Physics
Boltzmann's most important scientific contributions were in kinetic theory, including the Maxwell–Boltzmann distribution for molecular speeds in a gas. In addition, Maxwell–Boltzmann statistics and the Boltzmann distribution over energies remain the foundations of classical statistical mechanics. They are applicable to the many phenomena that do not require quantum statistics and provide a remarkable insight into the meaning of temperature.
Much of the physics establishment did not share his belief in the reality of atoms and molecules — a belief shared, however, by Maxwell in Scotland and Gibbs in the United States; and 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 and molecules as anything other than convenient theoretical constructs. Only a couple of years after Boltzmann's death, Perrin's studies of colloidal suspensions (1908–1909), based on Einstein's theoretical studies of 1905, confirmed the values of Avogadro's number and Boltzmann's constant, and convinced the world that the tiny particles really exist.
To quote Planck, "The logarithmic connection between entropy and probability was first stated by L. Boltzmann in his kinetic theory of gases". This famous formula for entropy S is
where k = 1.3806505(24) × 10−23 J K−1 is Boltzmann's constant, and the logarithm is taken to the natural base e. W is the Wahrscheinlichkeit, the frequency of occurrence of a macrostate or, more precisely, the number of possible microstates corresponding to the macroscopic state of a system — number of (unobservable) "ways" in the (observable) thermodynamic state of a system can be realized by assigning different positions and momenta to the various molecules. Boltzmann’s paradigm was an ideal gas of N identical particles, of which Ni are in the ith microscopic condition (range) of position and momentum. W can be counted using the formula for permutations
where i ranges over all possible molecular conditions. ( denotes factorial.) The "correction" in the denominator is because identical particles in the same condition are indistinguishable.
Boltzmann was also one of the founders of quantum mechanics due to his suggestion in 1877 that the energy levels of a physical system could be discrete.
The equation for S is engraved on Boltzmann's tombstone at the Vienna Zentralfriedhof — his second grave.
Read more about this topic: Ludwig Boltzmann
Famous quotes containing the word physics:
“The fundamental laws of physics do not describe true facts about reality. Rendered as descriptions of facts, they are false; amended to be true, they lose their explanatory force.”
—Nancy Cartwright (b. 1945)
“Now the twitching stops. Now you are still. We are through with physiology and theology, physics begins.”
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“He who is conversant with the supernal powers will not worship these inferior deities of the wind, waves, tide, and sunshine. But we would not disparage the importance of such calculations as we have described. They are truths in physics because they are true in ethics.”
—Henry David Thoreau (1817–1862)