Quantum entanglement, interaction, and the classical limit

Two or more quantum systems are said to be in an entangled or non-factorisable state if their joint (supposedly pure) wave-function is not expressible as a product of individual wave functions but is instead a superposition of product states. It is only when the systems are in a factorisable state that they can be considered to be separated (in the sense of Bell). We show that whenever two quantum systems interact with each other, it is impossible that all factorisable states remain factorisable during the interaction unless the full Hamiltonian does not couple these systems so to say unless they do not really interact. We also present certain conditions under which particular factorisable states remain factorisable although they represent a bipartite system whose components mutually interact. We identify certain quasi-classical regimes that satisfy these conditions and show that they correspond to classical, pre-quantum, paradigms associated to the concept of particle

Estimate of the weight of empty space based on astronomical observations

As a consequence of the equivalence principle and of the existence of a negative vacuum energy, we show how a weak but universal linear response of the vacuum to a local gravitational potential suffices to explain the main features of so-called Pioneer anomalies as well as the apparent departure from the third Kepler law which has been observed at the level of numerous galaxies.Comment: submitted to EP

Generalized guidance equation for peaked quantum solitons: the single particle case

We study certain non-linear generalisations of the Schr{\"o}dinger equation which admit static solitonic 2 solutions in absence of external potential acting on the particle. We consider a class of solutions that can be written as a product of a solution of the linear Schr{\"o}dinger equation with a peaked quantum soliton, in a regime where the size of the soliton is quite smaller than the typical scale of variation of the linear wave. In the non-relativistic limit, the solitons obey a generalized de Broglie-Bohm (dB-B) guidance equation. In first approximation, this guidance equation reduces to the dB-B guidance equation according to which they move at the so-called de Broglie-Bohm velocity along the hydrodynamical flow lines of the linear Schr{\"o}dinger wave. If we consider a spinorial electronic wave function a la Dirac, its barycentre is predicted to move exactly in accordance with the dB-B guidance equation.Comment: The second version of this paper will be published in 2017 in a special issue devoted to the Double Solution Program of Louis de Broglie under the title: "de Broglie's double solution and self-gravitation