Splitra: Schwinger Effect
Electromagnetism & Plasma arc, page 81 of 193. Back to The Pixelated Physics Universe
Who they are
Splitra opens her hands in a storm of electric field and tears a gleaming electron and positron out of empty space.
Splitra is a character of the Electromagnetism & Plasma arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
A strong enough electric field should pull electron–positron pairs out of the vacuum. In Dirac's picture an electron in the negative-energy sea must tunnel across a gap of 2mc², and the field tilts that gap. The rate is exponentially suppressed unless the field approaches a critical value, where the field does work mc² over one reduced Compton wavelength. Sauter found the tunnelling factor in 1931, Heisenberg and Euler built the effective theory in 1936, and Julian Schwinger gave the full QED result in Phys. Rev. 82, 664 (1951).
$$ \begin{gathered} E_c = \frac{m^{2}c^{3}}{e\hbar} \approx 1.32\times10^{18}\ \mathrm{V/m} \\ \text{pair rate} \propto \exp\!\left(-\frac{\pi E_c}{E}\right) \quad (\text{leading factor only}) \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $E_c$ | critical (Schwinger) field | V/m |
| $m$ | electron mass | kg |
| $c$ | speed of light, 299 792 458 m/s (exact) | m/s |
| $e$ | elementary charge, 1.602 176 634 × 10⁻¹⁹ C (exact) | C |
| $\hbar$ | reduced Planck constant | J·s |
| $E$ | applied electric field | V/m |
Honest caveat: The exponential is the leading factor only. The effect has not yet been seen directly in the vacuum with a static field, because no lab field comes close to E_c. A “Schwinger-like” production of electron–hole plasma reported in graphene superlattices (Berdyugin et al., Science 2022) is an analogue in a material, not the vacuum effect. The pair's energy comes from the field, not from nothing.
Sources
- Sauter (1931) Über das Verhalten eines Elektrons im homogenen elektrischen Feld nach der relativistischen Theorie Diracs, Z. Phys. 69, 742
- Heisenberg & Euler (1936) Folgerungen aus der Diracschen Theorie des Positrons, Z. Phys. 98, 714
- Schwinger (1951) On Gauge Invariance and Vacuum Polarization, Phys. Rev. 82, 664
Crossovers
Splitra meets Marina Dirac (Dirac Sea). 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.
Splitra meets The Vertex Smith (Quantum Electrodynamics Vertex). Splitra's pair production needs a field near the Schwinger value, about 1.3 × 10¹⁸ V/m. The Vertex Smith's coupling, the fine-structure constant α, is one reason the effect is exponentially suppressed below that field.
Wear the lore
Concept keywords: Schwinger Effect, Splitra, Electromagnetism & Plasma, physics lore, Pixelated Physics