Schwinger Effect: Vacuum Pair Production in a Strong Field

Applied Field

Field strength E / E_crit 0.90

Vacuum fluctuation rate 20/s

Simulation speed 1.0×

Live Readouts

Tunneling prob. / attempt

4.32%

Real pairs escaped

Pair-production rate Γ/V (natural units)

How it works

The QED vacuum is not empty — virtual electron-positron pairs constantly pop in and out of existence within the Heisenberg time limit Δt ~ ℏ/(2mc²). Normally they always recombine. But in a strong uniform electric field E, the two opposite charges are pulled apart by the field faster than they can recombine, and quantum tunneling lets the pair "borrow" enough energy from the field to become real, on-shell particles — the Schwinger effect.

Critical field:   E_crit = m²c³/(eℏ)  (≈ 1.3×10¹⁸ V/m for electrons)
WKB tunneling prob. per attempt:
                  p ≈ exp(−π · E_crit/E)
Pair-production rate (leading term, natural units m=c=ℏ=e=1):
                  Γ/V ≈ (E² / 4π³) · exp(−π/E)

Field strength slider — sets E as a multiple of the critical Schwinger field E_crit. Below E_crit production is exponentially suppressed (virtual pairs almost always re-annihilate); near and above E_crit the tunneling probability rises sharply and real pairs escape to the plates.
Vacuum fluctuation rate — how many tunneling attempts per second are sampled in the visualization (a display-pacing choice, decoupled from the true astronomically small real-world attempt rate so the effect stays visible).
Blue spheres are electrons (pulled toward the + plate), red spheres are positrons (pulled toward the − plate). A pair that fails its tunneling roll shrinks back to nothing; a pair that succeeds separates and drifts to the plates, incrementing the escaped-pairs counter.

Real-world relevance: E_crit is far beyond any lab magnet or capacitor, but ultra-intense lasers (ELI-NP, XCELS) and the near-field of heavy-ion collisions approach it, and Hawking radiation is a curved-spacetime cousin of the same tunneling mechanism.

Electron (e⁻) Positron (e⁺) Field lines

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