790 research outputs found
Semi-classical limit and minimum decoherence in the Conditional Probability Interpretation of Quantum Mechanics
The Conditional Probability Interpretation of Quantum Mechanics replaces the
abstract notion of time used in standard Quantum Mechanics by the time that can
be read off from a physical clock. The use of physical clocks leads to apparent
non-unitary and decoherence. Here we show that a close approximation to
standard Quantum Mechanics can be recovered from conditional Quantum Mechanics
for semi-classical clocks, and we use these clocks to compute the minimum
decoherence predicted by the Conditional Probability Interpretation.Comment: 8 pages, references adde
A realist interpretation of quantum mechanics based on undecidability due to gravity
We summarize several recent developments suggesting that solving the problem
of time in quantum gravity leads to a solution of the measurement problem in
quantum mechanics. This approach has been informally called "the Montevideo
interpretation". In particular we discuss why definitions in this approach are
not "for all practical purposes" (fapp) and how the problem of outcomes is
resolved.Comment: 7 pages, IOPAMS style, no figures, contributed to the proceedings of
DICE 2010, Castiglioncello, slightly improved versio
Lattice knot theory and quantum gravity in the loop representation
We present an implementation of the loop representation of quantum gravity on
a square lattice. Instead of starting from a classical lattice theory,
quantizing and introducing loops, we proceed backwards, setting up constraints
in the lattice loop representation and showing that they have appropriate
(singular) continuum limits and algebras. The diffeomorphism constraint
reproduces the classical algebra in the continuum and has as solutions lattice
analogues of usual knot invariants. We discuss some of the invariants stemming
from Chern--Simons theory in the lattice context, including the issue of
framing. We also present a regularization of the Hamiltonian constraint. We
show that two knot invariants from Chern--Simons theory are annihilated by the
Hamiltonian constraint through the use of their skein relations, including
intersections. We also discuss the issue of intersections with kinks. This
paper is the first step towards setting up the loop representation in a
rigorous, computable setting.Comment: 23 pages, RevTeX, 14 figures included with psfi
How the Jones Polynomial Gives Rise to Physical States of Quantum General Relativity
Solutions to both the diffeomorphism and the hamiltonian constraint of
quantum gravity have been found in the loop representation, which is based on
Ashtekar's new variables. While the diffeomorphism constraint is easily solved
by considering loop functionals which are knot invariants, there remains the
puzzle why several of the known knot invariants are also solutions to the
hamiltonian constraint. We show how the Jones polynomial gives rise to an
infinite set of solutions to all the constraints of quantum gravity thereby
illuminating the structure of the space of solutions and suggesting the
existance of a deep connection between quantum gravity and knot theory at a
dynamical level.Comment: 7p
Consistent canonical quantization of general relativity in the space of Vassiliev knot invariants
We present a quantization of the Hamiltonian and diffeomorphism constraint of
canonical quantum gravity in the spin network representation. The novelty
consists in considering a space of wavefunctions based on the Vassiliev knot
invariants. The constraints are finite, well defined, and reproduce at the
level of quantum commutators the Poisson algebra of constraints of the
classical theory. A similar construction can be carried out in 2+1 dimensions
leading to the correct quantum theory.Comment: 4 pages, RevTex, one figur
The Extended Loop Group: An Infinite Dimensional Manifold Associated with the Loop Space
A set of coordinates in the non parametric loop-space is introduced. We show
that these coordinates transform under infinite dimensional linear
representations of the diffeomorphism group. An extension of the group of loops
in terms of these objects is proposed. The enlarged group behaves locally as an
infinite dimensional Lie group. Ordinary loops form a subgroup of this group.
The algebraic properties of this new mathematical structure are analized in
detail. Applications of the formalism to field theory, quantum gravity and knot
theory are considered.Comment: The resubmited paper contains the title and abstract, that were
omitted in the previous version. 42 pages, report IFFI/93.0
Vacuum stability conditions of the economical 3-3-1 model from copositivity
By applying copositivity criterion to the scalar potential of the economical
model, we derive necessary and sufficient bounded-from-below conditions
at tree level. Although these are a large number of intricate inequalities for
the dimensionless parameters of the scalar potential, we present general
enlightening relations in this work. Additionally, we use constraints coming
from the minimization of the scalar potential by means of the orbit space
method, the positivity of the squared masses of the extra scalars, the Higgs
boson mass, the gauge boson mass and its mixing angle with the SM
boson in order to further restrict the parameter space of this model.Comment: 22 pages, 7 figures, added text and references. Matches published
versio
No black hole information puzzle in a relational universe
The introduction of a relational time in quantum gravity naturally implies
that pure quantum states evolve into mixed quantum states. We show, using a
recently proposed concrete implementation, that the rate at which pure states
naturally evolve into mixed ones is faster than that due to collapsing into a
black hole that later evaporates. This is rather remarkable since the
fundamental mechanism for decoherence is usually very weak. Therefore the
``black hole information puzzle'' is rendered de-facto unobservable.Comment: 4 pages, no figures, revte
Yang-Mills analogues of the Immirzi ambiguity
We draw parallels between the recently introduced ``Immirzi ambiguity'' of
the Ashtekar-like formulation of canonical quantum gravity and other
ambiguities that appear in Yang-Mills theories, like the ambiguity. We
also discuss ambiguities in the Maxwell case, and implication for the loop
quantization of these theories.Comment: 5 pages, revtex, no figure
Relational physics with real rods and clocks and the measurement problem of quantum mechanics
The use of real clocks and measuring rods in quantum mechanics implies a
natural loss of unitarity in the description of the theory. We briefly review
this point and then discuss the implications it has for the measurement problem
in quantum mechanics. The intrinsic loss of coherence allows to circumvent some
of the usual objections to the measurement process as due to environmental
decoherence.Comment: 19 pages, RevTex, no figure
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