is the Dirac sea a conventional or controversial model of the vacuum?
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I would describe it as "outdated". It is formally equivalent to the more modern, quantum field-based description, but I think people don't like the way it poses things conceptually.
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What’s the pop-science level distinction between the two interpretations?
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The idea of the Dirac sea was really meant to explain the origin of the positron, which acts just like an electron except it has positive charge. A positron can be created out of nothing so long as an electron is created simultaneously.
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The Dirac Sea idea is that what we call "empty space" is really an infinite sea of electrons with "negative energy". If you hit one of those electrons in the sea very hard, it gets promoted up to positive energy, leaving behind a hole in the sea.
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Think of it like making a bubble by removing a drop of water out of a glass.
In the Dirac sea interpretation, the "bubble" is the newly-created positron and the "drop" is the newly-created electron.
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The modern interpretation is more like what I wrote here: ribbonfarm.com/2015/09/24/sam
We think of empty space as having structure that admits two opposite kinds of defects. One is an electron, and its opposite is the positron.
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The zipper metaphor seems more like an information state than an energy balance
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I'm not entirely sure what you mean by that, but I know that there are people who think about the universe from an "everything is information" perspective, and they would probably agree with you.
I'm more of an "everything is energy" person.
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I mean something like you could view the 2 as bit strings that would xor to all 1s. Ie if electron is 1010 and positron is 0101 xor becomes 1111, which has no info content.

