324 research outputs found
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
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
Spacetime could be simultaneously continuous and discrete in the same way that information can
There are competing schools of thought about the question of whether
spacetime is fundamentally either continuous or discrete. Here, we consider the
possibility that spacetime could be simultaneously continuous and discrete, in
the same mathematical way that information can be simultaneously continuous and
discrete. The equivalence of continuous and discrete information, which is of
key importance in information theory, is established by Shannon sampling
theory: of any bandlimited signal it suffices to record discrete samples to be
able to perfectly reconstruct it everywhere, if the samples are taken at a rate
of at least twice the bandlimit. It is known that physical fields on generic
curved spaces obey a sampling theorem if they possess an ultraviolet cutoff.
Most recently, methods of spectral geometry have been employed to show that
also the very shape of a curved space (i.e., of a Riemannian manifold) can be
discretely sampled and then reconstructed up to the cutoff scale. Here, we
develop these results further, and we here also consider the generalization to
curved spacetimes, i.e., to Lorentzian manifolds
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
String Cosmology
An overview is given of the formulation of low-energy string cosmologies
together with examples of particular solutions, successes and problems of the
theory.Comment: 12 pages, Latex. Invited paper to appear in the special issue of the
Journal of Chaos, Solitons and Fractals on "Superstrings, M, F, S... Theory",
eds. C. Castro and M.S. El Naschi
On the Significance of the Weyl Curvature in a Relativistic Cosmological Model
The Weyl curvature includes the Newtonian field and an additional field, the
so-called anti-Newtonian. In this paper, we use the Bianchi and Ricci
identities to provide a set of constraints and propagations for the Weyl
fields. The temporal evolutions of propagations manifest explicit solutions of
gravitational waves. We see that models with purely Newtonian field are
inconsistent with relativistic models and obstruct sounding solutions.
Therefore, both fields are necessary for the nonlocal nature and radiative
solutions of gravitation.Comment: 15 pages, incorporating proof correction
Shear-free rotating inflation
We demonstrate the existence of shear-free cosmological models with rotation
and expansion which support the inflationary scenarios. The corresponding
metrics belong to the family of spatially homogeneous models with the geometry
of the closed universe (Bianchi type IX). We show that the global vorticity
does not prevent the inflation and even can accelerate it.Comment: Revtex, 12 pages; to appear in Phys. Rev.
Is Turing's Thesis the Consequence of a More General Physical Principle?
We discuss historical attempts to formulate a physical hypothesis from which
Turing's thesis may be derived, and also discuss some related attempts to
establish the computability of mathematical models in physics. We show that
these attempts are all related to a single, unified hypothesis.Comment: 10 pages, 0 figures; section 1 revised, other minor change
Existential witness extraction in classical realizability and via a negative translation
We show how to extract existential witnesses from classical proofs using
Krivine's classical realizability---where classical proofs are interpreted as
lambda-terms with the call/cc control operator. We first recall the basic
framework of classical realizability (in classical second-order arithmetic) and
show how to extend it with primitive numerals for faster computations. Then we
show how to perform witness extraction in this framework, by discussing several
techniques depending on the shape of the existential formula. In particular, we
show that in the Sigma01-case, Krivine's witness extraction method reduces to
Friedman's through a well-suited negative translation to intuitionistic
second-order arithmetic. Finally we discuss the advantages of using call/cc
rather than a negative translation, especially from the point of view of an
implementation.Comment: 52 pages. Accepted in Logical Methods for Computer Science (LMCS),
201
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