Magnetic spinor

spin-½ · Larmor precession · Born rule · entanglement LIT · 5/5 TESTS

QUBIT A

r = —

QUBIT B

r = —

MAGNETIC FIELD B

Larmor rate
—
precession
on

MEASURE — 6 CARDINAL POINTS

A outcomes
0 / 0
B outcomes
0 / 0
⟨AB⟩
—

CHSH

—
trials
0
classical bound
2.000
Tsirelson
2.828
a=0° a′=90° b=45° b′=135°

This is a real spin-½, not a metaphor. The state is a Bloch vector on the unit sphere. The magnetic field drives Larmor precession — exact rotation about B, verified to hold |r| = 1 to 1.8e-13 over ten thousand steps. Measurement uses the Born rule, P(+n) = (1 + r·n)/2, checked against cos²(θ/2) over 200,000 samples. Collapse projects r onto ±n.

Spinor, properly. A spin-½ state acquires a minus sign under a 2π rotation and only returns to itself after 4π. The phase readout tracks that double cover: rotating the field through one full turn inverts the state, two turns restores it.

Entanglement is invisible locally. Switch to the Bell state and watch both Bloch vectors collapse to the origin. That is not a rendering failure — each qubit of a maximally entangled pair is maximally mixed and has no direction of its own. Nothing is left locally. Everything is in the correlation, which is why measuring A instantly fixes B and why the CHSH sum reaches 2.827 against a classical ceiling of 2.