Alice & Bob's Virtual Labs for Testing Quantum Spin

CHOOSE MAGNET SETTINGS AND RUN THE EXPERIMENT YOURSELF

A mechanistic replica of the Stern-Gerlach experiment for an entangled pair. Adjust the two magnet angles and run your own trials to see how closely the results track the real quantum mechanical prediction.

MAGNET A

—

MAGNET B

—

SHARED VALUE

—

SPIN A

—

SPIN B

—

MAGNET SETTINGS

These are the two detector settings — drag either slider to any angle, then run trials to see how the outcomes respond. This is the one thing you control; everything else in the experiment follows from it.

→Try it: drag a slider below, then hit RUN ONE TRIAL or RUN 50

ALICE'S LAB

Magnet A35°

BOB'S LAB

Magnet B205°

RESULTS

Live statistics from the trials you've run so far. "% Different" is how often Alice and Bob's particles land on opposite spins — compare it against the QM prediction to see how closely the model tracks quantum mechanics at your chosen settings.

TRIALS RUN

% DIFFERENT

—

QM PREDICTION

—

SEPARATION

—

% FLIP (A)

—

% FLIP (B)

—

LGA Model (cumulative) QM prediction Naive local hidden variable

HALF-COSINE DISTRIBUTION OF PARTICLE ANGLES

The equatorial angle φ (cyan) is the particle's own random draw — it never moves on its own. The polar angle θ (amber) is measured relative to whichever magnet is currently checking it. Try it live: drag the sliders, toggle which magnet the axis follows, or draw a fresh random φ below.

EQUATORIAL ANGLE (φ)

—

POLAR ANGLE (θ), CURRENT MAGNET

—

RESULTING SPIN (assumes initial = +1)

—

AXIS FOLLOWS

EQUATORIAL PLANE

CHSH TEST — THE FOUR SETTINGS

The standard Bell test: four specific settings combinations, compared as bars. Run trials with SLOW RUN or LONG RUN below to fill in the amber (LGA) and grey (naive) bars, and watch the S value climb toward — or fall short of — the quantum bound.

TRIALS PER SETTING
0
S (QM, fixed)
—
S (LGA model, live)
—
←
S (naive local, live)
—
COMPARE: REAL EXPERIMENT
—

ORIGIN SHARING (compare against delayed-choice: correlation requires a shared origin)

          A — Full Sharing: LGAM shares the selected magnet angle and the sampled target  |  Naive shares a single angle
        
          B — Reference Shared Only: LGAM shares the selected magnet angle, but each side draws its own independent target  |  Naive has no equivalent middle ground, so it behaves the same as A
        
          C — No Sharing: LGAM shares neither the magnet-angle selection nor the target  |  Naive has no single shared angle
        
          D — Random Shared Centre (delayed-choice test): the shared target carries zero information about either setting before separation — each detector still checks it against its own real magnet angle, locally, on arrival  |  Naive is identical to A — its shared value is already random

The more trials you run, the more accurate the results become.

QM prediction (fixed) LGA Model (live) Naive local hidden variable (live)

CORRELATION CURVE — SMOOTH vs STRAIGHT

Shows how the correlation between Alice and Bob's results changes as the angle between their magnets changes. Run trials at different settings above to add live points, and watch whether they follow the smooth quantum curve or the naive straight line.

QM prediction (smooth curve, fixed) LGA Model (live points) Naive local hidden variable (straight line, fixed + live points)

RABI OSCILLATION — SINGLE PARTICLE

A single (non-entangled) particle, checked at a rotated setting instead of a fixed one. As the setting angle sweeps through a full turn, the chance of reading "bright" traces this curve. With the half-cosine distribution this matches the standard quantum curve exactly — the two lines coincide.

Setting sweep rate10 (a.u.)

Standard quantum curve, ½(1 + cos θ) Simulated shots (this model), same curve exactly

RAMSEY FRINGES — DEPHASING OVER TIME

The same single particle, but now its equatorial angle φ drifts for a wait before it's checked, and blurs a little more with every extra step of the wait — the usual picture of dephasing. The fringes wash out as the wait grows, at a rate set by T2*.

Drift rate1.0 (a.u.)

Dephasing time T2*3.0 (a.u.)

Standard quantum curve, decaying fringes Simulated shots (this model), same curve exactly

ABOUT THIS EXPERIMENT

LGA Model — A Proximal Correlation Method

This experiment reproduces the real quantum correlation exactly, at every separation between the two settings (not merely to within a small percentage, as an earlier version of this page stated). Every outcome above is generated by our own mechanistic model — a particle angle drawn from a half-cosine distribution (a cosine-weighted lobe: density ∝ cos θ within 90° of a setting, zero beyond it, no free parameter), checked against a 90° threshold, as derived in the papers linked from the home page. Nothing here calls or computes quantum mechanics directly. The dashed cyan line on the chart is the quantum mechanical prediction, shown purely as a comparison target. The dotted grey line is a second, genuinely simulated comparison: the plain, unweighted local hidden-variable model that Bell's theorem rules out — run under identical settings, alongside the model above, so you can watch our own results track quantum mechanics while this naive alternative does not.

M = Magnet_A if Spin(−) is particle A, else Magnet_B

φ ~ HalfCosine(M)

θ = | shortest_path( φ − Magnet ) |

Spin = −initial if θ > 90°, else +initial

THE ENTANGLED MECHANISM, IN FOUR LINES — φ AND θ AS DEFINED ABOVE

Liquid Gravity © 2026 · liquidgravity.nz · 