Derivation of the Planck Frequency from Generalized Mass as Twisted Time (G-MaTT): Implications for Quantum Gravity and the Emergence of Time

Abstract We derive the Planck frequency \[\Omega_0 = \frac{c^5}{\hbar G}\] 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 \(\mathcal{M}_\mu\). In G-MaTT, reality begins with \(\mathcal{M}_\mu\)—a pre-geometric, dimensionless potential identical to the source of mass and time—defined over a configuration space \(\chi\) with no prior spacetime. Time emerges as \[t = \frac{1}{\Omega_0} \int \mathcal{M}_\mu \, d\chi^\mu,\] making \(\Omega_0\) the conversion factor between torsional phase and physical time. We show that \(\Omega_0\) arises from the unification scale of quantum mechanics (\(\hbar\)), 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 \(\Omega_0\), 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.