Composition of velocities and momentum transformations in a scator-deformed Lorentz metric
Lab. de Óptica Cuántica, Depto. de Física, Universidad A. Metropolitana - Iztapalapa, Ap. postal. 55-534, 09340, México, D.F., Mexico
Accepted: 22 June 2020
Published online: 4 July 2020
The transformations of coordinates, velocities and momenta between inertial frames are described via real scator algebra. This algebra imposes a hyperbolic metric that is identical to the Lorentz metric in dimensions but becomes deformed in higher dimensions. Differences in the transformations of transverse quantities arise due to this departure in two and three spatial dimensions. The structure admits velocities arbitrarily close to c in orthogonal directions, but nonetheless, the scator velocity magnitude is always subluminal. The transformation between frames is described by an isometric scator product mapping. The product operation satisfies commutative group properties in a restricted subspace. Due to these properties, a sequence of Lorentz boosts can be synthesized as a single Lorentz boost without involving a rotation. A consequence of this algebraic structure is that the scator composition of velocities does not produce a Thomas rotation. The scenarios where this deformed metric could play a relevant role have not been yet assessed.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020