If you’ve ever watched dust-motes dancing in a sunbeam then you’ve observed Brownian motion. It is the jerky, fluttering motion of particles in fluids such as air or water. While the effect was known as least since the ancient Greeks, it is named after the botanist Robert Brown, who in 1827 first described the motion in detail. He demonstrated that it was not caused by some living organism, but was never able to determine its cause. While there were suspicions that the motion was caused by the collision of atoms against the particles, it wasn’t confirmed until Einstein’s 1905 paper “Investigations on the theory of Brownian Movement.”

Although it’s now common knowledge that things are made up of atoms, the idea was long seen as controversial. In the early 1800s John Dalton proposed that matter consists of indestructible spherical particles known as atoms, and that these atoms came in various types called elements. Dalton was mainly trying to address the fact that chemical reactions between different types of materials (elements) seemed to occur in particular ratios. The atomic model explained this process well, but required atoms to be so extraordinarily tiny that we had no hope of observing them. By the late 1800s Ludwig Boltzmann had expanded the idea into a kinetic theory of gases, in which he proposed that the properties of a gas, such as its temperature and pressure, were due to the the motion and interactions of atoms and molecules. This provided a theoretical way to connect heat (thermodynamics) with the Newtonian ideas of work and energy.

The diffusion of food coloring in water. Credit: Wikipedia

Throughout the 1800s, scientists were divided between “atomists” such as Dalton and Boltzmann, and their opponents such as Ernst Mach. At the heart of the debate was the fact that atoms couldn’t be measured. You could speculate about their existence all you wanted, but the atomic hypothesis was untestable. Which brings us to Einstein’s paper on brownian motion. Einstein wasn’t the first to propose atomic collisions as a solution to brownian motion, but what made his paper so powerful was that it connected physical properties of atoms to something we could actually measure. His paper focuses on a property of fluids known as diffusion. If you put drops of food coloring in water, it will spread out over time. This is due to the fact that the coloring is bouncing around with the water molecules. Since the molecule collisions are random, the coloring will move with a pattern known as a random walk. You can think of it as taking a step, then turning in a random direction and taking another. On average the position of the coloring will stay the same, but by chance some will drift outward. Thus, over time the coloring diffuses.

What Einstein showed was that the diffusion of an object undergoing Brownian motion will diffuse at a particular rate (known as the mean squared displacement), and that this rate depended upon the number of atoms or molecules in a mole of the fluid in which the object is suspended (Avogadro’s number). From this one could determine the size of molecules or atoms. For the first time, a measurable quantity allowed us to probe the atomic realm. It wasn’t just the idea, but rather the precision of Einstein’s results that many scientists found so convincing.

Einstein’s work settled a dispute that had raged for nearly a century, and it placed kinetic theory on an experimental foundation. From this work, Newtonian physics, chemistry, and thermodynamics were connected.

Tomorrow: Not content with bringing together three separate areas of science, Einstein takes on the the bizarre realm of the quantum with the photoelectric effect.

Paper: Einstein, Albert. Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Annalen der Physik 17 (8): 549–560 (1905)

The post Shake, Rattle and Roll appeared first on One Universe at a Time.

If you’ve ever watched dust-motes dancing in a sunbeam then you’ve observed Brownian motion. It is the jerky, fluttering motion of particles in fluids such as air or water. The botanist Robert Brown first described the motion in detail. He demonstrated that it was not caused by some living organism, but was never able to determine its cause. That answer came from Albert Einstein, who proved that Brownian motion was due to molecules of the fluid colliding with the Brownian particle.  Brownian motion was definitive proof of the atomic theory of matter. Even though we couldn’t (at that time) see the atoms which make up matter, we could see the effect of their existence.

What does all this have to do with black holes? Well it turns out black holes also undergo Brownian motion, and astronomers can use that fact to their advantage.

Brownian motion animation. Source: Wikimedia

Within most galaxies is a supermassive black hole. These typically have a mass a hundred thousand to a billion times larger than our sun. They reside in the center of the galaxy, surrounded by a dense cluster of stars. Just as a dust-mote is knocked about by the tiny atoms surrounding it, the black hole is knocked about by the (relatively) tiny stars surrounding it. Obviously we can’t observe this motion in real time, but its effect is clearly measurable.

There is an important difference between dust-motes and black holes. For traditional Brownian motion, the atoms move very much like billiard balls. An atom moves freely through space until it collides with the dust-mote, the collision happens very quickly, and then the atom moves freely again. But stars surrounding a black hole do not interact like billiard balls. For stars and black holes, the interaction varies depending on how close a star is to the black hole. This means that while the billiard-ball type model for Brownian motion can’t be used to model stars and black holes, you also have to take into account how the black hole’s gravity affects the distribution of stars in the first place.

Typically, the Brownian motion of a black hole has been modeled by starting with a galaxy of stars in an equilibrium state, then adding the black hole to the model to see what happens. But fellow RIT faculty David Merritt and his team modeled a galaxy of stars in equilibrium with the central black hole from the beginning. What they were able to show was that this new approach makes a significant difference in your predicted outcomes. Essentially, the presence of the black hole means that closer stars have more kinetic energy on average than more distant stars, and these closer stars in turn create most of the Brownian motion of the black hole.

The reason this matters is that Brownian motion can be used to determine the mass of the black hole in the center of our Milky Way galaxy. Measure the distribution of stellar speeds near the center of our galaxy and you can determine the mass of the central black hole. Merritt and co. determined the mass of our galactic black hole to be about 1.2 million solar masses. Pretty big, but smaller than older measurements which gave a value of about 3 million solar masses.

All this from treating a huge black hole as a cosmic speck of dust.

The post Black Holes, Brownian Motion appeared first on One Universe at a Time.