A violation of the spatial quantum inequality

Abstract: In classical physics the energy density of a field, such as the electromagnetic field, is always positive. However, in quantum field theory it has been shown that the energy density can be negative. There are restrictions, called the quantum inequalities, on the amount of negative energy that can exist in some region of space and time. In this paper we will focus on the spatial quantum inequality as it applies to a massless scalar field in 1-1 dimensional space-time. The spatial quantum inequality is a restriction on the amount of negative energy that can exist in a region of space at a given time. It will be shown that we can specify a quantum state which violates the spatial quantum inequality.