Abstract
In the following paper, translated from German by Arons and Peppard in 1965, Einstein extends Planck’s quantum concept, claiming that not only the emission and absorption of radiant energy, but even light itself is quantized. Essentially, Einstein treats light not as a classical electromagnetic wave, but rather as a gas of corpuscles, each of which carries a discrete amount of energy that depends on its wavelength. At the outset of the reading selection, Einstein introduces his paradoxical new concept of light. Then in the next several sections, Einstein motivates and explains this concept by applying Boltzmann’s principle of entropy to a gas of light corpuscles. These sections are rather technical, so feel free to skim over them for now; you might come back and re-read these after having studied a bit of quantum theory, variational calculus and statistical mechanics. In the mean time, be sure to carefully study Sect. 16.2.8, wherein Einstein describes how his concept of the light quantum may be used to understand the photoelectric effect. This curious emission of cathode rays (electrons) from illuminated metal bodies had been observed and noted by Heinrich Hertz in the 1880’s. Einstein’s novel theory of the photoelectric effect was originally published in 1905; it earned him a Nobel Prize in physics 16 year later.
The energy of a light ray spreading out from a point source is not continuously distributed over an increasing space but consists of a finite number of energy quanta which are localized at points in space, which move without dividing, and which can only be produced and absorbed as complete units.
—A. Einstein
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Notes
- 1.
The problem of blackbody radiation was mentioned briefly in Chap. 14 of the present volume.
- 2.
See Planck’s lecture in Chap. 15 of the present volume.
- 3.
Recall, however, that the concept of a light corpuscle was introduced some 300 years earlier by Isaac Newton in Book III of his Opticks; see, for example, Chap. 18 of volume III.
- 4.
This assumption is equivalent to the supposition that the average kinetic energies of gas molecules and electrons are equal to each other at thermal equilibrium. It is well known that, with the help of this assumption, Herr Drude derived a theoretical expression for the ratio of thermal and electrical conductivities of metals.
- 5.
M. Planck, Ann. Physik 1, 99 (1900).
- 6.
This problem can be formulated in the following manner. We expand the \(Z\) component of the electrical force (\(Z\)) at an arbitrary point during the time interval between \(t\, =\,0\) and \(t\, =\,T\) in a Fourier series in which \(A_{\nu }\, \geq \, 0\) and \(0\, \leq \, \alpha_{\nu }\, \leq 2 \pi \); the time \(T\) is taken to be very large relative to all the periods of oscillation that are present:
$$Z = \sum_{\nu = 1}^{\nu = \infty} A_{\nu} \sin{\left( 2 \pi \nu \frac{t}{T} + \alpha_{\nu} \right)}.$$(16.2)If one imagines making this expansion arbitrarily often at a given point in space at randomly chosen instants of time, one will obtain various sets of values of \(A_\nu \) and \(\alpha_{\nu }\). There then exist for the frequency of occurrence of different sets of values of \(A_{\nu }\) and \(\alpha_{\nu }\) (statistical) probabilities dW of the form;
$$dW = f(A_1,A_2 \dots \alpha_1, \alpha_2)dA_1\,dA_2 \dots d\alpha_1\,d\alpha_2$$(16.3)The radiation is then as disordered as conceivable if
$$f(A_1, A_2 \dots \alpha_1, \alpha_2 \dots) = F_1(A_1)F_2(A_2) \dots f_1(\alpha_1) f_2(\alpha_2) \dots,$$(16.4)i.e., if the probability of a particular value of \(A\) or \(\alpha \) is independent of other values of \(A\) or \(\alpha \). The more closely this condition is fulfilled (namely, that the individual pairs of values of \(A_{\nu }\) and \(\alpha_{\nu }\) are dependent upon the emission and absorption processes of specific groups of oscillators) the more closely will radiation in the case being considered approximate a perfectly random state.
- 7.
M. Planck, Ann. Physik 4, 561 (1901).
- 8.
This assumption is an arbitrary one. One will naturally cling to this simplest assumption as long as it is not controverted by experiment.
- 9.
If \(E\) is the energy of the system, one obtains:
$$ S-S_0=R(n/N) \ln{(v/vo)}. $$(16.33)therefore
$$ S-S_0=R(n/N) \ln{(v/vo)}. $$(16.34) - 10.
P. Lenard, Ann. Physik 8, 169, 170 (1902).
- 11.
If one assumes that the individual electron is detached from a neutral molecule by light with the performance of a certain amount of work, nothing in the relation derived above need be changed; one can simply consider \(P'\) as the sum of two terms.
- 12.
P. Lenard, Ann. Physik 8, pp. 165, 184 and Table I, Fig. 2 (1902).
- 13.
P. Lenard, Ref. 9, p. 150 and p. 166–168.
- 14.
Should be \(\Pi E\) (translator’s note).
- 15.
P. Lenard, Ann. Physik 12, 469 (1903).
- 16.
J. Stark, Die Elektrizität in Gasen (Leipzig, 1902), p. 57.
- 17.
In the interior of gases the ionization potential for negative ions is, however, five times greater.
- 18.
A complete Photoelectric Apparatus (Model EP-07)—containing a phototube, an amplifier and three color filters—is available form Daedalon, Downeast Maine. Additional light sources, such as a mercury arc and a He-Ne laser may be used to extend the measurements to additional wavelengths. A digital voltmeter is also required.
- 19.
See Ex. 16.1, above.
- 20.
For precise measurements of the Planck’s constant using the photoelectric effect for several surfaces, see Millikan, R. A., A direct photoelectric determination of Planck’s “h”, Physical Review, 7(3), 355, 1916.
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Kuehn, K. (2016). Corpuscles of Light. In: A Student's Guide Through the Great Physics Texts. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-21828-1_16
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