Schwinger Effect: Vacuum Pair Production

Applied Field

Field strength E / E_c 1.00

Live Readouts

Field E / E_c

1.00

Rate Γ/V (rel.)

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Pairs produced

Pairs in flight

Suppression exponent −π·E_c/E

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How it works

The vacuum is not empty — it seethes with virtual electron-positron pairs that normally recombine before they can be observed. A strong enough electric field tilts the energy landscape so a virtual pair can quantum-tunnel through the "mass gap" (2m_ec²) and become real, on-shell particles that the field then rips apart. This is the Sauter-Schwinger effect, predicted in 1931/1951 and only directly observed via ultra-intense lasers and heavy-ion collisions.

The real leading-order Schwinger pair-production rate per unit volume per unit time, in terms of the field ratio x = E/E_c:

Γ/V ∝ E² · exp(−π·E_c/E) = x² · exp(−π/x)
E_c = m_e²c³/(eℏ) ≈ 1.3×10¹⁸ V/m   (the true QED critical field)

This simulator works entirely in the normalized ratio x = E/E_c so the real exponential survives in floating point — computing directly with 10¹⁸ V/m would just underflow to zero. The physics is unchanged: below x ≈ 0.3 the exponent is so deeply negative that essentially no pairs appear no matter how long you wait; production only becomes appreciable as x approaches and passes 1, and rises steeply from there. Nothing here is a linear ramp — it is the genuine tunnelling threshold.

Low field (x ≲ 0.3) — the vacuum stays essentially inert; the vast majority of virtual pairs never make it past the mass gap.
x ≈ 1 — the exponential suppression is still severe (e^−π ≈ 0.043) but occasional real pairs now tunnel through and separate visibly.
x ≳ 2 — the suppression collapses and pair production becomes copious — this is the field strength found for a fraction of a second near the focus of the most intense lasers ever built, and is thought to occur naturally at the surface of magnetars.
Once real, the electron (−e) and positron (+e) feel opposite forces from the same field and accelerate apart along the field direction — exactly what the particle trails below show.

Electron (e⁻) Positron (e⁺) Γ/V(E) curve · current field