arXiv subjects

James B. Hartle

Publications and source records attributed to James B. Hartle.

At least 73 records · Page 4Linked to original sources

arXiv2004

What Connects Different Interpretations of Quantum Mechanics?

We investigate the idea that different interpretations of quantum mechanics can be seen as restrictions of the consistent (or decoherent) histories quantum mechanics of closed systems to particular classes of histories,together with the approximations and descriptions of these histories that the restrictions permit. (Talk at the the workshop Quo Vadis Quantum Mechanics, Center for Frontier Sciences, Temple University, Philadelphia, PA, September 24--27, 2002.)

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arXiv2004

The Physics of 'Now'

The world is four-dimensional according to fundamental physics, governed by basic laws that operate in a spacetime that has no unique division into space and time. Yet our subjective experience is divided into present, past, and future. This paper discusses the origin of this division in terms of simple models of information gathering and utilizing systems (IGUSes). Past, present, and future are not properties of four-dimensional spacetime but notions describing how individual IGUSes process information. Their origin is to be found in how these IGUSes evolved or were constructed. The past, present, and future of an IGUS is consistent with the four-dimensional laws of physics and can be described in four-dimensional terms. The present, for instance, is not a moment of time in the sense of a spacelike surface in spacetime. Rather there is a localized notion of present at each point along an IGUS' world line. The common present of many localized IGUSes is an approximate notion appropriate when they are sufficiently close to each other and have relative velocities much less than that of light. But modes of organization that are different from present, past and future can be imagined that are consistent with the physical laws. We speculate why the present, past, and future organization might be favored by evolution and therefore a cognitive universal.

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arXiv2004

Generalized Quantum Theory of Recollapsing Homogeneous Cosmologies

A sum-over-histories generalized quantum theory is developed for homogeneous minisuperspace type A Bianchi cosmological models, focussing on the particular example of the classically recollapsing Bianchi IX universe. The decoherence functional for such universes is exhibited. We show how the probabilities of decoherent sets of alternative, coarse-grained histories of these model universes can be calculated. We consider in particular the probabilities for classical evolution defined by a suitable coarse-graining. For a restricted class of initial conditions and coarse grainings we exhibit the approximate decoherence of alternative histories in which the universe behaves classically and those in which it does not. For these situations we show that the probability is near unity for the universe to recontract classically if it expands classically. We also determine the relative probabilities of quasi-classical trajectories for initial states of WKB form, recovering for such states a precise form of the familiar heuristic "J dΣ" rule of quantum cosmology, as well as a generalization of this rule to generic initial states.

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arXiv2004

Bohmian Histories and Decoherent Histories

The predictions of the Bohmian and the decoherent (or consistent) histories formulations of the quantum mechanics of a closed system are compared for histories -- sequences of alternatives at a series of times. For certain kinds of histories, Bohmian mechanics and decoherent histories may both be formulated in the same mathematical framework within which they can be compared. In that framework, Bohmian mechanics and decoherent histories represent a given history by different operators. Their predictions for the probabilities of histories therefore generally differ. However, in an idealized model of measurement, the predictions of Bohmian mechanics and decoherent histories coincide for the probabilities of records of measurement outcomes. The formulations are thus difficult to distinguish experimentally. They may differ in their accounts of the past history of the universe in quantum cosmology.

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arXiv2002

Theories of Everything and Hawking's Wave Function of the Universe

If a cat, a cannonball, and an economics textbook are all dropped from the same height, they fall to the ground with exactly the same acceleration under the influence of gravity. This equality of gravitational accelerations of different things is one of the most accurately tested laws of physics. That law, however, tells us little about cats, cannonballs, or economics. This lecture expands on this theme to address the question of what features of our world are predicted by a fundamental ``theory of everything'' governing the regularities exhibited universally by all physical systems. This may consist of two parts: a dynamical law governing regularities in time (e.g superstring theory) and a law of cosmological initial condition governing mostly regularities in space (e.g. Hawking's no-boundary initial condition). The lecture concludes that: (1) ``A theory of everything'' is not a theory of everything in a quantum mechanical universe. (2) If the laws are short enough to be discoverable then they are probably too short to predict everything. (3) The regularities of human history, economics, biology, geology, etc are consistent with the fundamental laws of physics but do not follow from them. (Public lecture given at The Future of Theoretical Physics and Cosmology: Stephen Hawking 60th Birthday Symposium.)

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arXiv1999

Classical Dynamics of the Quantum Harmonic Chain

The origin of classical predictability is investigated for the one dimensional harmonic chain considered as a closed quantum mechanical system. By comparing the properties of a family of coarse-grained descriptions of the chain, we conclude that local coarse-grainings in this family are more useful for prediction than nonlocal ones. A quantum mechanical system exhibits classical behavior when the probability is high for histories having the correlations in time implied by classical deterministic laws. But approximate classical determinism holds only for certain coarse-grainings and then only if the initial state of the system is suitably restricted. Coarse-grainings by the values of the hydrodynamic variables (integrals over suitable volumes of densities of approximately conserved quantities) define the histories usually used in classical physics. But what distinguishes this coarse-graining from others? This paper approaches this question by analyzing a family of coarse-grainings for the linear harmonic chain. At one extreme in the family the chain is divided into local groups of $N$ atoms. At the other extreme the $N$ atoms are distributed nonlocally over the whole chain. Each coarse-graining follows the average (center of mass) positions of the groups and ignores the ``internal'' coordinates within each group, these constituting a different environment for each coarse-graining. We conclude that noise, decoherence, and computational complexity favor locality over nonlocality for deterministic predictability.

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arXiv1999

Entropy of Classical Histories

We consider a number of proposals for the entropy of sets of classical coarse-grained histories based on the procedures of Jaynes, and prove a series of inequalities relating these measures. We then examine these as a function of the coarse-graining for various classical systems, and show explicitly that the entropy is minimized by the finest-grained description of a set of histories. We propose an extension of the second law of thermodynamics to the entropy of histories. We briefly discuss the implications for decoherent or consistent history formulations of quantum mechanics.

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arXiv1998

Generalized Quantum Theory and Black Hole Evaporation

Usually quantum theory is formulated in terms of the evolution of states through spacelike surfaces. However, a generalization of this formulation is needed for field theory in spacetimes not foliable by spacelike surfaces, or in quantum gravity where geometry is not definite but a quantum variable. In particular, a generalization of usual quantum theory is needed for field theory in the spacetimes that model the process of black hole evaporation. This paper discusses a spacetime generalization of usual quantum theory that is applicable to evaporating black hole spacetimes. In this generalization, information is not lost in the process of evaporation. Rather, complete information is distributed about four-dimensional spacetime. Black hole evaporation is thus not in conflict with the principles of quantum theory when suitably generally stated. (Talk presented at the 49th Yamada Conference: Black Holes and High Energy Astrophysics, Kyoto Japan, April 7-10, 1998.)

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arXiv1997

Quantum Pasts and the Utility of History

From data in the present we can predict the future and retrodict the past. These predictions and retrodictions are for histories -- most simply time sequences of events. Quantum mechanics gives probabilities for individual histories in a decoherent set of alternative histories. This paper discusses several issues connected with the distinction between prediction and retrodiction in quantum cosmology: the difference between classical and quantum retrodiction, the permanence of the past, why we predict the future but remember the past, the nature and utility of reconstructing the past(s), and information theoretic measures of the utility of history. (Talk presented at the Nobel Symposium: Modern Studies of Basic Quantum Concepts and Phenomena, Gimo, Sweden, June 13-17, 1997)

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arXiv1997

Generalized Quantum Theory in Evaporating Black Hole Spacetimes

Quantum mechanics for matter fields moving in an evaporating black hole spacetime is formulated in fully four-dimensional form according to the principles of generalized quantum theory. The resulting quantum theory cannot be expressed in a 3+1 form in terms of a state evolving unitarily or by reduction through a foliating family of spacelike surfaces. That is because evaporating black hole geometries cannot be foliated by a non-singular family of spacelike surfaces. A four-dimensional notion of information is reviewed. Although complete information may not be available on every spacelike surface, information is not lost in a spacetime sense in an evaporating black hole spacetime. Rather complete information is distributed about the four-dimensional spacetime. Black hole evaporation is thus not in conflict with the principles of quantum mechanics when suitably generally stated. (Talk presented at Black Holes and Relativistic Stars: A Symposium in Honor of S. Chandrasekhar, Chicago, Dec 14-15,1996.)

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arXiv1997

Comment on ``Consistent Sets Yield Contrary Inferences in Quantum Theory''

In a recent paper Kent has pointed out that in consistent histories quantum theory it is possible, given initial and final states, to construct two different consistent families of histories, in each of which there is a proposition that can be inferred with probability one, and such that the projectors representing these two propositions are mutually orthogonal. In this note we stress that, according to the rules of consistent history reasoning two such propositions are not contrary in the usual logical sense namely, that one can infer that if one is true then the other is false, and both could be false. No single consistent family contains both propositions, together with the initial and final states, and hence the propositions cannot be logically compared. Consistent histories quantum theory is logically consistent, consistent with experiment as far as is known, consistent with the usual quantum predictions for measurements, and applicable to the most general physical systems. It may not be the only theory with these properties, but in our opinion, it is the most promising among present possibilities.

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arXiv1997

Sources of Predictability

Sources of predictability in the basic laws of physics are described in the most general theoretical context -- the quantum theory of the universe as a whole. (To appear in the Proceedings of the conference on Fundamental Sources of Unpredictability held at the Santa Fe Institute, March 28 to 30, 1996 to be published by Complexity.)

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arXiv1997

Comparing Formulations of Generalized Quantum Mechanics for Reparametrization-Invariant Systems

A class of decoherence schemes is described for implementing the principles of generalized quantum theory in reparametrization-invariant `hyperbolic' models such as minisuperspace quantum cosmology. The connection with sum-over-histories constructions is exhibited and the physical equivalence or inequivalence of different such schemes is analyzed. The discussion focuses on comparing constructions based on the Klein-Gordon product with those based on the induced (a.k.a. Rieffel, Refined Algebraic, Group Averaging, or Spectral Analysis) inner product. It is shown that the Klein-Gordon and induced products can be simply related for the models of interest. This fact is then used to establish isomorphisms between certain decoherence schemes based on these products.

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arXiv1997

Signature of the Simplicial Supermetric

We investigate the signature of the Lund-Regge metric on spaces of simplicial three-geometries which are important in some formulations of quantum gravity. Tetrahedra can be joined together to make a three-dimensional piecewise linear manifold. A metric on this manifold is specified by assigning a flat metric to the interior of the tetrahedra and values to their squared edge-lengths. The subset of the space of squared edge-lengths obeying triangle and analogous inequalities is simplicial configuration space. We derive the Lund-Regge metric on simplicial configuration space and show how it provides the shortest distance between simplicial three-geometries among all choices of gauge inside the simplices for defining this metric (Regge gauge freedom). We show analytically that there is always at least one physical timelike direction in simplicial configuration space and provide a lower bound on the number of spacelike directions. We show that in the neighborhood of points in this space corresponding to flat metrics there are spacelike directions corresponding to gauge freedom in assigning the edge-lengths. We evaluate the signature numerically for the simplicial configuration spaces based on some simple triangulations of the three-sphere (S^3) and three-torus (T^3). For the surface of a four-simplex triangulation of S^3 we find one timelike direction and all the rest spacelike over all of the simplicial configuration space. For the triangulation of T^3 around flat space we find degeneracies in the simplicial supermetric as well as a few gauge modes corresponding to a positive eigenvalue. Moreover, we have determined that some of the negative eigenvalues are physical, i.e. the corresponding eigenvectors are not generators of diffeomorphisms. We compare our results with the known properties of continuum superspace.

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arXiv1997

Quantum Cosmology: Problems for the 21st Century

Two fundamental laws are needed for prediction in the universe: (1) a basic dynamical law and (2) a law for the cosmological initial condition. Quantum cosmology is the area of basic research concerned with the search for a theory of the initial cosmological state. The issues involved in this search are presented in the form of eight problems. (To appear in Physics 2001, ed. by M. Kumar and in the Proceedings of the 10th Yukawa-Nishinomiya Symposium}, November 7-8, 1996, Nishinomiya, Japan.)

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arXiv1996

Solutions of the Regge Equations on some Triangulations of CP^2

Simplicial geometries are collections of simplices making up a manifold together with an assignment of lengths to the edges that define a metric on that manifold. The simplicial analogs of the Einstein equations are the Regge equations. Solutions to these equations define the semiclassical approximation to simplicial approximations to a sum-over-geometries in quantum gravity. In this paper, we consider solutions to the Regge equations with cosmological constant that give Euclidean metrics of high symmetry on a family of triangulations of CP^2 presented by Banchoff and Kuhnel. This family is characterized by a parameter p. The number of vertices grows larger with increasing p. We exhibit a solution of the Regge equations for p=2 but find no solutions for p=3. This example shows that merely increasing the number of vertices does not ensure a steady approach to a continuum geometry in the Regge calculus.

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arXiv1996

Equivalent Sets of Histories and Multiple Quasiclassical Realms

We consider notions of physical equivalence of sets of histories in the quantum mechanics of a closed system. We show first how the same set of histories can be relabeled in various ways, including the use of the Heisenberg equations of motion and of passive transformations of field variables. In the the usual approximate quantum mechanics of a measured subsystem, two observables re- presented by different Hermitian operators are physically distinguished by the different apparatus used to measure them. In the quantum mechanics of a closed system, however, any apparatus is part of the system and the notion of physically distinct situations has a different character. We show that a triple consisting of an initial condition, a Hamiltonian, and a set of histories is physically equivalent to another triple if the operators representing these initial conditions, Hamiltonians, and histories are related by any fixed unitary transformation. We apply this result to the question of whether the universe might exhibit physically inequivalent quasiclassical realms (which we earlier called quasiclassical domains), not just the one that includes familiar experience. We describe how the probabilities of alternative forms, behaviors, and evolutionary histories of information gathering and utilizing systems (IGUSes) using the usual quasiclassical realm could in principle be calculated in quantum cosmology, although it is, of course, impractical to perform the computations. We discuss how, in principle, the probabilities of occurence of IGUSes could be calculated in realms distinct from the usual quasiclassical one. We discuss how IGUSes adapted mainly to two different realms could draw inferences about each other using a hybrid realm consisting of alternatives drawn from each.

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arXiv1996

Nearly Instantaneous Alternatives in Quantum Mechanics

Usual quantum mechanics predicts probabilities for the outcomes of measurements carried out at definite moments of time. However, realistic measurements do not take place in an instant, but are extended over a period of time. The assumption of instantaneous alternatives in usual quantum mechanics is an approximation whose validity can be investigated in the generalized quantum mechanics of closed systems in which probabilities are predicted for spacetime alternatives that extend over time. In this paper we investigate how alternatives extended over time reduce to the usual instantaneous alternatives in a simple model in non-relativistic quantum mechanics. Specifically, we show how the decoherence of a particular set of spacetime alternatives becomes automatic as the time over which they extend approaches zero and estimate how large this time can be before the interference between the alternatives becomes non-negligible. These results suggest that the time scale over which coarse grainings of such quantities as the center of mass position of a massive body may be extended in time before producing significant interference is much longer than characteristic dynamical time scales.

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