# Why is the Dirac Sea concept taught in physics courses without explaining that is fundamentally flawed? [closed]

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.

• Why is the Bohr model still taught? – BioPhysicist Jan 4 '19 at 13:36
• All kinds of things are taught that are found to be "wrong" when looked at more deeply. One learns to realize that the models have their limitations, and those limitations are the places to start looking for new stuff. – Jon Custer Jan 4 '19 at 13:50
• Near duplicate without rant. – Cosmas Zachos Jan 4 '19 at 15:58
• @my2cts The point is, when you quantize a negative frequency fermionic mode, you get two energy levels, one higher than the other, and the lower one is occupied in the vacuum state. That is the unambiguous prediction of QFT. You can choose to call the higher energy level "the presence of a positron" or "the absence of a negative-energy electron", but these are merely words. All of the equations are the same. – knzhou Jan 4 '19 at 20:23
• If my bank account goes up by a hundred dollars, I could call it "the gain of a hundred dollars" or "the loss of a hundred dollars of debt". There's no difference. I still have the same amount of money either way. – knzhou Jan 4 '19 at 20:24

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.

• "making an assumption here that it is not explained" I stated "in courses" not "in all/most courses". I suspect that it may happen often but do not have access to any statistics on this. I give examples of textbooks that I believe are frequently used in courses. – my2cts Jan 4 '19 at 19:23
• "the texts can't resist the opportunity to show that Dirac was capable of mistakes" This is certainly possible. It may also be a way to evade the question of the meaning of negative frequency. It seems to have this effect in the texts I have seen. – my2cts Jan 4 '19 at 19:28
• If you have any references where the flaws of the Dirac sea concept are discussed I would be interested. – my2cts Jan 4 '19 at 19:33
• Sincere apologies, I didn't read the post properly. I wrote a kinda/sorta related post (in the sense that nothing much is done about it today), regarding the word spin and the confusion it causes. – user214814 Jan 4 '19 at 19:36
• As far as texts go, QFT Demystified , McMahon, says flatly that there is no sea, but you are absolutely correct, I have not seen anything along the lines of "if there was a sea......" – user214814 Jan 4 '19 at 19:40