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

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.

10pp, close to PRD version

References in corpus (7)

• A Spin Entanglement Witness for Quantum Gravity
• Gravitationally-induced entanglement between two massive particles is sufficient evidence of quantum effects in gravity
• Present status and future challenges of non-interferometric tests of collapse models
• Principle of least decoherence for Newtonian semi-classical gravity
• Collapse Models: a theoretical, experimental and philosophical review
• General quantum-classical dynamics as measurement based feedback
• Relativistic GKLS master equation?

Cited by in corpus (5)

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• Quantum state of fields in $SU(\infty )$ Quantum Gravity ($SU(\infty )$-QGR)