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

TL;DR

This paper demonstrates that the localization of a massive scalar boson on spacelike hyperplanes extends uniquely to all achronal hyperplanes through high boost limits, establishing a covariant framework and deriving Lorentz contraction.

Contribution

It introduces a covariant method for extending scalar boson localization from spacelike to all achronal hyperplanes using high boost limits, emphasizing causality and Lorentz contraction.

Findings

Localization extends uniquely to all achronal hyperplanes.

Normalization is preserved under high boost limits.

Lorentz contraction naturally arises from causality considerations.

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.