It is said that if the space is homogeneous then momentum is conserved. But I've been thinking in the following situation:
Consider a parallel plates capacitor. In between the plates there is a uniform electric field so that the space is homogeneous. There is no point in between the plates that differs from any other. However an electric charged particle would feel an electric force and its momentum would change.
I know that the potential energy (PE) is not uniform, but at same time I understand PE as just a bookkeeping device (In the sense of section 4-1 of Feynman's lectures of physics, vol 1). Is this true or it has an underlying reality (in the sense PE existence cannot be avoided).
Edit: Another way to put it. Suppose we never used the concept of energy in physics. We only use forces, momentum or anything we can measure directly. How could we say the space in between the plates is not homogeneous so that momentum does not conserve?