Leslie Ballentine

(1940-)

Leslie 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 Statistical Interpretation of Quantum Mechanics," *Rev. Mod. Phys.*, Vol.42, No.4, 1970, p.358)

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 Ψ_{12} collapses for both particles when either particle is measured, or indeed when any interaction *disentangles* (decoheres) the two particles. There is always only one measurement, not two. All the properties of both particles become definite on the first measurement

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.
( *ibid.*, p.379)

Uncertainty Principle

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.
( *ibid.*, p.379)

References

The Statistical Interpretation of Quantum Mechanics,

*Physical Review*, 1970.

Einstein’s Interpretation of Quantum Mechanics, *American Journal of Physics*, 1972.

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