Einstein’s description of wave-particle duality is as good as anything written today. He saw the relation between the wave and the particle as the relation between probable possibilities and the realization of one possibility as an actual event. He saw the wave spreading out in space and giving us the probable number of particles in different locations. Where Einstein saw the particle as concrete and material, he described the wave as a “ghostly field,” which is exactly right according to the information interpretation of quantum mechanics. The wave is neither matter nor energy, but pure abstract information about locating concrete matter and energy.
The information about probabilities and possibilities in the wave function is immaterial, but that abstract information has real causal powers. The wave’s interference with itself predicts null points where no particles should be found. And experiments confirm that no particles are found there. Immaterial information is a kind of modern “spirit.” Einstein also described the wave function as a “ghost field” (Gespensterfeld) or a “guiding field” (Führungsfeld), an idea taken up later by Louis de Broglie as his “pilot waves.” Following de Broglie, Schrödinger developed his equation that describes how the probability wave function moves through space deterministically. This restoration of some determinism was a brief bright moment for Einstein. He saw a possible return to a deterministic theory for quantum mechanics and his continuous field theory. But it was not to be, despite the large number of present-day physicists who are still pursuing Einstein’s and Schrödinger’s deterministic dreams, by denying indeterminism and “quantum jumping.”
Einstein could never accept most of his quantum discoveries because they conflicted with his basic idea that nature is best described by a continuous field theory using differential equations that are functions of “local” variables, primarily the space-time four-vector of his general relativistic theory. Einstein’s idea of a “local” reality is one where “action-at-a-distance” is limited to causal effects that propagate at or below the speed of light, according to his theory of relativity.
Einstein believed that quantum theory, as good as it is (and he never saw anything better), is “incomplete.” This is so, because its statistical predictions (phenomenally accurate in the limit of large numbers of identical experiments – “ensembles” Einstein called them), tell us nothing but “probabilities” about individual systems. Even worse, he thought that the wave functions of entangled two-particle systems predict faster-than-light correlations of properties between events in a space-like separation. He mistakenly thought this violated his theory of relativity. Although this was the heart of his famous EPR paradox paper in 1935, we shall see that Einstein was already concerned about faster-than-light transfer of energy and that he saw spherical light waves “collapsing” instantaneously in his very first paper on quantum theory in 1905 and in his second 1909 paper on wave-particle duality.