The Quantum Mechanical Arrows of Time

The familiar textbook quantum mechanics of laboratory measurements incorporates a quantum mechanical arrow of time --- the direction in time in which state vector reduction operates. This arrow is usually assumed to coincide with the direction of the thermodynamic arrow of the quasiclassical realm of everyday experience. But in the more general context of cosmology we seek an explanation of all observed arrows, and the relations between them, in terms of the conditions that specify our particular universe. This paper investigates quantum mechanical and thermodynamic arrows in a time-neutral formulation of quantum mechanics for a number of model cosmologies in fixed background spacetimes. We find that a general universe may not have well defined arrows of either kind. When arrows are emergent they need not point in the same direction over the whole of spacetime. Rather they may be local, pointing in different directions in different spacetime regions. Local arrows can therefore be consistent with global time symmetry.Comment: 9 pages, 4 figures, revtex4, typos correcte

Letter from J.B. Mann to James B. Finley

Mann invites Finley to deliver a course of lectures to the Milford Center (Union County) Sons of Temperance. Abstract Number - 1184https://digitalcommons.owu.edu/finley-letters/2165/thumbnail.jp

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.Comment: 40pages, UCSBTH92-0

Conditional probabilities in Ponzano-Regge minisuperspace

We examine the Hartle-Hawking no-boundary initial state for the Ponzano-Regge formulation of gravity in three dimensions. We consider the behavior of conditional probabilities and expectation values for geometrical quantities in this initial state for a simple minisuperspace model consisting of a two-parameter set of anisotropic geometries on a 2-sphere boundary. We find dependence on the cutoff used in the construction of Ponzano-Regge amplitudes for expectation values of edge lengths. However, these expectation values are cutoff independent when computed in certain, but not all, conditional probability distributions. Conditions that yield cutoff independent expectation values are those that constrain the boundary geometry to a finite range of edge lengths. We argue that such conditions have a correspondence to fixing a range of local time, as classically associated with the area of a surface for spatially closed cosmologies. Thus these results may hint at how classical spacetime emerges from quantum amplitudes.Comment: 26 pages including 10 figures, some reorganization in the presentation of results, expanded discussion of results in the context of 2+1 gravity in the Witten variables, 3 new reference

The quasiclassical realms of this quantum universe

The most striking observable feature of our indeterministic quantum universe is the wide range of time, place, and scale on which the deterministic laws of classical physics hold to an excellent approximation. This essay describes how this domain of classical predictability of every day experience emerges from a quantum theory of the universe's state and dynamics.Comment: 24 pages, revtex4, minor change

Some Remarks on Quantum Coherence

There are many striking phenomena which are attributed to ``quantum coherence''. It is natural to wonder if there are new quantum coherence effects waiting to be discovered which could lead to interesting results and perhaps even practical applications. A useful starting point for such discussions is a definition of ``quantum coherence''. In this article I give a definition of quantum coherence and use a number of illustrations to explore the implications of this definition. I point to topics of current interest in the fields of cosmology and quantum computation where questions of quantum coherence arise, and I emphasize the impact that interactions with the environment can have on quantum coherence.Comment: 25 pages plain LaTeX, no figures. More references have been added and typos have been corrected. Journal of Modern Optics, in press. Imperial/TP/93-94/1

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.Comment: 47pages, 2 figures, UCSBTH 94-0

Comparison of Estimated-1RM and 225-lb (102-kg) bench press performance between starters and non-starters among a NCAA Division I college football team

The estimated one-repetition maximum (1RM) bench press and NFL-225 (225-lb or 102-kg) repetition test are commonly used to assess upper-body muscular strength and endurance among football players. However, little research has been focused on the relationship of these tests to playing status. Therefore, the purpose of this study was to determine if significant relationships exist between these tests and playing status in Division I football athletes. Archival data from 31 NCAA Division I football players (age: 20.1±1.4 yrs., height: 188.07 ± 5.93 cm, body mass: 112.4 ± 19.5 kg) on the 1RM Bench press test, NFL-225 test and playing status were utilized for this analysis. A one-way ANOVA was used to detect any differences in 1RM and NFL-225 performance between skill groups: big (linemen), medium (linebackers, quarterbacks, tight ends) and small (receivers, backs, and corners) (p < 0.05). Playing status (starters vs. non-starters) were compared within position groups. A point bi-serial correlation was then utilized to examine the relationship in test performance between groups, as well as between starters and non-starters. Significant differences were discovered in NFL-225 test performance between big and small skill groups. Moderate-to-strong relationships between playing status and performance on the 1RM bench press (r = .660) and the NFL-225 test (r = .685) for the big skills group. The results of this study suggest that playing status and upper-body strength and endurance are strongly related for the big skills position group

Classical paths in systems of fermions

We implement in systems of fermions the formalism of pseudoclassical paths that we recently developed for systems of bosons and show that quantum states of fermionic fields can be described, in the Heisenberg picture, as linear combinations of randomly distributed paths that do not interfere between themselves and obey classical Dirac equations. Every physical observable is assigned a time-dependent value on each path in a way that respects the anticommutative algebra between quantum operators and we observe that these values on paths do not necessarily satisfy the usual algebraic relations between classical observables. We use these pseudoclassical paths to define the dynamics of quantum fluctuations in systems of fermions and show that, as we found for systems of bosons, the dynamics of fluctuations of a wide class of observables that we call "collective" observables can be approximately described in terms of classical stochastic concepts. Finally, we apply this formalism to describe the dynamics of local fluctuations of globally conserved fermion numbers.Comment: to appear in Pys. Rev.

The black hole final state

We propose that in quantum gravity one needs to impose a final state boundary condition at black hole singularities. This resolves the apparent contradiction between string theory and semiclassical arguments over whether black hole evaporation is unitary.Comment: 17 pages, harvmac, 1 figure, v2: comment about interactions and references adde