Quantum Physics

   

Spin as a Real Vector from Internal Photon-Sphere Motion: Geometric Origin of U(1) Gauge and SU(2) Periodicity

Authors: Satoshi Hanamura

We present a time-dependent model of electron spin in which the spin angular momentum arises from internal oscillatory motion rather than from a static pseudovector. This work corrects a dimensional inconsistency in our previous formulation by explicitly introducing the unit vector e_z along the z-axis, ensuring proper vector notation for the angular velocity Ω(t) = -(1/4c²)sin(2ωt)·e_z. Inspired by a reinterpretation of Thomas precession, we emphasize that angular momentum can emerge even in non-circular or reciprocating motion, such as a simple harmonic oscillator. This leads us to treat the spin as a real vector whose z-component evolves as sin(2ωt), reflecting an intrinsic 4π periodicity. The model is built upon a closed internal phase space—specifically, the 0-Sphere kernel structure—and provides a deterministic evolution of spin orientation in internal time. Spin quantization is reinterpreted as a geometric effect of phase evolution, eliminating the need for a predefined spin direction. The formulation reproduces the SU(2) double-covering property in a natural and geometric manner, offering new insight into the origin of spin and its fundamental symmetries. Moreover, the model provides a novel interpretation of the anomalous g-factor as a relativistic effect arising from Lorentz contraction in internal oscillatory motion. The conventional SU(2) symmetry is shown to emerge geometrically from an underlying U(1) phase evolution, suggesting that spin behavior reflects continuous internal dynamics rather than discrete quantum states. This corrected formulation offers a deterministic foundation for understanding spin measurements and the 720-degree rotation symmetry of spin-1/2 particles.

Comments: 10 Pages.

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[v1] 2025-06-13 17:03:08

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