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Leslie Ballentine develops in QM: A Modern Development an interpretation based on the ensemble interpretation, and responds to most criticisms.

My question: what criticisms still exist against this interpretation such that it is not recognized as the standard interpretation within the physics community?

What problems still exist?

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L. Ballentine[1970] The Statistical Interpretation of Quantum Mechanics – user44342 Sep 4 at 20:52

3 Answers 3

The problem with Ensemble interpretation is that the quantum state of a uranium atom in its ground state, including the nucleus and the electrons, is a property of one atom, not of an ensemble. You don't need to measure the electron position, you can just subject the atom to external forces, and see how it moves. This motion is predicted by the wavefunction of the one atom, not of any ensemble.

It is logically possible to reject this position, of course, but then you are claiming that a quantum description cannot be given to an individual system, and you renounce the ability to map physical objects to mathematical objects so that the behavior of one is isomorphic to the behavior of the other. This is an enormous weakening of the goal of physical science, that there would be no point in doing physics. Also, it throws away the many cases where quantum mechanics makes firm predictions about the behavior of individual systems.

The Wikipedia page erronously claims that Einstein supported the Ensemble idea. This is false, but there is a quote that makes it seem true. Einstein was referring to hidden variables here, and the reason he states it in terms of ensembles is because he believed that the wavefunction described a statistical pattern for hidden variables which is analogous to statistical mechanical distributions. These statistical distributions do not describe a single particle (at least not in a straightforward interpretation), because the particle has a hidden position deep down underneath. The averages of many position measurements require an ensemble, and these measure the wavefunction. Einstein used the term "ensemble" in the context of quantum mechanics to emphasize the probabilistic nature of the wavefunction, not the inability to describe an individual system.

Einstein also believed that the quantum mechanical description of an individual system, inasmuch as it was deterministic, was correct. It was only the probabilistic aspects of the description that required hidden variables, of course, just like classical theormodynamics. You don't need an ensemble to describe the motion of piston pushing a gas, only for the statistically random motion of individual molecules.

A true ensemble interpretation renounces the description of a physical system entirely, leaving only the description of the statistics of identical measurment. It is not what Einstein had in mind, and it is not reasonable in the majority of cases where quantum systems are in their ground state, and changing adiabatically, so that they essentially reproduce deterministic classical behavior.

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This assumes you can actually do experiments with one single atom. – nbubis Jan 22 '14 at 2:59
@ron state describes part of the description of similarly prepared systems(Which is called an ensemble) according to the ensemble interpretation. In this case the system should be the Uranium itself. Here the ensemble is similarly prepared uranium atoms.If you want to talk about the state of an electrons in the uranium atom, then that means u have to consider similarly obtained electrons (Ballentine[1970]) – user44342 Sep 4 at 21:00
I'm confused why you say "you can just subject the atom to external forces, and see how it moves. This motion is predicted by the wavefunction of the one atom, not of any ensemble." QM would not predict the result of any single position measurement of a single uranium atom (unless the distribution is a dirac delta), it would only speak of the distribution of position measurements made on similarly prepared but different uranium atoms. – David Santo Pietro Oct 17 at 16:09
I'm confused when you say "This is an enormous weakening of the goal of physical science, that there would be no point in doing physics". Haven't we always had to verify QM and QFT with measurements on similarly prepared systems (which could be similarly prepared single particles) anyways? I don't see how adopting an ensemble interpretation would actually change how we do physics at all. It might change how we think about physics or feel about physics, but at the end of the day would we not still do physics in the lab the same way we always did it? – David Santo Pietro Oct 17 at 16:16

The different components of the wave function interfere constructively and destructively under time evolution. Translated into the ensemble interpretation, it would mean different elements of the ensemble can and will interfere with each other with the phase information preserved intact.

What preferred basis should the definite outcomes of the elements of the ensemble be in? Maybe we have an ensemble over all possible bases to avoid being forced to make an arbitrary choice point blank. In an ensemble of Schroedinger cats, there will be bases mixing up live and dead cats.

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-1: this is completely wrong. The ensemble in the interpretation is not a bunch of particles doing the same thing, it is an ensemble of experiments which give a meaning to the probabilities in a non-deterministic theory. It does not postulate an actual ensemble underneath quantum mechanics. – Ron Maimon Oct 11 '11 at 15:55

Think of the double slit experiment. It is possible to make the particle beam as weak as you want, e.g. so that you have less than one particle per second. So there is - with certainty - only one patricle in the apparatus at each moment in time. Nevertheless, the wave parts of the function for each slit interfere. So you can't assume it is an ensemle of particles where the wave functions of different particles interfere.

(@Ron: There is no ensemble postulate at all. The ensemble interpretation was just a try to understand QM, from the 30s of the last century. An ensemble of experiments seems not to lead to such problems, right - but thats not what was meant with ensemble interpretation.)

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