The Two Postulates

Gabriel Catren

We propose the conjecture according to which the fact that quantum me-chanics does not admit sharp value attributions to both members of a com-plementary pair of observables can be understood in the light of the symplec-tic reduction of phase space in constrained Hamiltonian systems. In order to unpack this claim, we propose a quantum ontology based on two inde-pendent postulates, namely the phase postulate and the quantum postulate. The phase postulate generalizes the gauge correspondence between first-class constraints and gauge transformations to the observables of unconstrained Hamiltonian systems. The quantum postulate specifies the relationship be-tween the numerical values of the observables that permit us to individualize a physical system and the symmetry transformations generated by the oper-ators associated to these observables. We argue that the quantum postulate and the phase postulate are formally implemented by the two independent stages of the geometric quantization of a symplectic manifold, namely the prequantization formalism and the election of a polarization of pre-quantum states respectively.

R. Shankar

Michele Cini

Andrei Yu. Khrennikov

We show that the projection postulate plays a crucial role in the discussion on the so called "quantum nonlocality," in particular in the EPR-argument. We stress that the original von Neumann projection postulate was crucially modified by extending it to observables with degenerate spectra (the Lüders postulate) and we show that this modification is highly questionable from a physical point of view, and it is the real source of "quantum nonlocality." The use of the original von Neumann postulate eliminates this problem: instead of "action at the distance"-nonlocality, we obtain a classical measurement nonlocality. The latter is related to the synchronization of two measurements (on the two parts of a composite system). It seems that EPR did mistake in their 1935-paper: if one uses correctly von Neumann projection postulate, no "elements of reality" can be assigned to entangled systems. Our analysis of the EPR and projection postulate makes clearer Bohr's considerations in his reply to Einstein.

Michele Cini

Andrei Yu. Khrennikov

We show that the projection postulate plays a crucial role in the discussion on the so-called quantum nonlocality, in particular, in the Einstein, Podolsky, and Rosen argument. We stress that the original von Neumann projection postulate was crucially modified by extending it to observables with degenerate spectra (the Lüders postulate) and we show that this modification is highly questionable from a physical point of view and is the real source of quantum nonlocality. The use of the original von Neumann postulate eliminates this problem: instead of an action at a distance nonlocality we obtain a classical measurement nonlocality, which is related to the synchronization of two measurements (on the two parts of a composite system).