Abstract
In all our well-established theories, it is assumed that events are embedded in a global causal structure such that, for every pair of events, the causal order between them is always fixed. However, the possible interplay between quantum mechanics and general relativity may require a revision of this paradigm. The process matrix framework keeps the validity of quantum physics locally but does not assume the existence of a global causal order. It allows to describe causal structures corresponding to a quantum superposition of ‘A is before B’ and ‘B is before A’. So far, the framework has been developed only for finite-dimensional systems, and a straightforward generalization to infinite dimensions leads to singularities. Such generalization is necessary for continuous-variable systems and is a prerequisite for quantum fields on indefinite causal structures. Here we develop the process-matrix framework for continuous-variable systems. We encounter and solve the problems of singularities. Moreover, we study an example of a process in infinite dimensions, and we derive correlations exhibiting intereference due to processes in which A is before B and B is before A.
Highlights
The notion of causality is deeply rooted in our understanding of nature
This familiar idea might be untenable at regimes at which the quantum mechanical properties of the systems under study are of comparable relevance to their gravitational properties [1,2,3], for instance if the metric tensor, and the causal relations, are subject to quantum fluctuations
The crucial role played by probability in quantum mechanics on the one hand, and the dynamical causal structure of general relativity on the other hand, led to the conjecture that a theory unifying general relativity and quantum mechanics should be a probabilistic theory on a dynamical causal structure [4]
Summary
Abstract the terms of the Creative In all our well-established theories, it is assumed that events are embedded in a global causal structure. The process matrix framework keeps the validity of quantum physics locally but does not assume the author(s) and the title of the work, journal citation existence of a global causal order. It allows to describe causal structures corresponding to a quantum and DOI. The framework has been developed only for finite-dimensional systems, and a straightforward generalization to infinite dimensions leads to singularities. Such generalization is necessary for continuous-variable systems and is a prerequisite for quantum fields on indefinite causal structures. We study an example of a process in infinite dimensions, and we derive correlations exhibiting intereference due to processes in which A is before B and B is before A
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
