You guys are probably going to get a few replies to this affect, and it’s been a while since I’ve studied any of this so my memory is very hazy, but Danielle hit the nail on the head when she said a Dirac sea is kind of a conceptual way of dealing with the consequence of mathematics.
The Dirac equation, which is a quantum field theory model of `matter’ particles like electrons, admits solutions with both positive and negative energies. This conflicts fundamentally with the ‘principle of least energy’ in physics; if there’s an infinite sea of negative energy values, then particles would want to lose energy and decay away into these negative energy states (also releasing an infinite amount of energy as radiation as they did so, would be a problem.)
Dirac’s solution to this is a conceptual one; the negative energy levels must all be occupied. Matter particles have an interesting property that no two can have exactly the same “state” (i.e. energy, momentum, and other properties) at any given time. (This is the “Pauli Exclusion Principle”) If all the negative energy levels are full, then its impossible for particles to lose energy and drop into a negative state, and the paradox is resolved. Dirac further stated this “sea” of fully occupied negative energy levels is basically just ‘the vacuum’, regular empty space as we observe it in the absence of any matter.
I guess when Eva evokes the Dirac sea it basically wants to suggest that some localised hole in it has opened up and just swallowd up all the regular matter particles into its low-energy states.
Edit: Further cool things: this also explains the phenomenon of ‘pair-creation’, the fact that sometimes a pair of anti-matter/matter particles can be created from a very energetic photon. In the Dirac Sea model, the photon was absorbed by one of the negative energy particles, which was then ‘excited’ up to a positive energy level. We observe the resulting ‘hole’ in the dirac sea as an antiparticle.
Edit 2: Just a note, the Pauli Exclusion Principle might sound arbitrary but it’s very important. Again, the least energy principle might suggest that everything would want to occupy the lowest energy level possible. But the PEP basically rules this out and explains why we observe any kind of structure in matter at all.
I have no idea what the imaginary number space is supposed to be though??