So taking the square root of $E^2 = (m_oc^2)^2 + p^2c^2$ yields two solutions.
The Dirac Sea treats the negative solution as an infinite space of electrons with negative energy.
All the observable electrons have positive energies. As an electron lose energy, another electron somewhere else in the universe gains energy, so that the total positive energy is balanced with the negative energy.
Seems to be a good explanation I can use for explaining the negative part of the Energy-Mass equivalence. What is it about this interpretation that people disagree with?