207 research outputs found
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-
Decoherence and classical predictability of phase space histories
We consider the decoherence of phase space histories in a class of quantum
Brownian motion models, consisting of a particle moving in a potential
in interaction with a heat bath at temperature and dissipation gamma, in
the Markovian regime. The evolution of the density operator for this open
system is thus described by a non-unitary master equation. The phase space
histories of the system are described by a class of quasiprojectors.
Generalizing earlier results of Hagedorn and Omn\`es, we show that a phase
space projector onto a phase space cell is approximately evolved under
the master equation into another phase space projector onto the classical
dissipative evolution of , and with a certain amount of degradation due
to the noise produced by the environment. We thus show that histories of phase
space samplings approximately decohere, and that the probabilities for these
histories are peaked about classical dissipative evolution, with a width of
peaking depending on the size of the noise.Comment: 34 pages, LATEX, revised version to avoid LATEX error
Decoherence Functional and Probability Interpretation
We confirm that the diagonal elements of the Gell-Mann and Hartle's
decoherence decoherence functional are equal to the relative frequencies of the
results of many identical experiments, when a set of alternative histories
decoheres. We consider both cases of the pure and mixed initial states.Comment: 9 pages, UCSBTH-92-40 and MMC-M-
Spacetime topology from the tomographic histories approach I: Non-relativistic Case
The tomographic histories approach is presented. As an inverse problem, we
recover in an operational way the effective topology of the extended
configuration space of a system. This means that from a series of experiments
we get a set of points corresponding to events. The difference between
effective and actual topology is drawn. We deduce the topology of the extended
configuration space of a non-relativistic system, using certain concepts from
the consistent histories approach to Quantum Mechanics, such as the notion of a
record. A few remarks about the case of a relativistic system, preparing the
ground for a forthcoming paper sequel to this, are made in the end.Comment: 19 pages, slight chang in title and corrected typos in second
version. To appear to a special proceedings issue (Glafka 2004) of the
International Journal of Theoretical Physic
Decoherence of Hydrodynamic Histories: A Simple Spin Model
In the context of the decoherent histories approach to the quantum mechanics
of closed systems, Gell-Mann and Hartle have argued that the variables
typically characterizing the quasiclassical domain of a large complex system
are the integrals over small volumes of locally conserved densities --
hydrodynamic variables. The aim of this paper is to exhibit some simple models
in which approximate decoherence arises as a result of local conservation. We
derive a formula which shows the explicit connection between local conservation
and approximate decoherence. We then consider a class of models consisting of a
large number of weakly interacting components, in which the projections onto
local densities may be decomposed into projections onto one of two alternatives
of the individual components. The main example we consider is a one-dimensional
chain of locally coupled spins, and the projections are onto the total spin in
a subsection of the chain. We compute the decoherence functional for histories
of local densities, in the limit when the number of components is very large.
We find that decoherence requires two things: the smearing volumes must be
sufficiently large to ensure approximate conservation, and the local densities
must be partitioned into sufficiently large ranges to ensure protection against
quantum fluctuations.Comment: Standard TeX, 36 pages + 3 figures (postscript) Revised abstract and
introduction. To appear in Physical Review
Topos Theory and Consistent Histories: The Internal Logic of the Set of all Consistent Sets
A major problem in the consistent-histories approach to quantum theory is
contending with the potentially large number of consistent sets of history
propositions. One possibility is to find a scheme in which a unique set is
selected in some way. However, in this paper we consider the alternative
approach in which all consistent sets are kept, leading to a type of `many
world-views' picture of the quantum theory. It is shown that a natural way of
handling this situation is to employ the theory of varying sets (presheafs) on
the space \B of all Boolean subalgebras of the orthoalgebra \UP of history
propositions. This approach automatically includes the feature whereby
probabilistic predictions are meaningful only in the context of a consistent
set of history propositions. More strikingly, it leads to a picture in which
the `truth values', or `semantic values' of such contextual predictions are not
just two-valued (\ie true and false) but instead lie in a larger logical
algebra---a Heyting algebra---whose structure is determined by the space \B
of Boolean subalgebras of \UP.Comment: 28 pages, LaTe
Consistent histories, quantum truth functionals, and hidden variables
A central principle of consistent histories quantum theory, the requirement
that quantum descriptions be based upon a single framework (or family), is
employed to show that there is no conflict between consistent histories and a
no-hidden-variables theorem of Bell, and Kochen and Specker, contrary to a
recent claim by Bassi and Ghirardi. The argument makes use of ``truth
functionals'' defined on a Boolean algebra of classical or quantum properties.Comment: Latex 10 pages, no figure
Histories quantisation of parameterised systems: I. Development of a general algorithm
We develop a new algorithm for the quantisation of systems with first-class
constraints. Our approach lies within the (History Projection Operator)
continuous-time histories quantisation programme. In particular, the
Hamiltonian treatment (either classical or quantum) of parameterised systems is
characterised by the loss of the notion of time in the space of true degrees of
freedom (i.e. the `problem of time'). The novel temporal structure of the HPO
theory (two laws of time transformation that distinguish between the temporal
logical structure and the dynamics) persists after the imposition of the
constraints, hence the problem of time does not arise. We expound the algorithm
for both the classical and quantum cases and apply it to simple models.Comment: 34 pages, Late
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