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According to my understanding of the dirac equation, there's an infinite sea of electrons occupying all negative energy states which prevents an electron from dropping to lower and lower energy states down to negative infinity.

Since these are electrons, they have obviously have a charge, and hence every electron sits in the potential of every other: essentially there is a collosal amount of energy in all of space from these sea electrons.

Shouldn't this energy contribute to gravity? I understand that the cosmological constant should be energy present at all points in space, which causes space to expand. Wouldn't this energy do the same?

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    $\begingroup$ Yup, it does, and it contribute negatively. That’s why exact supersymmetry would give us zero vacuum energy, the fermions would cancel out the bosons. $\endgroup$ – knzhou Aug 15 '18 at 20:41
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    $\begingroup$ The "Dirac sea" is an obsolete concept. Now that we have a proper understanding of quantum field theory, it is not necessary anymore. To be clear: the modern paradigm does not include the Dirac sea as one of its ingredients. See also physics.stackexchange.com/q/309972/84967, physics.stackexchange.com/q/315603/84967. $\endgroup$ – AccidentalFourierTransform Aug 15 '18 at 20:52
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    $\begingroup$ @AccidentalFourierTransform As usual I have to disagree. The Dirac sea is a perfectly self-consistent story that provides valuable intuition. Only a purist would categorically reject it! $\endgroup$ – knzhou Aug 15 '18 at 21:00
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    $\begingroup$ Another issue with the Dirac sea story is that bosons can have antiparticles just as easily as fermions, but the Dirac sea can't explain bosonic antiparticles at all. $\endgroup$ – tparker Aug 15 '18 at 21:20
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    $\begingroup$ I do agree with @AccidentalFourierTransform in that the Dirac sea is not necessary: it’s just words you would use to fix up the situation if you did the quantization naively. (Basically we define the creation and annihilation operators backward by accident, get the wrong vacuum state, and then put in the Dirac sea to get the right vacuum.) But I do think it’s useful for at least some intuition. How would you intuitively show the SUSY vacuum energy vanishes otherwise? And it’s the most naive thing to do if you’ve never quantized a fermionic field, so the most natural for first-time learners. $\endgroup$ – knzhou Aug 15 '18 at 21:42
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Do not confuse models with reality/data.

The hypothesis of infinite seas of electrons has been left behind because better mathematical models were developed, and the problems of real electrons in infinite seas are model problems.

The solutions of the Dirac equation described fermions for us and started the way to quantum field theory which is the present tool of studying particle physics.

In the standard model of particle physics, all the point elementary particles in the table cover all of space as fields, on which operators creating and annihilating the particles act. Thus charged massive particles exist only where the creation operators act, the dirac model is not applicable. What is kept from the dirac equation is the plane wave solution for fermions,(the maxwell for photons,...) which represents the quantum field of the particle at all points in space, i.e. the electron field in your case.

The vacuum expectation value for all these fields is zero, except for the Higgs boson.

(It is important to keep in mind that this is the quantum framework, where wavefunctions lead to probabilities of interaction, not certitudes.)

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  • $\begingroup$ what is the reason for downvote? looks reasonable to me... $\endgroup$ – wcc Aug 18 '18 at 3:58
  • $\begingroup$ @IamAStudent if you continue your studies in physics you will realize that there are people who have their own physics in mind, not mainstream. A down vote may also mean that I am not answering the question asked."if this is true should it not..." in a vague cosmological allusion. I am answering that this model is no longer valid, and do not bother with cosmological implications. $\endgroup$ – anna v Aug 18 '18 at 4:10

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