Is Quantum Mechanics Incomplete? Einstein Thought Dirac’s Statistical Theory Was Perfect, Though Not A Field Theory

In 1931, Einstein said of Paul Dirac

“Dirac, to whom, in my opinion, we owe the most perfect exposition, logically, of this [quantum] theory, rightly points out that it would probably be difficult, for example, to give a theoretical description of a photon such as would give enough information to enable one to decide whether it will pass a polarizer placed (obliquely) in its way or not.” Maxwell’s Influence on the Evolution of the Idea of Physical Reality…1931, Ideas and Opinions, p.270

Four years later, in the infamous EPR paper, Einstein said quantum theory appears tp be “incomplete.” He believed that quantum theory, as good as it is (and he never saw anything better), is incomplete 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 saw 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 most general histories, and in the brief histories included in modern quantum mechanics textbooks, the problems raised by Einstein are usually presented as arising after the “founders” of quantum mechanics and their Copenhagen Interpretation in the late 1920’s. Modern attention to Einstein’s work on quantum physics often starts with the Einstein-Podolsky-Rosen paper of 1935, when the mysteries of nonlocality, nonseparability, and entanglement are first clearly understood by Einstein’s opponents. Physicists today think of quantum mechanics as beginning with the Heisenberg (particle) formulation and the Schrödinger (wave) formulation. The popular image of Einstein post-EPR is either in the role of critic trying to expose fundamental flaws in the “new” quantum mechanics or as an old man who simply didn’t understand the new quantum theory. Both these images of Einstein are seriously flawed, as we shall see.

Many histories of quantum theory, most starting from the Copenhagen perspective of Bohr, Heisenberg, Born, Jordan, and Pauli, focus on Einstein’s failed attempts in debates with Bohr to challenge the uncertainty principle. EPR is described as failing to show that quantum mechanics is “incomplete.” This is a verbal quibble. Quantum mechanics is indeed incomplete in that it cannot predict simultaneously the position and momentum of a particle, nor the “real” path of a particle between measurements. Most important, QM is only a statistical theory, as Einstein maintained. Its results are only confirmed by large numbers of identical experiments. Continuous matter and radiation only appear when we average over large numbers of discrete particles.

Few histories point out that it was Einstein who over three decades invented (or discovered) nonlocality and entanglement, as well as the ontological chance in quantum mechanics that is the real basis of acausality that Heisenberg thought he saw in his uncertainty principle.

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