This is a good start and finally
asks the important question about the fine structure of space itself once you
throw 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 as
smoothness and continuity are way more tricky than has been assumed. Enough in fact to revisit the whole of
calculus to establish an empirical version of calculus.
At present, I expect the electron
to be formed far more complexly than presently suggested but that is a lot of
simulation away.
Otherwise I am pleased to see
where we are at now and see the value of my ideas emerging from this cloud of
work. It looks like we will be able to measure
fine structure through the manipulation of graphene which is exciting.
Is space like a chessboard?
March 18, 2011 By
Jennifer Marcus
Electrons are thought to spin, even though they are pure point
particles with no surface that can possibly rotate. Recent work on graphene
shows that the electron's spin might arise because space at very small
distances is not smooth, but rather segmented like a chessboard with triangular
tiles. (Image: UCLA CNSI)
(PhysOrg.com) -- 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.
Electrons are thought to spin, even though they are pure point
particles with no surface that can possibly rotate. Recent work on graphene
shows that the electron’s spin might arise because space at very small
distances is not smooth, but rather segmented like a chessboard. The standard
cartoon of an electron shows a spinning sphere with positive or negative
angular momentum, as illustrated in blue or gold above. However, such cartoons
are fundamentally misleading: compelling experimental evidence indicates that
electrons are ideal point particles, with no finite radius or internal
structure that could possibly “spin”. A quantum mechanical model of electron
transport in graphene, a single layer of graphite (shown as a black honeycomb),
presents a possible resolution to this puzzle. An electron in graphene hops
from carbon atom to carbon atom as if moving on a chessboard with triangular
tiles. At low energies the individual tiles are unresolved, but the electron acquires
an “internal” spin quantum number which reflects whether it is on the blue or
the gold tiles. Thus the electron’s spin could arise not from rotational motion
of its substructure, but rather from the discrete, chessboard-like structure of
space. (Image: Chris Regan/CNSI)
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."
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