1306.5492 (David H. Oaknin)

Solving the EPR paradox with pseudo-classical paths    [PDF]

David H. Oaknin

We discuss a novel interpretation of the Heisenberg picture of Quantum Mechanics, which allows to integrate the principle of locality and an extended notion of physical realism and, hence, might solve the outstanding issue about the completeness of the theoretical framework. The discussion is presented in the context of Bohm's two photons system in which the Einstein-Podolski-Rosen paradox is commonly addressed. We show that quantum states can be described as statistical mixtures of non-interfering paths that obey pseudo-classical equations of motion and have well defined bayesian probabilities. Each one of these paths represents a post-selection of the system in one of the eigenstates of a complete set of commuting observables, so that, any other physical observable takes along the path its corresponding weak value. The weak value of a physical observable was first introduced by Y.Aharonov et al as the average output of a weak measurement in pre- and post-selected quantum systems. Hence, these statistical paths seems to be experimentally accessible. As weak values are not constrained either to belong to the spectrum of eigenvalues of their physical observables nor to fulfill standard classical algebraic relationships and they may even be complex, this statistical description of quantum states is not constrained by Bell's theorem and, indeed, it successfully reproduces all quantum mechanical correlations. Different choices of the complete set of commuting observables that fixes the post-selection conditions on the family of paths lead to symmetrically equivalent statistical descriptions of the quantum state.

View original: http://arxiv.org/abs/1306.5492