Causality in Schwinger’s Picture of Quantum Mechanics

Abstract

This paper begins the study of the relation between causality and quantum mechanics, taking advantage of the groupoidal description of quantum mechanical systems inspired by Schwinger’s picture of quantum mechanics. After identifying causal structures on groupoids with a particular class of subcategories, called causal categories accordingly, it will be shown that causal structures can be recovered from a particular class of non-selfadjoint class of algebras, known as triangular operator algebras, contained in the von Neumann algebra of the groupoid of the quantum system. As a consequence of this, Sorkin’s incidence theorem will be proved and some illustrative examples will be discussed.

The space of light rays: Causality and L–boundary

“…As part of that goal, Penrose has pioneered various theories that have been remarkably successful for their achievements and originality, for instance, the study of causal relations [27,59], in the sense of describing the global properties of spacetime depending on what events influence to (or are influenced by) others. Most of the tools used in this field are quite simple, but the idea is powerful enough so that it has been very fruitful and still remains active today [1,14,33]. Non-spacelike curves are one of these tools, so if we would want to characterize the causality in any geometrical new model of the spacetime, then it will be necessary to describe such curves.…”

The space of light rays: Causality and $L$-boundary

“…As part of that goal, Penrose has pioneered various theories that have been remarkably successful for their achievements and originality, for instance, the study of causal relations [27], [59], in the sense of describing the global properties of spacetime depending on what events influence to (or are influenced by) others. Most of the tools used in this field are quite simple, but the idea is powerful enough so that it has been very fruitful and still remains active today [1], [33], [14]. Non-spacelike curves are one of these tools, so if we would want to characterize the causality in any geometrical new model of the spacetime, then it will be necessary to describe such curves.…”