9 research outputs found
The mathematical basis for deterministic quantum mechanics
If there exists a classical, i.e. deterministic theory underlying quantum
mechanics, an explanation must be found of the fact that the Hamiltonian, which
is defined to be the operator that generates evolution in time, is bounded from
below. The mechanism that can produce exactly such a constraint is identified
in this paper. It is the fact that not all classical data are registered in the
quantum description. Large sets of values of these data are assumed to be
indistinguishable, forming equivalence classes. It is argued that this should
be attributed to information loss, such as what one might suspect to happen
during the formation and annihilation of virtual black holes.
The nature of the equivalence classes is further elucidated, as it follows
from the positivity of the Hamiltonian. Our world is assumed to consist of a
very large number of subsystems that may be regarded as approximately
independent, or weakly interacting with one another. As long as two (or more)
sectors of our world are treated as being independent, they all must be
demanded to be restricted to positive energy states only. What follows from
these considerations is a unique definition of energy in the quantum system in
terms of the periodicity of the limit cycles of the deterministic model.Comment: 17 pages, 3 figures. Minor corrections, comments and explanations
adde
A symmetry for vanishing cosmological constant
Two different realizations of a symmetry principle that impose a zero
cosmological constant in an extra-dimensional set-up are studied. The symmetry
is identified by multiplication of the metric by minus one. In the first
realization of the symmetry this is provided by a symmetry transformation that
multiplies the coordinates by the imaginary number i. In the second realization
this is accomplished by a symmetry transformation that multiplies the metric
tensor by minus one. In both realizations of the symmetry the requirement of
the invariance of the gravitational action under the symmetry selects out the
dimensions given by D = 2(2n+1), n=0,1,2,... and forbids a bulk cosmological
constant. Another attractive aspect of the symmetry is that it seems to be more
promising for quantization when compared to the usual scale symmetry. The
second realization of the symmetry is more attractive in that it is posible to
make a possible brane cosmological constant zero in a simple way by using the
same symmetry, and the symmetry may be identified by reflection symmetry in
extra dimensions.Comment: Talk in the conference IRGAC 2006, 2nd International Conference on
Quantum Theories and Renormalization Group in Gravity and Cosmology,
Barcelon
Complex Lagrangians and phantom cosmology
Motivated by the generalization of quantum theory for the case of
non-Hermitian Hamiltonians with PT symmetry, we show how a classical
cosmological model describes a smooth transition from ordinary dark energy to
the phantom one. The model is based on a classical complex Lagrangian of a
scalar field. Specific symmetry properties analogous to PT in non-Hermitian
quantum mechanics lead to purely real equation of motion.Comment: 11 pages, to be published in J.Phys.A, refs. adde
Brane Induced Gravity, its Ghost and the Cosmological Constant Problem
"Brane Induced Gravity" is regarded as a promising framework for addressing
the cosmological constant problem, but it also suffers from a ghost instability
for parameter values that make it phenomenologically viable. We carry out a
detailed analysis of codimension > 2 models employing gauge invariant variables
in a flat background approximation. It is argued that using instead a curved
background sourced by the brane would not resolve the ghost issue, unless a
very specific condition is satisfied (if satisfiable at all). As for other
properties of the model, from an explicit analysis of the 4-dimensional
graviton propagator we extract a mass, a decay width and a momentum dependent
modification of the gravitational coupling for the spin 2 mode. In the flat
space approximation, the mass of the problematic spin 0 ghost is instrumental
in filtering out a brane cosmological constant. The mass replaces a background
curvature that would have had the same function. The optical theorem is used to
demonstrate the suppression of graviton leakage into the uncompactified bulk.
Then, we derive the 4-dimensional effective action for gravity and show that
general covariance is spontaneously broken by the bulk-brane setup. This
provides a natural realization of the gravitational Higgs mechanism. We also
show that the addition of extrinsic curvature dependent terms has no bearing on
linearized brane gravity.Comment: v2: LaTeX, JHEP style, 41 pages, 3 eps figures. Partly rewritten to
improve presentation, results unchanged, published versio
Nonsaturated Holographic Dark Energy
It has been well established by today that the concept of holographic dark
energy (HDE) does entail a serious candidate for the dark energy of the
universe. Here we deal with models where the holographic bound for dark energy
is not saturated for a large portion of the history of the universe. This is
particularly compelling when the IR cutoff is set by the Hubble scale, since
otherwise a transition from a decelerated to an accelerated era cannot be
obtained for a spatially flat universe. We demonstrate by three generic but
disparate dynamical models, two of them containing a variable Newton constant,
that transition between the two eras is always obtained for the IR cutoff in
the form of the Hubble scale and the nonsaturated HDE. We also give arguments
of why such a choice for the dark energy is more consistent and favored over
the widely accepted saturated form.Comment: 9 pages, minor revision, to appear in JCA
Invariance under complex transformations, and its relevance to the cosmological constant problem
In this paper we study a new symmetry argument that results in a vacuum
state with strictly vanishing vacuum energy. This argument exploits the well-known
feature that de Sitter and Anti- de Sitter space are related by analytic continuation.
When we drop boundary and hermiticity conditions on quantum fields, we get as many
negative as positive energy states, which are related by transformations to complex space.
The paper does not directly solve the cosmological constant problem, but explores a new
direction that appears worthwhile