Leslie BallentineLeslie Ballentine is a professor of physics emeritus at Simon Fraser University in British Columbia, Canada. He is best known for his careful description and defense of Albert Einstein's "ensemble" or "statistical" interpretation of quantum mechanics.
The Statistical Interpretation of quantum theory is formulated for the purpose of providing a sound interpretation using a minimum of assumptions. Several arguments are advanced in favor of considering the quantum state description to apply only to an ensemble of similarity prepared systems, rather than supposing, as is often done, that it exhaustively represents an individual physical system. Most of the problems associated with the quantum theory of measurement are artifacts of the attempt to maintain the latter interpretation. The introduction of hidden variables to determine the outcome of individual events is fully compatible with the statistical predictions of quantum theory. However, a theorem due to Bell seems to require that any such hidden-variable theory which reproduces all of quantum mechanics exactly (i.e., not merely in some limiting case) must possess a rather pathological character with respect to correlated, but spacially separated, systems.The "pathological character" is nonlocality, which Einstein saw as early as 1905, and nonseparability, which he described in his 1935 EPR paper. When entangled systems are measured, their properties are perfectly correlated even though they show up at large spatial separations after the measurement. Ballentine does not seem to see that "correlated" measurements are actually made synchronously (in a special frame) as the two-particle wave function Ψ12 collapses for both particles when either particle is measured, or indeed when any interaction disentangles (decoheres) the two particles. All the properties of both particles become definite on the first measurement. A second measurement, on a now-distant particle, must conserve the total spin since spin is a constant of the motion. If spin was not conserved, it would be a much greater violation of the fundamental principles of physics than the appearance of Einstein's "spooky action at a distance." Ballentine is convinced that Einstein understood quantum mechanics as well or better than most of his colleagues, a point also made by Arthur Fine a few years later.
A serious reading of Einstein’s Reply [to Critics, in Schilpp volume] should clear up any misconceptions to the effect that he rejected quantum theory or misunderstood its foundations. In fact, he understood the essentially statistical nature of quantum theory as well as any of his contemporaries, and better than many. His only objection was against the assumption that a wave function or state vector could exhaustively describe an individual system, which we have seen to be an unwarranted and troublesome assumption. This fact, and the fact that Einstein advocated a fully viable interpretation of quantum theory (essentially the Statistical Interpretation of this paper although he expressed himself more briefly), do not seem to have been appreciated by his critics.Ballentine also questions the common interpretation of Werner Heisenberg's uncertainty principle as resulting from a "disturbance" made by the measuring apparatus.
The Uncertainty Principle finds its natural interpretation as a lower bound on the statistical dispersion among similarily prepared system (this interpretation being deduced, not introduced ad hoc), and is not in any real sense related to the possible disturbance of a system by a measurement. The distinction between measurement and state preparation is essential for clarity. It is possible to extend the formalism of quantum theory by the introduction of joint probability distributions for position and momentum. This demonstrates that there is no conflict with quantum theory in thinking of a particle as having definite (but, in general, unknown) values of both position and momentum, contrary to an earlier interpretation of the uncertainty principle.
ReferencesThe Statistical Interpretation of Quantum Mechanics, Physical Review, 1970. Einstein’s Interpretation of Quantum Mechanics, American Journal of Physics, 1972. Normal | Teacher | Scholar