The classical-quantum hybrid canonical dynamics and its difficulties with special and general relativity

TL;DR

This paper examines the challenges of formulating a consistent classical-quantum hybrid dynamics compatible with special and general relativity, highlighting issues with decoherence and diffusion terms.

Contribution

It provides an improved formalism for nonrelativistic hybrid dynamics and discusses the incompatibility of Markovian decoherence with relativistic extensions.

Findings

Decoherence and diffusion terms diverge in relativistic extensions.

Renormalization methods may not reconcile Markovian decoherence with relativity.

Relativistic postquantum gravity remains unresolved in current hybrid theories.

Abstract

We discuss the Hamiltonian hybrid coupling between a classical and a quantum subsystem. If applicable to classical gravity coupled to quantized matter, this hybrid theory might realize a captivating `postquantum' alternative to full quantum-gravity. We summarize the nonrelativistic hybrid dynamics in improved formalism adequate to Hamiltonian systems. The mandatory decoherence and diffusion terms become divergent in special and general relativistic extensions. It is not yet known if any renormalization method might reconcile Markovian decoherence and diffusion with relativity. Postquantum gravity could previously only be realized in the Newtonian approximation. We argue that pending problems of the recently proposed general relativistic postquantum theory will not be solved if Markovian diffusion/decoherence are truly incompatible with relativity.