The set of principles formulated in 1915-1918, and now collectively called the old quantum theory... more The set of principles formulated in 1915-1918, and now collectively called the old quantum theory, were successfully applied to a number of problems in atomic and X-ray spectroscopy. The three most notable successes are all associated with the Munich school headed by Arnold Sommerfeld. First, there was the derivation of a relativistic fine-structure formula which predicted splittings of stationary state energies for orbits of varying eccentricity at a given principal quantum number. These splittings were empirically verified by Paschen for ionized helium, and constituted the first quantitative confirmation of the special relativistic mechanics introduced by Einstein a decade earlier. The relativistic fine-structure formula was also applied successfully to the splitting of lines in the X-ray spectra of atoms of widely varying atomic number. Finally, the principles of the old quantum theory (in particular, the use of Schwarzschild quantization in combination with Hamilton-Jacobi metho...
The development of the complex of assumptions and methods now referred to as the “old quantum the... more The development of the complex of assumptions and methods now referred to as the “old quantum theory” mainly took place in the first five years following the introduction of the Bohr atomic model in 1913. Three guiding principles emerged that were used, sometimes in overlapping ways, to explain the flood of spectroscopic data that needed to be explained. First, quantization rules (or conditions) were proposed to single out the allowed orbital motions of electrons in atoms. These rules were derived in various forms by Planck, Sommerfeld, and Wilson, but were put into their most general form by Schwarzschild, who recognized the underlying principle as the quantization of the action variables of a multiply periodic classical system. Second, the special role of the action variables in quantization was given convincing support by the transfer of the adiabatic principle of mechanics to quantum theory (work primarily due to Paul Ehrenfest). Third, the correspondence principle, or statement...
The Oxford Handbook of the History of Quantum Interpretations
We trace the evolution of quantization conditions from Max Planck’s introduction of a new fundame... more We trace the evolution of quantization conditions from Max Planck’s introduction of a new fundamental constant (h) in his treatment of blackbody radiation in 1900 to Werner Heisenberg’s interpretation of the commutation relations of modern quantum mechanics in terms of his uncertainty principle in 1927.
On November 23, 2021, the Einstein-Besso manuscript on the perihelion motion of Mercury will be a... more On November 23, 2021, the Einstein-Besso manuscript on the perihelion motion of Mercury will be auctioned at Christie’s. Expected to fetch around $3M, it promises to be the most expensive scientific manuscript ever sold at auction. In this preprint, we present the parts of our forthcoming book, How Einstein Found His Field Equations. Sources and Interpretation (Springer, 2021) dealing with Einstein’s attempts, in 1913 and in 1915, to account for the anomalous advance of Mercury’s perihelion. In 1913, as documented in the Einstein-Besso manuscript, Einstein and his friend Michele Besso found that the Einstein-Grossmann or Entwurf (= outline or draft) theory, a preliminary version of general relativity, could only account for 18 of the 43 seconds-of-arc-per-century discrepancy between Newtonian theory and observation. In November 1915, however, putting the techniques developed in his collaboration with Besso to good use, Einstein showed that his new general theory of relativity could ...
In 1913, Albert Einstein and Michele Besso tried to explain the anomalous advance of Mercury'... more In 1913, Albert Einstein and Michele Besso tried to explain the anomalous advance of Mercury's perihelion on the basis of the precursor theory of general relativity. A manuscript bundle documents their work. This manuscript was recently auctioned for a record amount. The paper gives a brief discussion of the significance and history of this manuscript.
In October 1924, The Physical Review, a relatively minor journal at the time, published a remarka... more In October 1924, The Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Van Vleck used Bohr’s correspondence principle and Einstein’s quantum theory of radiation to find quantum formulae for the emission, absorption, and dispersion of radiation. The paper is similar but in many ways superior to the well-known paper by Kramers and Heisenberg published the following year that is widely credited to have led directly to Heisenberg’s Umdeutung paper. As such, it clearly shows how strongly the discovery of matrix mechanics depended on earlier work on the application of the correspondence principle to the interaction of matter and radiation.
After three papers on statistical mechanics, mostly duplicating work by Boltzmann and Gibbs, Eins... more After three papers on statistical mechanics, mostly duplicating work by Boltzmann and Gibbs, Einstein relied heavily on arguments from statistical mechanics in the most revolutionary of his famous 1905 papers, the one introducing the light‐quantum hypothesis. He showed that the equipartition theorem inescapably leads to the classical Rayleigh‐Jeans law for black‐body radiation and the ultraviolet catastrophe (as Ehrenfest later called it). Einstein and Ehrenfest were the first to point this out but the physics community only accepted it after the venerable H.A. Lorentz, came to the same conclusion in 1908. The central argument for light quanta in Einstein’s 1905 paper involves a comparison between fluctuations in black‐body radiation in the Wien regime and fluctuations in an ideal gas. From this comparison Einstein inferred that black‐body radiation in the Wien regime behaves as a collection of discrete, independent, and localized particles. We show that the same argument works for ...
The Nachlass of Einstein’s close friend and confidant Michele Besso (1873–1955) contains four pag... more The Nachlass of Einstein’s close friend and confidant Michele Besso (1873–1955) contains four pages, written on a folded sheet, with what appear to be Besso’s notes of discussions with Einstein about a preliminary version of general relativity known in the historical literature as the “Entwurf” (“outline”) theory.1 The first two pages of this Besso memo are reproduced in facsimile in Figs. 1 and 2.2 Of the various points recorded in the memo two in particular are bound to catch the eye of a modern historian of relativity. First, under point “b) 2.” on the first page, Besso writes:
Inspired by the Monty Hall Problem and a popular simple solution to it, we present a simple solut... more Inspired by the Monty Hall Problem and a popular simple solution to it, we present a simple solution to the notorious Sleeping Beauty Problem. We replace the awakenings of Sleeping Beauty by contestants on a game show like Monty Hall’s and we increase the number of awakenings/contestants in the same way that the number of doors in the Monty Hall Problem is increased to make it easier to see what the solution to the problem is. We show that the Sleeping Beauty Problem and variations on it can be solved through simple applications of Bayes’s theorem. This means that we will phrase our analysis in terms of credences or degrees of belief. We will also rephrase our analysis, however, in terms of relative frequencies. Overall, our paper is intended to showcase, in a simple yet non-trivial example, the efficacy of a tried-andtrue strategy for addressing problems in philosophy of science, i.e., develop a model for the problem and vary its parameters. Given that the Sleeping Beauty Problem, ...
The set of principles formulated in 1915-1918, and now collectively called the old quantum theory... more The set of principles formulated in 1915-1918, and now collectively called the old quantum theory, were successfully applied to a number of problems in atomic and X-ray spectroscopy. The three most notable successes are all associated with the Munich school headed by Arnold Sommerfeld. First, there was the derivation of a relativistic fine-structure formula which predicted splittings of stationary state energies for orbits of varying eccentricity at a given principal quantum number. These splittings were empirically verified by Paschen for ionized helium, and constituted the first quantitative confirmation of the special relativistic mechanics introduced by Einstein a decade earlier. The relativistic fine-structure formula was also applied successfully to the splitting of lines in the X-ray spectra of atoms of widely varying atomic number. Finally, the principles of the old quantum theory (in particular, the use of Schwarzschild quantization in combination with Hamilton-Jacobi metho...
The development of the complex of assumptions and methods now referred to as the “old quantum the... more The development of the complex of assumptions and methods now referred to as the “old quantum theory” mainly took place in the first five years following the introduction of the Bohr atomic model in 1913. Three guiding principles emerged that were used, sometimes in overlapping ways, to explain the flood of spectroscopic data that needed to be explained. First, quantization rules (or conditions) were proposed to single out the allowed orbital motions of electrons in atoms. These rules were derived in various forms by Planck, Sommerfeld, and Wilson, but were put into their most general form by Schwarzschild, who recognized the underlying principle as the quantization of the action variables of a multiply periodic classical system. Second, the special role of the action variables in quantization was given convincing support by the transfer of the adiabatic principle of mechanics to quantum theory (work primarily due to Paul Ehrenfest). Third, the correspondence principle, or statement...
The Oxford Handbook of the History of Quantum Interpretations
We trace the evolution of quantization conditions from Max Planck’s introduction of a new fundame... more We trace the evolution of quantization conditions from Max Planck’s introduction of a new fundamental constant (h) in his treatment of blackbody radiation in 1900 to Werner Heisenberg’s interpretation of the commutation relations of modern quantum mechanics in terms of his uncertainty principle in 1927.
On November 23, 2021, the Einstein-Besso manuscript on the perihelion motion of Mercury will be a... more On November 23, 2021, the Einstein-Besso manuscript on the perihelion motion of Mercury will be auctioned at Christie’s. Expected to fetch around $3M, it promises to be the most expensive scientific manuscript ever sold at auction. In this preprint, we present the parts of our forthcoming book, How Einstein Found His Field Equations. Sources and Interpretation (Springer, 2021) dealing with Einstein’s attempts, in 1913 and in 1915, to account for the anomalous advance of Mercury’s perihelion. In 1913, as documented in the Einstein-Besso manuscript, Einstein and his friend Michele Besso found that the Einstein-Grossmann or Entwurf (= outline or draft) theory, a preliminary version of general relativity, could only account for 18 of the 43 seconds-of-arc-per-century discrepancy between Newtonian theory and observation. In November 1915, however, putting the techniques developed in his collaboration with Besso to good use, Einstein showed that his new general theory of relativity could ...
In 1913, Albert Einstein and Michele Besso tried to explain the anomalous advance of Mercury'... more In 1913, Albert Einstein and Michele Besso tried to explain the anomalous advance of Mercury's perihelion on the basis of the precursor theory of general relativity. A manuscript bundle documents their work. This manuscript was recently auctioned for a record amount. The paper gives a brief discussion of the significance and history of this manuscript.
In October 1924, The Physical Review, a relatively minor journal at the time, published a remarka... more In October 1924, The Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Van Vleck used Bohr’s correspondence principle and Einstein’s quantum theory of radiation to find quantum formulae for the emission, absorption, and dispersion of radiation. The paper is similar but in many ways superior to the well-known paper by Kramers and Heisenberg published the following year that is widely credited to have led directly to Heisenberg’s Umdeutung paper. As such, it clearly shows how strongly the discovery of matrix mechanics depended on earlier work on the application of the correspondence principle to the interaction of matter and radiation.
After three papers on statistical mechanics, mostly duplicating work by Boltzmann and Gibbs, Eins... more After three papers on statistical mechanics, mostly duplicating work by Boltzmann and Gibbs, Einstein relied heavily on arguments from statistical mechanics in the most revolutionary of his famous 1905 papers, the one introducing the light‐quantum hypothesis. He showed that the equipartition theorem inescapably leads to the classical Rayleigh‐Jeans law for black‐body radiation and the ultraviolet catastrophe (as Ehrenfest later called it). Einstein and Ehrenfest were the first to point this out but the physics community only accepted it after the venerable H.A. Lorentz, came to the same conclusion in 1908. The central argument for light quanta in Einstein’s 1905 paper involves a comparison between fluctuations in black‐body radiation in the Wien regime and fluctuations in an ideal gas. From this comparison Einstein inferred that black‐body radiation in the Wien regime behaves as a collection of discrete, independent, and localized particles. We show that the same argument works for ...
The Nachlass of Einstein’s close friend and confidant Michele Besso (1873–1955) contains four pag... more The Nachlass of Einstein’s close friend and confidant Michele Besso (1873–1955) contains four pages, written on a folded sheet, with what appear to be Besso’s notes of discussions with Einstein about a preliminary version of general relativity known in the historical literature as the “Entwurf” (“outline”) theory.1 The first two pages of this Besso memo are reproduced in facsimile in Figs. 1 and 2.2 Of the various points recorded in the memo two in particular are bound to catch the eye of a modern historian of relativity. First, under point “b) 2.” on the first page, Besso writes:
Inspired by the Monty Hall Problem and a popular simple solution to it, we present a simple solut... more Inspired by the Monty Hall Problem and a popular simple solution to it, we present a simple solution to the notorious Sleeping Beauty Problem. We replace the awakenings of Sleeping Beauty by contestants on a game show like Monty Hall’s and we increase the number of awakenings/contestants in the same way that the number of doors in the Monty Hall Problem is increased to make it easier to see what the solution to the problem is. We show that the Sleeping Beauty Problem and variations on it can be solved through simple applications of Bayes’s theorem. This means that we will phrase our analysis in terms of credences or degrees of belief. We will also rephrase our analysis, however, in terms of relative frequencies. Overall, our paper is intended to showcase, in a simple yet non-trivial example, the efficacy of a tried-andtrue strategy for addressing problems in philosophy of science, i.e., develop a model for the problem and vary its parameters. Given that the Sleeping Beauty Problem, ...
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