Ludwig Boltzmann

"Boltzmann’s Lectures on Gas Theory is an acknowledged masterpiece of theoretical physics... still... [of] considerable scientific value today. It contains a comprehensive exposition of the kinetic theory of gases by a scientist who devoted a large pail of his own career to it, and brought it very nearly to completion as a fundamental part of modern physics. ...Ludwig Boltzmann ...played a leading role in the nineteenth-century movement toward reducing the phenomena of heat, light, electricity, and magnetism to "matter and motion"—in other words, to atomic models based on Newtonian mechanics. His own greatest contribution was to show how... mechanics... previously ...regarded as deterministic and reversible in time, could be used to describe irreversible phenomena in the real world on a statistical basis. His original papers on the statistical interpretation of thermodynamics, the H-theorem, transport theory, , the of gases... occupy about 2,000 pages... [N]ot even the handful of experts on kinetic theory could claim to have read everything he wrote. ...Boltzmann decided to publish his lectures, in which the most important parts of the theory, including his ...contributions, were carefully explained. ...[H]e included his mature reflections and speculations on such questions as the nature of irreversibility and the justification for using statistical methods in physics. His Vorlesungen über Gastheorie was... the standard reference... for advanced researchers, ...[and] a popular textbook ...for the first quarter of the [20th] century ..."

"The influence of Quetelet's ideas spread throughout the sciences, even to the physical sciences. The two primary founders of the modern kinetic theory of gases, based on considerations of probability, were James Clerk Maxwell and Ludwig Boltzmann. Both acknowledged their debt to Quetelet. ...historians generally consider the influence of the natural sciences on the social sciences, whereas in the case of Maxwell and Boltzmann, there is an influence of the social sciences on the natural sciences, as Theodore Porter has shown."

"Ludwig Boltzmann, who spent much of his life studying statistical mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study statistical mechanics. Perhaps it will be wise to approach the subject cautiously."

"Boltzmann summarized most (but not all) of his work in a two volume treatise Vorlesungen Uber Gastheorie [1896, 1898]. This is one of the greatest books in the history of exact sciences and the reader is strongly advised to consult it. It is tough going but the rewards are great."

"In 1902 he returned to his chair in theoretical physics... In addition to... mathematical physics, Boltzmann was given Mach's philosophy course to teach. His philosophy lectures quickly became famous with the audience... too large for the biggest lecture hall available. ...Boltzmann's fame is based on his invention of statistical mechanics... independently of Willard Gibbs. Their theories connected the properties and behaviour of atoms and molecules with... [those of] the substances of which they were the building blocks. ...Boltzmann obtained the in 1871 ...In 1884 ...Boltzmann ...showed how Josef Stefan's empirical T4 law for black body radiation ...could be derived from the principles of thermodynamics. ...[T]he Second Law of Thermodynamics...he derived from the principles of mechanics in the 1890s."

"In 1895, at a scientific meeting... presented a paper... which... stated... The actual irreversibility of natural phenomena thus proves the existence of processes that cannot be described by mechanical equations, and with this the verdict on scientific materialism is settled. Sommerfeld... described the resulting battle between Ostwald and Boltzmann. ...Boltzmann was seconded by Felix Klein. The battle resembled the... bull with the supple fighter. However... the bull was victorious... Boltzmann carried the day. We, the young mathematicians of the time, were all on the side of Boltzmann... Boltzmann's ideas ...were opposed by many European scientists... not fully grasping the statistical nature of his reasoning."

"Maxwell... during the 1860s... showed that when the [molecular] velocities reached the bell-shaped distribution, no further net change was likely. (...Ludwig Boltzmann further elaborated... and strengthened Maxwell's results). Any specific molecule would speed up or slow down, but... other molecules would change in speed to compensate. When a gas reached that state... the gas was at equilibrium. ...[T]his notion of equilibrium is precisely analogous to the Nash equilibrium in game theory. ...[J]ust as the Nash equilibrium is typically a mixed set of strategies, a gas seeks an equilibrium state with a mixed distribution of molecular velocities."

"Maxwell, and then Boltzmann, and then... J. Willard Gibbs consequently expended enormous intellectual effort in devising... , or... . The uses... extend far beyond gases... describing electric and magnetic interactions, chemical reactions, phase transitions... and all other manner of exchanges of matter and energy. The success... has driven the belief among many physicists that it could be applied with similar success to society. ...[E]verything from the flow of funds in the stock market to the flow of traffic on interstate highways ..."

"Boltzmann... felt that all that we were really doing when we stated physical laws was using a series of linguistic representations of reality. To relate force and mass, as Newton had done in his laws of motion, was to relate labels in such a way that we could use the relations for predictive purposes. To read anything more into the terms force and mass was to presume more than we can know."

"Boltzmann was a martyr to his ideas."

"Boltzmann stands as a link between... James Clerk Maxwell... and Albert Einstein... Maxwell... first found the formula for the probability distribution of velocities of particles in a gas in equilibrium... but... Boltzmann... derived the equation governing the dynamical evolution of the probability distribution, according to which the state of a gas, not necessarily in equilibrium, will... change. Boltzmann's ideas were central to... Planck's... analysis of black body radiation... in which he introduced the quantum of action, thereby... the quantum revolution. In 1905 Einstein... developed it further (...showing that the "atomic hypothesis" applied even to light ..!) but was also influenced by Boltzmann's concepts in two... papers of 1905, one... a method of determining molecular dimensions and the other... explained... ... Both gave enormous support to the "atomic hypothesis"..."

"Die Möglichkeit einer mechanischen Erklärung der ganzen Natur ist nicht bewiesen, ja, dass wir dieses Ziel vollkommen erreichen werden, kaum denkbar."