Time and space transformations in a scator deformed Lorentz metric

On the Geometry of the Hyperbolic Scator Space in 1+2 Dimensions

“…Results produced by the multiplication formula for higher dimensions can be interpreted as a deformation of the standard Lorentz metric. The latter is obtained in the limit a 0 → ∞, b 0 → ∞ [4]. Therefore, the scator structure is compatible with the standard physical interpretation only in the 1 + 1 case.…”

“…However, the norm of the product of two scators is just the product of their norms [9], which is very useful in this context. In this paper we present new results concerning the metric structure of the scator space, extending results of [4,9].…”

“…As opposite, here we perform a classification in terms of the deformed metric (1.6) only, what has its formal consequences in the appearance of some new causal realms, with potential physical interpretations. For instance, we indicate that the bipyramid considered in [4] has some kind of time-like "wings" around, described by the regime a We point out that the existence of such wings is not mentioned in the paper [4]. Probably this possibility was excluded from considerations by assumption.…”

“…It was shown in [4] that this algebra may be given physical interpretation corresponding to some ideas of special relativity, although the metric in the scator space is different from the standard metric of Minkowski space. This scator metric (defined below) is called a scator-deformed Lorentz metric.…”

“…By the way, the scator appearing on the right-hand side of (1.5) will be referred to as dual to o c (see Definition 2.1 below). Many properties of the scator product (1.2) were widely investigated in many contexts [1,8,9], also physical [4]. To gain some insight in possible physical interpretation of the scator algebra, we recall here some basic terminology from [1] The classification proposed above is analogous to what is well known from special relativity.…”