Physicists Extend Einstein's 1905 Theory to the Universe's First Fluid

Where does Einstein's theory fall short?

That general relationship dates to 1905, when Einstein built a theory around an observation made by the botanist Robert Brown in 1827: grains of pollen suspended in still water jittered and swirled randomly. This jittering, later named Brownian motion, arises from invisible microscopic forces.

Einstein showed that a particle's motion balances two effects: the drag the fluid exerts to slow the particle down, and random kicks delivered by the atoms and molecules of the fluid itself. His theory implies a bell-shaped probability distribution, in which gentle kicks are common and extreme kicks sit vanishingly far out in the tails.

"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," Du Plessis said. "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."

What did the new calculation find?

The researchers calculated the forces a heavy quark would experience flying through quark-gluon plasma at relativistic speeds. They computed the strong nuclear force, the fundamental force binding quarks and gluons, starting with a manageable scenario: a heavy quark passing through a gas of weakly interacting quarks and gluons.

The result was a curve describing the probability of kicks of various strengths. For small kicks, it matched Einstein's bell shape. For large kicks, the bell tilted. The tails at either end grew uneven, meaning a heavy kick that slows the quark down more than drag alone predicts is more likely than an equally large kick that speeds it up.

"The usual Brownian picture assumes that large kicks become exceedingly rare," Du Plessis said. "For heavy quarks, however, these rare kicks are more common than the bell curve predicts, and are not equally likely in opposite directions."

The team repeated the calculation in plasmas made of different particles. The same tilted curve appeared every time, and the same structure turned out to be hiding in an earlier calculation for a strongly coupled plasma, despite different microscopic physics.

"This is the first time that this seemingly universal structure was realized and really formalized," Du Plessis said. "This gives a concrete path forward for how to better understand the quark-gluon plasma, using heavy quarks."

As for the universe's first fluid, Du Plessis says it was likely more strongly interacting than the Brownian picture suggests, more like a liquid and less like a gas.

The work remains theoretical. The next step is comparing its predictions against accelerator experiments. The Office of Nuclear Physics in the U.S. Department of Energy's Office of Science, the U.S. National Science Foundation, and the Simons Foundation supported the research.

A pollen grain in water once revealed the atom; a quark in plasma may now reveal the universe's first moment.