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Non-Einsteinian Interpretations of the Photoelectric Effect

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Non-Einsteinian Interpretations of the Photoelectric Effect NON-EINSTEINIAN INTERPRETATIONS ------ROGER H. STUEWER------ serveq spectral distribution for black-body radiation, and it led inexorably ~o _the ~latantl~ f::se conclusion that the total radiant energy in a cavity is mfimte. (This ultra-violet catastrophe," as Ehrenfest later termed it, was point~d out independently and virtually simultaneously, though not Non-Einsteinian Interpretations of the as emphatically, by Lord Rayleigh.2) Photoelectric Effect Einstein developed his positive argument in two stages. First, he derived an expression for the entropy of black-body radiation in the Wien's law spectral region (the high-frequency, low-temperature region) and used this expression to evaluate the difference in entropy associated with a chan.ge in volume v - Vo of the radiation, at constant energy. Secondly, he Few, if any, ideas in the history of recent physics were greeted with ~o~s1dere? the case of n particles freely and independently moving around skepticism as universal and prolonged as was Einstein's light quantum ms1d: a given v~lume Vo _and determined the change in entropy of the sys­ hypothesis.1 The period of transition between rejection and acceptance tem if all n particles accidentally found themselves in a given subvolume spanned almost two decades and would undoubtedly have been longer if v ~ta r~ndomly chosen instant of time. To evaluate this change in entropy, Arthur Compton's experiments had been less striking. Why was Einstein's Emstem used the statistical version of the second law of thermodynamics hypothesis not accepted much earlier? Was there no experimental evi­ in _c?njunction with his own strongly physical interpretation of the prob­ dence that suggested, even demanded, Einstein's hypothesis? If so, why ~b1ht~. He found that the expression for this change in entropy is formally was it met with such profound skepticism? identical to the one he had derived earlier for black-body radiation, and Questions such as these, which relate to the processes by which scien­ from this fact he drew what to him was the unavoidable conclusion: tific theories gain acceptance, are less popular with historians of science monochro~atic black-body radiation in the Wien's law spectral region than they ought to be. A good deal of insight into the nature of science, behaves with respect to thermal phenomena as if it consists of independ­ especially into the interplay between theory and experiment, may be ob­ ently moving particles or quanta of radiant energy. It was also clear from tained from a study of these transition periods. This point may be illus­ his arguments that the energy of each quantum is proportional to its trated immediately by briefly sketching Einstein's arguments for his light· frequency. quantum hypothesis, its relationship to the photoelectric effect, and the Einstein's light quantum hypothesis (his "heuristic point of view") was experimental evidence on the photoelectric effect available to physicists therefore a necessary consequence of very fundamental assumptions: in in the early years of this century. no sense did he propose it in an ad hoc fashion to "explain" certain experi­ Einstein gave two powerful arguments for light quanta, one negative, ments. If, however, under certain circumstances light indeed exhibited a the other positive. His negative argument was that classical radiatio11 quantum structure, this ought to be experimentally verifiable. Einstein theory was fundamentally inadequate; it could not account for the oh-, gave a detailed discussion of three experimental applications, one of which was the photoelectric effect. The famous equation he derived showed that AUTHOR'S NOTE : I am especially grateful to Professor Martin J. Klein for his numero11:. and illuminating comments, and I should also like to thank Professor Howard Stein for I lie maximum kinetic energy T of the photoelectrons depends linearly his helpful suggestions. 011 the frequency v of the incident radiation. In modern notation, T = 1 Uber einen die Erzeugung und Verwandlung des Lichtes betreffenden hc11 fr. tischen Gesichtspunkt," Annalen der Physik, 17 ( 1905), 132-148; translated in H. A. Ii,, - wo, where his Planck's constant and w0 is the work function of the Boorse and L. Motz, eds., The World of the Atom, vol. l (New York: Basic Boob, pl1otosensitive surface. (It is worth noting that Einstein himself used a 1966) , pp. 545-5 57. For a detailed historical discussion, see Martin J. Klein, "l•'.i11 rnmhination of other constants instead of the single constant h, which stein's First Paper on Quanta," The Natural Philosopher (New York), 2' ( 1963), 57 86; "Thermodynamics in Einstein's Thought," Science, 157 (1967), 509-516. My 111 ercl y cmpl1;i sizes the fact that Einstein did not, as many believe, build brief discussion of Einstein's paper draws heavily on Klein 's work. "'The Dy11amieal T"hco1y of C:iscs :ind of Radiation ," Nature, 72 ( 1905), 55. 246 247 Roger H. Stuewer NON-EINSTEINIAN INTERPRETATIONS on Planck's earlier work.) Einstein also pointed out that the intensity of ceptance of quanta to imply rejection of classical electrodynamics-this in the incident radiation should determine only the number and not the spite of Einstein's 1909 proof that a necessary consequence of Planck's law energy of the ejected photoelectrons, predictions which were consistent is the coexistence of quanta and waves in black-body radiation.11 (Ein­ with Lenard's "trailblazing" 1902 experiments.3 stein's proof rested on his analysis of energy and momentum fluctuations But what about Einstein's extremely bold prediction that the maximum in black-body radiation, a proof his contemporaries were unprepared to photoelectron energy depends linearly on the frequency of the incident accept or even understand.) Maxwell's theory had been repeatedly con­ radiation? Here the experimental situation was highly uncertain. Thus, firmed, by Hertz's electromagnetic wave experiments, Lebedev's (and Lenard had found only a general increase in electron energy with incident Nichols and Hull's) radiation pressure experiments, and all interference frequency; and several years later in 1907 Ladenburg concluded4 that the and diffraction experiments.12 The heuristic value of MaxweII's theory energy varied quadratically with the frequency. While Joffe was quick to was beyond question. To believe that it would not eventually encompass 5 point out that Ladenburg's experiments were also consistent with Ein­ photoelectric phenomena appeared to most of Einstein's contemporaries stein's linear relationship, it developed that they were also consistent with -the exception was Johannes Stark13-to be most unreasonable. a frequency to the~ power variation proposed in 1911 by F. A. Linde­ Given the belief (to a large degree unjustified by the experimental evi­ mann.6 A year later in 1912 0. W. Richardson and K. T. Compton,7 as dence, as we have seen) in the validity of the linear relationship between well as A. L. Hughes, 8 reasserted the validity of the linear relationship. But ener~y and frequency, as well as the disbelief in Einstein's interpretation their experiments were immediately challenged by Pohl and Pringsheim, 9 of it, a natural question arose: Were there perhaps other, less radical, in­ who maintained that the best fit to Richardson and Compton's data could terpretations of the photoelectric effect? A historical examination of the be obtained with a logarithmic relationship. It was not until 1915-16 that answers proposed to this question will form the main thrust of my paper, R. A. Millikan settled the issue.10 but before I begin I should like to make two general remarks. First, we Now the remarkable fact is that these disparate experimental results, as shall evidently be discussing theories formulated not primarily in response we shall see, did not lead those who opposed Einstein's interpretation of to a troublesome experimental observation,14 but rather in response to an the photoelectric effect to seriously question the validity of Einstein's linear relationship. Their opposition stemmed from a different quarter. unpalatable interpretation. Second, while revolutionary new theories tend They failed to see that Einstein's light quantum hypothesis was a neces­ to be generated by young minds, and while it is therefore natural to at­ sary consequence of Einstein's assumptions, and they tended to take ac- tribute any resistance to them to the "old guard," we do not seem to have such a situation here. We do not seem to have an example of Planck's con­ • P. Lenard, "Ueber die lichtelektrische Wirkung," Annalen der Physik, 8 ( 1902), 149-198. tention that "a new scientific truth does not triumph by convincing its • E. Ladenburg, "Uber Aufangsgeschwindigkeit un~. Menge der photoelek~rischc~~ opponents and making them see the light, but rather because its oppo­ Elektronen in ihrem Zusammenhange mit der W ellenlange der Auslosenden ~1ch.tc s . Berichte der deutschen physikalischen Gesellschaft, 9 (1907), 504-515; Phys1kal1sc11c nents eventually die, and a new generation grows up that is familiar with Zeitschrift, 8 (1907), 590-594. 11 "Zurn gegenwartigen Stand des Strahlungsproblems," Physikalische Zeitschrift, 10 •A. Joffe, "Eine Bemerkung zu der Arbeit van E. Lade~burg," B.ayn.sche Akaden~"· der Wissenschaften, Miinchen, Sitzungberichte, rnathernatisch·phys1kal1sche Klasse, ) 7 ( 1909), 185-193; "Uber die Entwicklung unserer Anschauungen Uber <las Wesen und ( 1907), 279-280; Annalen der Physik, 24 ( 1907), 939-940. di e Konstitution der Strahlung," Physikalische Zeitschrift, 10 (1909), 817-826. See • "Uber die Berechnung der Eigenfrequenzen der Elektronen 1m selekhven Pho I• 1 also Martin J. Klein, "Einstein and the Wave-Particle Duality," The Natural Philos­ effect," Berichte der deutschen physikalischen Gesellschaft, 13 ( 1911 ) , 482-488. opher, 3 ( 1963), 3-49. 1 "The Photoelectric Effect," Philosophical Magazine, 24 (1912), 575-594. "For discussion and references, see E. T. Whittaker, A History of the Theories of •"On the Long-Wave Limits of the Normal Photoelectric Effect," Philosopl1irn l Act/1cr and Electricity, vol.
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