Mass as a Relativistic Quantum Observable
  A field state containing photons propagating in different directions has a non vanishing mass which is a quantum observable. We interpret the shift of this mass under transformations to accelerated frames as defining space-time observables canonically conjugated to energy-momentum observables. Shifts of quantum observables differ from the predictions of classical relativity theory in the presence of a non vanishing spin. In particular, quantum redshift of energy-momentum is affected by spin. Shifts of position and energy-momentum observables however obey simple universal rules derived from invariance of canonical commutators. 
Marc-Thierry Jaekel (Laboratoire de Physique Th\'eorique de l'Ecole   Normale Sup\'erieure) and Serge Reynaud (Laboratoire K...