' two-valued spin can arise from
> having two types of tiles  light and dark  in a chessboard-like space. And
> they developed this quantum mechanical model while working on the
> surprisingly practical problem of how to make better transistors out of a
> new material called graphene.
> 
> Graphene, a single sheet of graphite, is an atomically-thin layer of
> carbon atoms arranged in a honeycomb structure. First isolated in 2004 by
> Andre Geim and Kostya Novoselov, graphene has a wealth of extraordinary
> electronic properties, such as high electron mobility and current
> capacity. In fact, these properties hold such promise for revolutionary
> advances that Geim and Novoselov were awarded the 2010 Nobel Prize a mere
> six years after their achievement.
> 
> Regan and Mecklenburg are part of a UCLA effort to develop extremely fast
> transistors using this new material.
> 
> "We wanted to calculate the amplification of a graphene transistor,"
> Mecklenburg said. "Our collaboration was building them and needed to know
> how well they were going to work."
> 
> This calculation involved understanding how light interacts with the
> electrons in graphene.
> 
> The electrons in graphene move by hopping from carbon atom to carbon atom,
> as if hopping on a chessboard. The graphene chessboard tiles are
> triangular, with the dark tiles pointing "up" and light ones pointing
> "down."  When an electron in graphene absorbs a photon, it hops from light
> tiles to dark ones. Mecklenburg and Regan showed that this transition is
> equivalent to flipping a spin from "up" to "down."
> 
> In other words, confining the electrons in graphene to specific, discrete
> positions in space gives them spin. This spin, which derives from the
> special geometry of graphene's honeycomb lattice, is in addition to and
> distinct from the usual spin carried by the electron. In graphene the
> additional spin reflects the unresolved chessboard-like structure to the
> space that the electron occupies.
> 
> "My adviser [Regan] spent his Ph.D. studying the structure of the
> electron," Mecklenburg said. "So he was very excited to see that spin can
> emerge from a lattice. It makes you wonder 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 particle or
> condensed matter physics," Regan said, "but it would be odd if graphene's
> honeycomb structure was the only lattice capable of generating spin."
> 
> The California NanoSystems Institute at UCLA is an integrated research
> facility located at UCLA and UC Santa Barbara. Its mission is to foster
> interdisciplinary collaborations in nanoscience and nanotechnology; to
> train a new generation of scientists, educators and technology leaders; to
> generate partnerships with industry; and to contribute to the economic
> development and the social well-being of California, the United States and
> the world. The CNSI was established in 2000 with $100 million from the
> state of California. An additional $850 million of support has come from
> federal research grants and industry funding. CNSI members are drawn from
> UCLA's College of Letters and Science, the David Geffen School of
> Medicine, the School of Dentistry, the School of Public Health and the
> Henry Samueli School of Engineering and Applied Science. They are engaged
> in measuring, modifying and manipulating atoms and molecules  the building
> blocks of our world. Their work is carried out in an integrated laboratory
> environment. This dynamic research setting has enhanced understanding of
> phenomena at the nanoscale and promises to produce important discoveries
> in health, energy, the environment and information technology.
> 
> For more news, visit the UCLA Newsroom and follow us on Twitter.
> 
> 
> ==
> email archive: http://sondheim.rupamsunyata.org/
> webpage http://www.alansondheim.org
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> ==
> 
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Simon Biggs
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