ABSTRACT
This chapter aims to express the deviation, the variance of outputs, in the simpler and more transparent form of a specific type of action uncertainty principle (AUP). It considers two simple examples of the application of AUP in quantum mechanics: position monitoring of a free particle and of a harmonic oscillator. The chapter considers only the case of a one-dimensional particle and oscillator. Both rougher and finer measurements are disadvantageous as compared with the optimal measurement, the former because of classical and the latter because of quantum measurement noise. The variance of the measurement outputs corresponding to the optimal level of measurement puts an absolute quantum limit on the given type of measurement. The path-integral approach has already been applied to measurements of quantum fields: an electromagnetic field and a gravitational field. Measurements of this type can be called continual because they are prolonged in time and protracted in space.
