Scale Law in Absolute Space: From Fine-Structure Constant to Dark Matter

Abstract

This paper starts from the basic assumption that light travels continuously at a fixed velocity within absolute space. Relying on experimental results of radiation pressure, we deduce a fundamental dynamic relation describing how light frequency shifts when moving through gravitational fields, and further obtain an exponential redshift expression that does not rely on the expansion of spacetime. By integrating gravitational effects along the light propagation path and adopting the critical gravitational limit condition for spherically symmetric objects, a universal scale law is established. This unified scale law is applicable across vastly different physical length scales. At atomic scales, it naturally explains the origin and numerical value of the fine-structure constant. When extended to cosmic dimensions, it gives a universal critical cosmic acceleration that matches the empirical critical acceleration parameter proposed by Modified Newtonian Dynamics. The effective gravitational acceleration revised by the scale law successfully accounts for the flat galactic rotation curves observed in the Milky Way, Andromeda Galaxy and Triangulum Galaxy, offering a geometric explanation for the dark matter puzzle without introducing new invisible particles. The theory also yields a theoretical value of the cosmological constant close to astronomical measurements, which can interpret the cosmic dark energy effect. For black hole research, the scale law perfectly reproduces the classic Hawking temperature relation at black hole horizons. It also predicts a singularity-free internal structure for black holes, featuring a linear mass-radius distribution inside the horizon and a quantum core at Planck scale. Furthermore, the scale law provides a consistent frequency ratio rule to unify the coupling strengths of all four fundamental interactions, and traces the physical source of quantum quantization to the standing-wave constraint of confined light waves, without requiring additional independent quantum postulates. Covering a range of 41 orders of magnitude from microscopic atomic scale to the entire observable universe, the scale law connects quantum phenomena, atomic physics, galactic dynamics, cosmology and black hole physics, forming a self-consistent unified dimensional theoretical framework.

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