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.
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.
We consider two interacting systems when one is treated classically while the other system remains quantum. Consistent dynamics of this coupling has been shown to exist, and explored in the context of treating space-time classically. Here, we prove that such hybrid dynamics necessarily results in decoherence of the quantum system, and a breakdown in predictability in the classical phase space. We further prove that a trade-off between the rate of this decoherence and the degree of diffusion induced in the classical system is a general feature of all classical quantum dynamics; long coherence times require strong diffusion in phase-space relative to the strength of the coupling. Applying the trade-off relation to gravity, we find a relationship between the strength of gravitationally-induced decoherence versus diffusion of the metric and its conjugate momenta. This provides an experimental signature of theories in which gravity is fundamentally classical. Bounds on decoherence rates arising from current interferometry experiments, combined with precision measurements of mass, place significant restrictions on theories where Einstein's classical theory of gravity interacts with quantum matter. We find that part of the parameter space of such theories are already squeezed out, and provide figures of merit which can be used in future mass measurements and interference experiments.
We consider two interacting systems when one is treated classically while the other system remains quantum. Consistent dynamics of this coupling has been shown to exist, and explored in the context of treating space-time classically. Here, we prove that any such hybrid dynamics necessarily results in decoherence of the quantum system, and a breakdown in predictability in the classical phase space. We further prove that a trade-off between the rate of this decoherence and the degree of diffusion induced in the classical system is a general feature of all classical quantum dynamics; long coherence times require strong diffusion in phase-space relative to the strength of the coupling. Applying the trade-off relation to gravity, we find a relationship between the strength of gravitationally-induced decoherence versus diffusion of the metric and its conjugate momenta. This provides an experimental signature of theories in which gravity is fundamentally classical. Bounds on decoherence rates arising from current interferometry experiments, combined with precision measurements of mass, place significant restrictions on theories where Einstein's classical theory of gravity interacts with quantum matter. We find that part of the parameter space of such theories are already squeezed out, and provide figures of merit which can be used in future mass measurements and interference experiments.
In hybrid classical-quantum theories, the dynamics of the classical system induce the classicality of the quantum system, meaning that such models do not necessarily require a measurement postulate to describe probabilistic measurement outcomes. It has recently been shown that covariant classical-quantum dynamics can be constructed using path integral methods, with the dynamics encoded in a combined action for the classical and quantum variables. This work introduces a classical-quantum model whereby quantum gravity interacts with a classical scalar field. The scalar field can be viewed as fundamentally classical or effectively classical due to the decoherence of a quantum gravity theory. The dynamics act to collapse quantum spacetimes according to their Ricci scalar, with corresponding diffusion in the scalar field due to the quantum back-reaction. In the classical limit, the diffusion in the scalar field manifests itself via stochastic fluctuations in the Newtonian potential. Because we couple a classical scalar field to perturbative quantum gravity, we find the theory is not renormalizable but is instead to be viewed as an effective field theory. However, it is an effective field theory that does not necessarily require a measurement postulate. More generally, our work shows it is possible to integrate collapse dynamics with high-energy physics and covariance.
A concise and self-contained derivation of hybrid quantum-classical dynamics is given in terms of Markovian master equations. Many previously known results are rederived and revised and some of them are completed or corrected. Using a method as simple as possible, our goal is a brief introduction to the state of the art of hybrid dynamics, with a limited discussion of the implications for foundations and without discussion of further relevance in the measurement problem, quantum gravity, chemistry, numeric methods, etc. Hybrid dynamics is defined as a special case of composite quantum dynamics where the observables of one of the two subsystems are restricted to the commuting set of diagonal operators in a fixed basis. With this restriction, the derivation of hybrid dynamical equations is clear conceptually and simple technically. Jump and diffusive dynamics follow in the form of hybrid master equations. Their stochastic interpretation (called unravelings) is derived. We discuss gauge-type ambiguities, problems of uniqueness, and covariance of the diffusive master equation. Also conditions of minimum noise and of monitoring the quantum trajectory are derived. We conclude that the hybrid formalism is equivalent to the standard Markovian theory of time-continuous quantum measurement (monitoring) on the one hand and is a motivating alternative formalism on the other.
The formulation of a consistent scheme for treating semiclassical systems is considered, giving particular emphasis to the case of gravity. A critical review of the semiclassical problem is first given, stressing the conceptual aspects of the topic; the theory usually adopted is found to be unsatisfactory, and the need to have an unambiguous interpretation of quantum mechanics before trying to give an alternative description is realized. Our way to arrive at such an interpretation is rather unusual, but it presents the advantage of being almost compelling in the choice to make: First, we reformulate the Schrodinger equation as a set of hydrodynamical equations involving quantities which formally play the role of mass density, velocity and pressure for a fluid; the problem of interpreting the wave function is thus reduced to that of interpreting these quantities. We then show how they can be derived from the Wigner distribution function exactly as in the usual formalism of kinetic theory, and discuss how this fact provides strong support in favour of the statistical interpretation of quantum theory, according to which the state vector describes only ensembles, and not individual systems. We also consider some implications of these results on the possible existence of a more fundamental theory underlying quantum mechanics. It is shown that reconsidering the semiclassical problem in the light of the statistical interpretation, one is led to distinguish between a strongly and a weakly semiclassical regime, which are essentially characterized by the size of the statistical dispersion induced in the observables of the classical subsystem by the coupling to the quantum one. It turns out that in the weakly semiclassical regime, in which this dispersion is not negligible, the concept of coupling equations cannot be successfully applied, and one has rather to define a probability distribution even for the values of the classical observables; an hypothesis which allows to specify such a distribution is enunciated. Several examples of the application of these general principles are considered, and it is shown how the treatment of semiclassical relativistic fields requires a much more sophisticated treatment of the quantum source. This is provided reformulating quantum theory in terms of a quasiprobability functional P[1] in the space of the histories of the system. It is shown how such a functional allows to reconstruct the usual phase space distributions when integrated over suitable sets of paths, in a way which clarify the relations between operator ordering, path integration and phase space treatment of quantum theory. The relativistic extension of p[f] is also constructed, and an explicitly covariant version of relativistic quantum theory is discussed in some details. It is shown how the latter allows, formally, to consider superpositions of different mass eigenstates, although such superpositions are not directly observable. Finally, the application of these new techniques to the treatment of semiclassical electromagnetism and gravity, as well as of a scalar field, are considered. It is shown how the usual semiclassical field equations, suitably reinterpreted in terms of averages of the field, are recovered either in linear cases or in the strongly semiclassical regime, but that they do not hold in general. Finally, some possible extensions and implications of the formalism are discussed.