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Many physics text books reference to the concept of the Dirac sea as explanation of negative frequency solutions of the Dirac equation. It is supposed to be a bottomless "sea" of filled electron states. The other physical implications of this theory of the vacuum are never explored in a more than handwaving detail. Clearly the concept implies infinite electron density. The associated infinite negative charge density must be compensated by an equally infinite positive charge density. Effects of electron correlation would likely alter the properties of the hole, giving an effective mass different from that of an electron. What are the n&k values of the Dirac sea? We observe that the vacuum is perfectly transparent. How can this be consistent with the omnipresence of an infinite electron density ? In view of this blatant lack of physical motivation, why is this idea still surfacing in physics at all?

See for example Greiner, Relativistic quantum mechanics. Wave Equations, page 112 and others.

my2cts
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Why is the Dirac Sea concept taught in physics courses without explaining that is fundamentally flawed?

I think you are making an assumption here that it is not explained. It could well be that it most cases, it is correctly dealt with, in taught courses.

If you are referring to texts, from those I've read, I would agree that for every one that says clearly "There is no Dirac Sea", there is another that treats the topic badly, leaving it ambiguous at best.

Such texts certainly confused me, but that's easily done.

I think the texts can't resist the opportunity to show that Dirac was capable of mistakes, and to try an answer a question that may have occurred to some its readers.

By mentioning it, text writers may feel they are preparing students for later, related concepts

It's also a chance to give a history lesson, in the same way that many textbooks mention that Schrödinger originally thought about the electron being described by what we now treat as a probability wave, or Einstein working through his various (wrong) interpretations of GR.