Some Relativistic Oddities in the Quantum Theory of Observation

Abstract

The orthodox quantum theory of observations is summarized and then applied to particle detection. Probabilities and state vectors are worked out for instantaneous observations, at stated times, by one counter, two counters, and three counters. The same cases are then examined in the context of a relativistic theory. It is found that, if attempts are made to detect a given particle in two space-time regions that have space-like separation, the nonrelativistic probability formulas have to be supplemented by additional conditions, and the wave function of the particle being detected becomes ambiguous and noncovariant. This ambiguity does not affect any probabilities for observations whose effect on the wave function has already been taken into account, and these are, by implication, the only observations whose probabilities could possibly be affected by the ambiguities in question. Possible consequences of these results are briefly discussed.