QUANTUM EVIDENCE / CHARGE

Oil-Drop Charge Measurement

Track one negative oil drop with the electric field off and on. Separate gravity, buoyancy, viscous drag and thermal wandering; infer a continuous charge from the recorded motion.

Synthetic overdamped motion of a spherical mineral-oil drop with a simple pressure-dependent slip correction, ideal uniform field and calibrated camera. Charge magnitude is continuously adjustable; integer charge is not imposed on the estimator. This is a measurement model, not a reconstruction of Millikan’s historical records or an independent proof of quantization.

Plate gap: 5 mm. Drop radius greatly enlarged. Upward height follows the latest camera record; this tracking camera is idealized. Light is scattered sideways into the microscope.

OBSERVE / KEEP THE RECORD

One drop. Two tracks.

Independent field-off and field-on tracks each start at the mid-plane. Physical time advances in 0.1 s increments; playback is accelerated. A plate contact ends that track and withholds the estimate.

Ready. Predict, then acquire.

CAMERA HEIGHT / MICROMETERS

Drift beneath the wandering.

$t/\mathrm{s},\quad z/\mathrm{\mu m}$

Teal: field off. Gold: field on. Dots and solid lines: camera records. Fine dashes: source mean drift. Purple dashes: endpoint drift estimates. Gray: saved observations.

INFER / SOURCE PARAMETERS EXCLUDED

A continuous charge estimate.

Inferred charge magnitude

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Inferred radius

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Stokes-only charge

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Off drift · estimate

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On drift · estimate

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Recorded frames

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$\Delta z/\mathrm{\mu m}$

The lower plot shows raw frame-to-frame displacements, including camera noise. Position errors along a Brownian track are correlated. Drift readouts include plug-in standard errors, not a charge confidence interval.

COMPARE / RESTORE

Latest six raw observations
#	Phase	Time / s	Height / µm

CSV includes raw observations, seed, units and source/instrument settings. Source settings are simulator metadata, excluded from inverse estimation. One saved run lasts for this page session.

MODEL / EVIDENCE

What this measurement leaves out.

\Delta z=v\Delta t+\sqrt{2D\Delta t}\,\xi,\quad \xi\sim\mathcal N(0,1)

A spherical, non-evaporating drop in still air at 293.15 K. Density 886 kg per cubic meter, air density 1.2, viscosity 0.0000182 Pa s, slip coefficient 0.0082 Pa m. Temperature, viscosity, density, gap and voltage calibration are treated as exact. No air currents, evaporation, transient inertia, charge jumps, image blur or field-edge effects. Camera noise is 0.3 micrometers per frame. Raw thermal paths are generated, not historical timings.

PASCO · AP-8210A manual · apparatus, slip model and nominal oil density; Brownian camera acquisition is our explicit extension.

Read the historical evidence Compare magnetic moments

Start with the essentials

Focus question: Watch the motion. Infer the charge.
One-sentence intuition: Keep source assumptions separate from estimates made from records.

Core mathematical model

Force and diffusion

\begin{aligned}v&=\frac{QU/d-W}{\zeta}\\W&=\frac{4\pi a^3}{3}(\rho_o-\rho_a)g\\D&=\frac{k_BT}{\zeta}\end{aligned}

Height is positive upward. The physical charge is negative; the positive magnitude multiplies the top-to-bottom voltage. Positive voltage produces an upward electric force.

Slip-corrected radius

\begin{aligned}c&=b/p,\quad R=\frac{9\eta v_f}{2(\rho_o-\rho_a)g}\\a&=\sqrt{c^2/4+R}-c/2\\\zeta&=\frac{6\pi\eta a}{1+c/a}\end{aligned}

Infer radius from field-off fall speed; pressure is in pascals in this formula. The Stokes-only analysis uses the same records.

Charge from two drifts

\widehat Q=\widehat\zeta\,(\widehat v_{\rm on}-\widehat v_{\rm off})\frac dU,\quad \widehat v=\frac{z(T)-z(0)}T

No integer rounding or input charge enters this estimate. Endpoint drifts respect the correlated Brownian positions.

Common difficulties

A simulation supplies its law

Typical misconceptionRecovering a source parameter independently confirms the law.

Better mental modelThese synthetic records test a measurement and inference workflow. They are not historical observations, a parameter confidence interval, or external scientific certification.

Run the experiment

01
Record both tracks
Acquire the field-off and field-on tracks, each restarted at the mid-plane.
What to observe: Compare the two drift directions and the thermal wandering.
02
Question the correction
Turn off slip correction after acquisition without clearing records.
What to observe: The same motion implies a different radius and charge under a different drag model.
03
Try a continuous charge
Save a run, select the continuous-charge preset and acquire again.
What to observe: The estimator follows the supplied continuous response; a synthetic result cannot establish charge quantization.