## Über einen der Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtpunkt. Offprint from Annalen der Physik, 4. Folge, 17. Band, 1905.

Leipzig: Johann Ambrosius Barth, 1905.

First Edition, very rare author’s presentation offprint, of Einstein’s paper on light quanta, for which (along with his 1912 paper on the photo-electric equation) he was awarded the 1921 Nobel Prize for physics. Completed in March of 1905 (Einstein’s *annus mirabilis*), ‘On a heuristic point of view about the creation and conversion of light’ was the first of four epochal scientific papers published by Einstein that year; the others were his paper on Brownian motion and two papers on the special theory of relativity. “No one before or since has widened the horizons of physics in so short a time as Einstein did in 1905” (Pais, p. 47). Einstein’s paper on light quanta was the only one of his works that he himself called ‘revolutionary,’ and for good reason: “The heuristic viewpoint of the title was nothing less than the suggestion that light be considered a collection of independent particles of energy … Einstein had his reasons for advancing such a bold suggestion, one that seemed to dismiss a century of evidence supporting the wave theory of light. First among these was a negative result: The combination of the electromagnetic theory of light with the (statistical) mechanics of particles was incapable of dealing with the problem of black-body radiation. It predicted that radiation in thermodynamic equilibrium within an enclosure would have a frequency distribution corresponding to an infinite amount of energy at the high-frequency end of the spectrum. This was incompatible with the experimental results, but, worse than that, it meant that the theory did not give an acceptable answer to the problem … Einstein showed that his strange proposal of light quanta could immediately account for several puzzling properties of fluorescence, photoionization, and especially of the photoelectric effect” (*DSB*). “He determined that a massless quantum of light, the photon, would have to impart the energy required according to Planck's radiation law to break the attractive forces holding the electrons in the metal. This theory was one of the milestones in the development of quantum mechanics, making Einstein the foremost pioneer in the field and opening the world of quantum physics” (Calaprice, *The Eintsein Almanac*, p. 14). Einstein submitted his light-quanta paper to *Annalen der Physik* immediately upon its completion; it was published in the first issue of Vol. 17, which was distributed on June 9, 1905. A letter from Einstein to his friend Conrad Habicht, written in April 1905, indicates that Einstein had received his allotment of offprints of the paper by that date; thus the offprint, rather than the journal article, represents the true first edition. In his bibliography of Einstein’s works, Weil states that “it seems to be certain that there were few [offprints of Einstein’s papers made] before 1914. They were given only to the author, and mostly ‘Überreicht vom Verfasser’ (Presented by the Author) is printed o**n **the wrapper [as in our copy]” (Weil, p. 4). ABPC/RBH lists six copies in the last half-century: Aguttes, 2019, €94,777 (‘dos fendu, papier fragile’); Sotheby’s, 2003, £1320; Christie’s, 2002, Plotnick copy, $8365 (spine reinforced, covers tissue-lined on versos); Sotheby’s, 1989, Garden copy, $4250; Sotheby’s, 1984, £495; Sotheby’s, 1971, $204. The present copy appears to be at least as fine, and possibly finer, than any other copy that has appeared on the market.

*Provenance*: ‘Falter’ written in pencil in upper right corner of front cover. This is possibly Ludwig Falter (born 15 June 1880 in Steinbuch, Odenwald, date of death unknown), German philosopher and mathematician. (We would like to thank Brian Markle for suggesting this provenance to us.)

Some time in the first half of the year 1905 Einstein wrote a letter to Conrad Habicht, in which he announced that he would soon send him copies of four different scientific papers: the first dealt with radiation [the offered paper]; the second with methods to determine the real dimensions of atoms; the third with the irregular motion of particles suspended in fluids; and the fourth with the electrodynamics of moving bodies … The first paper … bore the title ‘On a heuristic point of view about the creation and conversion of light’ … ‘It is on radiation and energy of light,’ he described its content [to Habicht], ‘and it is very revolutionary, as you will see yourself’” (*The Historical Development of Quantum Theory*, vol. 1, pp. 70-72).

“In describing four of his 1905 papers, Einstein characterized only the one on the quantum hypothesis as revolutionary. It is now regarded as revolutionary in challenging the unlimited validity of Maxwell’s theory of light and suggesting the existence of light quanta. The paper shows that, at a sufficiently high frequency, the entropy of equilibrium thermal (or ‘black-body’) radiation behaves as if the radiation consists of a gas of independent ‘quanta of light energy’, each with energy proportional to the frequency. Einstein showed how to explain several otherwise puzzling phenomena by assuming that the interaction of light with matter consists of the emission or absorption of such energy quanta …

“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].

“Although Einstein expressed misgivings about Planck’s approach in 1901, he did not mention Planck or black-body radiation in his papers until 1904. A study of the foundations of statistical physics, which he undertook between 1902 and 1904, provided Einstein with the tools he needed to analyze Planck’s derivation and to explore its consequences. At least three elements of Einstein’s ‘general molecular theory of heat’ were central to his subsequent work on the quantum hypothesis: the introduction of the canonical ensemble; the interpretation of probability in Boltzmann’s principle; and the study of energy fluctuations in thermal equilibrium.

“In an analysis of the canonical ensemble, Einstein proved that the equipartition theorem holds for any system in thermal equilibrium. In 1905 he showed that, when applied to an ensemble of charged harmonic oscillators in equilbrium with thermal radiation, the equipartition theorem leads to a black-body distribution law now known as the Rayleigh-Jeans law [and that Planck’s derivation would also lead to this law on the assumption that all ‘complexions’ were equally probable] … Einstein showed that, if the energies available to a canonical ensemble of oscillators are arbitrarily restricted to multiples of the energy element *hv*, then all possible complexions are not equally probable, and Planck’s law results.

“A third element of Einstein’s work on statistical physics that is central to his work on the quantum hypothesis is his method for calculating mean square fluctuations in the state variables of a system in thermal equilibrium. He employed the canonical ensemble to calculate such fluctuations in the energy of mechanical systems, and then applied the result to a nonmechanical system – black-body radiation, deducing a relation that agrees with Wien’s displacement law. This agreement confirms the applicability of statistical concepts to radiation, and may have suggested to him the possibility that radiation could be treated as a system with a finite number of degrees of freedom, a possibility he raised at the outset of his first paper on the quantum hypothesis …

“Among Einstein’s papers on the quantum hypothesis, the 1905 paper is unique in arguing for the notion of light quanta without using either the formal apparatus of his statistical papers or Planck’s law … In order to suggest what new concepts might be needed, he focused on the problematic Wien region. Using Wien’s law, 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 (within the range of validity of Wien's radiation formula) 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 …

“In addition to their contributions to theory, each of Einstein’s first three papers on the quantum hypothesis also provides ingenious explanations of observed phenomena or predictions of new ones. [The offered paper] examines three interactions of light with matter, treated ‘as if light consisted of such energy quanta’: Stokes’s rule for fluorescence; the ionization of gases by ultraviolet light; and the photoelectric effect … [It] proposes what later became known as Einstein’s photoelectric equation … Although his derivation of this equation was later considered to be a leading achievement of that paper – it is cited in his 1922 Nobel Prize award – for almost two decades the argument failed to persuade most physicists of the validity of the light quantum hypothesis. Lenard’s experimental studies, to which Einstein referred, only provide qualitative evidence … For almost a decade the quantitative relationship between electron energy and radiation frequency was in doubt. By about 1914, there was a substantial body of evidence tending to support [Einstein’s photoelectric equation]. Millikan’s studies clinched the case for almost all physicists. But even the confirmation of Einstein’s photoelectric equation did not bring about widespread acceptance of the concept of light quanta. Alternative interpretations of the photoelectric effect still received general support for a number of years” (*The Collected Papers of Albert Einstein*, vol. 2, pp. 134-142).

“During World War II, Dr Ludwig Falter worked as a mathematician, cryptanalyst and English interpreter, initially working in the English Referat of In 7/VI, the signals intelligence agency of the Wehrmacht, before and during World War II. He would later work for the General der Nachrichtenaufklärung, the successor organization to the In 7/VI, specifically undertaking analytical research from the summer of 1944 in Group IV. Falter was son of a farmer Heinrich Falter at Steinbuch within the Odenwald mountain road. Falter enrolled and registered at the University of Giessen on 30 April 1898, as student of mathematics and was ex-matriculated a year later on the 12 May 1899. Falter had another go at the university and enrolled for a second time at Gießen and registered at 28 October 1899 as student of mathematics and de-registered at 19.06.1902. From February 1899 he worked sometimes as a teacher of mathematics at the Pädagogium in Wiesbaden. Little is known about Falter after this period, except that he was promoted to Dr. phil at Gießen with a thesis titled *Die erkenntnistheoretischen Grundlagen der Mathematik bei Kant und Hume* on 29 December 1903. His doctoral advisor and mentor was the philosopher, Hermann Siebeck.

Weil 6*. Pais, *Subtle is the Lord,* pp. 364-68. See *Printing and the Mind of Man *391.

8vo (222 x 144 mm), pp. [1], 132-148. Original printed wrappers with “A. Einstein. Überreicht vom Verfasser” printed in bold type on the front wrapper, “Falter” in ms. in upper corner (a bit spotted, outer corners lightly creased). A fine untouched copy, housed in a full morocco silk-lined box.

Item #4983

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Price:
$280,000.00
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