754 research outputs found
Physical Logic
In R.D. Sorkin's framework for logic in physics a clear separation is made
between the collection of unasserted propositions about the physical world and
the affirmation or denial of these propositions by the physical world. The
unasserted propositions form a Boolean algebra because they correspond to
subsets of an underlying set of spacetime histories. Physical rules of
inference, apply not to the propositions in themselves but to the affirmation
and denial of these propositions by the actual world. This physical logic may
or may not respect the propositions' underlying Boolean structure. We prove
that this logic is Boolean if and only if the following three axioms hold: (i)
The world is affirmed, (ii) Modus Ponens and (iii) If a proposition is denied
then its negation, or complement, is affirmed. When a physical system is
governed by a dynamical law in the form of a quantum measure with the rule that
events of zero measure are denied, the axioms (i) - (iii) prove to be too rigid
and need to be modified. One promising scheme for quantum mechanics as quantum
measure theory corresponds to replacing axiom (iii) with axiom (iv) Nature is
as fine grained as the dynamics allows.Comment: 14 pages, v2 published version with a change in the title and other
minor change
Growth factor in f(T) gravity
We derive the evolution equation of growth factor for the matter over-dense
perturbation in gravity. For instance, we investigate its behavior in
power law model at small redshift and compare it to the prediction of
CDM and dark energy with the same equation of state in the framework
of Einstein general relativity. We find that the perturbation in gravity
grows slower than that in Einstein general relativity if \p f/\p T>0 due to
the effectively weakened gravity.Comment: 15 pages,1 figure; v2,typos corrected; v3, discussions added,
accepted by JCA
SAperI: Approaching Gender Gap Using Spatial Ability Training Week in High-School Context
The purpose of this paper is to describe the structure of a girls summer school, “SAperI – Spatial Ability per l’Ingegneria” (in English, “Knowledge – Spatial Ability for Engineering”), and to illustrate its impact on spatial ability development and future career preferences on those who participated in the week long summer school compared to a control group that did not participate.The 5 days school,organized by Politecnico di Torino (Italy), was included in a larger project addressing 17 years old high-school students. Thirtyseven girls actively took part in a summer school, while 167 students (both males and females) were tested as a controlled group.For those who attended the summer school, significant gains were observed in four measures of spatial ability - mental rotation, spatialvisualization, mental cutting and paper folding. For a minority of participants, scores on one of these tests, paper folding, were lower when measured at the end of the summer school but this was an exception. Furthermore, when tested several months after the summer school, the gains in spatial ability that were made during the course were maintained indicating stability over time with regard to the improvement in spatial ability.In terms of the experience of taking the course, the feedback provided was very positive and all but one participant would recommend the summer school to othergirls at this stage of high school
The universe formation by a space reduction cascade with random initial parameters
In this paper we discuss the creation of our universe using the idea of extra
dimensions. The initial, multidimensional Lagrangian contains only metric
tensor. We have found many sets of the numerical values of the Lagrangian
parameters corresponding to the observed low-energy physics of our universe.
Different initial parameters can lead to the same values of fundamental
constants by the appropriate choice of a dimensional reduction cascade. This
result diminishes the significance of the search for the 'unique' initial
Lagrangian. We also have obtained a large number of low-energy vacua, which is
known as a 'landscape' in the string theory.Comment: 17 pages, 1 figur
Degeneracy in Candecomp/Parafac and Indscal Explained For Several Three-Sliced Arrays With A Two-Valued Typical Rank
The Candecomp/Parafac (CP) method decomposes a three-way array into a prespecified number R of rank-1 arrays, by minimizing the sum of squares of the residual array. The practical use of CP is sometimes complicated by the occurrence of so-called degenerate sequences of solutions, in which several rank-1 arrays become highly correlated in all three modes and some elements of the rank-1 arrays become arbitrarily large. We consider the real-valued CP decomposition of all known three-sliced arrays, i.e., of size p×q×3, with a two-valued typical rank. These are the 5×3×3 and 8×4×3 arrays, and the 3×3×4 and 3×3×5 arrays with symmetric 3×3 slices. In the latter two cases, CP is equivalent to the Indscal model. For a typical rank of {m,m+1}, we consider the CP decomposition with R=m of an array of rank m+1. We show that (in most cases) the CP objective function does not have a minimum but an infimum. Moreover, any sequence of feasible CP solutions in which the objective value approaches the infimum will become degenerate. We use the tools developed in Stegeman (2006), who considers p×p×2 arrays, and present a framework of analysis which is of use to the future study of CP degeneracy related to a two-valued typical rank. Moreover, our examples show that CP uniqueness is not necessary for degenerate solutions to occur
Hamiltonian dynamics and Noether symmetries in Extended Gravity Cosmology
We discuss the Hamiltonian dynamics for cosmologies coming from Extended
Theories of Gravity. In particular, minisuperspace models are taken into
account searching for Noether symmetries. The existence of conserved quantities
gives selection rule to recover classical behaviors in cosmic evolution
according to the so called Hartle criterion, that allows to select correlated
regions in the configuration space of dynamical variables. We show that such a
statement works for general classes of Extended Theories of Gravity and is
conformally preserved. Furthermore, the presence of Noether symmetries allows a
straightforward classification of singularities that represent the points where
the symmetry is broken. Examples of nonminimally coupled and higher-order
models are discussed.Comment: 20 pages, Review paper to appear in EPJ
Adiabatic following criterion, estimation of the nonadiabatic excitation fraction and quantum jumps
An accurate theory describing adiabatic following of the dark, nonabsorbing
state in the three-level system is developed. An analytical solution for the
wave function of the particle experiencing Raman excitation is found as an
expansion in terms of the time varying nonadiabatic perturbation parameter. The
solution can be presented as a sum of adiabatic and nonadiabatic parts. Both
are estimated quantitatively. It is shown that the limiting value to which the
amplitude of the nonadiabatic part tends is equal to the Fourier component of
the nonadiabatic perturbation parameter taken at the Rabi frequency of the
Raman excitation. The time scale of the variation of both parts is found. While
the adiabatic part of the solution varies slowly and follows the change of the
nonadiabatic perturbation parameter, the nonadiabatic part appears almost
instantly, revealing a jumpwise transition between the dark and bright states.
This jump happens when the nonadiabatic perturbation parameter takes its
maximum value.Comment: 33 pages, 8 figures, submitted to PRA on 28 Oct. 200
Particle motion in the field of a five-dimensional charged black hole
In this paper, we have investigated the geodesics of neutral particles near a
five-dimensional charged black hole using a comparative approach. The effective
potential method is used to determine the location of the horizons and to study
radial and circular trajectories. This also helps us to analyze the stability
of radial and circular orbits. The radius of the innermost stable circular
orbits have also been determined. Contrary to the case of massive particles for
which, the circular orbits may have up to eight possible values of specific
radius, we find that the photons will only have two distinct values for the
specific radii of circular trajectories. Finally we have used the dynamical
systems analysis to determine the critical points and the nature of the
trajectories for the timelike and null geodesics.Comment: 15 pages, accepted for publication in Astrophysics and Space Scienc
Cosmological model with interactions in the dark sector
A cosmological model is proposed for the current Universe consisted of
non-interacting baryonic matter and interacting dark components. The dark
energy and dark matter are coupled through their effective barotropic indexes,
which are considered as functions of the ratio between their energy densities.
It is investigated two cases where the ratio is asymptotically stable and their
parameters are adjusted by considering best fits to Hubble function data. It is
shown that the deceleration parameter, the densities parameters, and the
luminosity distance have the correct behavior which is expected for a viable
present scenario of the Universe.Comment: 6 pages, 8 figure
Dynamically avoiding fine-tuning the cosmological constant: the "Relaxed Universe"
We demonstrate that there exists a large class of action functionals of the
scalar curvature and of the Gauss-Bonnet invariant which are able to relax
dynamically a large cosmological constant (CC), whatever it be its starting
value in the early universe. Hence, it is possible to understand, without
fine-tuning, the very small current value of the CC as compared to its
theoretically expected large value in quantum field theory and string theory.
In our framework, this relaxation appears as a pure gravitational effect, where
no ad hoc scalar fields are needed. The action involves a positive power of a
characteristic mass parameter, M, whose value can be, interestingly enough, of
the order of a typical particle physics mass of the Standard Model of the
strong and electroweak interactions or extensions thereof, including the
neutrino mass. The model universe emerging from this scenario (the "Relaxed
Universe") falls within the class of the so-called LXCDM models of the cosmic
evolution. Therefore, there is a "cosmon" entity X (represented by an effective
object, not a field), which in this case is generated by the effective
functional and is responsible for the dynamical adjustment of the cosmological
constant. This model universe successfully mimics the essential past epochs of
the standard (or "concordance") cosmological model (LCDM). Furthermore, it
provides interesting clues to the coincidence problem and it may even connect
naturally with primordial inflation.Comment: LaTeX, 63 pp, 8 figures. Extended discussion. Version accepted in
JCA
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