Localizability and the Planck mass

Andrés J. Kálnay

Arthur S. Wightman

Lawrence Paul Horwitz

Friedwardt Winterberg

Yuval Ne’eman

Abstract We combine the assumption of environmental decoherence, as the mechanism generating the classical (i.e. no quantum interferences) nature of spacetime, with the limit on its other classical feature, point-like continuity, namely Planck length. As a result, quantum extended objects with masses larger than the Planck mass have to derive their quantum behaviour from long-range correlations; objects with masses smaller than the Planck mass cannot display classical behaviour.

Eugenios Angelopoulos, F. Bayen, Mosh� Flato

Wightman's reformulation of the Wigner-Newton position operators and localizability of a massive particle is generalized so as to include zero mass particles. Different a priori procedures of generalizations are examined: we first prove some negative results based upon a projective induction technique. We then present some positive results which state that in some sense zero-mass particles are localizable and that their corresponding position operators are candidates for observables. Our treatment–which is group theoretical and kinematical in the same sense as that of Wightman–ends with suggestions for further possible developments.