Cross-Scale Relativity : Unifed Description of Quantum Nonlocality and Cosmological Redshift via Scale-Derived Rapidity

Based on the hierarchical structure of the universe spanning from the subnuclear scale to the observable cosmic horizon, this paper systematically develops a theoretical framework of Cross-Scale Relativity, whose core contribution is **extending the Lorentz transformation of special relativity—traditionally confined to the velocity transformation of objects—to the transformations between cosmic scale hierarchies**. This extension, a groundbreaking advancement, reveals that the Lorentz symmetry inherent in special relativity is not limited to inertial reference frames describing object motion, but also universally applies to the relationships between different cosmic scales, which has long been overlooked in traditional physics. Additionally, the framework explicitly incorporates the scale-dependence of measurement—another critical issue neglected by conventional theories—integrating it with the extended Lorentz transformation as the dual core of the theoretical construction.By inheriting the local constancy of the speed of light and Lorentz symmetry from special relativity, the framework generalizes the concept of rapidity from inertial reference frames to scale reference frames, defining a cross-scale rapidity as the natural logarithm of the ratio of characteristic lengths between adjacent scales. This definition is the key to realizing the extension of Lorentz transformation to cosmic scale hierarchies, as it enables linear superposition of multi-scale Lorentz transformations while strictly ensuring that local physical velocities remain subluminal at all scales—thus preserving the core principles of special relativity while expanding its scope to cross-scale scenarios.This extension of Lorentz transformation to cosmic scale hierarchies, combined with the consideration of measurement scale-dependence, provides a natural explanation for apparent superluminal phenomena in quantum systems (including quantum entanglement, quantum tunneling, and wavefunction collapse). These phenomena are not genuine superluminal propagation, but rather cross-scale time dilation effects arising from the extended multi-scale Lorentz transformations, caused by the mismatch between the measurement scale of macroscopic observers and the microscopic physical scale when measuring microscopic proper time.In terms of cosmological research, it is crucial to clarify that current physical measurements are fundamentally based on the atomic scale, as atomic clocks—operating at the atomic scale—serve as the de facto standard for all experimental measurements. Traditional physics overlooks the scale disparity between this atomic-scale measurement standard and cosmic scales, leading to biased calculations and misinterpreting redshift as evidence for cosmic expansion. Notably, when interpreted within the framework of Cross-Scale Relativity (relying on the extended Lorentz transformation across scale hierarchies), there is no cosmic expansion: the observed redshift arises entirely from the correction of measurement biases via the extended multi-scale Lorentz transformation, without invoking the cosmic expansion hypothesis. The framework incorporates an intrinsic rapidity offset (linked to measurement scale-dependence) as a correction term, and the resulting redshift formula is observationally indistinguishable from the standard ΛCDM model, consistent with supernovae, galaxy surveys, and cosmic microwave background data. Overall, the theory requires no free parameters, preserves quantum mechanics and special relativity, achieves a unified description of physics across , and its core innovation lies in extending the Lorentz transformation of special relativity from object velocity transformation to transformations between cosmic scale hierarchies.