663 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
Anti-de Sitter wormhole kink
The metric describing a given finite sector of a four-dimensional
asymptotically anti-de Sitter wormhole can be transformed into the metric of
the time constant sections of a Tangherlini black hole in a five-dimensional
anti-de Sitter spacetime when one allows light cones to tip over on the
hypersurfaces according to the conservation laws of an one-kink. The resulting
kinked metric can be maximally extended, giving then rise to an instantonic
structure on the euclidean continuation of both the Tangherlini time and the
radial coordinate. In the semiclassical regime, this kink is related to the
existence of closed timelike curves.Comment: 10 pages, to appear in IJMP
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-
Scalar Perturbations in Scalar Field Quantum Cosmology
In this paper it is shown how to obtain the simplest equations for the
Mukhanov-Sasaki variables describing quantum linear scalar perturbations in the
case of scalar fields without potential term. This was done through the
implementation of canonical transformations at the classical level, and unitary
transformations at the quantum level, without ever using any classical
background equation, and it completes the simplification initiated in
investigations by Langlois \cite{langlois}, and Pinho and Pinto-Neto
\cite{emanuel2} for this case. These equations were then used to calculate the
spectrum index of quantum scalar perturbations of a non-singular
inflationary quantum background model, which starts at infinity past from flat
space-time with Planckian size spacelike hypersurfaces, and inflates due to a
quantum cosmological effect, until it makes an analytical graceful exit from
this inflationary epoch to a decelerated classical stiff matter expansion
phase. The result is , incompatible with observations.Comment: 10 pages, 2 figures, accepted version to Physical Review D 7
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
Pound-Rebka experiment and torsion in the Schwarzschild spacetime
We develop some ideas discussed by E. Schucking [arXiv:0803.4128] concerning
the geometry of the gravitational field. First, we address the concept
according to which the gravitational acceleration is a manifestation of the
spacetime torsion, not of the curvature tensor. It is possible to show that
there are situations in which the geodesic acceleration of a particle may
acquire arbitrary values, whereas the curvature tensor approaches zero. We
conclude that the spacetime curvature does not affect the geodesic
acceleration. Then we consider the the Pound-Rebka experiment, which relates
the time interval of two light signals emitted at a position
, to the time interval of the signals received at a
position , in a Schwarzschild type gravitational field. The experiment is
determined by four spacetime events. The infinitesimal vectors formed by these
events do not form a parallelogram in the (t,r) plane. The failure in the
closure of the parallelogram implies that the spacetime has torsion. We find
the explicit form of the torsion tensor that explains the nonclosure of the
parallelogram.Comment: 16 pages, two figures, one typo fixed, one paragraph added in section
Quantum Physics and Human Language
Human languages employ constructions that tacitly assume specific properties
of the limited range of phenomena they evolved to describe. These assumed
properties are true features of that limited context, but may not be general or
precise properties of all the physical situations allowed by fundamental
physics. In brief, human languages contain `excess baggage' that must be
qualified, discarded, or otherwise reformed to give a clear account in the
context of fundamental physics of even the everyday phenomena that the
languages evolved to describe. The surest route to clarity is to express the
constructions of human languages in the language of fundamental physical
theory, not the other way around. These ideas are illustrated by an analysis of
the verb `to happen' and the word `reality' in special relativity and the
modern quantum mechanics of closed systems.Comment: Contribution to the festschrift for G.C. Ghirardi on his 70th
Birthday, minor correction
``Weighing'' a closed system and the time-energy uncertainty principle
A gedanken-experiment is proposed for `weighing'' the total mass of a closed
system from within the system. We prove that for an internal observer the time
, required to measure the total energy with accuracy , is
bounded according to . This time-energy uncertainty
principle for a closed system follows from the measurement back-reaction on the
system. We generally examine what other conserved observables are in principle
measurable within a closed system and what are the corresponding uncertainty
relations.Comment: 8 page
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.Comment: 24 pages, RevTeX, 4 eps Figures. Submitted to Classical Quantum
Gravit
No Way Back: Maximizing survival time below the Schwarzschild event horizon
It has long been known that once you cross the event horizon of a black hole,
your destiny lies at the central singularity, irrespective of what you do.
Furthermore, your demise will occur in a finite amount of proper time. In this
paper, the use of rockets in extending the amount of time before the collision
with the central singularity is examined. In general, the use of such rockets
can increase your remaining time, but only up to a maximum value; this is at
odds with the ``more you struggle, the less time you have'' statement that is
sometimes discussed in relation to black holes. The derived equations are
simple to solve numerically and the framework can be employed as a teaching
tool for general relativity.Comment: 7-pages, 5 figures, accepted for publication in the Publications of
the Astronomical Society of Australia (Journal name corrected.
- …