419 research outputs found
On the Concept of a Notational Variant
In the study of modal and nonclassical logics, translations have frequently been employed as a way of measuring the inferential capabilities of a logic. It is sometimes claimed that two logics are ânotational variantsâ if they are translationally equivalent. However, we will show that this cannot be quite right, since first-order logic and propositional logic are translationally equivalent. Others have claimed that for two logics to be notational variants, they must at least be compositionally intertranslatable. The definition of compositionality these accounts use, however, is too strong, as the standard translation from modal logic to first-order logic is not compositional in this sense. In light of this, we will explore a weaker version of this notion that we will call schematicity and show that there is no schematic translation either from first-order logic to propositional logic or from intuitionistic logic to classical logic
Josephson Junctions defined by a Nano-Plough
We define superconducting constrictions by ploughing a deposited Aluminum
film with a scanning probe microscope. The microscope tip is modified by
electron beam deposition to form a nano-plough of diamond-like hardness, what
allows the definition of highly transparent Josephson junctions. Additionally a
dc-SQUID is fabricated to verify appropriate functioning of the junctions. The
devices are easily integrated in mesoscopic devices as local radiation sources
and can be used as tunable on-chip millimeter wave sources
String Supported Wormhole Spacetimes and Causality Violations
We construct a static axisymmetric wormhole from the gravitational field of
two Schwarzschild particles which are kept in equilibrium by strings (ropes)
extending to infinity. The wormhole is obtained by matching two
three-dimensional timelike surfaces surrounding each of the particles and thus
spacetime becomes non-simply connected. Although the matching will not be exact
in general it is possible to make the error arbitrarily small by assuming that
the distance between the particles is much larger than the radius of the
wormhole mouths. Whenever the masses of the two wormhole mouths are different,
causality violating effects will occur.Comment: 12 pages, LaTeX, 1 figur
A Godel-Friedman cosmology?
Based on the mathematical similarity between the Friedman open metric and
Godel's metric in the case of nearby distances, we investigate a new scenario
for the Universe's evolution, where the present Friedman universe originates
from a primordial Godel universe by a phase transition during which the
cosmological constant vanishes. Using Hubble's constant and the present matter
density as input, we show that the radius and density of the primordial Godel
universe are close, in order of magnitude, to the present values, and that the
time of expansion coincides with the age of the Universe in the standard
Friedman model. In addition, the conservation of angular momentum provides, in
this context, a possible origin for the rotation of galaxies, leading to a
relation between the masses and spins corroborated by observational data.Comment: Extended version, accepted for publication in Physical Review
The lightcone of G\"odel-like spacetimes
A study of the lightcone of the G\"odel universe is extended to the so-called
G\"odel-like spacetimes. This family of highly symmetric 4-D Lorentzian spaces
is defined by metrics of the form ,
together with the requirement of spacetime homogeneity, and includes the
G\"odel metric. The quasi-periodic refocussing of cone generators with
startling lens properties, discovered by Ozsv\'{a}th and Sch\"ucking for the
lightcone of a plane gravitational wave and also found in the G\"odel universe,
is a feature of the whole G\"odel family. We discuss geometrical properties of
caustics and show that (a) the focal surfaces are two-dimensional null surfaces
generated by non-geodesic null curves and (b) intrinsic differential invariants
of the cone attain finite values at caustic subsets.Comment: 19 pages, 1 figur
Set Theory and its Place in the Foundations of Mathematics:a new look at an old question
This paper reviews the claims of several main-stream candidates to be the foundations of mathematics, including set theory. The review concludes that at this level of mathematical knowledge it would be very unreasonable to settle with any one of these foundations and that the only reasonable choice is a pluralist one
Programmability of Chemical Reaction Networks
Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a well-stirred solution according to standard chemical kinetics equations. SCRNs have been widely used for describing naturally occurring (bio)chemical systems, and with the advent of synthetic biology they become a promising language for the design of artificial biochemical circuits. Our interest here is the computational power of SCRNs and how they relate to more conventional models of computation. We survey known connections and give new connections between SCRNs and Boolean Logic Circuits, Vector Addition Systems, Petri Nets, Gate Implementability, Primitive Recursive Functions, Register Machines, Fractran, and Turing Machines. A theme to these investigations is the thin line between decidable and undecidable questions about SCRN behavior
Superenergy and Supermomentum of Goedel Universes
We review the canonical superenergy tensor and the canonical angular
supermomentum tensors in general relativity and calculate them for space-time
homogeneous G\"odel universes to show that both of these tensors do not, in
general, vanish. We consider both an original dust-filled pressureless acausal
G\"odel model of 1949 and a scalar-field-filled causal G\"odel model of Rebou\c
cas and Tiomno. For the acausal model, the non-vanishing components of
superenergy of matter are different from those of gravitation. The angular
supermomentum tensors of matter and gravitation do not vanish either which
simply reflects the fact that G\"odel universe rotates. However, the axial
(totally antisymmetric) and vectorial parts of supermomentum tensors vanish. It
is interesting that superenergetic quantities are {\it sensitive} to causality
in a way that superenergy density of gravitation in the acausal
model is {\it positive}, while superenergy density in the causal
model is {\it negative}. That means superenergetic quantities might serve as
criterion of causality in cosmology and prove useful.Comment: an amended version, REVTEX, 26 pages, no figures, to appear in
Classical and Quantum Gravit
Stability of Closed Timelike Curves in Goedel Universe
We study, in some detail, the linear stability of closed timelike curves in
the Goedel metric. We show that these curves are stable. We present a simple
extension (deformation) of the Goedel metric that contains a class of closed
timelike curves similar to the ones associated to the original Goedel metric.
This extension correspond to the addition of matter whose energy-momentum
tensor is analyzed. We find the conditions to have matter that satisfies the
usual energy conditions. We study the stability of closed timelike curves in
the presence of usual matter as well as in the presence of exotic matter
(matter that does satisfy the above mentioned conditions). We find that the
closed timelike curves in Goedel universe with or whithout the inclusion of
regular or exotic matter are also stable under linear perturbations. We also
find a sort of structural stability.Comment: 12 pages, 11 figures, RevTex, several typos corrected. GRG, in pres
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