By Olivier Darrigol

The background of quantum concept is a maze of conceptual difficulties, by which Olivier Darrigol presents a lucid and discovered advisor, monitoring the position of formal analogies among classical and quantum conception. From Planck's first creation of the quantum of motion to Dirac's formula of quantum mechanics, Darrigol illuminates not just the background of quantum idea but additionally the function of analogies in clinical pondering and idea swap. in contrast to past works, that have tended to target qualitative, worldwide arguments, Darrigol's examine follows the strains of mathematical reasoning and symbolizing and so is ready to convey the motivations of early quantum theorists extra preciselyand provocativelythan ever ahead of. Erudite and unique, From c- Numbers to q-Numbers units a brand new average as a philosophically perceptive and mathematically particular background of quantum mechanics. For future years it's going to impression old and philosophical discussions of twentieth-century physics.

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**Extra info for From c-Numbers to q-Numbers: The Classical Analogy in the History of Quantum Theory (California Studies in the History of Science)**

**Sample text**

In the gas case the Boltzmann equation provided by itself the equilibrium distribution, and the method of complexions gave hardly more than "an illustration of the mathematical meaning of the quantity H" of the H -theorem, as Boltzmann wrote in his Gastheorie . [80] This is why Planck decided to turn to the combinatorial method. However, he consistently rejected the probabilistic context of Boltzmann's original considerations. One could well call a certain mathematical function of the state of a system a "probability" without having to consider the increase of this function in time as a matter of probability.

Yet, F2 is not zero, because the gradient of Be contributes a term of the same order (in ) as F1 . This term is Because of the rotational invariance of d S × E, only the part contributes to this integral. Taking into account Maxwell's equation an elementary calculation then yields Equating the two expressions (44) and (45) of F now gives of , ― 35 ― or In the latter equation one can consider the time to be the only variable since, according to (39), f (t — r/c ) can be replaced with f (t ) whenever .

Planck nevertheless studied Maxwell's kinetic theory, if only as a part of his duties as editor of Kirchhoff's lectures on thermodynamics, which included this topic. The resulting book, published in 1894, contained an unfortunate mistake in the proof of Maxwell's distribution law, which stirred a short but instructive polemic with Boltzmann. Planck proposed a better proof and in the process became acquainted with, though not convinced by, Boltzmann's idea of molecular chaos. On this occasion he might also have felt the need of an alternative microscopic foundation of thermodynamics.