The Planck Scale Fallacy

This paper challenges the conventional treatment of the Planck scale (lP ≈ 1.616 × 10⁻³⁵ m) as a fundamental physical property of spacetime. Instead, the work demonstrates that the Planck scale functions as an ad-hoc "emergency brake" and artificial cutoff patch engineered to prevent continuous mathematical field models and differential calculus from collapsing into unphysical infinities and singularities (R → ∞). The paper argues that enforcing discrete regularizations onto a smooth manifold (R⁴) constitutes a fundamental self-goal—proving that the continuous paradigm itself is flawed. By evaluating the history of ultraviolet divergences through an Aristotelian and Feynman-inspired critique, the author highlights how continuous models mask their own mathematical breakdowns, paving the way for natively discrete physical frameworks.