  It is generally known that the energy density can be negative in quantum
field theory. It is also believed that there are limits on this negative energy
density. These limits are known as the quantum inequalities. In a recent paper
[8] an example was provided of a system which violated the quantum
inequalities. Here we will demonstrate a violation of the spatial quantum
inequality for a scalar field with zero mass in 1-1 dimensional space-time. In
addition we will show that the system presented here also violates the quantum
interest conjecture.
