0. Introduction A Bézier surface is defined using mathematical spline functions whereby the resulting surface has a compact analytic description. This enables such surfaces to be easily manipulated, and they also have greater continuity properties. Bézier curves and surfaces are commonly used in computer-aided design [1,2], image processing [3,4], and finite elementmodeling (e.g. [5–7]). Many o...

We ask, and answer, the question of what’s computable by Turing machines equipped with time travel into the past: that is, closed timelike curves or CTCs (with no bound on their size). We focus on a model for CTCs due to Deutsch, which imposes a probabilistic consistency condition to avoid grandfather paradoxes. Our main result is that computers with CTCs can solve exactly the problems that are...

In this paper, we investigate the possibility of using closed timelike curves (CTCs) in relativistic hypercomputation. We introduce a wormhole based hypercomputation scenario which is free from the common worries, such as the blueshift problem. We also discuss the physical reasonability of our scenario, and why we cannot simply ignore the possibility of the existence of spacetimes containing CTCs.

I survey a number of interesting tests of quantum chromodynamics at the amplitude level which can be carried out in electron-positron annihilation and in photon-photon collisions at low energy. Some of the tests require e+e− center of mass energy as small as √ s = 2 GeV. Other tests which involve a spectrum of energies can be carried out advantageously at high energy facilities using the radiat...

Recent developments in the formulation of causality restrictions on the S matrix are reviewed, with attention focused on the behavior of matrix elements of the translation operator between suitably localized in and out states. Rapid decrease for large translations outside the timelike velocity cone of the center of momentum follows from Poincaré invariance and boundedness of S, as a result of a...

The existence of initial singularities in expanding universes is proved without assuming the timelike convergence condition. The assumptions made in the proof are ones likely to hold both in open universes and in many closed ones. (It is further argued that at least some of the expanding closed universes that do not obey a key assumption of the theorem will have initial singularities on other g...

Spacetimes with collisionless matter evolving from data on a compact Cauchy surface with hyperbolic symmetry are shown to be timelike and null geodesically complete in the expanding direction, provided the data satisfy a certain size restriction.

General Relativity is the study of Lorentz 4-manifolds (M, g) whose metric arises from a solution to the Einstein equations. We will take the signature of the metric to be (− + ++), where the minus sign indicates the time component. Then the tangent space at any point may be divided into three different types of vectors, namely timelike, spacelike, and null vectors whose lengths squared respect...

The Adler function [1] plays a key role in particle physics. Specifically, theoretical description of some strong interaction processes (e.g., electron– positron annihilation into hadrons [2] and inclusive τ lepton decay [3,4]) is inherently based on this function. Besides, Adler function is essential for confronting the precise experimental measurements of some electroweak observables (e.g., m...

We calculate the transformation and inverse transformation, in the form of Taylor expansions, from arbitrary coordinates to Fermi-Walker coordinates in tubular neighborhoods of arbitrary timelike paths for general spacetimes. Explicit formulas for coefficients and the Jacobian matrix are given.