1,538 research outputs found
Godel-type space-time metrics
A simple group theoretic derivation is given of the family of space-time
metrics with isometry group SO(2,1) X SO(2) X R first described by Godel, of
which the Godel stationary cosmological solution is the member with a
perfect-fluid stress-energy tensor. Other members of the family are shown to be
interpretable as cosmological solutions with a electrically charged perfect
fluid and a magnetic field.Comment: Heavly rewritten respect to the orginal version, corrected some typos
due to files transfer in the last submitted versio
Godel Type Metrics in Randall Sundrum Model
Anisotropic cosmological models such as the G\"{o}del universe and its
extensions - G\"{o}del type solutions, are embedded on a visible 3-brane in the
Randall-Sundrum 1 model. The size of the extra dimension is stabilized by
tuning the rotation parameter to a very small value so that hierarchy problem
can be solved. A limiting case also yields the Randall-Sundrum 2 model. The
rotation parameter on the visible brane turns out to be of order ,
which implies that visible brane essentially lacks rotation.Comment: 10 pages, typos corrected and references adde
Cosmological Models with Shear and Rotation
Cosmological models involving shear and rotation are considered, first in the
General Relat ivistic and then in the Newtonian framework with the aim of
investigating singularities in them by using numerical and analytical
techniques. The dynamics of these rotating models ar e studied. It is shown
that singularities are unavoidable in such models and that the centr ifugal
force arising due to rotation can never overcome the gravitational and shearing
forc e over a length of time.Comment: 17 pages, 6 figures Journal Ref: J. Astrophys. Astr. (1999) 20, 79-8
Classical Mathematics for a Constructive World
Interactive theorem provers based on dependent type theory have the
flexibility to support both constructive and classical reasoning. Constructive
reasoning is supported natively by dependent type theory and classical
reasoning is typically supported by adding additional non-constructive axioms.
However, there is another perspective that views constructive logic as an
extension of classical logic. This paper will illustrate how classical
reasoning can be supported in a practical manner inside dependent type theory
without additional axioms. We will see several examples of how classical
results can be applied to constructive mathematics. Finally, we will see how to
extend this perspective from logic to mathematics by representing classical
function spaces using a weak value monad.Comment: v2: Final copy for publicatio
Essential Incompleteness of Arithmetic Verified by Coq
A constructive proof of the Goedel-Rosser incompleteness theorem has been
completed using the Coq proof assistant. Some theory of classical first-order
logic over an arbitrary language is formalized. A development of primitive
recursive functions is given, and all primitive recursive functions are proved
to be representable in a weak axiom system. Formulas and proofs are encoded as
natural numbers, and functions operating on these codes are proved to be
primitive recursive. The weak axiom system is proved to be essentially
incomplete. In particular, Peano arithmetic is proved to be consistent in Coq's
type theory and therefore is incomplete.Comment: This paper is part of the proceedings of the 18th International
Conference on Theorem Proving in Higher Order Logics (TPHOLs 2005). For the
associated Coq source files see the TeX sources, or see
<http://r6.ca/Goedel20050512.tar.gz
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 “notational variants” 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
Vacuum energy and Universe in special relativity
The problem of cosmological constant and vacuum energy is usually thought of
as the subject of general relativity. However, the vacuum energy is important
for the Universe even in the absence of gravity, i.e. in the case when the
Newton constant G is exactly zero, G=0. We discuss the response of the vacuum
energy to the perturbations of the quantum vacuum in special relativity, and
find that as in general relativity the vacuum energy density is on the order of
the energy density of matter. In general relativity, the dependence of the
vacuum energy on the equation of state of matter does not contain G, and thus
is valid in the limit when G tends to zero. However, the result obtained for
the vacuum energy in the world without gravity, i.e. when G=0 exactly, is
different.Comment: LaTeX file, 7 pages, no figures, to appear in JETP Letters, reference
is adde
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
Consistent use of paradoxes in deriving constraints on the dynamics of physical systems and of no-go-theorems
The classical methods used by recursion theory and formal logic to block
paradoxes do not work in quantum information theory. Since quantum information
can exist as a coherent superposition of the classical ``yes'' and ``no''
states, certain tasks which are not conceivable in the classical setting can be
performed in the quantum setting. Classical logical inconsistencies do not
arise, since there exist fixed point states of the diagonalization operator. In
particular, closed timelike curves need not be eliminated in the quantum
setting, since they would not lead to any paradoxical outcome controllability.
Quantum information theory can also be subjected to the treatment of
inconsistent information in databases and expert systems. It is suggested that
any two pieces of contradicting information are stored and processed as
coherent superposition. In order to be tractable, this strategy requires
quantum computation.Comment: 10 pages, latex, no figure
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