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Home , Paul Dirac, Zitterbewegung

THESIS

Dirac gets the jitters In 1928, British Paul Dirac could help to change that, bringing up an arbitrary electronic state. In a derived his famous equation for some of the strangest eff ects fi nally semiconducting nanowire, a similar the relativistic within experimental reach. eff ect takes place for with of -1/2 particles. Following his In 1930, Erwin Schrödinger components in both conduction and unique aesthetic sense for math- showed that Dirac’s equation implies valence bands. In some type III–V ematical elegance, Dirac sought a an unexpected relativistic interaction , in particular, the linear diff erential equation with only between an ’s translational lack of symmetry of the electron a fi rst-order derivative in time, akin and spin, which should lead hamiltonian under spatial inver- to the Schrödinger equation, that to a violent oscillation of the particle sion of the atomic lattice induces an would refl ect the electron’s intrinsic at very high frequencies and over IT MIGHT BE interaction between an electron’s spin and also lead to the relativistic distances of roughly one Compton POSSIBLE TO spin and momentum — as in the relationship between energy and wavelength. Th is phenomenon of PROBE A CLOSE . momentum, E2 = p2c2 + m2c4. Dirac zitterbewegung — from the German ANALOGUE OF Calculations, and simulations, found his equation; and much more. word for ‘jitter’ — has never been ZITTERBEWEGUNG suggest that an electron travel- Dirac’s equation has an infi nite observed directly. Given its predicted BY RECREATING ling along a narrow quantum wire number of solutions with negative frequency (about 1021 Hz), it might THE should undergo a semiconduct- energies. Th is obviously needs some be some time before a physicist, MATHEMATICS ing version of zitterbewegung — a explaining, as real electrons of posi- in the manner of botanist Robert OF DIRAC’S fl uctuating motion in a direction tive energy exist stably in free space, Brown, peers through a microscope EQUATION IN A perpendicular to the wire. Its ampli- and never seem to plunge into that of some design to see the electron QUANTUM WIRE. tude should grow with the electron’s abyss of negativity. Dirac supposed erratically bouncing around. wavelength, and with the steep- that an invisible sea of negative-ener- But, as several have ness of the wire’s potential walls. gy electrons fi lls that abyss, prevent- recently proposed, it might soon be Experimentalists may soon be able ing ordinary electrons from falling possible to probe a close analogue to measure this eff ect. into it. Incredibly, this idea led him of zitterbewegung by recreating the Quantum-wire zitterbewegung to predict the existence of the posi- mathematics of Dirac’s equation in even has a relatavistic origin tron, discovered fi ve years later. a quantum wire (J. Schliemann et al. — linked to very strong electric Dirac’s equation can no longer Phys. Rev. Lett. 94, 206801; 2005). fi elds near atomic cores. Th e eff ect be considered mysterious, given its For Dirac’s electrons, zitter- illustrates, again, the surprising fl ex- central position in modern phys- bewegung takes place whenever the ibility of nanostruc- ics. But 60 years later, some of the electron wavefunction includes both tures in exploring novel and oft en equation’s features have yet to be positive and com- exotic phenomena — even some explored experimentally. Mod- ponents; this is generally the case, that were predicted 75 years ago. ern semiconductor technologies as it takes both sets of states to build Mark Buchanan Lost in Los Angeles I was driving around Los Angeles status that warrants a whole year eral relativity, depending on their a few weeks ago, lost, and relying being named in his honour. position in the Earth’s gravitational on a global positioning system was per- fi eld. Without correcting for that, receiver to guide me through the haps the most objectively cerebral GPS would not work properly. maze of freeways and unfamiliar theoretical development in modern Einstein didn’t develop general streets. In the unending traffi c jams, . It was not a response to an relativity because he wanted to I had plenty of time to ponder and, experimental problem (the preces- fi nd a better way to track his own surprisingly perhaps, my thoughts sion of the perihelion of Mercury position, even if the technology turned to Einstein. didn’t seem to need a revolution had been available. But it is hard to 2005 has been named World in physics to explain it), and direct WITHOUT think of a better example than this Year of Physics, to celebrate the laboratory confi rmation only took EINSTEIN’S of the cross-germination between centenary of ’s ‘mira- place over a quarter century aft er EXOTIC THEORY fundamental scientifi c investiga- cle year’, in which he wrote fi ve the theory was fi rst written down. OF SPACETIME, I tion and technological innovation. seminal papers. Th e whole world is But without that exotic theory WOULDN’T HAVE In this World Year of Physics, familiar with E = mc2, but really it of spacetime, I wouldn’t have been BEEN ABLE TO as economic pressures have led to was Einstein’s development of gen- able to fi nd my way around LA. FIND MY WAY cuts in funding for fundamental eral relativity a decade later — and Global positioning systems rely on AROUND LA. research in many industrialized the dramatic confi rmation in 1919 the timing of signals sent from sev- countries, it is worth refl ecting on of the predicted bending of , a eral satellites located thousands of this connection — at least the next consequence of interpreting gravity miles apart. However, the internal time you’re caught in traffi c and as a curvature of space — that cata- clocks of GPS satellites tick at rates looking for an alternative route. pulted him to the kind of superstar that are shift ed, according to gen- Lawrence M. Krauss physics | VOL 1 | OCTOBER 2005 | www.nature.com/naturephysics 5

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