We investigate the meaning of gravity-induced decoherence in quantum theory, known as `intrinsic' or `fundamental' decoherence in the literature. We explore a range of issues relevant to this problem, including the meaning of modified uncertainty relations, the interpretations of the Planck scale, the distinction between quantum and stochastic fluctuations and the role of the time variable in quantum mechanics. We examine the specific physical assumptions that enter into different approaches to the subject. In particular, we critique two representative approaches that identify time fluctuations as the origin of intrinsic or fundamental decoherence: one that models the fluctuations by stochastic process and one that purports to derive decoherence from the quantum fluctuations of real clocks.
We review the difference between standard environmental decoherence and 'intrinsic decoherence', which is taken to be an ineluctable process of Nature. Environmental decoherence is typically modeled by spin bath or oscillator modes - we review some of the unanswered questions not captured by these models, and also the application of them to experiments. Finally, a sketch is given of a new theoretical approach to intrinsic decoherence, and this scheme is applied to the discussion of gravitational decoherence.
Four models of energy decoherence are discussed from the common perspective of intrinsic time-uncertainty. The four authors -- Milburn, Adler, Penrose, and myself -- have four different approaches. The present work concentrates on their common divisors at the level of the proposed equations rather than at the level of the interpretations. General relationships between time-uncertainty and energy-decoherence are presented in both global and local sense. Global and local master equations are derived. (The local concept is favored.)
Quantum decoherence can arise due to classical fluctuations in the parameters which define the dynamics of the system. In this case decoherence, and complementary noise, is manifest when data from repeated measurement trials are combined. Recently a number of authors have suggested that fluctuations in the space-time metric arising from quantum gravity effects would correspond to a source of intrinsic noise, which would necessarily be accompanied by intrinsic decoherence. This work extends a previous heuristic modification of Schrödinger dynamics based on discrete time intervals with an intrin…
We give a first principles derivation of a master equation for the evolution of a quantum matter field in a linearly perturbed Minkowski spacetime, based solely on quantum field theory and general relativity. We make no additional assumptions nor introduce extra ingredients, as is often done in alternative quantum theories. When the quantum matter field is projected to a one-particle state, the master equation for a non-relativistic quantum particle in a weak gravitational field predicts decoherence in the energy basis, in contrast to most existing theories of gravitational decoherence. We poi…
To investigate the possibility that intrinsic gravitational decoherence can be theoretically demonstrated within canonical quantum gravity, we develop a model of a self-gravitating interferometer. We search for evidence in the resulting interference pattern that would indicate coherence is fundamentally limited due to general relativistic effects. To eliminate the occurence of gravitational waves, we work in spherical symmetry, and construct the "beam" of the interferometer out of WKB states for an infinitesimally thin shell of matter. For internal consistency, we encode information about the …
An increasing number of papers have appeared in recent years on decoherence in quantum gravity at the Planck energy. We discuss the meaning of decoherence in quantum gravity starting from the common notion that quantum gravity is a theory for the microscopic structures of spacetime, and invoking some generic features of quantum decoherence from the open systems viewpoint. We dwell on a range of issues bearing on this process including the relation between statistical and quantum, noise from effective field theory, the meaning of stochasticity, the origin of non-unitarity and the nature of nonl…
We present a general relativistic model of a spherical shell of matter with a perfect fluid on its surface coupled to an internal oscillator, which generalizes a model recently introduced by the authors to construct a self-gravitating interferometer [1]. The internal oscillator evolution is defined with respect to the local proper time of the shell, allowing the oscillator to serve as a local clock that ticks differently depending on the shell's position and momentum. A Hamiltonian reduction is performed on the system, and an approximate quantum description is given to the reduced phase space.…
In Crull (2015) it is argued that, in order to confront outstanding problems in cosmology and quantum gravity, interpretational aspects of quantum theory can by bypassed because decoherence is able to resolve them. As a result, Crull (2015) concludes that our focus on conceptual and interpretational issues, while dealing with such matters in Okon and Sudarsky (2014), is avoidable and even pernicious. Here we will defend our position by showing in detail why decoherence does not help in the resolution of foundational questions in quantum mechanics, such as the measurement problem or the emergen…
We scrutize the commonly used criteria for classicality and examine their underlying issues. The two major issues we address here are that of decoherence and fluctuations. We borrow the insights gained in the study of the semiclassical limit of quantum cosmology to discuss the three criteria of classicality for a quantum closed system: adiabaticity, correlation and decoherence. We then use the Brownian model as a paradigm of quantum open systems to discuss the relation of quantum and thermal fluctuations and their role in the transition from quantum to classical. We derive the uncertainty rela…
One of the biggest problems faced by those attempting to combine quantum theory and general relativity is the experimental inaccessibility of the unification scale. In this paper we show how incoherent conformal waves in the gravitational field, which may be produced by quantum mechanical zero-point fluctuations, interact with the wavepackets of massive particles. The result of this interaction is to produce decoherence within the wavepackets which could be accessible in experiments at the atomic scale. Using a simple model for the coherence properties of the gravitational field we derive an e…
The notion of time is given a different footing in Quantum Mechanics and General Relativity, treated as a parameter in the former and being an observer dependent property in the later. From a operational point of view time is simply the correlation between a system and a clock, where an idealized clock can be modelled as a two level systems. We investigate the dynamics of clocks interacting gravitationally by treating the gravitational interaction as a classical information channel. In particular, we focus on the decoherence rates and temporal resolution of arrays of $N$ clocks showing how the…
We give a short, critical review of the issue of decoherence. We establish the most general framework in which decoherence can be discussed, how it can be quantified and how it can be measured. We focus on environment induced decoherence and its degree of usefulness for the interpretation of quantum theory. We finally discuss the emergence of a classical world. An overall emphasis is given in pointing at common fallacies and misconceptions.
We review a number of issues in foundations of quantum theory and quantum cosmology including, in particular, the problem of the preferred basis in the many-worlds interpretation of quantum mechanics, the relation between this interpretation and the decoherence phenomenon, application of decoherence approach to quantum cosmology, the relation between the many-worlds interpretation and Anthropic Principle along with the notion of quantum-classical duality. We also discuss the concept of fundamentally mixed quantum state of the Universe represented by a special microcanonical density matrix and …
One of the biggest unsolved problems in physics is the unification of quantum mechanics and general relativity. The lack of experimental guidance has made the issue extremely evasive, though various attempts have been made to relate the loss of matter wave coherence to quantum spacetime fluctuations. We present a new approach to the gravitational decoherence near the Planck scale, made possible by recently discovered conformal structure of canonical gravity. This leads to a gravitational analogue of the Brownian motion whose correlation length is given by the Planck length up to a scaling fact…
We address the issue of recovering the time-dependent Schrödinger equation from quantum gravity in a natural way. To reach this aim it is necessary to understand the nonoccurrence of certain superpositions in quantum gravity. We explore various possible explanations and their relation. These are the delocalisation of interference terms through interaction with irrelevant degrees of freedom (decoherence), gravitational anomalies, and the possibility of $θ$ states. The discussion is carried out in both the geometrodynamical and connection representation of canonical quantum gravity.
We have recently argued that if one introduces a relational time in quantum mechanics and quantum gravity, the resulting quantum theory is such that pure states evolve into mixed states. The rate at which states decohere depends on the energy of the states. There is therefore the question of how this can be reconciled with Galilean invariance. More generally, since the relational description is based on objects that are not Dirac observables, the issue of covariance is of importance in the formalism as a whole. In this note we work out an explicit example of a totally constrained, generally co…
While the issues of dissipation, fluctuations, noise and decoherence in open quantum systems (with autocratic divide) analyzed via Langevin dynamics are familiar subjects, the treatment of corresponding issues in closed quantum systems is more subtle, as witnessed by Boltzmann's explanation of dissipation in a macroscopic system made up of many equal constituents (a democratic system). How to extract useful physical information about a closed democratic system with no obvious ways to distinguish one constituent from another, nor the existence of conservation laws governing certain special kind…
Decoherence and dissipation in quantum systems has been studied extensively in the context of Quantum Brownian Motion. Effective decoherence in coarse grained quantum systems has been a central issue in recent efforts by Zurek and by Hartle and Gell-Mann to address the Quantum Measurement Problem. Although these models can yield very general classical phenomenology, they are incapable of reproducing relevant characteristics expected of a local environment on a quantum system, such as the characteristic dependence of decoherence on environment spatial correlations. I discuss the characteristics…
The statistical mechanical properties of interacting quantum fields in terms of the dynamics of the correlation functions are investigated. We show how the Dyson - Schwinger equations may be derived from a formal action functional, the n-particle irreducible ($nPI, n \to \infty$) or the `master' effective action. It is related to the decoherence functional between histories defined in terms of correlations. Upon truncation of the Dyson - Schwinger hierarchy at a certain order, the master effective action becomes complex, its imaginary part arising from the higher order correlation functions, t…
We discuss two classes of semi-microscopic theoretical models of stochastic space-time foam in quantum gravity and the associated effects on entangled states of neutral mesons, signalling an intrinsic breakdown of CPT invariance. One class of models deals with a specific model of foam, initially constructed in the context of non-critical (Liouville) string theory, but viewed here in the more general context of effective quantum-gravity models. The relevant Hamiltonian perturbation, describing the interaction of the meson with the foam medium, consists of off-diagonal stochastic metric fluctuat…
