Analysis reveals Planck's constant as a geometric curvature invariant, indicating new quantization insights.
In this paper, we show that Planck’s constant [Formula: see text] arises as an intrinsic curvature invariant rather than as a fundamental postulate of quantization. Within Chronon Field Theory (CFT) — a pre-geometric framework based on a microscopic temporal alignment field [Formula: see text] — quantization, spin and statistics emerge from the symplectic geometry governing causal order and phase coherence. The same curvature dynamics that stabilize Lorentzian structure also quantize the action and fix the unit of intrinsic angular momentum. In this framework, [Formula: see text] is identified as a universal curvature modulus: the minimal symplectic flux of the chronon manifold that underlies canonical commutation relations, spin quantization and photon polarization. Stabilized solitonic configurations dynamically generate this finite action quantum. Analytically, we establish the existence and stability of finite-energy solitons in [Formula: see text] dimensions. Numerically, a [Formula: see text]-dimensional study demonstrates soliton formation and the freezing of an effective action scale, while in a solvable [Formula: see text]-dimensional illustrative model, the plateau value of the effective action satisfies [Formula: see text], confirming the geometric and dynamical origin of Planck’s constant.
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Bin Li (2026) studied this question.
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