Vacuum Polarization: the Running Coupling of QED

Probe the Vacuum

Probe distance r 1.00 λ_C

Vacuum fluctuation rate 1.0×

Live Readouts

α(r) = α / (1 − (2α/3π)·ln(λ_C/r))

Probe distance386.2 fm

Effective coupling α(r)1 / 137.04

Charge screening0.0%

How it works

QED's vacuum is not empty. Heisenberg's energy–time uncertainty ΔE·Δt ≳ ħ/2 lets virtual electron–positron pairs briefly pop into existence anywhere, including right around a real charge. The real charge's electric field polarizes each pair — pulling the virtual positron slightly closer and pushing the virtual electron slightly farther — so the vacuum behaves like a dielectric: a cloud of induced dipoles that partially screens the bare charge, exactly like polarized molecules screening a charge in water.

A probe far outside the cloud sees the fully screened charge and measures the familiar low-energy fine-structure constant α ≈ 1/137.036. A probe that gets closer than the electron's reduced Compton wavelength λ_C ≈ 386 fm starts to penetrate the screening cloud and resolves more of the bare charge underneath, so the effective coupling grows. To leading order (one electron loop) this is:

α(r) = α / (1 − (2α/3π)·ln(λ_C/r)),   r ≤ λ_C
α(r) = α,                             r > λ_C  (pair production suppressed)

Probe distance — sets how close the yellow probe sphere sits to the bare charge; the formula above is re-evaluated live from this distance.
Vacuum fluctuation rate — only changes how fast virtual pairs are shown popping in and out; it has no effect on α(r), it just visualizes the ΔE·Δt uncertainty more or less vividly.
Field lines — toggles radial field-line strands whose brightness tracks the effective field strength ∝ α(r) at the current probe radius.

This is a real, measured effect: the running of α has been confirmed at particle colliders, where α climbs from 1/137.036 at everyday energies to about 1/128 near the Z-boson mass (≈ 91 GeV, r ≈ 2×10⁻³ fm) once muon, tau and quark loops are included alongside the electron loop. This simulation shows only the leading electron-loop contribution, so its numbers run more gently than the full experimental result — the mechanism (charge screening by vacuum polarization) is the same physics in both cases.

Bare charge (−e) Virtual e⁺ (pulled in) Virtual e⁻ (pushed out) Probe

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