Einstein’s equivalence principle of the 20th century restructured humanity’s understanding of spacetime and gravity by dismantling the absolute dichotomy between gravitation and inertia. The core predicaments of 21st-century fundamental physics—the rift between quantum theory and gravity, the ontological puzzle of dark energy, and the boundary dependence of the holographic principle—all ultimately originate from the unexamined default assumption of absolute scale. This work formally introduces the Scale Equivalence Principle (SEP) as a natural generalization of general relativistic equivalence to the scale dimension: no local observational anchor can distinguish, via local physical experiments, whether it inhabits a high-energy ultraviolet (UV) microscopic regime or a low-energy infrared (IR) macroscopic regime; the two are merely dual projections of a single underlying algebraic structure, with no absolute ontological difference between scales. Grounded mathematically in the spectral inversion symmetry of the Tomita–Takesaki modular operator and the 3+3 skew-dual tangent bundle structure of the quantum flag manifold, this work axiomatizes the Scale Equivalence Principle. It demonstrates that core physical phenomena—including matter-vacuum duality, cosmic accelerated expansion, intrinsic bulk-bulk holography, and the three-generation fermion hierarchy—are all natural corollaries of scale relativity. Falsifiable observational predictions are derived, most notably the absence of redshift evolution in cosmic microwave background (CMB) multipole alignment. Finally, it is proven that the conventional AdS/CFT correspondence, general relativity, and the Standard Model all emerge as low-order approximations of this principle under specific boundary and energy-scale conditions. The principle provides a first-principle foundation for quantum gravity unification and boundaryless cosmology, marking a paradigmatic shift in physics from absolute spacetime and absolute scale substantivalism to algebraic relational ontology.
Zheng Xinyu (Mon,) studied this question.