1,085 research outputs found
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
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
No Time Asymmetry from Quantum Mechanics
With CPT-invariant initial conditions that commute with CPT-invariant final
conditions, the respective probabilities (when defined) of a set of histories
and its CPT reverse are equal, giving a CPT-symmetric universe. This leads me
to question whether the asymmetry of the Gell-Mann--Hartle decoherence
functional for ordinary quantum mechanics should be interpreted as an asymmetry
of {\it time} .Comment: 14 pages, Alberta-Thy-11-9
An Analysis of the Representations of the Mapping Class Group of a Multi-Geon Three-Manifold
It is well known that the inequivalent unitary irreducible representations
(UIR's) of the mapping class group of a 3-manifold give rise to ``theta
sectors'' in theories of quantum gravity with fixed spatial topology. In this
paper, we study several families of UIR's of and attempt to understand the
physical implications of the resulting quantum sectors. The mapping class group
of a three-manifold which is the connected sum of with a finite number
of identical irreducible primes is a semi-direct product group. Following
Mackey's theory of induced representations, we provide an analysis of the
structure of the general finite dimensional UIR of such a group. In the picture
of quantized primes as particles (topological geons), this general
group-theoretic analysis enables one to draw several interesting qualitative
conclusions about the geons' behavior in different quantum sectors, without
requiring an explicit knowledge of the UIR's corresponding to the individual
primes.Comment: 52 pages, harvmac, 2 postscript figures, epsf required. Added an
appendix proving the semi-direct product structure of the MCG, corrected an
error in the characterization of the slide subgroup, reworded extensively.
All our analysis and conclusions remain as befor
Relativistic quantum measurement
Does the measurement of a quantum system necessarily break Lorentz
invariance? We present a simple model of a detector that measures the spacetime
localization of a relativistic particle in a Lorentz invariant manner. The
detector does not select a preferred Lorentz frame as a Newton-Wigner
measurement would do. The result indicates that there exists a Lorentz
invariant notion of quantum measurement and sheds light on the issue of the
localization of a relativistic particle. The framework considered is that of
single-particle mechanics as opposed to field theory. The result may be taken
as support for the interpretation postulate of the spacetime-states formulation
of single-particle quantum theory.Comment: 9 pages, no figures: Revision: references adde
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
Dynamical coherent states and physical solutions of quantum cosmological bounces
A new model is studied which describes the quantum behavior of transitions
through an isotropic quantum cosmological bounce in loop quantum cosmology
sourced by a free and massless scalar field. As an exactly solvable model even
at the quantum level, it illustrates properties of dynamical coherent states
and provides the basis for a systematic perturbation theory of loop quantum
gravity. The detailed analysis is remarkably different from what is known for
harmonic oscillator coherent states. Results are evaluated with regard to their
implications in cosmology, including a demonstration that in general quantum
fluctuations before and after the bounce are unrelated. Thus, even within this
solvable model the condition of classicality at late times does not imply
classicality at early times before the bounce without further assumptions.
Nevertheless, the quantum state does evolve deterministically through the
bounce.Comment: 30 pages, 3 figure
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
Time-of-arrival probabilities and quantum measurements: II Application to tunneling times
We formulate quantum tunneling as a time-of-arrival problem: we determine the
detection probability for particles passing through a barrier at a detector
located a distance L from the tunneling region. For this purpose, we use a
Positive-Operator-Valued-Measure (POVM) for the time-of-arrival determined in
quant-ph/0509020 [JMP 47, 122106 (2006)]. This only depends on the initial
state, the Hamiltonian and the location of the detector. The POVM above
provides a well-defined probability density and an unambiguous interpretation
of all quantities involved. We demonstrate that for a class of localized
initial states, the detection probability allows for an identification of
tunneling time with the classic phase time. We also establish limits to the
definability of tunneling time.
We then generalize these results to a sequential measurement set-up: the
phase space properties of the particles are determined by an unsharp sampling
before their attempt to cross the barrier. For such measurements the tunneling
time is defined as a genuine observable. This allows us to construct a
probability distribution for its values that is definable for all initial
states and potentials. We also identify a regime, in which these probabilities
correspond to a tunneling-time operator.Comment: 26 pages--revised version, small changes, to appear in J. Math. Phy
Origin of the inflationary Universe
We give a consistent description of how the inflationary Universe emerges in
quantum cosmology. This involves two steps: Firstly, it is shown that a
sensible probability peak can be obtained from the cosmological wave function.
This is achieved by going beyond the tree level of the semiclassical expansion.
Secondly, due to decoherence interference terms between different semiclassical
branches are negligibly small. The results give constraints on the particle
content of a unified theory.Comment: LATEX, 6 pages, selected for honorable mention in the 1999 Essay
Competition of the Gravity Research Foundation. To appear in Mod. Phys. Lett.
- …