arXiv subjects

James B. Hartle

Publications and source records attributed to James B. Hartle.

78 records · Page 5Linked to original sources

arXiv1996

Scientific Knowledge from the Perspective of Quantum Cosmology

Existing physical theories do not predict every feature of our experience but only certain regularities of that experience. That difference between what could be observed and what can be predicted is one kind of limit on scientific knowledge. Such limits are inevitable if the world is complex and the laws governing the regularities of that world are simple. Another kind of limit on scientific knowledge arises because even simple theories may require intractable or impossible computations to yield specific predictions. A third kind of limit concerns our ability to know theories through the process of induction and test. Quantum cosmology -- that part of science concerned with the quantum origin of the universe and its subsequent evolution -- displays all three kinds of limits. This paper briefly describes quantum cosmology and discusses these limits. The place of the other sciences in this most comprehensive of physical frameworks is described.

gr-qc↗

arXiv1995

Strong Decoherence

We introduce a condition for the strong decoherence of a set of alternative histories of a closed quantum-mechanical system such as the universe. The condition applies, for a pure initial state, to sets of homogeneous histories that are chains of projections, generally branch-dependent. Strong decoherence implies the consistency of probability sum rules but not every set of consistent or even medium decoherent histories is strongly decoherent. Two conditions characterize a strongly decoherent set of histories: (1) At any time the operators that effectively commute with generalized records of history up to that moment provide the pool from which -- with suitable adjustment for elapsed time -- the chains of projections extending history to the future may be drawn. (2) Under the adjustment process, generalized record operators acting on the initial state of the universe are approximately unchanged. This expresses the permanence of generalized records. The strong decoherence conditions (1) and (2) guarantee what we call ``permanence of the past'' -- in particular the continued decoherence of past alternatives as the chains of projections are extended into the future. Strong decoherence is an idealization capturing in a general way this and other aspects of realistic physical mechanisms that destroy interference, as we illustrate in a simple model. We discuss the connection between the reduced density matrices that have often been used to characterize mechanisms of decoherence and the more general notion of strong decoherence. The relation between strong decoherence and a measure of classicality is briefly described.

gr-qc↗

arXiv1995

Time and Time Functions in Parametrized Non-Relativistic Quantum Mechanics

The ``evolving constants'' method of defining the quantum dynamics of time-reparametrization-invariant theories is investigated for a particular implementation of parametrized non-relativistic quantum mechanics (PNRQM). The wide range of time functions that are available to define evolving constants raises issues of interpretation, consistency, and the degree to which the resulting quantum theory coincides with, or generalizes, the usual non-relativistic theory. The allowed time functions must be restricted for the predictions of PNRQM to coincide with those of usual quantum theory. They must be restricted to have a notion of quantum evolution in a time-parameter connected to spacetime geometry. They must be restricted to prevent the theory from making inconsistent predictions for the probabilities of histories. Suitable restrictions can be introduced in PNRQM but these seem unlikely to apply to a reparametrization invariant theory like general relativity.

gr-qc↗

arXiv1994

Conservation Laws in the Quantum Mechanics of Closed Systems

We investigate conservation laws in the quantum mechanics of closed systems. We review an argument showing that exact decoherence implies the exact conservation of quantities that commute with the Hamiltonian including the total energy and total electric charge. However, we also show that decoherence severely limits the alternatives which can be included in sets of histories which assess the conservation of these quantities when they are not coupled to a long-range field arising from a fundamental symmetry principle. We then examine the realistic cases of electric charge coupled to the electromagnetic field and mass coupled to spacetime curvature and show that when alternative values of charge and mass decohere, they always decohere exactly and are exactly conserved as a consequence of their couplings to long-range fields. Further, while decohering histories that describe fluctuations in total charge and mass are also subject to the limitations mentioned above, we show that these do not, in fact, restrict {\it physical} alternatives and are therefore not really limitations at all.

gr-qc↗

arXiv1994

Spacetime Information

In usual quantum theory, the information available about a quantum system is defined in terms of the density matrix describing it on a spacelike surface. This definition must be generalized for extensions of quantum theory which do not have a notion of state on a spacelike surface. It must be generalized for the generalized quantum theories appropriate when spacetime geometry fluctuates quantum mechanically or when geometry is fixed but not foliable by spacelike surfaces. This paper introduces a four-dimensional notion of the information available about a quantum system's boundary conditions in the various sets of decohering histories it may display. The idea of spacetime information is applied in several contexts: When spacetime geometry is fixed the information available through alternatives restricted to a spacetime region is defined. The information available through histories of alternatives of general operators is compared to that obtained from the more limited coarse- grainings of sum-over-histories quantum mechanics. The definition of information is considered in generalized quantum theories. We consider as specific examples time-neutral quantum mechanics with initial and final conditions, quantum theories with non-unitary evolution, and the generalized quantum frameworks appropriate for quantum spacetime. In such theories complete information about a quantum system is not necessarily available on any spacelike surface but must be searched for throughout spacetime. The information loss commonly associated with the ``evolution of pure states into mixed states'' in black hole evaporation is thus not in conflict with the principles of generalized quantum mechanics.

gr-qc↗

arXiv1993

Unitarity and Causality in Generalized Quantum Mechanics for Non-Chronal Spacetimes

Spacetime must be foliable by spacelike surfaces for the quantum mechanics of matter fields to be formulated in terms of a unitarily evolving state vector defined on spacelike surfaces. When a spacetime cannot be foliated by spacelike surfaces, as in the case of spacetimes with closed timelike curves, a more general formulation of quantum mechanics is required. In such generalizations the transition matrix between alternatives in regions of spacetime where states {\it can} be defined may be non-unitary. This paper describes a generalized quantum mechanics whose probabilities consistently obey the rules of probability theory even in the presence of such non-unitarity. The usual notion of state on a spacelike surface is lost in this generalization and familiar notions of causality are modified. There is no signaling outside the light cone, no non-conservation of energy, no ``Everett phones'', and probabilities of present events do not depend on particular alternatives of the future. However, the generalization is acausal in the sense that the existence of non-chronal regions of spacetime in the future can affect the probabilities of alternatives today. The detectability of non-unitary evolution and violations of causality in measurement situations are briefly considered. The evolution of information in non-chronal spacetimes is described.

gr-qc↗