Spinor Double Cover of SO(3)
Belt trick · Dirac's scissors · 720° = identity
Rotation angle θ:
0°
Rotation axis
X
Y
Z
Belt count:
3
0°
SU(2) phase (θ/2)
▶ Auto-rotate
720° Demo
α = 1.000 + 0.000i
β = 0.000 + 0.000i
SU(2) → SO(3):
2-to-1 covering map. A 2×2 unitary matrix U(θ) rotates a spinor, but U(θ+2π) = −U(θ).
Belt trick:
Physical object connected by belts to fixed frame — 360° twist is topologically non-trivial, but 720° unwinds without moving the object.
π₁(SO(3)) = ℤ/2 — the Dirac string trick demonstrates this.