Ludwig Boltzmann

Austrian physicist

• Born: February 20, 1844; Vienna, Austria
• Died: October 5, 1906; Duino, Austria (now Italy)

Austrian physicist Ludwig Boltzmann is best remembered for inventing the field of physics now known as statistical mechanics. Boltzmann’s discoveries in thermodynamics and electromagnetism were important contributions to the later development of quantum mechanics. He was particularly interested in the relationship between heat and entropy (a concept that he helped to define) and of particles in gases.

Primary field: Physics

Specialties: Statistical mechanics; kinetics; thermodynamics

Early Life

Ludwig Eduard Boltzmann was born on February 20, 1844 in Vienna, Austria. His father, who worked as a tax official, moved the family out of Vienna shortly after the birth of his son. Boltzmann went to high school in the city of Linz and developed an aptitude for science. He was particularly drawn to the study of botany and butterflies. In 1863, he returned to Vienna to attend university, where he concentrated in physics and mathematics. At the University of Vienna, Boltzmann found a mentor in Josef Stefan, a professor of physics who encouraged his interest in progressive scientific theories.

Life’s Work

Having received his doctorate in 1866, Boltzmann embarked on a career that would be marked by frequent life-changes. He spent a few years serving as an assistant to his old teacher Stefan, after which he was offered a full professorship at the University of Graz. After four years, he returned to the University of Vienna to become the chair of the mathematics department in 1873. Three years later, he found himself in Graz once again, where he lectured in experimental physics instead of theoretical physics.

Boltzmann also spent time in Heidelberg, where he studied under German chemist and physicist Robert Bunsen, for whom the Bunsen burner is named. In Berlin, he worked with Gustav Kirchhoff, an expert on electricity and radiation. In fact, in 1888 Boltzmann accepted an offer to take Kirchhoff’s place at the university there, only to change his mind and move to the University of Munich. He returned to Vienna by the end of the century.

In the first half of the twentieth century, the study of physics began to undergo some very dramatic changes. One of the ways in which physics was starting to change involved a paradigm shift from “deterministic” thinking to what we call “probabilistic” thinking. For scientists, the shift from deterministic to probabilistic analysis meant letting go of the idea that the universe behaves in a rational, ordered fashion, and that people can determine everything about its behavior with certainty.

A physicist using probabilistic analysis has to admit that in some ways the universe behaves in a random, unpredictable fashion, and that people can only talk about the probability, or chance, that something will happen one way or another. In the late nineteenth and early twentieth century, Boltzmann was a pioneer of this kind of analysis, specifically as it related to thermodynamics.

In 1877, Boltzmann wrote what would become the most famous paper of his career. It consisted of a new interpretation of the second law of thermodynamics, a topic that he had been working on for several years. The word thermodynamics comes from two Greek words meaning “heat” and “power,” and it refers to the relationship between the temperature of a system and the amount of mechanical energy it can produce. Scientists knew that heat energy could be converted into mechanical energy and that mechanical energy could be converted into heat. But at the time there were still many questions to answer about the details of this process. The first law of thermodynamics states that energy can never be created or destroyed, only transformed from one form into another. The second law of thermodynamics, which was first formulated by Rudolf Clausius in 1850, can be stated in several different ways. One way is to say that heat energy always moves from a hotter place to a colder one. Another, more complex way is to say that the entropy of a closed system will always increase and never decrease.

It was this second statement that Boltzmann wanted to explore. What is this strange quantity in the mathematics of the second law that we call entropy? And what does it mean for it to be always increasing? Since Boltzmann was an atomist, he thought about these questions in terms of atoms and molecules; specifically, he thought about the atoms and molecules that make up a gas.

Boltzmann’s breakthrough was realizing that in order to understand the second law of thermodynamics, one had to pay attention to the total number of different ways the particles in a gas could be arranged. Then, he gave “entropy” a precise mathematical definition, as well as an intuitive explanation. Boltzmann said that entropy was essentially the same thing as disorder. In other words, if all the atoms and molecules in a container of gas were arranged neatly along one side, the system would be very ordered, and its entropy would be low. But if all the gas particles were randomly distributed within the whole space, the system would be chaotic, and its entropy would be high.

Because there are so few possible “ordered” arrangements compared to “disordered” arrangements, any closed system always moves toward being in a disordered state. Imagine asking a class full of children to line up against a wall. It is possible that they will end up standing in order of height, or weight, or age. But it is very much more likely that they will end up standing in some other, completely random, order.

Boltzmann realized that he could not use mechanical theory to explain the second law, not only because entropy typically increased, but because the energy reversion process was too lengthy for him to measure practically. Instead, he turned to probability theory. Though Boltzmann elucidated his evolving understanding of thermodynamics in hundreds of articles and papers, he did not produce a concise, unified explanation of the second law.

Boltzmann described himself as a restless, moody person whose emotions were as unpredictable as his changes of address. This agitated internal landscape, combined with a certain amount of criticism he received regarding his work on the second law of thermodynamics, ultimately contributed to his downfall. On October 5 1906, he died by suicide while on holiday with his wife and children. His contributions to physics and the correctness of his theories have since been widely acknowledged.

Impact

Boltzmann’s work provided a link between nineteenth-century physics and later physics, helping shape the scientific world of the twentieth and twenty-first centuries. His theories and mathematical models were so advanced for his time that some of them, such as his equation for predicting the motion of gas molecules, have only recently been proven. Boltzmann furthered the work of nineteenth-century theoretical physicist James Clerk Maxwell, who wrote a formula for the probability distribution of the velocity of gas particles in equilibrium. Boltzmann’s work also influenced Max Planck’s quantum theory, as well as German physicist Albert Einstein’s method for calculating the dimensions of molecules and his work on Brownian motion.

Bibliography

Aron, Jacob. “Proof at Last for Boltzmann’s 140-Year-Old Gas Equation.” New Scientist 206.2761 (2010): 14. Print. Discusses how Boltzmann’s equation for predicting the motion of gas molecules was finally proven by twenty-first-century mathematicians.

Boltzmann, Ludwig, and Bertram Schwarzschild, trans. “A German Professor’s Trip to El Dorado.” Physics Today 45.1 (1992): 44. Print. Presents an abridged and translated version of Boltzmann’s humorous essay about his 1905 travels in California.

Broda, Engelbert. Ludwig Boltzmann: Man, Physicist, Philosopher. Trans. Larry Gay and Engelbert Broda. Woodbridge, CT: Ox Bow, 1983. Print. Discusses Boltzmann’s achievements, analyzes his contributions, and comments on his philosophy.

Cercignani, Carlo. Ludwig Boltzmann: The Man Who Trusted Atoms. Oxford: Oxford UP, 1998, 2006. Print. Examines Boltzmann’s life and death, his work, and his influence on twenty-first-century physics.