Nelson’s stochastic quantum mechanics provides an ideal arena to test how the Born rule is established from an initial probability distribution that is not identical to the square modulus of the wavefunction. Here, we investigate numerically this problem for three relevant cases: a double-slit interference setup, a harmonic oscillator, and a quantum particle in a uniform gravitational field. For all cases, Nelson’s stochastic trajectories are initially localized at a definite position, thereby violating the Born rule. For the double slit and (...) harmonic oscillator, typical quantum phenomena, such as interferences, always occur well after the establishment of the Born rule. In contrast, for the case of quantum particles free-falling in the gravity field of the Earth, an interference pattern is observed before the completion of the quantum relaxation. This finding may pave the way to experiments able to discriminate standard quantum mechanics, where the Born rule is always satisfied, from Nelson’s theory, for which an early subquantum dynamics may be present before full quantum relaxation has occurred. Although the mechanism through which a quantum particle might violate the Born rule remains unknown to date, we speculate that this may occur during fundamental processes, such as beta decay or particle-antiparticle pair production. (shrink)

In his article on « Vampires », in the Dictionnaire philosophique, Voltaire both evokes the phenomenon of the so-called « vampire plague » which hit Central Europe during the 1730s and recalls the controversial interpretations of this phenomenon in France and abroad. He takes advantage of the occasion to renew his anti-religious polemic, with a caustic irony that doesn’t spare even a sincere Voltairian like Jean Baptiste Boyer d’Argens, who had offered a penetrating analysis of this phenomenon in his Lettres (...) Juives. In his text, Voltaire chooses satire rather than an inquiry into causes of the phenomenon, revealing a superficial anthropological approach as well as the limits of an argument conceived as pure ideology. (shrink)