Jean Pierre Vigier

Dirac's aether in relativistic quantum mechanics

The introduction by Dirac of a new aether model based on a stochastic covariant distribution of subquantum motions (corresponding to a “vacuum state” alive with fluctuations and randomness) is discussed with respect to the present experimental and theoretical discussion of nonlocality in EPR situations. It is shown (1) that one can deduce the de Broglie waves as real collective Markov processes on the top of Diracs aether; (2) that the quantum potential associated with this aethers modification, by the presence of EPR photon pairs, yields a relativistic causal action at a distance which interprets the superluminal correlations recently established by Aspect et al.; (3) that the existence of the Einstein-de Broglie photon model (deduced from Diracs aether) implies experimental predictions which conflict with the Copenhagen interpretation in certain specific testable interference experiments.

Causal non-local character of quantum statistics

Abstract Developing Tersoff and Bayers ideas one shows that quantum statistics result from distinguishable particles correlated by causal non-local actions-at-a-distance. The difference between classical and quantum statistics thus results from the uncontrollable non-local character of stochastic interactions connecting particles imbedded in Diracs random aether.

Elimination of negative probabilities within the causal stochastic interpretation of quantum mechanics

Abstract Negative probabilities resulting from the Klein-Gordon equation are eliminated from quantum theory within the stochastic interpretation of quantum theory (SIQM) for spin-zero particles. The assumption of real physical paths in E 4 implies that only particles (antiparticles) of positive energies move forward in time with positive probability densities.

Causal stochastic interpretation of Fermi—Dirac statistics in terms of distinguishable non-locally correlated particles

Abstract Like in the Bose—Einstein case, Fermi—Dirac statistics are shown to correspond to subquantal, causal, space—time behaviour of distinguishable particles correlated by actions-at-a-distance. This justifies the introduction of the non-local hidden parameters introduced by Bohm and Vigier in the stochastic interpretation of quantum mechanics.

Proposed neutron interferometry test of Einstein's “Einweg” assumption in the Bohr-Einstein controversy

Abstract Recent technical progress of neutron detection is shown to allow the simultaneous observation of interference and individual energy losses in neutron interferometric double resonance experiments. This detection which is also predicted by the present mathematical formalism of quantum mechanics is shown to support Einsteins “Einweg” point of view in double slit experiments provided the proposed experiments satisfy the predictions of the said formalism.

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.

Positive probabilities and the principle of equivalence for spin-zero particles in the causal stochastic interpretation of quantum mechanics

SummaryThe effect of gravity on spin-0 particles is discussed in the context of the causal stochastic interpretation of quantum mechanics (SIQM). It is shown through the use of the quantum potential that, for positive probabilities which result from SIQM, the weak principle of equivalence breaks down. The theory nevertheless remains compatible with the geometrical character of quantum gravity.RiassuntoSi discute ’effetto della gravità sulle particelle con spin 0 nel contesto dell’interpretazione causale stocastica della meccanica quantistica (SIQM). Si mostra attraverso l’uso del potenziale quantistico che per probabilità positive che risultano da SIQM il principio di equivalenza debole è violato. La teoria ciò nondimeno resta compatibile con il carattere geometrico della gravità quantistica.РезюмеОбсуждается влияние гравитации на частицы с нулевым спином в связи с причинной стохастической интерпретацией квантовой механики. Используя кванговый потенциал, показывается, что для положительных вероятностей, которые являются следствием стохастической интерпретации квантовой механики, слабый принцип эквивалентности нарушается. Тем не менее, теория остается совместимой с геометрическим характером квантовой гравитации.

Illustration of the causal model of quantum statistics

As an illustration of the causal stochastic interpretation of quantum statistics it is shown, in the case of two particles in two harmonic oscillator wavepackets, that the different results for observables obtained with different statistics can be explained in terms of distinguishable particle motions correlated by the quantum potential.

Cosmology and the causal interpretation of quantum mechanics

Abstract We answer the objections raised recently by Tipler to the trajectory interpretation of quantum mechanics by analyzing in detail the scattering of a particle from a semi-transparent surface. We conclude that the notion of the “wavefunction of the universe” poses no particular problems for this interpretation.

Stable states of a relativistic harmonic oscillator imbedded in a random stochastic thermostat

An analysis in phase space of the behavior of a relativistic four-dimensional harmonic oscillator undergoing stochastic interactions shows that the group of linear canonical transformations in phase space which leaves invariant the Poisson brackets is anSp(12,4) group, withSp(12,4)⊃U(6,2)⊃SU(1,1)⊗SO(6,2). The application of Cartans treatment to its behavior implies a classification of its stable states characterized by a set of discrete numbers.