Roland Omnès, Université de Paris XI
Two kinds of results regarding local properties of entanglement are given in this work and applied to the problem of collapse: 1. Strong cluster properties of local entanglement in a macroscopic system result directly from the Schrödinger equation when there is interaction with another system. These properties, which cannot be expressed by observables, are nevertheless associated with well-defined local probabilities, though different from standard quantum probabilities. They evolve with a finite velocity under nonlinear wave equations, until complete entanglement between the two systems. 2. When these local properties are extended to the interactions of a macroscopic system with its environment, and especially to fluctuations in these interactions, they induce a substantial level of incoherence in the quantum state of the system. These properties of clustering and of incoherence can combine together during a quantum measurement, to generate an explicit mechanism of random collapse in which randomness derives from incoherence and the associated outcomes of collapse are governed by Born’s probability rule. Although these results are partly conjectural, they seem suggestive enough for proposing their trend as a renovated strategy for approaching the collapse problem. Full text