Quantum Cellular Automata, the Epr Paradox and the Stages Paradigm

Abstract

In 1935 Einstein, Podolsky and Rosen proposed a thought experiment designed to highlight the incompleteness of quantum mechanics. There have since been a number of variants on the original EPR theme, but the set-up considered in this report consists of a neutral pion decaying to an electron-positron pair, π⁰ → e ^- + e ⁺. Electrons and positrons possess spin components of ±½ (denoted by ‘up’ and ‘down’ in some frame) whereas pions are spinless, so by conservation of angular momentum a spin-up electron is partnered by a spin-down positron, and vice versa. Given that Hidden Variables types of interpretation have been empirically ruled out, quantum mechanics states that before the spin of one of the particles is measured, both it and its partner are in both spin states simultaneously, and the outgoing wavefunction | Ψ〉 is described by a linear superposition:

$$ \left| \psi \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| \uparrow \right\rangle e \otimes \left| \downarrow \right\rangle _p - \left| \downarrow \right\rangle e \otimes \left| \uparrow \right\rangle _p } \right). $$

((1))