A Probabilistic Model of Spin and Spin Measurements

Justo Pastor Lambare

William G. Faris

Amir Pishkoo, Yosra Sharifi, Ali Khotanloo

In this paper we study the system of non-interacting spins like electrons by using notions probability, soft sets and probabilistic soft sets. Electrons are indistinguishable identical particles whose spin is one of their features like mass of electron, charge of electron etc. We also compare two systems of non-interacting spins by defining two soft spin sets and calculating their similarity measure.

Peter Kienzler

Ana Marı́a Cetto

The electron spin correlation is shown to be expressible in terms of a bona fide probability distribution function with an associated geometric representation. With this aim, an analysis is presented of the probabilistic features of the spin correlation within the quantum formalism, which helps clarify the concepts of contextuality and measurement dependence. The dependence of the spin correlation on conditional probabilities allows for a clear separation between system state and measurement context; the latter determines how the probability space should be partitioned in calculating the correlation. A probability distribution function ρ(ϕ) is then proposed, which reproduces the quantum correlation for a pair of single-particle spin projections and is amenable to a simple geometric representation that gives meaning to the variable ϕ. The same procedure is shown to be applicable to the bipartite system in the singlet spin state. This endows the spin correlation with a clear probabilistic meaning and leaves the door open for a possible physical picture of the electron spin, as discussed at the end of the paper.

Franklin E. Schroeck