In his 1916's first paper on gravitational waves Einstein began to speculate on interactions between the principles of the old quantum theory and his theory of gravitation. With this contribution Einstein has stimulated a lot of similar speculations, during the dawn and the development of Quantum Mechanics. These speculations have culminated with the first attempt to quantize the gravitational field, that was provided by Rosenfeld in 1930. In this paper we briefly explain why this period (1916)(1917)(1918)(1919)(1920)(1921)(1922)(1923)(1924)(1925)(1926)(1927)(1928)(1929)(1930) should be inserted into the history of Quantum Gravity and then we focus on Klein's approach to the problem of reconciling Wave Mechanics with gravity, during the two-years period [1926][1927]. His attempt should be looked as the prehistory of Quantum Field Theory in a curved background. 1 Recent results [2] give approximately (4.354 ± 0.012) × 10 17 s. 2 See [4] for a commented English translation.3 Rosenfeld refers to this formalism as "the one-body theory proposed by Weyl [7]". 4 In those years physicists were used to talk about c-numbers (classical) and q-numbers (quantum). 7 We refer to Oskar Klein, not to be confused with Felix Klein. 8 In the old quantum theory there were two main approaches [25]: the particle approach and the wave approach. They led to the birth of Matrix Mechanics in 1925, developed by Heisenberg, Born and Jordan, and to the birth of Wave Mechanics at the beginning of 1926, developed by Schrödinger, respectively. 9 Klein himself admitted that his program failed because "as Dirac may well say, my main trouble came from trying to solve too many problems at a time!" [11].
In June 1888, Oliver Heaviside received by mail an officially unpublished pamphlet, which was written and printed by the American author Willard J. Gibbs around 1881-1884. This original document is preserved in the Dibner Library of the History of Science and Technology at the Smithsonian Institute in Washington DC. Heaviside studied Gibbs's work very carefully and wrote some annotations in the margins of the booklet. He was a strong defender of Gibbs's work on vector analysis against quaternionists, even if he criticized Gibbs's notation system. The aim of our paper is to analyse Heaviside's annotations and to investigate the role played by the American physicist in the development of Heaviside's work.
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