On noise-resolution uncertainty in quantum field theory

Abstract

An uncertainty inequality is presented that establishes a lower limit for the product of the variance of the time-averaged intensity of a mode of a quantized electromagnetic field and the degree of its spatial localization. The lower limit is determined by the vacuum fluctuations within the volume corresponding to the width of the mode. This result also leads to a generalized form of the Heisenberg uncertainty principle for boson fields in which the lower limit for the product of uncertainties in the spatial and momentum localization of a mode is equal to the product of Planck's constant and a dimensionless functional which reflects the joint signal-to-noise ratio of the position and momentum of vacuum fluctuations in the region of the phase space occupied by the mode. Experimental X-ray synchrotron measurements provide an initial verification of the proposed theory in the case of Poisson statistics.