## Zur Theorie der Lichterzeugung und Lichtabsorption. Offprint from Annalen der Physik, 4. Folge, 20. Bd., 1906.

Leipzig: Barth, 1906.

First edition, rare author’s presentation offprint with “Überreicht vom Verfasser” printed on front wrapper, of this brilliant follow-up to Einstein’s landmark 1905 paper on the photoelectric effect. In the 1905 paper, ‘On a heuristic point of view concerning the production and transformation of light,’ Einstein had explained the photoelectric effect—the emission of electrons from a metal when irradiated by light—by making the revolutionary proposal that light, rather than consisting of continuous waves, was instead made up of discrete particles of energy (“light quanta”), which transferred their entire payload of energy to an electron on impact. In the 1905 paper Einstein made use of Planck’s formula for blackbody radiation, which had introduced the concept of energy quantization. “In a companion paper, published in 1906 [offered here], Einstein exposed appeal to the quantum as fundamentally counter to the ethos of classical physics: ‘the theoretical bases on which Planck’s radiation theory rests are different from those of Maxwell’s theory’. Planck had not initially intended to quantify light-radiation itself, but Einstein demonstrated that his own ‘light-quantum hypothesis’ was implicit in Planck’s earlier work” (Honner, p. 31). In his 1906 paper Einstein “used his statistical mechanics to demonstrate that when light interacts with matter, Planck’s entire formula can arise only from the existence of light quanta—not from waves” (Cassidy). Einstein had realized, as he stated in the present paper, that “‘Planck’s theory makes implicit use of the . . . light-quantum hypothesis’ . . . his acceptance of Planck’s [formula], albeit as a hypothesis, led to a major advance in his own work” (Pais*, *p. 378). In 1921 Einstein was awarded the Nobel Prize in physics for his work on the photoelectric effect.

“Einstein started to study black-body radiation well before 1905. Mach’s *Wärmelehre*, which Einstein read in 1897 or shortly thereafter, contains two chapters on thermal radiation, culminating in a discussion of Kirchhoff's work. Kirchhoff showed that the energy emission spectrum of a perfectly black body (defined as one absorbing all incident radiation) at a given temperature is a universal function of the temperature and wavelength. He inferred that equilibrium thermal radiation in a cavity with walls maintained at a certain temperature behaves like radiation emitted by a black body at the same temperature.

“H. F. Weber, Einstein’s physics professor at the ETH, attempted to determine the universal black-body radiation function. He made measurements of the energy spectrum and proposed an empirical formula for the distribution function … anticipating Wien’s formulation of the displacement law for black-body radiation. Weber described his work in a course at the ETH given during the winter semester of 1898-1899, for which Einstein registered.

“By March 1899, Einstein had started to think seriously about the problem of radiation. In the spring of 1901, he was closely following Planck’s work on black-body radiation. Originally, Planck had hoped to explain irreversibility by studying electromagnetic radiation, but came to recognize that this could not be done without introducing statistical elements into the argument. In a series of papers published between 1897 and 1900, Planck utilized Maxwell’s electrodynamics to develop a theory of thermal radiation in interaction with one or more identical, charged harmonic oscillators within a cavity. He was only able to account for the irreversible approach to thermal equilibrium by employing methods analogous to those Boltzmann used in kinetic theory. Planck introduced the notion of ‘natural’ (that is, maximally disordered) radiation, which he defined in analogy with Boltzmann’s definition of molecular chaos …

“Planck calculated the average energy of an oscillator by making assumptions about the entropy of the oscillators that enabled him to derive Wien’s law for the blackbody spectrum, which originally seemed well supported by the experimental evidence. But by the turn of the century new observations showed systematic deviations from Wien’s law for large values of [temperature].

“Planck [in 1900] presented a new energy density distribution formula that agreed closely with observations over the entire spectrum … this expression, now known as Planck’s law or Planck’s formula, [involves] a new constant *h *(later called Planck’s constant). To derive this formula, Planck calculated the entropy of the oscillators, using what Einstein later called ‘the Boltzmann principle’: *S = k* log *W*, where *S* is the entropy of a macroscopic state of the system, the probability of which is *W* [and *k* is ‘Boltzmann’s constant’]. Following Boltzmann, Planck took *W* proportional to the number of ‘complexions,’ or possible microconfigurations of the system corresponding to its state. He calculated this number by dividing the total energy of the state into a finite number of elements of equal magnitude, and counting the number of possible ways of distributing these energy elements among the individual oscillators. If the size of the energy elements is set equal to *hv*, where *v* is the frequency of the oscillators, an expression for the entropy of an oscillator results that leads to [Planck’s formula] ...

“[In the 1905 paper], Einstein showed that the expression for the volume dependence of the entropy of radiation at a given frequency is similar in form to that of the entropy of an ideal gas. He concluded that ‘monochromatic radiation of low density behaves thermodynamically as though it consisted of quanta of energy, which are independent of one another’ … Einstein opened the paper by pointing out the ‘fundamental formal distinction’ between current theories of matter, in which the energy of a body is represented as a sum over a finite number of degrees of freedom, and Maxwell’s theory, in which the energy is a continuous spatial function having an infinite number of degrees of freedom. He suggested that the inability of Maxwell’s theory to give an adequate account of radiation might be remedied by a theory in which radiant energy is distributed discontinuously in space. Einstein formulated ‘the light quantum hypothesis’ that the energy of a light ray emitted from a point [is] not continuously distributed over an ever 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 … Einstein asserted that Planck’s derivation implicitly assumes quantization of the energies of charged oscillators” (*Papers*, pp. 134-142).

“In 1905, Einstein could not make sense of Planck’s derivation of Planck’s law. In fact, he seems to have deliberately avoided any reference to Planck’s law in his reasoning … The following year, Einstein ceased to avoid Planck’s law as he discovered a new way to justify Planck’s formal steps toward this law. If a resonator of frequency *ν* can only emit or absorb full light quanta, Einstein reasoned, then its energy can only be an integral multiple of *hν* and Planck’s characterization of the complexions for a set of resonators receives a dynamical justification. The only remaining difficulty is that Planck’s derivation of the relation between the average energy of a resonator and the spectral density of radiation becomes void. Einstein expressed the need of a new derivation based on some quantized dynamics for the interaction between matter and radiation. Ten years elapsed, however, before he filled the gap” (Janssen & Lehner, p. 126).

In the final section of this paper, Einstein gives a new application of his ‘heuristic principle’, to the explanation of the ‘Volta effect’ – that when two different metals are placed in contact, a potential difference between them is observed.

Weil *12. Shields, “Writings of Albert Einstein” (in *Albert Einstein: Philosopher-Scientist *[1948], pp. 689-758), no. 13; also included in Shields’ “Chronological list of principal works” on p. 757. *The Cambridge Companion to Einstein* (Janssen & Lehner, eds.), 2014. *The Collected Papers of Albert Einstein*, *Vol. 2: The Swiss Years: Writings 1900-1909*. Cassidy, “Einstein on the Photoelectric Effect.” *Einstein: Image and Impact*. American Institute of Physics, n.d. Honner, *The Description of Nature*, 1988. Pais, *Subtle is the Lord,* 1982.

8vo (222 x 144 mm), pp. 199-206. Original printed wrappers (a little chipped and sunned, spine partly split).

Item #5070

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Price:
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