Time and space 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
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Accepted: 14 August 2014
Published online: 16 September 2014
The invariant transformations of a deformed Lorentz metric are explored. These transformations are described by the product operation with a unit magnitude element in hyperbolic scator algebra. The real scator set forms a group under the addition and product operations in a restricted space. However, the product is not distributive over addition. The restricted space condition is equivalent to the time-like subspace in special relativity. In 1+1 dimensions (time and one spatial variable), the deformation vanishes and the scator metric becomes identical to the Lorentz metric. In higher dimensions, time dilation and parallel space contraction are preserved albeit with slight quantitative modification. However, the deformed transformation also exhibits a transverse spatial elongation.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2014