Legendrian links, causality, and the Low conjecture

Let $(X^{m+1}, g)$ be a globally hyperbolic spacetime with Cauchy surface diffeomorphic to an open subset of $\mathbb R^m$. The Legendrian Low conjecture formulated by Nat\'ario and Tod says that two events x,y\in\ss are causally related if and only if the Legendrian link of spheres $\mathfrak S_x, \mathfrak S_y$ whose points are light geodesics passing through $x$ and $y$ is non-trivial in the contact manifold of all light geodesics in $X$. The Low conjecture says that for $m=2$ the events $x,y$ are causally related if and only if $\mathfrak S_x, \mathfrak S_y$ is non-trivial as a topological link. We prove the Low and the Legendrian Low conjectures. We also show that similar statements hold for any globally hyperbolic $(X^{m+1}, g)$ such that a cover of its Cauchy surface is diffeomorphic to an open domain in $\mathbb R^m.$Comment: Version 3 - minor improvements, references added 11 pages, 1 figur

Linking and causality in globally hyperbolic spacetimes

The linking number $lk$ is defined if link components are zero homologous. Our affine linking invariant $alk$ generalizes $lk$ to the case of linked submanifolds with arbitrary homology classes. We apply $alk$ to the study of causality in Lorentz manifolds. Let $M^m$ be a spacelike Cauchy surface in a globally hyperbolic spacetime $(X^{m+1}, g)$. The spherical cotangent bundle $ST^*M$ is identified with the space $N$ of all null geodesics in $(X,g).$ Hence the set of null geodesics passing through a point $x\in X$ gives an embedded $(m-1)$-sphere $S_x$ in $N=ST^*M$ called the sky of $x.$ Low observed that if the link $(S_x, S_y)$ is nontrivial, then $x,y\in X$ are causally related. This motivated the problem (communicated by Penrose) on the Arnold's 1998 problem list to apply link theory to the study of causality. The spheres $S_x$ are isotopic to fibers of $(ST^*M)^{2m-1}\to M^m.$ They are nonzero homologous and $lk(S_x,S_y)$ is undefined when $M$ is closed, while $alk(S_x, S_y)$ is well defined. Moreover, $alk(S_x, S_y)\in Z$ if $M$ is not an odd-dimensional rational homology sphere. We give a formula for the increment of \alk under passages through Arnold dangerous tangencies. If $(X,g)$ is such that $alk$ takes values in $\Z$ and $g$ is conformal to $g'$ having all the timelike sectional curvatures nonnegative, then $x, y\in X$ are causally related if and only if $alk(S_x,S_y)\neq 0$. We show that $x,y$ in nonrefocussing $(X, g)$ are causally unrelated iff $(S_x, S_y)$ can be deformed to a pair of $S^{m-1}$-fibers of $ST^*M\to M$ by an isotopy through skies. Low showed that if (\ss, g) is refocussing, then $M$ is compact. We show that the universal cover of $M$ is also compact.Comment: We added: Theorem 11.5 saying that a Cauchy surface in a refocussing space time has finite pi_1; changed Theorem 7.5 to be in terms of conformal classes of Lorentz metrics and did a few more changes. 45 pages, 3 figures. A part of the paper (several results of sections 4,5,6,9,10) is an extension and development of our work math.GT/0207219 in the context of Lorentzian geometry. The results of sections 7,8,11,12 and Appendix B are ne

The potential impact of orange-fleshed sweetpotatoes on vitamin A intake in Sub-Saharan Africa.

A recent ex ante impact assessment indicates that orangefleshed sweetpotatoes can make a major contribution to alleviating vitamin A malnutrition in Sub-Saharan Africa. Replacing the white-fleshed varieties now grown by farmers with new high ß-carotene cultivars that meet local preferences would benefit an estimated 50 million children under age 6 who are currently at risk. The majority of children in Burundi, Rwanda and Uganda would benefit, as would about half of the children in Tanzania. Children in Ethiopia, Kenya and South Africa would also be affected, though to a lesser degree. The study did not take into account the benefits of the new cultivars to pregnant and lactating women, a population whose health is also likely to improve from the availability of the new plant types. Vitamin A deficiency is a major public health problem throughout the region and is responsible for tens of thousands of deaths annually among young children

Search for a T_20 Analyzer for Deuterons

This work was supported by the National Science Foundation Grant NSF PHY 81-14339 and by Indiana Universit

The twin paradox and Mach's principle

The problem of absolute motion in the context of the twin paradox is discussed. It is shown that the various versions of the clock paradox feature some aspects which Mach might have been appreciated. However, the ultimate cause of the behavior of the clocks must be attributed to the autonomous status of spacetime, thereby proving the relational program advocated by Mach as impracticable.Comment: Latex2e, 11 pages, 6 figures, 33 references, no tables. Accepted for publication in The European Physical Journal PLUS (EPJ PLUS

Theorising Disability: Beyond Common Sense

This article seeks to introduce the topic of disability to political theory via a discussion of some of the literature produced by disability theorists. The author argues that these more radical approaches conceptualise disability in ways that conflict with ‘common-sense’ notions of disability that tend to underpin political theoretical considerations of the topic. Furthermore, the author suggests that these more radical conceptualisations have profound implications for current debates on social justice, equality and citizenship that highlight the extent to which these notions are also currently underpinned by ‘common-sense’ notions of ‘normality’

Measurements of d+p Elastic Scattering Analyzing Powers at 80 MeV

This research was sponsored by the National Science Foundation Grant NSF PHY 87-1440

Some Properties of a Transient New Coherent Condition of Matter Formed in High--Energy Hadronic Collisions

We investigate the dynamical possibility for the formation of a transient new coherent condition of matter in high--energy hadronic collisions. The coherent bosonic amplitude is characterized by a non--zero momentum and is sustained by $P$--wave interactions of quasi--pions in a dense fermionic medium. We make quantitative estimates of several essential properties: the condensate momentum and the fermionic density, the size of the coherent amplitude and the negative energy density contributed by the condensate, a characteristic proper time for the system to exist prior to breakdown into a few pions, and a characteristic extension of the system over the plane perpendicular to the collision axis. These quantities then allow us to make definite estimates of new signals: a few pions with anomalously small transverse momenta $\leq 50$ MeV/c; and a possible anomalous bremsstrahlung of very soft photons with characteristic transverse momenta as low as about 4 MeV/c.Comment: 23 pages, LaTeX. A complete postscript file is available via anonymous ftp at ttpux2.physik.uni-karlsruhe.de (129.13.102.139) as /ttp94-18 /ttp94-18.ps, Local preprint# TTP94-1

Oxidised cosmic acceleration

We give detailed proofs of several new no-go theorems for constructing flat four-dimensional accelerating universes from warped dimensional reduction. These new theorems improve upon previous ones by weakening the energy conditions, by including time-dependent compactifications, and by treating accelerated expansion that is not precisely de Sitter. We show that de Sitter expansion violates the higher-dimensional null energy condition (NEC) if the compactification manifold M is one-dimensional, if its intrinsic Ricci scalar R vanishes everywhere, or if R and the warp function satisfy a simple limit condition. If expansion is not de Sitter, we establish threshold equation-of-state parameters w below which accelerated expansion must be transient. Below the threshold w there are bounds on the number of e-foldings of expansion. If M is one-dimensional or R everywhere vanishing, exceeding the bound implies the NEC is violated. If R does not vanish everywhere on M, exceeding the bound implies the strong energy condition (SEC) is violated. Observationally, the w thresholds indicate that experiments with finite resolution in w can cleanly discriminate between different models which satisfy or violate the relevant energy conditions.Comment: v2: corrections, references adde