Localization of the massive scalar boson on achronal hyperplanes, derivation of Lorentz contraction

Abstract

It is shown that the causal localizations of the massive scalar boson on spacelike hyperplanes extend uniquely to all achronal hyperplanes. The extension occurs by means of the high boost limit in a covariant manner. Towards a localization in maximal achronal surfaces a simple but emblematic case shows that normalization, demanded by causality, is preserved. Moreover the existence of the high boost limit, as a consequence of causality, implies the phenomenon of Lorentz contraction discussed in detail. In conclusion, these considerations constitute a clear plea for the concept of achronal localization.