How Closed Space Breaks the Quantum Rules of Rotation ⚡ экспресс
For space with periodic boundaries, the orbital angular momentum spectrum splits into two parts: traditional integer values and a continuous zone generated by regions “edge” with respect to the rotation axis. This leads to the appearance of half-integer (previously thought forbidden) and irrational numbers in the spectrum. Notably, this result is independent of spatial size. Although these components are undetectable at laboratory scales, they can produce measurable effects at cosmological distances, particularly in the anisotropy of the cosmic microwave background.
Orbital angular momentum—the measure of an object's rotation around a point—usually appears discrete in quantum physics: like climbing a staircase where each step is a whole number. This rule was considered unshakable. But if space has periodic boundaries, looping back on itself like the surface of a donut, the staircase turns into a smooth ramp. On it, rotation can take any value—from fractions to irrational numbers like √2.
Interestingly, the effect doesn't depend on size: even on the scale of the entire Universe, rotation can lose its quantum strictness. It's not yet detectable in the lab, but traces could show up in the cosmic microwave background—the ancient light after the Big Bang. Finding them would confirm the nontrivial structure of our spacetime.
🎯 For a long time, physicists believed that orbital angular momentum could only be integer, and half-integer values were characteristic only of spin—a particle's intrinsic rotation. The new discovery shows that the boundaries of space can mix these properties.