Measured by the lab
1.5998e-19
Is electric charge a continuous quantity you can have any amount of, or does it come in indivisible lumps — and if so, how big is the lump?
Units: C (the elementary charge e)
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Electric charge is quantized: the oil-drop charges are not a continuum but integer multiples of one quantum, whose size — recovered blind from noisy fall/rise velocities across 24 seeds — is e = (1.600 ± 0.008)×10⁻¹⁹ C, matching the elementary charge, while a forward-modelled continuous-charge world fails to quantize under the identical recovery (Millikan 1913)
Forward-model 60 charged oil drops between two horizontal plates 6 mm apart at 480 V. Each drop carries a true charge n·e for a small integer n (1–6). Field OFF: buoyancy-corrected gravity balances Stokes drag at the terminal fall speed v_f = m'g/6πη a, so the fall speed alone MEASURES the radius, a = √(9η v_f/2(ρ_oil−ρ_air)g). Field ON: the electric force qE shifts the terminal velocity to v_E = v_f − qE/6πη a, giving q = 6πη a (v_f − v_E)/E. Add 1.5% Gaussian velocity noise, recover q for every drop, then recover the quantum e WITHOUT being told it — a 1-D scan for the divisor that makes every charge a near-integer multiple, then a least-squares refine e = Σ(n·q)/Σ(n²). Sweep 24 independent seeds for an uncertainty. The elementary charge is loaded from scripts/oracles/millikan.reference.json ONLY to score the recovered quantum and to synthesise the true charges — it never enters the divisor scan or the refine. Decisive control: run the IDENTICAL recovery on a forward-modelled continuous-charge world (charges any real multiple of e) and show it CANNOT be made to quantize.
field OFF: m'g = 6πη a v_f, m' = (4/3)π a³(ρ_oil−ρ_air) ⇒ a = √(9η v_f/2(ρ_oil−ρ_air)g); field ON: v_E = v_f − qE/6πη a ⇒ q = 6πη a (v_f−v_E)/E; the {q} are integer multiples n·e
8.3000e-22
-0.0015
0.0103
The recovered VALUE of the quantum (1.600×10⁻¹⁹ C, within 0.15% of the injected e) is a 'recover-what-you-simulate' fidelity check of the blind divisor-scan + LSQ machinery under 1.5% velocity noise — e is the unit injected into the synthetic true charges, so this is not an independent metrological measurement of e. What is genuinely non-circular and falsifiable is the QUANTIZATION (remainder RMS 0.15 vs the 0.29 continuum) and its control: those are structural facts about whether charge is discrete, independent of e's numerical value. TAMPER NOTE (2026-07-23 refinement): this same circularity previously made the tamper self-test vacuous — a tampered known_value was tracked by the recovery and the derisk still passed. The determinism pins added with the on-screen reconciliation restore tamper sensitivity (see result.tamper_repair).
Pre-existing gap found during this refinement: because e is the unit injected into the forward-modelled charges (q = n*e), a tampered known_value is TRACKED by the blind recovery (scan window 0.6-2.6e-19 brackets it), so all four original gates stayed green under the mandatory tamper self-test — tamper => exit 0, a silent violation of the oracle standard. The new on-screen determinism pins break that degeneracy: they are fixed fingerprints in the reference, so a tampered known_value shifts the generated charges, moves e_screen off the pin, and the derisk exits 1. Verified both ways: known_value 1.602->1.702e-19 => exit 1 (pin rel-miss 6.3e-2); pin tampered alone => exit 1 (rel-miss 1.4e-3); restored => exit 0, 9/9.
Millikan's 1913 oil-drop determination (R. A. Millikan, Phys. Rev. 2, 109; Nobel 1923) — the proof that electric charge is quantized in integer multiples of the elementary charge e, the last classical 'continuous quantity' to fall. It VALIDATES, not derives: the lab assumes the classical force balance on a Stokes-drag sphere (buoyancy-corrected gravity vs drag, plus qE) and shows that the charges recovered from noisy fall/rise velocities do not form a continuum but land on equally spaced integer bands, whose spacing — recovered blind by a divisor scan the elementary charge never enters — is e = (1.600 ± 0.008)×10⁻¹⁹ C over 24 seeds (mean error 0.15%, worst seed 1.0%). It is made non-circular by the continuous-charge control: the identical recovery run on a forward-modelled continuum leaves the fractional-remainder RMS at ≈0.25 (near the 0.289 uniform value) on every seed, cleanly separated from the quantized data's 0.15, so the fitter cannot manufacture quantization — the discreteness is physical. Honest scope: because the true charges are synthesised as n·e, recovering ~e is a fidelity check of the blind recovery machinery, not an independent measurement of e; the genuinely value-independent, falsifiable result is the quantization itself. It does NOT derive e from deeper theory, model non-spherical drops or Cunningham slip corrections, or account for the real experiment's known systematic (Millikan's low viscosity biased his e ~0.2% high). The lab's charge-quantization pillar of the early-quantum arc (?world=blackbody … ?world=rutherford … ?world=franckhertz … ?world=sterngerlach), where the others quantize energy, reveal the nucleus, and quantize spin — this one quantizes charge.
npm run derisk -- millikan (scripts/millikan-derisk.mjs)scripts/oracles/millikan.reference.jsonR. A. Millikan, 'On the Elementary Electrical Charge and the Avogadro Constant', Phys. Rev. 2, 109 (1913) — the oil-drop determination of e and the proof of charge quantization (Nobel 1923); H. Fletcher, contemporaneous collaborator. Air viscosity η = 1.81×10⁻⁵ Pa·s, oil density ρ_oil = 920 kg/m³, plate gap 6 mm, 480 V. CODATA/SI-2019 elementary charge e = 1.602176634×10⁻¹⁹ C (exact since the 2019 SI redefinition).