Einstein’s Miraculous Argument of 1905
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Einstein’s Miraculous Argument of 1905
June 30.2005; rev. July 17.20. 2005Atoms, Entropy, Quanta:Einstein’s Miraculous Argument of 1905John D. NortonDepartment of History and Philosophy of Einstein’s Miraculous Argument of 1905 Science University of PittsburghPittsburgh PA 15260www.pitt.edu/~jdnortonTo appear in Studies ill History and Philosophy of Modern Physics. For related web material see: www.pitt.edu/~jdnorton/GoodiesKeywords: Einstein quanta atoms entropy 1905In the sixth section of his light quantum paper of 1905 Einstein’s Miraculous Argument of 1905. Einstein presented the miraculous argument, as 1 shall call it. Pointing out an analogy with ideal gases and dilute solutions, he showed that the maEinstein’s Miraculous Argument of 1905
croscopic, thermodynamic properties of high frequency heat radiation earn a distinctive signature of finitely many, spatially localized, independent cJune 30.2005; rev. July 17.20. 2005Atoms, Entropy, Quanta:Einstein’s Miraculous Argument of 1905John D. NortonDepartment of History and Philosophy of Einstein’s Miraculous Argument of 1905he 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, w hi 1c the ideal gas law w as a secure signature Einstein’s Miraculous Argument of 1905oflI am grateful to Jos Uffmk for helpful comments on an earlier version of this paper and for penetrating queries that led to the material in SectionEinstein’s Miraculous Argument of 1905
2.2.independence, it was harder to use as an indicator that there arc finitely many components and that they arc spatially localized. Further, since June 30.2005; rev. July 17.20. 2005Atoms, Entropy, Quanta:Einstein’s Miraculous Argument of 1905John D. NortonDepartment of History and Philosophy of Einstein’s Miraculous Argument of 1905component quanta vary in number in most processes. So Einstein needed and found another, more powerful signature of discreteness applicable to hear radiation and which indicated all these properties. It used one of the few processes, volume fluctuation, in which heat radiation does not alter the num Einstein’s Miraculous Argument of 1905ber of quanta.1. IntroductionIn a mildly worded series of papers in the Annalen der Physik of 1905? Einstein established the reality of atoms, announcEinstein’s Miraculous Argument of 1905
ed special relativity and the inertia of energy and proposed the light quantum. These works of his annus niirabilis. his year of miracles, contain manJune 30.2005; rev. July 17.20. 2005Atoms, Entropy, Quanta:Einstein’s Miraculous Argument of 1905John D. NortonDepartment of History and Philosophy of Einstein’s Miraculous Argument of 1905nchronize clocks. From it. Einstein coaxed forth the relativity of simultaneity and. from that, the compatibility of the principle of relativity and the constancy of the speed of light of Maxwell’s electrodynamics. In his (1905c). Einstein imagined a body symmetrically emitting electromagnetic radia Einstein’s Miraculous Argument of 1905tion and. from that simple arrangement, inferred that every unit of energy E carries a mass m according to the formula. E=mc3.Yet nothing in these papEinstein’s Miraculous Argument of 1905
ers quite matches the audacity of the light quantum paper (Einstein. 1905a). the first paper published in the series. Both special relativity and the June 30.2005; rev. July 17.20. 2005Atoms, Entropy, Quanta:Einstein’s Miraculous Argument of 1905John D. NortonDepartment of History and Philosophy of Einstein’s Miraculous Argument of 1905in the perfected electrodynamics and were just awaiting an Einstein to find them. The light quantum paper is quite different. Its basic proposal that light sometimes behaves as if it consisted of independent, spatially localized quanta of energy—stands in direct contradiction with that most perfect Einstein’s Miraculous Argument of 1905product of nineteenth century science. No doubt that is why Einstein chose to single out this paper alone among the works of2Translations of text fromEinstein’s Miraculous Argument of 1905
these papers are from Stachcl (1998).21905 as "ven,- revolutionary” in his famous letter of May 1905 to his friend Conrad Hahicht (Papers, Vol. 5. DoJune 30.2005; rev. July 17.20. 2005Atoms, Entropy, Quanta:Einstein’s Miraculous Argument of 1905John D. NortonDepartment of History and Philosophy of Einstein’s Miraculous Argument of 1905ation, an empirically based expression for the entropy of a volume of high frequency heat radiation. In a few deft inferences he converts this expression into a simple, probabilistic formula whose unavoidable interpretation is that the energy of radiation is spatially localized in finitely many, ind Einstein’s Miraculous Argument of 1905ependent points. We are startled, wondering what happened to the waves of light of the nineteenth century theory and marveling al how Einstein could sEinstein’s Miraculous Argument of 1905
ec the signature of atomic discreteness in the bland formulae of thermodynamics. This inference is Einstein's miraculous argument, as 1 shall call it June 30.2005; rev. July 17.20. 2005Atoms, Entropy, Quanta:Einstein’s Miraculous Argument of 1905John D. NortonDepartment of History and Philosophy of Einstein’s Miraculous Argument of 1905roproperties of heat radiation to its microstructure. The more usual inference proceeds in the opposite direction. We tend to think of the microstructure as something hidden and inaccessible; we must hypothesize or conjecture it and then from that supposition infer empirically testable macroproperti Einstein’s Miraculous Argument of 1905es that no longer bear any obvious imprint of the microstructure. The sense of novelty of Einstein's strategy is heightened by the company his argumenEinstein’s Miraculous Argument of 1905
t keeps. It comes in a paper whose principle theses are without precedent. It is the first paper of the new century that unequivocally argues that claJune 30.2005; rev. July 17.20. 2005Atoms, Entropy, Quanta:Einstein’s Miraculous Argument of 1905John D. NortonDepartment of History and Philosophy of Einstein’s Miraculous Argument of 1905of the foundational results of nineteenth century physics.My purpose in this paper is to describe how Einstein's strategy in this miraculous argument did have an important precedent and one that was integrated into his other work of 1905.* That a thermal system conforms to the ideal gas law is the s Einstein’s Miraculous Argument of 1905ignature of a particular3A casual reader of Planck's papers of 1900. innocent of w hat is to come, would have no real inkling that they arc beginningEinstein’s Miraculous Argument of 1905
to pull the thread dial will unravel classical physics—a fact correctly emphasized by Kuhn < 1978).4Irons (2004) also stresses the connection of EinstJune 30.2005; rev. July 17.20. 2005Atoms, Entropy, Quanta:Einstein’s Miraculous Argument of 1905John D. NortonDepartment of History and Philosophy of Einstein’s Miraculous Argument of 1905f particle like volume fluctuations for radiation. For a general view of Einstein's statistical papers of 1905. sec the editorial headnotes of Slachel Ct al. (1989) and. for recent3microstructure: the system consists of finitely many, spatially localized, independent components. This idea had become Einstein’s Miraculous Argument of 1905 part of the standard repertoire of Einstein’s statistical physics of 1905. His statistical papers of 1905 his doctoral dissertation (1905b) and his BEinstein’s Miraculous Argument of 1905
rownian motion paper (1905c) used it for ideal gases, dilute solutions and suspensions: and the Brownian motion paper contained a quite serviceable deJune 30.2005; rev. July 17.20. 2005Atoms, Entropy, Quanta:Einstein’s Miraculous Argument of 1905John D. NortonDepartment of History and Philosophy of Einstein’s Miraculous Argument of 1905ions of the independence of microscopic components. Eor that was just the simplest case of the problem he had dealt with at length in his first two publications (1901, 1902). There he had sought empirical evidence for a particular law for intermolecular forces in the phenomena of capillarity and ele Einstein’s Miraculous Argument of 1905ctrolysis. Independence is just the simplest case of no intermolecular forces. One theoretical device, introduced casually into the work of 1905. hadEinstein’s Miraculous Argument of 1905
been developed with much greater caution in his work of 1902. It was the notion that one could equilibrate the osmotic pressure of solutes (or partialJune 30.2005; rev. July 17.20. 2005Atoms, Entropy, Quanta:Einstein’s Miraculous Argument of 1905John D. NortonDepartment of History and Philosophy of Einstein’s Miraculous Argument of 1905r under their random thermal motions.So the recognition in the light quantum paper of the signature of finitely many, spatially localized, independent components in the macroscopic properties of heat radiation is a natural extension of what was already in Einstein's work on molecular reality and Bro Einstein’s Miraculous Argument of 1905wnian motion. The result is astonishing: the approach and method is not.However. 1 will also argue that Einstein's use of this signature in the case oEinstein’s Miraculous Argument of 1905
f heat radiation presented a novel challenge. For the ideal gas law was a good signature for the independence of components, but harder to use withoutJune 30.2005; rev. July 17.20. 2005Atoms, Entropy, Quanta:Einstein’s Miraculous Argument of 1905John D. NortonDepartment of History and Philosophy of Einstein’s Miraculous Argument of 1905l gases, dilute solutions and suspensions were based on the assumption that these systems had fixed numbers of components. That assumption failed if the components were the quanta of heat radiation, for these quanta can be created by as simple a process as an isothermal expansion. Einstein's real in Einstein’s Miraculous Argument of 1905novation in his miraculous argument were these. He discovered a new signature for this same microscopic fact that could be used for thermal systems wiEinstein’s Miraculous Argument of 1905
th variable numbers of components. His new signature made much more transparent that the components are spatiallyscholarship. Howard and Stachcl <2000Gọi ngay
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