In this paper we apply the concept of radar time (popularised by Bondi in his work on k-calculus) to the well-known relativistic twin `paradox’. Radar time is used to define hypersurfaces of simultaneity for a class of travelling twins, fr … Continued
new form of the Kerr solution is presented. The solution involves a time coordinate which represents the local proper time for free-falling observers on a set of simple trajectories. Many physical phenomena are particularly clear when related to this time … Continued
The late 18th and 19th centuries were times of great mathematical progress. Many new mathematical systems and languages were introduced by some of the millenium’s greatest mathematicians. Amongst these were the algebras of Clifford (1878) and Grassmann (1877). While these … Continued
We consider topological contributions to the action integral in a gauge theory formulation of gravity. Two topological invariants are found and are shown to arise from the scalar and pseudoscalar parts of a single integral. Neither of these action integrals … Continued
It is argued that geometric algebra, in the form of the multiparticle spacetime algebra, is well-suited to the study of multiparticle quantum theory, with advantages over conventional techniques both in ease of calculation and in providing an intuitive geometric understanding … Continued
A new method for modelling spherically symmetric inhomogeneities is applied to the formation of clusters in an expanding Universe. We impose simple initial velocity and density perturbations of finite extent and we investigate the subsequent evolution of the density field. … Continued
A new method is proposed for modelling spherically symmetric inhomogeneities in the Universe. The inhomogeneities have finite size and are compensated, so they do not exert any measurable gravitational force beyond their boundary. The region exterior to the perturbation is … Continued
A new gauge theory of gravity is presented. The theory is constructed in a flat background spacetime and employs gauge fields to ensure that all relations between physical quantities are independent of the position and orientation of the matter fields. … Continued
We discuss a coordinate-free approach to the geometry of computer vision problems. The technique we use to analyse the 3-dimensional transformations involved will be that of geometric algebra: a framework based on the algebras of Clifford and Grassmann. This is … Continued
It is shown that higher-weighted representations of rotation groups can be constructed using multilinear functions in geometric algebra. Methods for obtaining the irreducible representations are found, and applied to the spatial rotation group, SO(3), and the proper Lorentz group, SO+(1,3). … Continued