A physical distinction between a covariant and non covariant reduction   process in relativistic quantum theories
  Causality imposes strong restrictions on the type of operators that may be observables in relativistic quantum theories. In fact, causal violations arise when computing conditional probabilities for certain partial causally connected measurements using the standard non covariant procedure. Here we introduce another way of computing conditional probabilities, based on an intrinsic covariant relational order of the events, which differs from the standard one when these type of measurements are included. This alternative procedure is compatible with a wider and very natural class of operators without breaking causality. If some of these measurements could be implemented in practice as predicted by our formalism, the non covariant, conventional approach should be abandoned. Furthermore, the description we promote here would imply a new physical effect where interference terms are suppressed as a consequence of the covariant order in the measurement process. 
Rodolfo Gambini and Rafael A. Porto