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Gerry's avatar

Big "small classical step, giant quantum leap" vibes. Also "Why does anything exist?" does real contemplative (as opposed to meditative) work.

Philip Madden's avatar

Unitary evolution assumption isn’t the controversial one?!

Marek Żukowski has a very thorough debunking of this.

“Most importantly |ψ⟩ is defined by the preparation process (essentially, a filtering measurement), plus perhaps the deterministic evolution described by a unitary transformation. It allows to calculate probabilities for all possible measurements and accounts for complementarity. This means that it does not give a joint distribution of outcomes of all possible measurements (in classical mechanics the joint probability of q→ and p→ always exists). Fully complementary observables are linked with mutually unbiased orthonormal bases.

|ψ⟩ represents an equivalence class of preparations of physical systems. However since it gives only probabilistic predictions and probabilities are defined for statistical ensembles, it is a description of a statistical ensemble of equivalently prepared systems. One may give other additional attributes to |ψ⟩, but this one is fundamental. Without it the quantum formalism makes no sense (see discussion in [2]). The additional attributes are, e.g. the claim that |ψ⟩describes the individual quantum systems of the ensemble (Copenhagen interpretation in its most common form, [66]), that it represents directly unobservable relations in so-called Quantum Relational Space [37], or that there are non-local hidden variables behind it, and therefore is only an epistemic tool to describe observable effects caused by these (Bohmian interpretation). Interestingly, as pointed by R. Werner [66], the view that wavefunction describes a statistical ensemble of equivalently prepared systems was acceptable for Einstein himself: (cited from [66], originally published in [58]):

“One arrives at very implausible theoretical conceptions, if one attempts to maintain the thesis that the statistical quantum theory is in principle capable of producing a complete description of an individual physical system. On the other hand, these difficulties of theoretical interpretation disappear, if one views the quantum mechanical description as the description of ensembles of systems. I reached this conclusion as the result of quite different types of considerations. I am convinced that everyone who will take the trouble to carry through such reflections conscientiously will find himself finally driven to this interpretation of quantum-theoretical description (the ψ-function is to be understood as the description not of a single system but of an ensemble of systems)”.

As emphasized by Werner, Einstein’s main motivation when constructing the EPR argument [25] was the rejection of the “individual system” interpretation of ψ. Note, that most of the discussions on the EPR paper concentrate not on the interpretation of the “ψ function” but rather on the question of existence of (local) elements of reality, as additional hidden variables.

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