1,012 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
Populating the Landscape: A Top Down Approach
We put forward a framework for cosmology that combines the string landscape
with no boundary initial conditions. In this framework, amplitudes for
alternative histories for the universe are calculated with final boundary
conditions only. This leads to a top down approach to cosmology, in which the
histories of the universe depend on the precise question asked. We study the
observational consequences of no boundary initial conditions on the landscape,
and outline a scheme to test the theory. This is illustrated in a simple model
landscape that admits several alternative inflationary histories for the
universe. Only a few of the possible vacua in the landscape will be populated.
We also discuss in what respect the top down approach differs from other
approaches to cosmology in the string landscape, like eternal inflation.Comment: 22 pages, 1 figur
Phase Space Representations and Perturbation Theory for Continuous-time Histories
We consider two technical developments of the formalism of continuous-time
histories. First, we provide an explicit description of histories of the simple
harmonic oscillator on the classical histories phase space, comparing and
contrasting the Q, P and Wigner representations; we conclude that a
representation based on coherent states is the most appropriate. Second, we
demonstrate a generic method for implementing a perturbative approach for
interacting theories in the histories formalism, using the quartic anharmonic
oscillator. We make use of the identification of the closed-time path (CTP)
generating functional with the decoherence functional to develop a perturbative
expansion for the latter up to second order in the coupling constant. We
consider both configuration space and phase space histories.Comment: 22 pages; slightly shortened, more concise argumentation; ref. adde
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
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
Quantum mechanics at the Planck scale
Usual quantum mechanics requires a fixed, background, spacetime geometry and its associated causal structure. A generalization of the usual theory may therefore be needed at the Planck scale for quantum theories of gravity in which spacetime geometry is a quantum variable. The elements of generalized quantum theory are briefly reviewed and illustrated by generalizations of usual quantum theory that incorporate spacetime alternatives, gauge degrees of freedom, and histories that move forward and backward in time. A generalized quantum framework for cosmological spacetime geometry is sketched. This theory is in fully four-dimensional form and free from the need for a fixed causal structure. Usual quantum mechanics is recovered as an approximation to this more general framework that is appropriate in those situations where spacetime geometry behaves classically. (Talk given at the Workshop on Physics at the Planck Scale, Puri, India, December 12-21, 1994. This talk is a precis of the author's 1992 Les Houches Lectures: Spacetime Quantum Mechanics and the Quantum Mechanics of Spacetime, gr-qc/9304006)
Universal quantum mechanics
If gravity respects quantum mechanics, it is important to identify the
essential postulates of a quantum framework capable of incorporating
gravitational phenomena. Such a construct likely requires elimination or
modification of some of the "standard" postulates of quantum mechanics, in
particular those involving time and measurement. This paper proposes a
framework that appears sufficiently general to incorporate some expected
features of quantum gravity. These include the statement that space and time
may only emerge approximately and relationally. One perspective on such a
framework is as a sort of generalization of the S-matrix approach to dynamics.
Within this framework, more dynamical structure is required to fully specify a
theory; this structure is expected to lack some of the elements of local
quantum field theory. Some aspects of this structure are discussed, both in the
context of scattering of perturbations about a flat background, and in the
context of cosmology.Comment: 15 pages. v2: minor clarifying comments adde
- …