20 May 2010

Einstein was wrong: Brownian speed can be measured

By
Cosmos Online
Over a century ago, Albert Einstein predicted that the random motion of tiny particles depended only on temperature, and not their size or mass. He also doubted that scientists would ever be able to prove this experimentally.
Brownian motion

Random trajectory for a micrometre-sized ellipsoid experiencing Brownian motion in water over a 20-second period. Credit: University of Pennsylvania

SYDNEY: Over a century ago, Albert Einstein predicted that the random motion of tiny particles depended only on temperature, and not their size or mass. He also doubted that scientists would ever be able to prove this experimentally.

Now, for the first time, a team of physicists at the University of Texas at Austin has measured the instantaneous velocity of particles as they move randomly in Brownian motion.

Named after the Scottish botanist Robert Brown, Brownian motion is the seemingly random movement of particles suspended in a fluid, or the mathematical model used to describe such random movements, often called a particle theory.

Out of reach

“There has been a lot of work on different aspects of Brownian motion, but the instantaneous velocity was generally considered to be out of reach,” said Mark Raizen, one of the authors of the study that appears in the U.S. journal Science.

In 1907, Einstein predicted that Brownian particles should obey the ‘equipartition theorem’, meaning that their kinetic energies are dependent solely upon temperature.

The great physicist, founder of the Theory of Relativity, felt that the time scale required to test this hypothesis was too short for experimentation.

Proven wrong

Raizen and colleagues have proven him wrong. They obtained their velocity measurements by suspending a silicon bead 3 microns in diameter in an ‘optical tweezer’.

They then created a trap with two laser beams and measured the bead’s movement as it drifted away from the centre.

The researchers are working toward studying the particle in a vacuum after cooling it into the quantum ground state, a low-energy system isolated from the environment.

But starting out with the bead in air, said Raizen, they realised they had a method of measuring the instantaneous velocity and achieving what Einstein deemed impossible.

Direct verification

“Our results provide direct verification of the energy equipartition theorem for a Brownian particle,” they wrote in the paper.

The authors said that this is an important step toward observing particles in the quantum state, where they expect the equipartition theorem will break down. “This will require more development, but appears within reach,” said Raizen.

Once in a quantum ground state, Brownian motion will cease, and physicists can test quantum theories for small particles. Additionally, an oscillating particle in this state could be used as a sensor for small forces, he said.

Wider implications

Phil Attard, a physicist at the University of Sydney, sees implications for this work outside of the quantum realm. “The present paper in Science for the first time bridges the gap between the instantaneous velocity and the long-time velocity [of Brownian particles] and is able to measure both,” he said.

In order for the equipartition theorem to work, Einstein had to distinguish the instantaneous from longer-term behaviour, when surrounding molecules affect the particle in question.

“The real significance of the paper, I believe, is not so much the verification of the equipartition theorem at short times, which no one seriously doubts,” said Attard.

Rather, he sees the potential to verify experimentally the probability distribution of Brownian particles over longer time scales.

About 100 years after Einstein worked out the principles of equipartition, scientists are only now starting to verify distributions more generally over time, said Attard.

Mathematics behind Brownian motion

The first person to describe the mathematics behind Brownian motion was Thorvald Thiele in 1880, followed independently by Louis Bachelier in 1900 in his thesis “The theory of speculation”, in which he presented a stochastic analysis of the stock and option markets.

However, it was Albert Einstein in his 1905 paper who brought the solution of the problem to the attention of physicists, and presented it as a way to indirectly confirm the existence of atoms and molecules.

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