arXiv:1109.3925 · Physical Review A

Interacting classical and quantum particles

Alvin J. K. Chua, Michael J. W. Hall, Craig M. Savage

Published Feb 7, 2012• 17 citations

Abstract

We apply Hall and Reginatto's theory of interacting classical and quantum ensembles to harmonically coupled particles, with a view to understanding its experimental implications. This hybrid theory has no free parameters and makes distinctive predictions that should allow it to be experimentally distinguished from quantum mechanics. It also bears on the questions of quantum measurement and quantum gravity.

DOI: 10.1103/physreva.85.022110

Related papers

Four questions for quantum-classical hybrid theory

Hans-Thomas Elze

Four questions are discussed which may be addressed to any proposal of a quantum-classical hybrid theory which concerns the direct coupling of classical and quantum mechanical degrees of freedom. In particular, we consider the formulation of hybrid dynamics presented recently in Ref. [1]. This linear theory differs from the nonlinear ensemble theory of Hall and Reginatto, but shares with it to fulfil all consistency requirements discussed in the literature, while earlier attempts failed. - Here, we additionally ask: Does the theory allow for superposition, separable, and entangled states originating in the quantum mechanical sector? Does it allow for "Free Will", as introduced, in this context, by Diósi [2]? Is it local? Does it provide hints for the emergence of quantum mechanics from dynamics beneath?

arXiv:1202.3448Journal of Physics Conference SeriesMay 10, 201223 citations

Linear dynamics of quantum-classical hybrids

Hans-Thomas Elze

A formulation of quantum-classical hybrid dynamics is presented which concerns the direct coupling of classical and quantum mechanical degrees of freedom. It is of interest for applications in quantum mechanical approximation schemes and may be relevant for the foundations of quantum mechanics, in particular, when it comes to experiments exploring the quantum-classical border. The present linear theory differs from the nonlinear ensemble theory of Hall and Reginatto but shares with it the fulfillment of all consistency requirements discussed in the literature, while earlier attempts have failed in this respect. Our work is based on the representation of quantum mechanics in the framework of classical analytical mechanics by A. Heslot, showing that notions of states in phase space, observables, Poisson brackets, and related canonical transformations can be naturally extended to quantum mechanics. This is suitably generalized for quantum-classical hybrids here.

arXiv:1111.2276Physical Review AMay 11, 2012124 citations

Interacting classical and quantum ensembles

Michael J. W. Hall, Marcel Reginatto

A consistent description of interactions between classical and quantum systems is relevant to quantum measurement theory and to calculations in quantum chemistry and quantum gravity. A solution is offered here to this long-standing problem, based on a universally applicable formalism for ensembles on configuration space. This approach overcomes difficulties arising in previous attempts and in particular allows for a back reaction on the classical ensemble, conservation of probability and energy, and the correct classical equations of motion in the limit of no interaction. Applications include automatic decoherence for quantum ensembles interacting with classical measurement apparatuses, a generalization of coherent states to hybrid harmonic oscillators, and an equation for describing the interaction of quantum matter fields with classical gravity, which implies that the radius of a Robertson-Walker universe containing a quantum massive scalar field can be sharply defined only for particular ``quantized'' values.

arXiv:quant-ph/0509134Physical Review ADec 9, 2005106 citations

Nonlocal signaling in the configuration space model of quantum-classical interactions

Michael J. W. Hall, Marcel Reginatto, Craig M. Savage

When interactions are turned off, the theory of interacting quantum and classical ensembles due to Hall and Reginatto is shown to suffer from a nonlocal signaling effect that is effectively action at a distance. This limits the possible applicability of the theory. In its present form, it is restricted to those situations in which interactions are always on, such as classical gravity interacting with quantized matter.

arXiv:1207.5305Physical Review ANov 8, 201212 citations

Distinguishable Consequence of Classical Gravity on Quantum Matter

Serhii Kryhin, Vivishek Sudhir

What if gravity is classical? If true, a consistent coexistence of classical gravity and quantum matter requires that gravity exhibit irreducible fluctuations. These fluctuations can mediate classical correlations, but not quantum entanglement, between the quantized motion of the gravitationally interacting matter. We use a consistent theory of quantum-classical dynamics in the Newtonian limit of gravity to show that experimentally relevant observables can conclusively test the hypothesis that gravity is classical. This can be done, for example, by letting highly coherent source masses interact with each other gravitationally, and performing precise measurements of the cross-correlation of their motion. Theory predicts a characteristic phase response that distinguishes classical gravity from quantum gravity, and from naive sources of decoherence. Such experiments are imminently viable.

arXiv:2309.09105Physical Review LettersFeb 12, 202516 citations

Gravitationally induced decoherence vs space-time diffusion: testing the quantum nature of gravity

Jonathan Oppenheim, Carlo Sparaciari, Barbara Šoda +1 more

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.

arXiv:2203.01982Mar 3, 20225 citations