MIT Physicists Extend Einstein's 1905 Brownian Motion Theory to Near-Light-Speed Particles

Physicists at MIT and the University of California, Santa Barbara have worked out where Albert Einstein's famous 1905 theory of random particle motion falls short for objects moving near the speed of light, and they have calculated what takes its place. The result, published in Physical Review Letters, could give experimenters a new way to probe the quark-gluon plasma, the primordial fluid of the early universe.

In the first fraction of a second after the Big Bang, matter was a trillion-degree plasma of quarks and gluons moving at close to the speed of light. It lasted only microseconds before the particles coalesced into protons and neutrons. Scientists re-create it by smashing ions together at accelerators such as the Relativistic Heavy Ion Collider at Brookhaven National Laboratory. The collisions create droplets of plasma roughly the size of an atomic nucleus that exist for tens of septillionths of a second.

One way to study the plasma is to track heavy quarks that pass through it without being part of it. How a heavy particle moves through a fluid reveals the fluid's microscopic structure, a relationship Einstein established in 1905 while explaining Brownian motion. In 1827 the botanist Robert Brown saw pollen grains jiggling in still water. Einstein showed the jiggle comes from a balance between the drag of the fluid and random kicks from atoms and molecules, which together let a particle settle to the same temperature as its surroundings.

Physicists have assumed the kicks in quark-gluon plasma follow a bell-shaped probability curve, with medium kicks most common and extreme kicks equally rare on either side. "Einstein showed that the drag and the random kicks must balance in just the right way for a particle eventually to come to the same temperature as its surroundings," said Jean Du Plessis, a graduate student in MIT's Center for Theoretical Physics. "For the types of fluids he was thinking about, he was correct. But for particles that are moving at relativistic velocities, this relationship breaks down. And we've known for 20 years that something is missing."

Du Plessis and Bruno Scheihing-Hitschfeld of UCSB's Kavli Institute for Theoretical Physics calculated the forces a relativistic heavy quark would feel, using the strong nuclear force that binds quarks and gluons. They started with a manageable case, a heavy quark flying through a gas of weakly interacting quarks and gluons, and computed how much its momentum is likely to change. That produced a new probability curve for the quark's changes in momentum.

The key finding is that the extreme kicks, the rare and unusually large changes in motion, carry information that the simple bell curve misses. "Our result reveals a new source of information carried by heavy quarks in rare, unusually large changes in their motion," Du Plessis said. "How often those large changes occur depends on the microscopic nature of the plasma, raising the possibility that they could provide a new way to learn what the quark-gluon plasma is actually like inside."

The calculation applies first to the idealized weakly interacting case, and the real plasma is strongly interacting, so the authors present it as a theoretical foundation rather than a final answer. They envision comparing its predictions with collider data on heavy quarks to characterize what kind of fluid existed in the universe's first moments.