Poincaré Invariant Quantum Theory

Abstract

It was stressed in section I.1 that “states” and “observables” in quantum theory have their physical counterparts in instruments which serve as sources of an ensemble or detectors of an event. Within the regime of special relativity we may distinguish two different types of information in the description of an instrument. On the one hand there is the intrinsic structure of the apparatus, given essentially by a workshop drawing. On the other hand, we have to specify where and how this equipment is to be placed within some established space-time reference system in the laboratory. We can put its center of mass in different positions, orient its axes, trigger the apparatus at a time of our choice, let it rest in the laboratory or move it with a constant velocity. There are altogether 10 parameters which specify the “placement”. They correspond to the 10 parameters of the Poincaré group. Poincaré invariance of the laws of nature means that the result of a complete experiment does not depend on the placement. Specifically, if both the source and the detector are subjected to the same shift of placement, then the counting rates will remain unaltered.