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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 Bohr model still taught? – BioPhysicist Jan 04 '19 at 13:36
  • @Aaon Stevens You could post this as a new question. In this way it would not divert from my question. – my2cts Jan 04 '19 at 13:41
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    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 04 '19 at 13:50
  • @Jon Custers Did we enter the post truth era in physics? I hope not. Please point out things that are wrong, yet taught. I am not talking about limited validity but invalidity. If a thing is totally wrong, not even wrong or wronger than wrong, it should not be taught. – my2cts Jan 04 '19 at 13:52
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    One thing was already pointed out above. And no, we are not in a 'post truth' era. Teaching is a difficult thing, and transitioning from, say, classical to quantum mechanics causes many students difficulty. The Bohr model, known to be wrong, helps many of them. Some get totally lost with it. Different students learn differently. Similarly, the jump from quantum mechanics to QFT loses others, yet we still have to try and bridge the gap. If a 'wrong' concept shows a way across the gap, it still may be useful pedagogically. – Jon Custer Jan 04 '19 at 14:24
  • @Jon Custers. I recognize that, hence my question. How is a fundamentally flawed concept judged to "help" students, especially without ever pointing out its overwhelming flaws? Bohr's theory as a first step towards quantum mechanics has clear pedagogical value. There is no pedagogical value in the Dirac sea especially when its flaws are not indicated. – my2cts Jan 04 '19 at 14:38
  • @Jon Custers Or are perhaps the teachers unaware of that the Dirac sea concept is nonsense? – my2cts Jan 04 '19 at 14:42
  • Perhaps some are - that certainly seems to be true for Bohr. Mine were quite aware and made sure to point it out (for both Bohr and Dirac and ...). – Jon Custer Jan 04 '19 at 14:44
  • I was trying to go along the lines of @JonCuster. I wasn't trying to ask a new question, and I am fairly sure you know this. Is it your experience that teachers spend much time on this concept? I know in the books I have read this concept is mentioned briefly and is not given much weight. – BioPhysicist Jan 04 '19 at 14:54
  • Related. – Cosmas Zachos Jan 04 '19 at 15:55
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    Near duplicate without rant. – Cosmas Zachos Jan 04 '19 at 15:58
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    Further near duplicate. – Cosmas Zachos Jan 04 '19 at 16:02
  • Dear all, I appreciate your comments. My position is that the Dirac sea model explains nothing and is fundamentally flawed. Nevertheless Greiner, Relativistic quantum mechanics, and Greiner and Reinhardt, Quantum Electrodynamics, extensively refer to the Dirac hole theory as a valid physical model. Does anybody, perhaps you yourself, believe that this is a valid model, and if so, why? – my2cts Jan 04 '19 at 17:27
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    I think you overstate the case against the Dirac sea. First, the Dirac sea is the intellectual forebearer of the Fermi sea, which is certainly real. Indeed, we now have Weyl metals in which the Fermi sea is a Dirac sea. Also, take something like the calculation of the one-loop calculation of the mass of a soliton coupled to fermions. This leads to a shift in the mass which is the sum of all the shifts of the states in the "Dirac sea". – Thomas Jan 04 '19 at 18:53
  • @Thomas All correct concepts probably have erroneous intellectual forbearers. I have no problem if such a concept is discussed with that context made explicit. There is no need to invoke exotic materials such as Weyl metals. The Dirac hole theory precedes the concept of a valence hole in e.g. silicon. However it is not a viable model of the positron at all and must not be presented as such. – my2cts Jan 04 '19 at 19:43
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    Quantum field theory gives unambiguous physical answers. The Dirac sea is one way of describing what it says with words -- it is an interpretation and not a separate theory. It's not "wrong" any more than the Copenhagen interpretation is. – knzhou Jan 04 '19 at 19:57
  • @knzhou It is not an interpretation. This is exactly my point. It has the status of interpretation of negative frequency solutions, while in fact it is the wrong theory that the vacuum contains infinitely many filled electron orbitals and that an unoccupied orbital represents a positron. – my2cts Jan 04 '19 at 20:18
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    @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 04 '19 at 20:23
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    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 04 '19 at 20:24
  • I was thinking of another example where Dirac sea description is entirely correct, and that’s the infinite hotel description of the chiral anomaly – Thomas Jan 05 '19 at 17:51
  • There is nothing opinion based about this question. Can the physics community handle criticism? Now that would be opinion based. – my2cts Mar 04 '19 at 20:57
  • @knzhou Have you ever studied many electron systems? – my2cts Mar 04 '19 at 21:02
  • @my2cts What about them? – knzhou Mar 04 '19 at 21:03
  • @knzhou A hole in in such a system is different from an electron due to relaxation and correlation effects between the remaining electrons. Also many electron systems require positive charge to compensate for the negative charge. In view of this, the Dirac sea concept is meaningless as an explanation of positrons. Fact, not opinion. – my2cts Mar 04 '19 at 21:08
  • @Thomas True, but you assertions are unrelated to the concept as an explanation of the positron. – my2cts Mar 04 '19 at 21:10
  • @knzhou The Infinite hotel explanation of the chiral anomaly in QED does apply to positrons – Thomas Mar 04 '19 at 22:02
  • @my2cts Many electron systems are very very different from your usual QFT. I am just stating that there are multiple ways of speaking about the excitations about the vacuum state of QFT, and one of those ways is the Dirac sea. In a many electron system, you're not expanding about the same vacuum state, instead you have a background of lots of electrons. There is still a hole picture story, but it's really logically independent of the one I was talking about. – knzhou Mar 04 '19 at 22:11
  • @knzhou In a Dirac sea you have more than "lots of" namely infinitely many electrons. I don't see the logic that in one case the many electron effects are absent and in the other not. And where is the positive background to keep the infinitely many electrons form flying apart? I recognise that the hole concept was a great, original idea for condensed matter physics. However it makes no sense as an explanation of antimatter. – my2cts Mar 04 '19 at 22:26

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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.

  • "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 04 '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 04 '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 04 '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. –  Jan 04 '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......" –  Jan 04 '19 at 19:40