By Olivier Darrigol

The background of quantum concept is a maze of conceptual difficulties, wherein Olivier Darrigol presents a lucid and realized advisor, monitoring the position of formal analogies among classical and quantum thought. From Planck's first advent of the quantum of motion to Dirac's formula of quantum mechanics, Darrigol illuminates not just the historical past of quantum idea but in addition the position of analogies in clinical considering and conception swap. not like earlier works, that have tended to target qualitative, worldwide arguments, Darrigol's research follows the traces of mathematical reasoning and symbolizing and so is ready to convey the motivations of early quantum theorists extra preciselyand provocativelythan ever prior to. Erudite and unique, From c- Numbers to q-Numbers units a brand new typical as a philosophically perceptive and mathematically certain heritage of quantum mechanics. For future years it is going to impact old and philosophical discussions of twentieth-century physics.

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

**Example text**

The only possible escape from this conclusion, Boltzmann suggested, would be—as he had done in gas theory—to shift to a statistical conception of irreversibility and to introduce a notion of "disordered" radiation that would be the counterpart of molecular chaos. " As a first step toward defining this notion, he introduced the relevant "directly measurable quantities," that is, certain quadratic time-averages, one for the electric moment of the resonator and one for the electric field at the place of the resonator.

The analogy with molecular chaos was transparent enough. In both cases there were two levels of description: the detailed micro-level, which includes uncontrollable features of the model (dynamics of molecular collisions/electrodynamic interaction between resonator and radiation), and the "physical" level of description, which involves only physically meaningful quantities (Maxwell's collision formula/Planck's fundamental equation). In order to deduce the second level of description from the first a special assumption must be made, molecular chaos in one case, natural radiation in the other.

Well aware of these developments, in 1895 Planck proposed that the electromagnetic interaction between matter and radiation could explain both thermodynamic irreversibility and the observed value of the blackbody spectrum. As the archetype of an energy-conserving, irreversible process, he imagined the scattering of a plane electromagnetic wave by a miniature version of a perfect Hertz resonator (small oscillating circuit with neither dissipation nor internal electromotive force). Planck then ― 38 ― proceeded to a quantitative evaluation of this effect.