Mathematical Foundations of G-MaTT: Toward a Full Quantum Field Theory from Pre-Geometric Torsion

Abstract We derive the Planck frequency Ω₀ = c⁵/ℏG from first principles in Generalized Mass as Twisted Time (G-MaTT), demonstrating that it is not a dimensional coincidence but the natural clock rate of the primordial mass-time torsional potential ℳ_μ. In G-MaTT, reality begins with ℳ_μ—a pre-geometric, dimensionless potential identical to the source of mass and time—defined over a configuration space χ with no prior spacetime. Time emerges as t = (1/Ω₀) ∫ ℳ_μ dχ^μ, making Ω₀ the conversion factor between torsional phase and physical time. We show that Ω₀ arises from the unification scale of quantum mechanics (ℏ), relativity (c), and gravity (G) within the mass–torsion correspondence. This derivation implies that: Time is emergent and discrete at the Planck scale, Spacetime is not fundamental but a low-energy condensate, UV divergences are avoided because no continuum exists above Ω₀, Quantum gravity is testable via torsion-amplified interference (e.g., neutron phase shifts). This work proves that G-MaTT is not merely interpretive—it is a predictive, falsifiable framework that resolves the measurement problem, explains the Standard Model, and redefines unification as torsion-first emergence.摘要 我们在扭曲时广义质量（Generalized Mass as Twisted Time，简称G-MaTT）框架下，从第一性原理推导出普朗克频率（Planck frequency）Ω₀ = c⁵/ℏG，证明其并非量纲巧合，而是原初质量-时间扭转势ℳ_μ的自然时钟速率。在G-MaTT框架中，实在性始于ℳ_μ——一种前几何、无量纲的势，同时也是质量与时间的起源——其定义于不含先验时空的位形空间χ之上。时间以t = (1/Ω₀) ∫ ℳ_μ dχ^μ的形式涌现，由此Ω₀成为扭转相位与物理时间之间的转换因子。我们证明，Ω₀源于质量-扭转对应关系下量子力学（quantum mechanics）、相对论（relativity）与引力（gravity）的统一能标。 该推导表明： 1. 时间在普朗克尺度下具有涌现性与离散性； 2. 时空并非基础实在，而是一种低能凝聚态； 3. 由于Ω₀之上不存在连续统，故可规避紫外发散； 4. 量子引力可通过扭转放大干涉（例如中子相移）进行实验检验。 本研究证明，G-MaTT并非仅具有解释性——它是一个可预测、可证伪的理论框架，能够解决测量问题、阐释标准模型（Standard Model），并将统一理论重新定义为以扭转为优先的涌现机制。