## A comparison of Whitehead's and Einstein's formulas (Eddington p. 192) WITH The law of dispersion and Bohr’s theory of spectra (Kramers p. 673-674) WITH Problems of Muscular Receptivity (Sherrington, pp. 892-894; 929-932) in Nature 113, 1924

London: Macmillan, 1924. 1st Edition. FIRST EDITION OF EDDINGTON’S PAPER PROPOSING A CHANGE IN COORDINATE SYSTEMS THAT WILL ELIMINATE THE SCHWARZSCHILD SINGULARITY.

The physical significance of this singularity, and whether this singularity could ever occur in nature, was debated for many decades” until the possibility of a black hole was accepted in the second half of the 20th century (Wikipedia). In this paper, Eddington made a coordinate change which transformed the Schwarzchild metric into a form which was not singular, thereby rejecting Schwarzchild’s implication of relativistic quantum mechanics rather than accept the possibility of black holes.

ALSO INCLUDED: FIRST EDITION OF KRAMERS’ LAW OF DISPERSION, A FORMULATION THAT CAME CLOSE TO PROVIDING A FORMULATION OF QUANTUM MECHANICS, BUT DID NOT DO SO. Prior to the development of matrix mechanics, a number of papers on the quantum theory of radiation and its dispersion came close to providing a formulation of quantum mechanics, and Kramer’s paper is one of those.

Electromagnetic radiation did not fit easily into the framework of the old quantum theory. “The task Kramers set himself was to fit dispersion phenomena into this framework, that is, to use the correspondence principle to derive expressions describing the reaction of material media to electromagnetic radiation. In face, he successfully derived such formulae which, moreover, contained only observable quantities and no longer contained attributes specific for the multiple periodic systems that he used as his model for the atoms” (ter Haar, Master of Modern Physics, 26).

“The path to quantum mechanics went over radiation theory, involving as an important component attempts to construct quantum-theoretical dispersion theories on the basis of difference rather than differential equations” (Kragh, Quantum Generations, 161). Kramers’s dispersion theory – an expression for the cross-section for scattering of a photon by an atomic electron -- was formulated in the context of the old quantum mechanics, then “introduce[d] quantum theory by invoking… the correspondence principle and first looking at the case of large quantum numbers” (Wikipedia; ter Haar).

“Kramers shows [in this paper] that a similar formula should hold in quantum theory. To each possible transition there corresponds a virtual oscillator with an effective value (e2/m) that can be calculated from the transition probabilities. For a transition to a higher level this value is positive but for a transition to a lower level it is negative, an entirely new feature closely related to Einstein’s stimulated emission” (CDSB).

Kragh argues that Kramers dispersion theory “can be seen as the first decisive step toward the new quantum mechanics” (Kragh,161).

ALSO INCLUDED: THE FIRST APPEARANCE IN PRINT OF CHARLES SHERRINGTON’S CLASSIC LINACRE LECTURE, “PROBLEMS OF MUSCULAR RECEPTIVITY”. Sherrington was the creator of many of the fundamental concepts of modern neurology, was a skilled experimentalist, and went on to win the Nobel Prize. Item #575

CONDITION & DETAILS: London: Macmillan. 4to. (11 x 8.25 inches; 275 x 206mm). Ex-libris bearing only minimal markings – a few stamps on the title page and none whatsoever on the spine. Full volume. Handsomely and professionally rebound in half leather. 5 raised bands at the spine, gilt-ruled. One red morocco label; one black morocco label; both gilt-lettered. Tightly and very solidly bound. Clean and bright throughout. Near fine condition.

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Price:
$450.00
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