Scientific Note on the Physical Necessity and Interpretation of the Lorentz Factor in the LHC within the Framework of Asymptotic Lorentz Relativity (ALR)

This note isolates the exact physical reason why established accelerator physics at the Large Hadron Collider (LHC) is phenomenologically compelled to apply Einstein's Special Relativity. Concurrently, it is demonstrated that the measured inertia factor of γ ≈ 10⁴ is not an intrinsic property of a point-like particle, but rather reflects the collective interaction of the highly excited vacuum. It is formally shown that the standard relativistic limit consideration constitutes a mathematical truncation artifact, whereas a rigorous separation of system levels entirely resolves the apparent contradictions of asymptotic field-theoretic approaches. The critical velocity threshold at which the standard SRT interpretation becomes physically untenable is located precisely at β ≈ 0.527.