A New Formula for Describing the Relative Intensity of the Casimir Force

Conventional vacuum fluctuation theory relies on energy borrowing and thus fails to rigorously satisfy energy conservation. Taking strict energy conservation as a fundamental premise, this work introduces quantum pairs of positive and negative mass with zero total energy to construct a new framework of vacuum fluctuations, and demonstrates that the Casimir force arises primarily from contributions in the far‑infrared regime. A new formula for the relative intensity of the Casimir force is proposed: Frel=3+R−k/C Using this formula, we calculate the Casimir force sequence of typical materials: Au≈Cu>Ag>Al>Ni>Pd>Cr>Si>ITO>Sapphire These results are consistent with available experiments. The model naturally explains several phenomena that are difficult to address within traditional theory, including the UV-tunable Casimir force in ITO and the temperature-dependent response in sapphire. The model provides testable predictions and offers a new microscopic interpretation and quantitative method for the Casimir effect.