134 research outputs found
Does Probability become Fuzzy in Small Regions of Spacetime?
In a recent paper, Buniy et al. have argued that a possible discretization of
spacetime leads to an unavoidable discretization of the state space of quantum
mechanics. In this paper, we show that this conclusion is not limited to
quantum theory: in any classical, quantum, or more general probabilistic
theory, states (i.e. probabilities or corresponding amplitudes) become discrete
or fuzzy for observers, as long as time evolution is reversible and entropy is
locally bounded.
Specifically, we show that the Bekenstein bound suggests that probabilities
in small closed regions of space carry an uncertainty inversely proportional to
the the square root of the system's effective radius and energy.Comment: 2 pages, published versio
Eccentric inflation and WMAP
For uniform arrangements of magnetic fields, strings, or domain walls
(together with the cosmological constant and non-relativistic matter), exact
solutions to the Einstein equations are shown to lead to a universe with
ellipsoidal expansion. We argue the results can be used to explain some
features in the WMAP data. The magnetic field case is the easiest to motivate
and has the highest possibility of yielding reliable constraints on
observational cosmology.Comment: 5 pages, 1 figur
Decomposition of geometric perturbations
For an infinitesimal deformation of a Riemannian manifold, we prove that the
scalar, vector, and tensor modes in decompositions of perturbations of the
metric tensor, the scalar curvature, the Ricci tensor, and the Einstein tensor
decouple if and only if the manifold is Einstein. Four-dimensional space-time
satisfying the condition of the theorem is homogeneous and isotropic.
Cosmological applications are discussed.Comment: 7 page
Discreteness and the origin of probability in quantum mechanics
Attempts to derive the Born rule, either in the Many Worlds or Copenhagen
interpretation, are unsatisfactory for systems with only a finite number of
degrees of freedom. In the case of Many Worlds this is a serious problem, since
its goal is to account for apparent collapse phenomena, including the Born rule
for probabilities, assuming only unitary evolution of the wavefunction. For
finite number of degrees of freedom, observers on the vast majority of branches
would not deduce the Born rule. However, discreteness of the quantum state
space, even if extremely tiny, may restore the validity of the usual arguments.Comment: 5 pages, revtex, 1 figure. Revised version, to appear in Physics
Letters B. (Small clarifcation, references added.
Construction of multi-instantons in eight dimensions
We consider an eight-dimensional local octonionic theory with the
seven-sphere playing the role of the gauge group. Duality conditions for two-
and four-forms in eight dimensions are related. Dual fields--octonionic
instantons--solve an 8D generalization of the Yang-Mills equation. Modifying
the ADHM construction of 4D instantons, we find general -instanton 8D
solutions which depends on effective parameters
Higher order topological actions
In classical mechanics, an action is defined only modulo additive terms which
do not modify the equations of motion; in certain cases, these terms are
topological quantities. We construct an infinite sequence of higher order
topological actions and argue that they play a role in quantum mechanics, and
hence can be accessed experimentally.Comment: 7 page
The Generalized Counting Rule and Oscillatory Scaling
We have studied the energy dependence of the elastic scattering data and
the pion-photoproduction data at 90 c.m. angle in light of the new
generalized counting rule derived for exclusive processes. We show that by
including the helicity flipping amplitudes (with energy dependence given by the
generalized counting rule) and their interference with the Landshoff amplitude,
we are able to reproduce the energy dependence of all cross-section and
spin-correlation (A) data available above the resonance region. The
pion-photoproduction data can also be described by this approach, but in this
case data with much finer energy spacing is needed to confirm the oscillations
about the scaling behavior.Comment: 5 pages, 4 figs, submitted to PRC rapid com
- âŠ