948 research outputs found
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
Influence of the Measure on Simplicial Quantum Gravity in Four Dimensions
We investigate the influence of the measure in the path integral for
Euclidean quantum gravity in four dimensions within the Regge calculus. The
action is bounded without additional terms by fixing the average lattice
spacing. We set the length scale by a parameter and consider a scale
invariant and a uniform measure. In the low region we observe a phase
with negative curvature and a homogeneous distribution of the link lengths
independent of the measure. The large region is characterized by
inhomogeneous link lengths distributions with spikes and positive curvature
depending on the measure.Comment: 12pg
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
An Invertible Linearization Map for the Quartic Oscillator
The set of world lines for the non-relativistic quartic oscillator satisfying
Newton's equation of motion for all space and time in 1-1 dimensions with no
constraints other than the "spring" restoring force is shown to be equivalent
(1-1-onto) to the corresponding set for the harmonic oscillator. This is
established via an energy preserving invertible linearization map which
consists of an explicit nonlinear algebraic deformation of coordinates and a
nonlinear deformation of time coordinates involving a quadrature. In the
context stated, the map also explicitly solves Newton's equation for the
quartic oscillator for arbitrary initial data on the real line. This map is
extended to all attractive potentials given by even powers of the space
coordinate. It thus provides classes of new solutions to the initial value
problem for all these potentials
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
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
Glen Cavaliero: Two Tributes
Two tribute pieces about Glen Cavaliero, a founder-member of the Sylvia Townsend Warner Society and for many years the referee for articles submitted to the Journal
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
Birth of the Universe as anti-tunnelling from the string perturbative vacuum
The decay of the string perturbative vacuum, if triggered by a suitable,
duality-breaking dilaton potential, can efficiently proceed via the parametric
amplification of the Wheeler-De Witt wave function in superspace, and can
appropriately describe the birth of our Universe as a quantum process of pair
production from the vacuum.Comment: 11 pages, Latex, three figures included using epsfig. Essay written
for the 2000 Awards for Essays on Gravitation (Gravity Research Foundation,
Wellesley Hills, MA), and selected for Honorable Mention. One reference
added. To appear in Int. J. Mod. Phys.
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
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