Authors: Carlos Castro
Born's Reciprocal Relativity in flat spacetimes is based on the principle of a maximal speed limit (speed of light) and a maximal proper force (which is also compatible with a maximal and minimal length duality) and where coordinates and momenta are unified on a single footing. We extend Born's theory to the case of curved spacetimes and construct a Reciprocal General Relativity theory (in curved spacetimes) as a local Gauge Theory of the Quaplectic Group and given by the semidirect product Q(1, 3) x U(1, 3) sH(1, 3), where the Nonabelian Weyl-Heisenberg group is H(1, 3). The gauge theory has the same structure as that of Complex Nonabelian Gravity. Actions are presented and it is argued why such actions based on Born's Reciprocal Relativity principle, involving a maximal speed limit and a maximal proper force, is a very promising avenue to Quantize Gravity that does not rely in breaking the Lorentz symmetry at the Planck scale, in contrast to other approaches based on deformations of the Poincare algebra, Quantum Groups. It is discussed how one could embed the Quaplectic gauge theory into one based on the U(1, 4),U(2, 3) groups where the observed cosmological constant emerges in a natural way. We conclude with a brief discussion of Complex coordinates and Finsler spaces with symmetric and nonsymmetric metrics studied by Eisenhart as relevant closed-string target space backgrounds where Born's principle may be operating.
Comments: recovered from sciprint.org
[v1] 5 Dec 2007
Unique-IP document downloads: 65 times
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.