1,241 research outputs found
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
Generalizing Quantum Mechanics for Quantum Gravity
`How do our ideas about quantum mechanics affect our understanding of
spacetime?' This familiar question leads to quantum gravity. The complementary
question is also important: `How do our ideas about spacetime affect our
understanding of quantum mechanics?' This short abstract of a talk given at the
Gafka2004 conference contains a very brief summary of some of the author's
papers on generalizations of quantum mechanics needed for quantum gravity. The
need for generalization is motivated. The generalized quantum theory framework
for such generalizations is described and illustrated for usual quantum
mechanics and a number of examples to which it does not apply. These include
spacetime alternatives extended over time, time-neutral quantum theory, quantum
field theory in fixed background spacetime not foliable by spacelike surfaces,
and systems with histories that move both forward and backward in time. A fully
four-dimensional, sum-over-histories generalized quantum theory of cosmological
geometries is briefly described. The usual formulation of quantum theory in
terms of states evolving unitarily through spacelike surfaces is an
approximation to this more general framework that is appropriate in the late
universe for coarse-grained descriptions of geometry in which spacetime behaves
classically. This abstract is unlikely to be clear on its own, but references
are provided to the author's works where the ideas can be followed up.Comment: 8 pages, LATEX, a very brief abstract of much wor
Generalized Sums over Histories for Quantum Gravity II. Simplicial Conifolds
This paper examines the issues involved with concretely implementing a sum
over conifolds in the formulation of Euclidean sums over histories for gravity.
The first step in precisely formulating any sum over topological spaces is that
one must have an algorithmically implementable method of generating a list of
all spaces in the set to be summed over. This requirement causes well known
problems in the formulation of sums over manifolds in four or more dimensions;
there is no algorithmic method of determining whether or not a topological
space is an n-manifold in five or more dimensions and the issue of whether or
not such an algorithm exists is open in four. However, as this paper shows,
conifolds are algorithmically decidable in four dimensions. Thus the set of
4-conifolds provides a starting point for a concrete implementation of
Euclidean sums over histories in four dimensions. Explicit algorithms for
summing over various sets of 4-conifolds are presented in the context of Regge
calculus. Postscript figures available via anonymous ftp at
black-hole.physics.ubc.ca (137.82.43.40) in file gen2.ps.Comment: 82pp., plain TeX, To appear in Nucl. Phys. B,FF-92-
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.Comment: 12 pages, harvmac, no figure
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
Coupled structural/thermal/electromagnetic analysis/tailoring of graded composite structures
Accomplishments are described for the third years effort of a 5-year program to develop a methodology for coupled structural/thermal/electromagnetic analysis/tailoring of graded composite structures. These accomplishments include: (1) structural analysis capability specialized for graded composite structures including large deformation and deformation position eigenanalysis technologies; (2) a thermal analyzer specialized for graded composite structures; (3) absorption of electromagnetic waves by graded composite structures; and (4) coupled structural thermal/electromagnetic analysis of graded composite structures
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.Comment: 7 pages, 3 figures, Revtex, minor correction
Decoherent Histories Quantum Mechanics with One 'Real' Fine-Grained History
Decoherent histories quantum theory is reformulated with the assumption that
there is one "real" fine-grained history, specified in a preferred complete set
of sum-over-histories variables. This real history is described by embedding it
in an ensemble of comparable imagined fine-grained histories, not unlike the
familiar ensemble of statistical mechanics. These histories are assigned
extended probabilities, which can sometimes be negative or greater than one. As
we will show, this construction implies that the real history is not completely
accessible to experimental or other observational discovery. However,
sufficiently and appropriately coarse-grained sets of alternative histories
have standard probabilities providing information about the real fine-grained
history that can be compared with observation. We recover the probabilities of
decoherent histories quantum mechanics for sets of histories that are recorded
and therefore decohere. Quantum mechanics can be viewed as a classical
stochastic theory of histories with extended probabilities and a well-defined
notion of reality common to all decoherent sets of alternative coarse-grained
histories.Comment: 11 pages, one figure, expanded discussion and acknowledgment
Bounds on the dragging rate and on the rotational mass-energy in slowly and differentially rotating relativistic stars
For relativistic stars rotating slowly and differentially with a positive
angular velocity, some properties in relation to the positiveness of the rate
of rotational dragging and of the angular momentum density are derived. Also, a
new proof for the bounds on the rotational mass-energy is given.Comment: 23 pages, latex. Submitted to J. Math. Phy
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.Comment: 22 pages, report UCSBTH-94-4, LA-UR-94-2101, CGPG-94/10-
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