## Quantentheorie des einatomigen idealen Gases [Quantum Theory of the Monatomic Ideal Gas]

FIRST EDITION IN ORIGINAL WRAPPERS OF THE FIRST PART OF ONE OF EINSTEIN’S GREAT CONTRIBUTIONS TO QUANTUM MECHANICS: THE DEVELOPMENT OF BOSE’S INSIGHTS TO CREATE “BOSE-EINSTEIN STATISTICS” AND “BOSE-EINSTEIN CONDENSATION”.

“Einstein made his own contribution [to quantum theory] when he received in June of that year [1924] a paper in English from a young physicist from India named Satyendra Nath Bose. It derived Planck’s blackbody radiation law by treating radiation as if it were a cloud of gas and then applying a statistical method of analyzing it. But there was a twist: Bose said that any two photons that had the same energy state were absolutely indistinguishable, in theory as well as fact, and should not be treated separately in the statistical calculations.

“Bose’s creative use of statistical analysis was reminiscent of Einstein’s youthful enthusiasm for that approach. He not only got Bose’s paper published, he also extended it with three papers of his own. In them, he applied Bose’s counting method, later called ‘Bose-Einstein statistics,’ to actual gas molecules, thus becoming the primary inventory of quantum-statistical mechanics.

“Bose’s paper dealt with photons, which have no mass. Einstein extended the idea by treating quantum particles *with mass* as being indistinguishable from one another for statistical purposes in certain cases...

“The key insight, which Einstein extracted from Bose’s initial paper, has to do with how you calculate the probabilities for each state of multiple quantum particles... When he applied [his] approach to a gas of quantum particles, Einstein discovered an amazing property: unlike a gas of classical particles, which will remain a gas unless the particles attract one another, a gas of quantum particles can condense into some kind of liquid even without a force of attraction between them.

“This phenomenon, now called Bose-Einstein condensation, was a brilliant and important discovery in quantum mechanics, and Einstein deserves most of the credit for it. Bose had not quite realized that the statistical mathematics he used represented a fundamentally new approach. As with the case of Planck’s constant, Einstein recognized the physical reality, and the significance, of a contrivance that someone else had devised” (Isaacson, pp. 327-329).

*Particle Physics, One Hundred Years of Discoveries*: “Extension of the Bose method to the monoatomic gases. Prediction of Bose-Einstein condensation effect.”

*Note*: Although in this paper Einstein provides the approach for the discovery of the condensation effect, he addresses it more explicitly in the later parts of the paper published in 1925.

IN: Sitzungsberichte der Preussischen Akademie der Wissenschaften, Vol XVIII-XXV. pp. 261-267. Berlin: Akademie der Wissenschaften, 1924. Quarto, original wrappers [the complete issue]; custom box. A little fading around wrapper edges, otherwise fine. Rare in original wrappers.

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