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Springer eBooks

Causality and Symmetry

Patrick Suppes, Mario Zanotti

Published Jan 1, 1984• 3 citations
Publisher
DOI
10.1007/978-94-009-6286-6_17

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(Anti)causal boundary conditions being imposed on the (seemingly) Hermitian Quantum Theory (HQT) as described in standard textbooks lead to an (Anti)Causal Quantum Theory ((A)CQT) with an indefinite metric. Therefore, an (anti)causal neutral scalar field is not Hermitian, as one (anti)causal neutral scalar field consists of a non-Hermitian linear combination of two (Hermitian) acausal fields. Fundamental symmetries in (A)CQT are addressed. The quantum theoretical (transition) probability and antiparticle concepts are revised. Imaginary parts of cross sections and refraction indices are related.

arXiv:hep-th/0310204•Oct 21, 2003•2 citations
This work addresses the problem of causation in physics, as for quantum fields, the fundamental theory describing elementary particle physics. Three basic elements are used as methodological concepts: a) the notion of mass-point and the notion of a field (as quantum field) describing a physical system (both concepts are used in physics to characterize elementary particles); b) the notion of state of a mass-point and of a field; c) the notion of causality among states, which are defined by symmetries. Then time and space changes include a space-like causality. These elements are discussed by using the definition of measurement, associated with the notion of symmetry. The derived results give rise to a generalization of the concept of causality, since a mechanical system includes mass-points, fields, and systems composed of mass-points and fields, together. In addition, conserved quantities, founding some causality theories, are generalized due to the notion of symmetry associated with causality.
In this paper, I argue that the Shrapnel-Costa no-go theorem undermines the last remaining viability of the view that the fundamental ontology of quantum mechanics is essentially classical: that is, the view that physical reality is underpinned by objectively real, counterfactually definite, uniquely spatiotemporally defined, local, dynamical entities with determinate valued properties, and where typically 'quantum' behaviour emerges as a function of our own in-principle ignorance of such entities. Call this view Einstein-Bell realism. One can show that the causally symmetric local hidden variable approach to interpreting quantum theory is the most natural interpretation that follows from Einstein-Bell realism, where causal symmetry plays a significant role in circumventing the nonclassical consequences of the traditional no-go theorems. However, Shrapnel and Costa argue that exotic causal structures, such as causal symmetry, are incapable of explaining quantum behaviour as arising as a result of noncontextual ontological properties of the world. This is particularly worrying for Einstein-Bell realism and classical ontology. In the first instance, the obvious consequence of the theorem is a straightforward rejection of Einstein-Bell realism. However, more than this, I argue that, even where there looks to be a possibility of accounting for contextual ontic variables within a causally symmetric framework, the cost of such an account undermines a key advantage of causal symmetry: that accepting causal symmetry is more economical than rejecting a classical ontology. Either way, it looks like we should give up on classical ontology.
(Anti)causal boundary conditions being imposed on the (seemingly) Hermitian Quantum Theory (HQT) as described in standard textbooks lead to an (Anti)Causal Quantum Theory ((A)CQT) with an indefinite metric. Therefore, an (anti)causal neutral scalar field is not Hermitian, as one (anti)causal neutral scalar field consists of a non-Hermitian linear combination of two (Hermitian) acausal fields. Fundamental symmetries in (A)CQT are addressed. The quantum theoretical (transition) probability and antiparticle concepts are revised. Imaginary parts of cross sections and refraction indices are related.