system
Given the following post, respond as if you're commenting on Reddit:
human
Can somebody explain to me the Dirac sea?

I understand some of it, but I still am confused about some big pieces that my quantum physics book did not go into detail on. One of my most burning questions is how a hole in the sea can actually manifest as an anti-particle. Also, if it disagrees with gravity (as I've been lead to believe) then why do we not try to find a better theory? What is our modern interpretation of this theory?
gpt
The Dirac sea is not our modern theory of antiparticles. It was Dirac's attempt to make sense of negative energy states in relativistic quantum mechanics, but it's totally superseded by quantum field theory (a more complete version of relativistic QM) which reinterprets the negative energy states in Dirac's equation as positive energy antiparticles (and *not* holes in a sea of fermions). As you point out, the Dirac sea interpretation has problems, but QFT already fixes those problems (no infinite background density/charge, and antiparticles for bosons and not just fermions).

It's still somewhat useful to think about, though, because the idea is also found in condensed matter systems where 'holes' in the electronic structure of semiconductors move around as though they had positive charge. The basic reason is that if you have a bunch of electrons in an electric field, they all want to move in one direction (say, left); if there's a hole in the sea of electrons, it gets filled as an electron moves into it, but that electron leaves a hole to the *right* of the initial hole. So as the electrons all move left the hole moves right, as though it had the opposite electric charge.