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AJP 1905 Photon.Pdf .-.-. AMERICAN AAPT JOURNAL n -v-51 r-i f :i. r.-.* i.: v o/PHYSICS Einstein's Proposal of the Photon Concept—a Translation of the Annalen der Physik Paper of 1905 A. B. Arons and M. B. Peppard Citation: Am. J. Phys. 33, 367 (1965); doi: 10.1119/1.1971542 View online: http://dx.doi.Org/10.1119/1.1971542 View Table of Contents: http://ajp.aapt.Org/resource/1/AJPIAS/v33/i5 Published by the American Association of Physics Teachers Additional information on Am. J. Phys. Journal Homepage: http://ajp.aapt.org/ Journal Information: http://ajp.aapt.org/about/about_theJournal Top downloads: http://ajp.aapt.org/most_downloaded Information for Authors: http://ajp.dickinson.edu/Contributors/contGenlnfo.html ADVERTISEMENT wNew Orleans JAAPT2013 AndAtt That Jazz Downloaded 18 Jan 2013 to 128.103.149.52. Redistribution subject to AAPT license or copyright; see http://ajp.aapt.org/authors/copyright_permission AMERICAN JOURNAL of PHYSICS A Journal Devoted to the Instructional and Cultural Aspects of Physical Science VOLUME 33, NUMBER 5 MAY 1965 Einstein's Proposal of the Photon Concept—a Translation of the Annalen der Physik Paper of 1905* A. B. ARONSf AND M. B. PEPPARD. Amherst College, Amherst, Massachusetts (Received 2 December 1964) Of the trio of famous papers that Albert Einstein sent to the Annalen der Physik in 1905 only the paper proposing the photon concept has been unavailable in English translation. The American Journal of Physics is publishing the following translation in recognition of the sixtieth anniversary of the appearance of the original work. Physics teachers may take particu­ lar interest in the following aspects: (1) Einstein's keen awareness of the heuristic character of his new conception. (2) His demonstration from thermodynamic and statistical considerations that electromagnetic radiation might be conceived as consisting of finite numbers of discrete corpuscles of energy hv. (3) His prediction of the linear relation between the stopping potential of photoelectrons and the frequency of the incident light. This latter aspect of the photo­ electric effect was not included among Lenard's early investigations. It remained for Millikan and others to develop the elegant experimental techniques that confirmed Einstein's bold pre­ diction. Readers interested in pursuing the background in greater depth will find it rewarding to refer to the critical analyses by Martin J. Klein in "Einstein's First Paper on Quanta," in The Natural Philosopher (Blaisdell Publishing Company, New York, 1963), Vol. II, and "Einstein and the Wave-Particle Duality," in The Natural Philosopher, Vol. Ill, 1964. We are grateful to Professor Klein for his criticism and advice regarding this translation and for his generosity in making available to us an unpublished translation of his own. CONCERNING AN HEURISTIC POINT OF spatial functions to describe the electromagnetic VIEW TOWARD THE EMISSION AND state of a given volume, and a finite number of TRANSFORMATION OF LIGHT parameters cannot be regarded as sufficient for BY A. EINSTEIN the complete determination of such a state. Ac­ PROFOUND formal distinction exists be­ cording to the Maxwellian theory, energy is to A tween the theoretical concepts which physi­ be considered a continuous spatial function in cists have formed regarding gases and other the case of all purely electromagnetic phenomena ponderable bodies and the Maxwellian theory of including light, while the energy of a ponderable electromagnetic processes in so-called empty object should, according to the present concep­ space. While we consider the state of a body to tions of physicists, be represented as a sum be completely determined by the positions and carried over the atoms and electrons. The energy velocities of a very large, yet finite, number of of a ponderable body cannot be subdivided into atoms and electrons, we make use of continuous arbitrarily many or arbitrarily small parts, while * Ann.. Physik 17, 132 (1905); Translation published the energy of a beam of light from a point source with the permission of Annalen der Physik. (according to the Maxwellian theory of light or, f Department of Physics. % Department of German. more generally, according to any wave theory) is 367 Downloaded 18 Jan 2013 to 128.103.149.52. Redistribution subject to AAPT license or copyright; see http://ajp.aapt.org/authors/copyright_permissic 368 A. B. ARONS AND M. B. PEPPARD continuously spread over an ever increasing be a number of electrons which are bound to volume. widely separated points by forces proportional The wave theory of light, which operates with to their distances from these points. The bound continuous spatial functions, has worked well in electrons are also to participate in conservative the representation of purely optical phenomena interactions with the free molecules and electrons and will probably never be replaced by another when the latter come very close. We call the theory. It should be kept in mind, however, that bound electrons "oscillators"; they emit and the optical observations refer to time averages absorb electromagnetic waves of definite periods. rather than instantaneous values. In spite of the According to the present veiw regarding the complete experimental confirmation of the theory origin of light, the radiation in the space we are as applied to diffraction, reflection, refraction, considering (radiation which is found for the case dispersion, etc., it is still conceivable that the of dynamic equilibrium in accordance with the theory of light which operates with continuous Maxwellian theory) must be identical with the spatial functions may lead to contradictions blackbody radiation—at least if oscillators of all with experience when it is applied to the phe­ the relevant frequencies are considered to be nomena of emission and transformation of light. present. It seems to me that the observations associated For the time being, we disregard the radiation with blackbody radiation, fluorescence, the emitted and absorbed by the oscillators and production of cathode rays by ultraviolet light, inquire into the condition of dynamical equilib­ and other related phenomena connected with the rium associated with the interaction (or collision) emission or transformation of light are more of molecules and electrons. The kinetic theory of readily understood if one assumes that the energy gases asserts that the average kinetic energy of of light is discontinuously distributed in space. an oscillator electron must be equal to the aver­ In accordance with the assumption to be con­ age kinetic energy of a translating gas molecule. sidered here, the energy of a light ray spreading If we separate the motion of an oscillator electron out from a point source is not continuously into three components at right angles to each distributed over an increasing space but consists other, we find for the average energy E of one of a finite number of energy quanta which are of these linear components the expression localized at points in space, which move without dividing, and which can only be produced and E=(R/N)T, absorbed as complete units. where R denotes the universal gas constant, N In the following I wish to present the line of denotes the number of "real molecules" in a thought and the facts which have led me to this gram equivalent, and T the absolute tempera­ point of view, hoping that this approach may be ture. The energy E is equal to two-thirds the useful to some investigators in their research. kinetic energy of a free monatomic gas particle because of the equality between the time average 1. CONCERNING A DIFFICULTY WITH REGARD TO values of the kinetic and potential energies of the THE THEORY OF BLACKBODY RADIATION oscillator. If through any cause—in our case We start first with the point of view taken in through radiation processes—it should occur that the Maxwellian and the electron theories and the energy of an oscillator takes on a time- consider the following case. In a space enclosed average value greater or less than E, then the by completely reflecting walls, let there be a collisions with the free electrons and molecules number of gas molecules and electrons which are would lead to a gain or loss of energy by the gas, free to move and which exert conservative forces different on the average from zero. Therefore, in on each other on close approach; i.e. they can the case we are considering, dynamic equilibrium collide with each other like molecules in the is possible only when each oscillator has the kinetic theory of gases.1 Furthermore, let there average energy E. 1 This assumption is equivalent to the supposition that known that, with the help of this assumption, Herr Drude the average kinetic energies of gas molecules and electrons derived a theoretical expression for the ratio of thermal are equal to each other at thermal equilibrium. It is well and electrical conductivities of metals. Downloaded 18 Jan 2013 to 128.103.149.52. Redistribution subject to AAPT license or copyright; see http://ajp.aapt.org/authors/copyright_permission EINSTEIN'S PROPOSAL OF THE PHOTON CONCEPT 369 We shall now proceed to present a similar argu­ and in the limit we obtain ment regarding the interaction between the oscillators and the radiation present in the R8TT 2 pvdv— -T ' I vHv = cavity. Herr Planck has derived the condition N U Jo for the dynamical equilibrium in this case under the supposition that the radiation can be con­ 2. CONCERNING PLANCK'S DETERMINATION sidered a completely random process.3 He found OF THE FUNDAMENTAL CONSTANTS We wish to show in the following that Herr Planck's determination of the fundamental where (Er) is the average energy (per degree constants is, to a certain extent, independent of of freedom) of an oscillator with eigenfrequency his theory of blackbody radiation.
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