Einstein

1906 · réf. 6413 — Leipzig: Johann Ambrosius Barth 1906. First edition. First edition a very rare author's presentation offprint with 'Überreicht vom Verfasser' from the library of the eminent German physicist Arnold Sommerfeld of this important sequel to Einstein's revolutionary 1905 paper introducing the light-quantum hypothesis - the foundation of quantum theory. In this follow- up work Einstein further develops the implications of his light-quantum hypothesis arguing that Max Planck's black-body radiation law implicitly relies on the same assumption: that light itself consists of discrete quanta of energy. . EINSTEIN ON HIS LIGHT-QUANTUM HYPOTHESIS . First edition very rare author's presentation offprint "Überreicht vom Verfasser" from the library of the great German physicist Arnold Sommerfeld of this brilliant follow-up to Einstein's landmark 1905 paper on the photoelectric effect for which he was awarded the 1921 Nobel Prize in physics. "Thomas Kuhn has argued that it is not to Planck in 1900 but to Einstein in 1905 that we owe the origins of quantum theory" Cassidy. 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. "At first Einstein believed that the light-quantum hypothesis was merely 'heuristic': light behaved only as if it consisted of discontinuous quanta . 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. As Einstein stated when he published the 1905 paper "Planck's theory of radiation seemed to me in a certain respect the antithesis of my own. New considerations which are presented in section 1 of this paper demonstrated to me however that the theoretical bases on which Planck's radiation theory rests are different from those of Maxwell's theory and of electron theory. The difference furthermore is precisely that Planck's theory implicitly makes use of the light-quantum hypothesis" p. 199 of the present paper translation from Kuhn p. 182. Later in the paper p. 203 Einstein is forced to make the following assumption: "Although Maxwell's theory is not applicable to elementary resonators the average energy of such a resonator in a radiation field is the same as that which one would compute from Maxwell's theory". "That statement marks the emergence of the basic paradox of the old quantum theory. The theory has recourse to both Maxwell's equations and those of classical mechanics but its further formulation is incompatible with one or both of those classical theories. Other physicists were to exploit the resulting inconsistency as an argument against any form of quantum discontinuity and Einstein himself was deeply disturbed by it . But neither he nor anyone else was successful in finding a classical resolution of the quantum paradox. When two decades later Bohr and others found a way to resolve it Einstein was unable to accept their fundamentally non-classical interpretation" Kuhn pp. 184-185. RBH lists 4 other copies: in the offprint collections of Einstein himself Christie's June 17 2008 lot 100 Richard Green Christie's June 17 2008 lot 101 Hans Albert Einstein Christie's June 14 2006 lot 264 and Harvey Plotnick Christie's October 4 2002 lot 105. This copy was presented by Einstein to one of the leading physicists of the time surely hoping to make himself known in the scientific world when he was still a technical expert in the Swiss Patent Office. Provenance: Arnold Sommerfeld 1868-1951 his signature and characteristic numbering in red pencil '8' on front cover. "The son of a physician Sommerfeld was educated at the University of Königsberg. After teaching briefly at the universities of Göttingen Clausthal and Aachen he was appointed professor of physics at the University of Münich in 1906. Sommerfeld should have retired in 1936 in favour of his pupil Werner Heisenberg. Opposition from the Nazi party to Heisenberg's appointment prolonged Sommerfeld's tenure and it was not in fact until late 1939 that he finally retired to be succeeded not by Heisenberg but by Wilhelm Müller a Nazi aerodynamicist without a single publication in physics to his credit. Although Sommerfeld and Heisenberg were not Jewish they were regarded by the Nazis as Jewish sympathizers. Sommerfeld however survived the war and returned to his Münich chair in 1945 continuing to work at physics until he died in a car accident in 1951" Oxford Reference. "Arnold Sommerfeld was one of the most distinguished representatives of the transition period between classical and modern theoretical physics. The work of his youth was still firmly anchored in the conceptions of the nineteenth century; but when in the first decennium of the century the flood of new discoveries experimental and theoretical broke the dams of tradition he became a leader of the new movement and in combining the two ways of thinking he exerted a powerful influence on the younger generation. This combination of a classical mind to whom clarity of conception and mathematical rigour are essential with the adventurous spirit of a pioneer are the roots of his scientific success while his exceptional gift of communicating his ideas by spoken and written word made him a great teacher" Max Born p. 275. "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. BRL 12; 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. Born 'Arnold Johannes Wilhelm Sommerfeld 1868-1951' Obituary Notices of Fellows of the Royal Society 8 1952 pp. 275-296. Cassidy "Einstein on the Photoelectric Effect." Einstein: Image and Impact. American Institute of Physics n.d. Honner The Description of Nature 1988. Kuhn Black-Body Theory and the Quantum Discontinuity 1894-1912 1978. Pais Subtle is the Lord 1982. 8vo 222 x 144 mm pp. 199-206. Original printed wrappers small chip from upper edge of front wrapper. Johann Ambrosius Barth unknown