l x x x v i I N T R O D U C T I O N T O V O L U M E 1 5 applied to a monochromatic plane light wave. He praised Heisenberg’s paper as signifying “a most meaningful contribution,” and discussed the connection be- tween quantum and classical physics in light of the uncertainty relations. We may detect here the seeds of Bohr’s version of the Copenhagen interpretation and the beginning of the enduring Einstein–Bohr dialogue on the interpretation and valid- ity of quantum mechanics. As far as we know, Einstein did not answer Bohr’s letter. But Born’s probabilis- tic interpretation of Schrödinger’s wave function and Heisenberg’s uncertainty re- lations were no doubt on his mind when, three weeks later, he completed a manuscript titled “Does Schrödinger’s Wave Mechanics Completely Determine the Motion of a System, or Only Statistically?” (Doc. 516). The paper contains many novelties. First, Einstein explores not only the properties of Schrödinger’s equation, but also takes up Schrödinger’s idea of using Riemannian geometry to better under- stand the structure of the configuration space on which the wave function ψ is defined. He defines a Riemannian metric on configuration space and calls the sec- ond covariant derivative of ψ (with respect to the derivative operator compatible with the metric) the “tensor of ψ-curvature” the twice-contracted “tensor of ψ- curvature” he calls the “scalar of ψ-curvature.” Second, Einstein spells out a notion of what it would mean to complement the description of a physical system described by the wave function in such a way that the description becomes “complete.” He assumes that the configuration space is n- dimensional, that is, he assumes that n particles move in one spatial dimension. Their description would be complete, Einstein argues, if one could associate n directions to the n dimensions of configuration space and if the energy of the total system could be written as a sum of n terms uniquely corresponding to the n direc- tions in configuration space. For one could then associate to each of these terms a corresponding velocity, and the sum of all these velocity vectors would be the ve- locity vector of the total system in configuration space. This latter vector would then be completely described. Third, Einstein implicitly defines a variational problem in terms of the scalar of ψ-curvature, and introduces Lagrange multipliers λ, which result in principal directions in configuration space, to solve the problem thus posed. It has been argued that by introducing principal directions of configuration space, Einstein effectively introduced what would today be called hidden variables. However, a distinction may be made between dynamical and nondynamical hidden variables
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