A categorial approach to relativistic locality

Abstract

Relativistic locality is interpreted in this paper as a web of conditions expressing the compatibility of a physical theory with the underlying causal structure of spacetime. Four components of this web are distinguished: spatiotemporal locality, along with three distinct notions of causal locality, dubbed CLIndependence, CL-Dependence, and CL-Dynamic. These four conditions can be regimented using concepts from the categorical approach to quantum field theory initiated by Brunetti, Fredenhagen, and Verch [1]. A covariant functor representing a general quantum field theory is defined to be causally local if it satisfies the three CL conditions. Any such theory is viewed as fully compliant with relativistic locality. We survey current results indicating the extent to which an algebraic quantum field theory satisfying the Haag-Kastler axioms is causally local.Keywords: Quantum field theory, category theory, operator algebra theory, causality The main claimsThe question of whether quantum theory is compatible with relativity theory is a central issue in philosophy and foundations of physics. The compatibility in question would manifest in quantum theory satisfying "relativistic locality" conditions that express harmony of quantum theory with the conceptual picture of the physical world according to theory of relativity. Whether such a harmony $ Forthcoming in Studies in History and Philosophy of Modern Physics.

Categorial Subsystem Independence as Morphism Co-possibility

“…According to this independence concept two objects are independent in a larger object with respect to a class of morphisms if any two morphisms on the two smaller objects have a joint extension to a morphism on the larger object. This independence notion appeared in [30] and was suggested in [31] as a possible axiom to require in Categorial Local Quantum Physics. Taking specific subclasses of the operations as the class of morphisms, one can recover the standard concepts of subsystem independence in the independence hierarchy as special cases of morphism co-possibility (see [30]).…”

“…The way subsystem independence as morphism co-possibility was formulated above and in the papers [30] and [31] is not entirely satisfactory however because it is not purely categorial: in a general category objects are not necessarily sets and morphisms are not necessarily functions -not every category is a concrete category (e.g. the real numbers R regarded as a poset category) [3].…”

Characterizing common cause closedness of quantum probability theories

“…By an embedding is meant here an injective ortholattice homomorphism h : L → L ′ which preserves ϕ in the sense ϕ ′ (h(A)) = ϕ(A) for all A ∈ L. Recently the notion of common cause has been given a general definition in terms of non-selective operations understood as completely positive, unit preserving linear maps on C * -algebras [35]. That definition makes it possible to formulate common cause closedness of quantum field theories on possibly nonflat spacetimes in the categorial approach to relativistic quantum field theory.…”

Bell’s Local Causality is a d-Separation Criterion

“…There is a renewed interest in Bell's notion of local causality (Norsen, 2009(Norsen, , 2011Maudlin 2014), its relation to separability (Henson, 2013b); the role of full specification in local causality (Seevinck and Uffink, 2011;Hofer-Szabó 2015a); its role in relativistic causality (Butterfield 2007;Earman and Valente, 2014;Rédei 2014); its status as a local causality principle (Henson, 2005;Rédei and San Pedro, 2012;Henson 2013a). A similar closely related topic, the Common Cause Principle is also given much attention (Rédei 1997;Rédei and Summers 2002;Vecsernyés 2012a, 2013a).…”