The conventionality of simultaneity in the light of the spinor representation of the lorentz group

Abstract

The assessment of the conventionality of simultaneity has commonly taken place so far within the traditional formulation of the special theory of relativity. The ε-synchrony transformation is presented within this context in a sufficiently general manner that explores the connection of spatiotemporal measures to the choice of an ε-simultaneity relation. Subsequently to the recent work of Zangari, the feasibility of the latter is then investigated in terms of the two-component spinor formulation of special relativity. This is motivated by the fact that the spinor formulation provides the most fundamental expression of a spacetime theory that is consistent with the principle of special relativity. It is shown within this context that the transformation elements of the spinor group (unlike its Lorentz counterparts) prevent the groups representations being extended to a representation of the ε-class of non-standard synchrony transformations in four-dimensional space. The underlying reasons are traced down and discussed at length, whereas the compatibility of this finding with a general version of the principle of general relativity that is applicable to both tensor and spinor quantities is also demonstrated. It is finally established that the standard simultaneity relations far from constituting just a sensible choice in a range of conventional possibilities, is uniquely and objectively singled out by the properties of a spinor structure in Minkowski spacetime. The desirability of such a structure is anticipated by its fundamental status.