Ludwig Eduard Boltzmann (1844-1906) Austrian Physicist who made many major contributions to statistical mechanics & thermodynamics. A Genius!! 1863-1866: Studied physics at the U. of Vienna. 1866: Received the PhD. Supervised by Josef Stefan. Thesis: Kinetic Theory of Gases. 1867: Became a Privatdozent (lecturer). Worked 2 years as Stefan’s assistant. Stefan introduced him to Maxwell's work on thermodynamics. Boltzmann as a young man

Ludwig Eduard Boltzmann (1844-1906) 1869: Age 25 (!), appointed Professor of Mathematical Physics at the U. of Graz, Austria. 1871: Worked in Berlin with Gustav Kirchhoff & Hermann von Helmholtz 1873: Joined U. of Vienna as Professor of Mathematics. Stayed until 1876. Boltzmann as a young man

Chair of Experimental Physics 1872: Long before women were admitted to Austrian universities, Boltzmann met Henriette von Aigentler, a mathematics & physics teacher. She was refused permission to unofficially audit lectures. Boltzmann advised her to appeal; she did, Successfully! July 17, 1876: Married Henriette von Aigentler; they had 3 daughters & 2 sons. 1876: Went to Graz again to be Chair of Experimental Physics Boltzmann in middle age

Chair of Experimental Physics President of the University of Graz!! 1876: At the U. of Graz as Chair of Experimental Physics Spent 14 years in Graz , where he developed his statistical concept of nature. 1885: Became a member of the Imperial Austrian Academy of Sciences. 1887: Became President of the University of Graz!! Boltzmann in middle age

Chair of Theoretical Physics Professor of Theoretical 1890: Was appointed Chair of Theoretical Physics at U. of Munich, Bavaria, Germany. 1893: At U. of Vienna, succeeded his teacher Stefan as Professor of Theoretical Physics Didn’t get along with some colleagues in Vienna, particularly Ernst Mach, professor of philosophy & history of sciences in 1895. Boltzmann in late middle age

Conflict With Mach (Summary) More Philosophy than Physics! Mach’s View: “Positivism”: Science should be based only on observable facts The pressure exerted by a gas on the walls of its container is an acceptable fact. “Explaining” that pressure in terms of invisible particles (atoms, molecules) is unacceptable, since the particles cannot be seen” Heat is also a primary phenomenon. “Explaining it in terms of the motion of unseen particles is unacceptable” For Mach, science is more description than understanding: For gases, study the relation between T & P, e.g. how does P change as T is increased? Then make a catalog of the results.

e.g. about how P changes if T is increased Boltzmann’s View Truth in science need not be seen directly, but is what can be consistently inferred from observations Even though we cannot see atoms directly, the atomic hypothesis makes predictions, e.g. about how P changes if T is increased If those predictions are confirmed by experiment, it provides support to the atomic hypothesis. If many predictions that follow from the atomic hypothesis are confirmed, we may believe in the existence of atoms In effect, we “see” atoms by their effects. This is the modern attitude Plus, today we can “see” atoms directly!

Boltzmann & Philosophy After Mach retired, Boltzmann returned to Vienna & was given Mach’s philosophy course to teach! These lectures became famous, in part for their strong, even personal attacks on various philosophies and philosophers! As an example: The actual proposed title of one of his lectures! “Proof that Schopenhauer is a stupid, ignorant philosophaster, scribbling nonsense and dispensing hollow verbiage that fundamentally and forever rots people’s brains”

1902: Back to Vienna after the retirement of Mach due to bad health. 1900: Moved U. of Leipzig. 1902: Back to Vienna after the retirement of Mach due to bad health. His students there included Paul Ehrenfest & Lise Meitner, both later Nobel Prize winners. Boltzmann in late middle age

the Austrian Emperor invited him for a reception at the Palace!! In Vienna, he became an important advocate for atomic theory when it was still highly controversial. He taught both physics & philosophy! His philosophy lectures were very popular! 1st one was a huge success!! It was in the largest lecture hall, but people still stood all the way down the stairs!! Boltzmann a little older Because of the great successes of his philosophy lectures, the Austrian Emperor invited him for a reception at the Palace!!

September 5, 1906: He committed suicide Boltzmann Was subject to rapid alternation of depressed moods with elevated, expansive or irritable moods. He likely had what today we call bipolar disorder. Meitner & others related that those who were close to him were aware of his severe depression & his suicide attempts. September 5, 1906: He committed suicide Boltzmann as an older man

The Atomic Model of Matter Boltzmann September 5, 1906: He committed suicide This happened during an attack of depression, while on a summer vacation with his family in Duino, near Trieste, Italy. Speculation is that this was because of vicious attacks he was receiving from the physics community for his advocating Kinetic Theory & The Atomic Model of Matter Boltzmann as an older man

Boltzmann’s most important scientific contributions were in kinetic theory. This includes the Maxwell-Boltzmann Distribution for molecular speeds in a gas. Maxwell-Boltzmann Statistics & the Boltzmann Distribution of energies are at the foundations of classical statistical mechanics. They’re applicable many phenomena that don’t require quantum statistics & provide insight into the meaning of temperature. The Boltzmann Transport Equation was the earliest attempt to treat NON-EQULIBRIUM transport. Still useful today!

Boltzmann’s contributions NOTE! Most in the physics establishment in his time rejected his theory of the reality of atoms & molecules! Belief in these was shared, by Maxwell in Scotland & Gibbs in the US; & by most chemists since the discoveries of John Dalton in 1808. He had a long-running dispute with the editor of the preeminent German physics journal of his day, who refused to let Boltzmann refer to atoms & molecules as anything other than “convenient theoretical constructs”.

that atoms & molecules really exist. Boltzmann’s contributions Shortly after Boltzmann's death, Perrin's studies of colloidal suspensions (1908-1909) confirmed the values of Avogadro's number & Boltzmann's constant, & convinced the world that atoms & molecules really exist.

on Boltzmann’s gravestone. The Entropy Equation on Boltzmann’s gravestone. Boltzmann’s gravestone is in the largest cemetery in Vienna. Note the equation for entropy at the top of the stone: S = klogW The more modern notation for entropy is S = kBlnΩ