N. Cufaro Petroni

A review of extended probabilities

Abstract Some results emerging from the formalism of quantum theory seem to indicate probabilities outside of the conventional range between 0 and 1. This article draws attention to arguments in favour of extended probalilites, reviews some approaches to a formal account and interpretation, and presents a collection of statements of distinguished scientists about this strange topic.

Stochastic derivation of Proca's equation in terms of a fluid of Weyssenhoff tops endowed with random fluctuations at the velocity of light

Abstract If one analyzes the stochastic behaviour of classical Weyssenhoff particles imbedded in a relativistic thermostat one obtains (for random jumps at the velocity of light) a probability distribution corresponding to Procas equations for nonzero-mass spin-one particles.

Mixtures in non stable Levy processes

We analyse the Lprocesses produced by means of two interconnected classes of nonstable, infinitely divisible distribution: the variance gamma and the Student laws. While the variance gamma family is closed under convolution, the Student one is not: this makes its time evolution more complicated. We prove that—at least for one particular type of Student processes suggested by recent empirical results, and for integral times—the distribution of the process is a mixture of other types of Student distributions, randomized by means of a new probability distribution. The mixture is such that along the time the asymptotic behaviour of the probability density functions always coincide with that of the generating Student law. We put forward the conjecture that this can be a general feature of the Student processes. We finally analyse the Ornstein-Uhlenbeck process driven by our Lnoises and show a few simulations of it.

A causal stochastic theory of spin-1/2 fields

SummaryA hydrodynamical analysis of the second-order wave equation of spin-1/2 fields is deduced from a Lagrangian formalism. The explicit form of the corresponding quantum potential is calculated: a basis to discuss causal nonlocal actions at a distance in EPR-type experiments. A stochastic derivation (following the lines of Nelson, Guerra, Ruggiero and Vigier) is presented, based on a model of extended bilocal subelements.RiassuntoSi deduce da un formalismo Lagrangiano un’analisi idrodinamica dell’equazione d’onda del second’ordine per campi di spin 1/2. Si calcola la forma esplicita del corrispondente potenziale quantistico: una base per la discussione di azioni a distanza causali e non locali negli esperimenti del tipo EPR. Si espone una derivazione stocastica (secondo la linea di Nelson, Guerra, Ruggiero e Vigier) basata su un modello a sottoelementi estesi e bilocali.РезюмеВ рамках лагранжева формализма проводится гидродинамический анализ волнового уравнения второго порядка для полей со спином 1/2. Вычисляется явная форма соответствующего квантового потенциала. Обсуждается причинное нелокальное действие на расстоянии в эксперименте EPR типа. Предлагается стохастический вывод, основанный на модели обобщенных билокальных субэлементов.

Stochastic mechanics and quantum interference

Abstract It is shown that in the framework of the stochastic interpretation of quantum mechanics it is always possible to determine correct real positive transition probabilities that can be added together to obtain the quantum interference patterns. The implication of this fact on the possibility that quantum micro-objects follow trajectories in space and time is discussed. A derivation is given of a path integral formula yielding these transition probabilities.

Stochastic derivation of the Dirac equation in terms of a fluid of spinning tops endowed with random fluctuations at the velocity of light

Abstract If one analyzes the stochastic behaviour of classical “rigid” tops imbedded in Diracs aether (relativistic thermostat) one obtains (for random jumps at the velocity of light) a probability distribution corresponding to the Feynman-Gell-Mann equation for relativistic spin 1 2 particles.

Markov Process at the Velocity of Light: The Klein-Gordon Statistic

The Markovian random walk of a point at the velocity of light on a two-dimensional invariant space-time lattice is shown to yield the quantum statistic associated with the Klein-Gordon equation. Quantum mechanics thus appears as a particular case of Markovian processes in velocity space: and one justifies the introduction of Diracs invariant “ether” as a possible physical stochastic subquantum level of matter which yields a realistic mechanical basis for recent attempts to reinterpret quantum mechanics in terms of material, causal, random behavior.

Causal space-time paths of individual distinguishable particle motions in N -body quantum systems: Elimination of negative probabilities

SummaryThe quantum Klein-GordonN-particle system is shown to admit a causal space-time description. In the frame of the stochastic interpretation of quantum mechanics, we show how an explicit world-line construction should be undertaken and prove that positive energy is always associated with positive probability densities.

Stochastic model for the motion of correlated photon pairs

Abstract If one analyzes the stochastic behaviour of two massive ( m γ ≠0) photons imbedded in Diracs vacuum one obtains (with stochastic jumps at velocity of light) the two-particle Proca equations which one can use to interpret (i) the first results of the Aspect experiment; (ii) the future issues of the complete Aspect and Rapisarda experiments, if they will violate Bells inequality.

An alternative derivation of the spin-dependent quantum potential

SummaryA new derivation, avoiding the difficulties of the old demonstrations, is given for the quantum potential form of spin-2/1 fields.