Marina Dirac: Dirac Sea
Quantum Foundations arc, page 15 of 193. Back to The Pixelated Physics Universe
Who they are
Marina Dirac rises from a sea of filled states, and the hole she leaves behind shines like a positive electron.
Marina Dirac is a character of the Quantum Foundations arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
Dirac's equation for a free electron allows negative as well as positive energies, separated by a gap of 2mc². Dirac proposed that every negative-energy state is already filled, so electrons cannot fall into them. An empty state, a hole, would move like a positively charged electron. Dirac proposed the sea in 1930 (he first suggested the holes were protons); C. D. Anderson reported the positron in cosmic rays in 1933. The gap is 2m_ec² ≈ 1.022 MeV.
$$ \begin{gathered} \left(i\hbar\,\gamma^{\mu}\partial_{\mu} - mc\right)\psi = 0 \\ E = \pm\sqrt{p^{2}c^{2} + m^{2}c^{4}} \\ 2m_e c^{2} \approx 1.022\ \mathrm{MeV} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $\hbar$ | reduced Planck constant | J·s |
| $\gamma^{\mu}$ | Dirac matrices | 1 |
| $\partial_{\mu}$ | spacetime derivative | 1/m |
| $m,\ m_e$ | electron mass | kg |
| $c$ | speed of light, 299 792 458 m/s (exact) | m/s |
| $\psi$ | electron wavefunction (four-component spinor) | m^(−3/2) |
| $E$ | energy | J |
| $p$ | momentum | kg·m/s |
Honest caveat: The sea is a historical picture. Quantum field theory keeps the positron and drops the sea.
Sources
- Dirac (1930) A Theory of Electrons and Protons, Proc. R. Soc. Lond. A 126, 360
- Anderson (1933) The Positive Electron, Phys. Rev. 43, 491
- NIST CODATA: electron mass energy equivalent in MeV
Crossovers
Marina Dirac meets Exclusor (Pauli Exclusion Principle / Degeneracy Pressure). Marina Dirac's sea of filled negative-energy states only stays filled because of Exclusor: no electron can drop into a state that is already taken. Knock one out and the hole behaves like a positron.
Marina Dirac meets Splitra (Schwinger Effect). Marina Dirac's sea has a gap of 2mc² between filled and empty states. Splitra's electric field, if strong enough, tilts the levels until an electron can tunnel across that gap, leaving a hole behind: one electron–positron pair from the vacuum.
Marina Dirac meets Sakhara (Baryon Asymmetry). Marina Dirac's theory predicted antimatter. Sakhara asks why the universe kept so little of it. The Standard Model seems to fall far short of explaining the excess, and its origin is unknown.
Wear the lore
Concept keywords: Dirac Sea, Marina Dirac, Quantum Foundations, physics lore, Pixelated Physics