Relativistic Stochastic Processes and Related Questions

Gian Fabrizio De Angelis, Maurizio Serva

R Ramanathan

A heuristic model of space time under the influence of an underlying stochastic background is presented. It is shown that it is possible to view the whole of relativistic quantum mechanics as a Markovian stochastic process under certain conditions in a complex five dimensional space which models the influence of the background. Compactification of the extra dimension leads to the Klein-Gordon equation with the probabilistic interpretation in-built in the theory. The question of positivity of the variance in the context of complex space-time is circumvented by suggesting that positivity can break down after compactification.

Marcello Baldo

The compatibility of special relativity and Quantum Mechanics has been questioned by several authors. The origin of this tension can be traced back mainly to the introduction of the measurement processes and the corresponding wave function reduction, which play a crucial role in Quantum Mechanics. We approach this problem with the help of a recent proposal for a model of Quantum Mechanics, where the measurement is explicitly described as a specific stochastic process. This implements ordinary Quantum Mechanics, where measurement and reduction are treated as phenomenological events of unknown origin without any physical justification. To state clearly the question in general, we first discuss and establish the effect of a Lorentz transformation on a generic wave function in space-time. Alongside the analysis we formulate the relativistic version of the model. We then consider few thought experiments in order to analyze to what extent Quantum Mechanics follows relativistic invariance and find the specific critical points where non invariance possibly occurs. The analysis can shade light to the interpretation of the existing experimental observations.

Francesco Guerra, P. Ruggieko

Maurizio Serva

Anedio Ranfagni, Daniela Mugnai

A stochastic model for tunneling processes that is based on a close correspondence between quantum relativistic and telegrapher's equations is proposed along the lines of a procedure similar to the one already adopted by Kac [Rocky Mountain J. Math 4, 497 (1974)]. It is hypothesized that reversals of motion imply the inversion of the (imaginary) time rather than of the space, as in the ordinary allowed processes. In this way, superluminal behavior can be predicted in limiting cases. The plausibility of the superluminal motions observed is then discussed on the basis of a signal analysis along the lines of the Sommerfeld-Brillouin criterion which has been suitably modified.