In the sixth section of his light quantum paper of 1905, Einstein presented the miraculous argument, as I shall call it. Pointing out an analogy with ideal gases and dilute solutions, he showed that the macroscopic, thermodynamic properties of high-frequency heat radiation carry a distinctive signature of finitely many, spatially localized, independent components and so inferred that it consists of quanta. I describe how Einstein's other statistical papers of 1905 had already developed and exploited the idea that the ideal gas (...) law is another macroscopic signature of finitely many, spatially localized, independent components and that these papers in turn drew on his first two, "worthless" papers of 1901 and 1902 on intermolecular forces. However, while the ideal gas law was a secure signature of independence, it was harder to use as an indicator that there are finitely many components and that they are spatially localized. Further, since his analysis of the ideal gas law depended on the assumption that the number of components was fixed, its use was precluded for heat radiation, whose component quanta vary in number in most processes. So Einstein needed and found another, more powerful signature of discreteness applicable to heat radiation and which indicated all these properties. It used one of the few processes, volume fluctuation, in which heat radiation does not alter the number of quanta. © 2005 Elsevier Ltd. All rights reserved. (shrink)

This is the second installment of a two-part paper on developments in quantum dispersion theory leading up to Heisenberg’s Umdeutung paper. In telling this story, we have taken a 1924 paper by John H. Van Vleck in The Physical Review as our main guide. In this second part we present the detailed derivations on which our narrative in the first part rests. The central result that we derive is the Kramers dispersion formula, which played a key role in the thinking (...) that led to Heisenberg’s Umdeutung paper. We derive classical formulae for the dispersion, emission, and absorption of radiation and use Bohr’s correspondence principle to construct their quantum counterparts both for the special case of a charged harmonic oscillator (Sect. 5) and for arbitrary non-degenerate multiply-periodic systems (Sect. 6). We then rederive these results in modern quantum mechanics (Sect. 7). (shrink)

In the sixth section of his light quantum paper of 1905, Einstein presented the miraculous argument, as I shall call it. Pointing out an analogy with ideal gases and dilute solutions, he showed that the macroscopic, thermodynamic properties of high frequency heat radiation carry a distinctive signature of finitely many, spatially localized, independent components and so inferred that it consists of quanta. I describe how Einstein’s other statistical papers of 1905 had already developed and exploited the idea that the ideal (...) gas law is another macroscopic signature of finitely many, spatially localized, independent components and that these papers in turn drew on his first two, “worthless” papers of 1901 and 1902 on intermolecular forces. However, while the ideal gas law was a secure signature of independence, it was harder to use as an indicator that there are finitely many components and that they are spatially localized. Further, since his analysis of the ideal gas law depended on the assumption that the number of components was fixed, its use was precluded for heat radiation, whose component quanta vary in number in most processes. So Einstein needed and found another, more powerful signature of discreteness applicable to heat radiation and which indicated all these properties. It used one of the few processes, volume fluctuation, in which heat radiation does not alter the number of quanta. (shrink)

The year 1905 has been called Einstein's annus mirabilis in virtue of three ground-breaking works completed over the span of a few months --- the light quantum paper (Einstein, 1905a), the Brownian motion paper (Einstein, 1905c), and the paper on the electrodynamics of moving bodies introducing the special theory of relativity (Einstein, 1905d). There are prima facie reasons for thinking that the origins of these papers cannot be understood in isolation from one another. Due to space limitations, we concentrate primarily (...) on the light quantum paper, since, in key respects, it marks the turning point for the annus mirabilis. The task is to probe, not just how the idea of the light quantum might have occurred to Einstein, but, more importantly, what convinced him that the idea was not just a quixotic hypothesis, but an unavoidable and demonstrable feature of radiation. The crucial development, we suggest, arose from comparing the energy fluctuations that following rigorously from the Stefan-Boltmann law, as well as from Wien's distribution formula for blackbody radiation, with what it is reasonable to expect from Maxwell's electromagnetic theory of light. A special case of this is addressed in (Einstein, 1904). The outcome for the general case leads naturally to the central theoretical argument of the light quantum paper, the expectation of Brownian-like motion, and several of the key results for the electrodynamics of moving bodies. (shrink)

(1980). The development of attitudes to the wave-particle duality of light and quantum theory, 1900–1920. Annals of Science: Vol. 37, No. 1, pp. 59-79.

Our object in this paper is to study the antecedents, contents, implications, and impact of a not well-known or appreciated paper by EHRENFEST in 1911 on the essential nature of the different quantum hypotheses in radiation theory. After a careful analysis of EHRENFEST’s notebooks, correspondence, and publications, we conclude that the essential points of EHRENFEST’s paper were not perceived to a large extent, and hence that its implications were not considered thoroughly. Specifically, we show that EHRENFEST contributed significantly to the (...) clarifications of the differences between PLANCK’s and EINSTEIN’s respective quantum hypotheses, as well as to those of the concepts ‘‘discontinuity,’’ ‘‘quantization,’’ and ‘‘corpuscularity.’’. (shrink)

Any advanced theory of physics contains modules defined as essential components that are themselves theories with different domains of application. Different kinds of modules can be distinguished according to the way in which they fit in the symbolic and interpretive apparatus of a theory. The number and kind of the modules of a given theory vary as the theory evolves in time. The relative stability of modules and the variability of their insertion in other theories play a vital role in (...) the application, comparison, construction, and communication of theories. Modularity conveys some global unity to physics through the sharing of modules by diverse theories. This alternative to rigid hierarchies and holistic totalities permits a dynamical, plastic, and symbiotic approach to physical theory. (shrink)