Differences in Doppler Shift Behavior between Flat and Expanding Spaces and Its Test of Hubble's Law

Traditional cosmology interprets galactic redshift as the Doppler effect caused by cosmic expansion and thus establishes Hubble's Law. In this paper, the theoretical relationships between Doppler shift and light source recession velocity are rigorously derived in both flat static space and uniformly expanding space, respectively. Taking the validity of Hubble's Law as a premise, the observed redshift-velocity correlation is deduced and compared with the theoretical results of the two types of spaces. The research shows that the Doppler shift has a linear relationship with the recession velocity in flat static space, while the redshift exhibits an exponential growth relationship with the recession velocity in uniformly expanding space. The linear redshift-velocity relationship of Hubble's Law is only self-consistent with the theoretical expectation of flat space, and there is an essential conflict with the theoretical characteristics of expanding space. This behavioral difference provides a clear observational criterion for testing the origin of redshift, the geometric properties of space, and the validity of Hubble's Law.