Is space just like a chessboard?

Washington: Researchers at the UCLA have discovered 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, the 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, 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 there 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," said Regan. 

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 have shown 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. 

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. 

The findings have been published in the journal Physical Review Letters.