A unified description of particles, strings and branes in Clifford spaces and p-brane/polyparticle duality

It is described how the Extended Relativity Theory in [Formula: see text]-spaces (Clifford spaces) allows a unified formulation of point particles, strings, membranes and [Formula: see text]-branes, moving in ordinary target spacetime backgrounds, within the description of a single polyparticle moving in [Formula: see text]-spaces. The degrees of freedom of the latter are provided by Clifford polyvector-valued coordinates (antisymmetric tensorial coordinates). A correspondence between the [Formula: see text]-brane ([Formula: see text]-loop) “Schrödinger-like” equations of Ansoldi–Aurilia–Spallucci and the polyparticle wave equation in [Formula: see text]-spaces is found via the polyparticle/[Formula: see text]-brane correspondence. This correspondence might provide another unexplored avenue to quantize [Formula: see text]-branes (a notoriously difficult and unsolved problem) from the more straightforward quantization of the polyparticle in [Formula: see text]-spaces, even in the presence of external interactions. We conclude with comments about the compositeness nature of the polyvector-valued coordinate operators in terms of ordinary [Formula: see text]-brane coordinates via the evaluation of [Formula: see text]-ary commutators.

Revisiting Barry Cox and James Hill's theory of superluminal motion: a possible solution to the problem of spinless tachyon localization

In 2012, Barry Cox and James Hill published a new and elegant way to deduce the formulae of extended relativity, developed by Erasmo Recami and others during the 1960s and 1970s. Extended relativity applies to superluminal or FTL (faster than light in the vacuum) particles, called tachyons by the late American physicist Gerald Feinberg. However, tachyons generate causality paradoxes in special relativity when used for signalling. These paradoxes are safely removed only in a space–time containing a preferred inertial reference frame. Moreover, quantum properties should be taken into account. They cause further trouble for tachyons because, for instance, spin-zero FTL particles satisfying the Klein–Gordon equation cannot be localized as pointlike particles, contrary to all other known fundamental constituents of matter. Perhaps the most interesting suggestion in Cox and Hill's paper is that a certain freedom is allowed in the theory of superluminal particles as no such particle has been reliably detected until now, so that it is worthwhile exploring theoretical alternatives. We shall prove that an idea from Cox and Hill's paper, when applied not in the context of extended relativity but in the framework of F. R. Tangherlini's absolute synchronization, allows the problem of tachyon localization for spinless particles to be solved.

THE CLIFFORD SPACE GEOMETRY BEHIND THE PIONEER AND FLYBY ANOMALIES

It is rigorously shown how the extended relativity theory in Clifford spaces (C-spaces) can explain the variable radial dependence ap(r) of the Pioneer anomaly; its sign (pointing towards the Sun); why planets do not experience the anomalous acceleration and why the present day value of the Hubble scale RH appears. It is the curvature–spin coupling of the planetary motions that hold the key. The difference in the rate at which clocks tick in C-space translates into the C-space analog of Doppler shifts which may explain the anomalous redshifts in cosmology, where objects which are not that far apart from each other exhibit very different redshifts. We conclude by showing how the empirical formula for the flybys anomalies obtained by Anderson et al.17 can be derived within the framework of Clifford geometry.