Mathematical Fitting and Physical Reality

Modern theoretical physics suffers from a fatal cognitive bias: equating numerically matched relations obtained by mathematical fitting with the fundamental physical truth of the universe. Most physical formulas developed in modern and contemporary times are typical phenomenological fitting models. Researchers adjust functional structures and calibrate empirical constants to achieve close alignment between calculated results and experimental data. All physical contradictions, unknown interaction mechanisms and ontological questions that the theory cannot explain are incorporated, concealed and encapsulated within empirical constants. Mathematical fitting can only realize numerical reproduction and engineering application of phenomena, and is by no means equivalent to revealing the real physical mechanisms of the objective world. The greatest fallacy in contemporary physics is the excessive deification of mathematical structures, even taking mathematical elegance and system self-consistency as criteria to judge the authenticity of physical theories. Quantum mechanics, the particle Standard Model and even the framework of general relativity jointly form a self-closed system built upon artificially presupposed mathematical objects. This problem goes beyond the logical limitation described by Gödel’s incompleteness theorems. Theoretical researchers define mathematical objects such as tensors and operators, perform deductions within presupposed axiomatic frameworks, and prove the self-consistency and completeness of the system using internal rules of the framework, forming a demonstration loop detached from objective reality. When theoretical predictions clearly conflict with physical reality, the academic community does not reflect on defects in the underlying framework. Instead, they constantly invent new hypotheses and add nested mathematical fitting schemes to resolve contradictions, patching the original theory layer by layer. To fit scattered, weak and transient high-energy experimental signals, researchers artificially posit more than sixty elementary particles. New assumptions and interpretations are continuously added, and mathematical degrees of freedom are expanded to construct a fully closed, self-consistent and self-validating theoretical system. This patched multi-layered model drives theoretical systems further away from the real world, and stripping away all additional mathematical constructs to return to physical reality has become extremely difficult. A large number of theoretical particles have no corresponding entities in physical reality, and many theoretical pictures are completely disconnected from the objective physical world. This paper strictly distinguishes the essential boundary between mathematical fitting tools and physical reality, reveals the core crux of over-fitting, repeated patching and reversed causality in modern physics, and rebuilds the underlying cognitive logic for seeking truth in fundamental physics.