On the Measurement of Observables in Relativistic Quantum Mechanics

Abstract

The paper discusses the question how far observables in quantum theory permit accurate measurement if no assumptions are made about the values of conjugate variables. The physical connection between the uncertainty principle and the commutation relations is briefly discussed. A treatment of the $\gamma -\mathrm{r}\mathrm{a}\mathrm{y}$ microscope makes it appear that even with small-angle diffraction no great improvement beyond the Compton wave-length can be obtained. An analysis of an ideal arrangement to measure electric field strengths leads to the result that, admitting the existence of arbitrarily constituted test bodies, the accuracy of the measurement still cannot exceed certain limits which are mainly defined by the wave-length of the field and the spatial and temporal domain of measurement. These restrictions are due to the properties of the "vacuum," which are changed as a consequence of the possibility of pair production.