The Sagnac effect can be interpreted as evidence of anisotropy in light speed as a first-order effect (proportional to the ratio of v to c) at the scale of Earth's rotation, but not at higher velocities such as Earth's orbital speed or its speed relative to the Cosmic Microwave Background (CMB). Logically, one would expect that Michelson interferometer-type experiments, which investigate second-order effects (proportional to the ratio of v^2 to c^2), would yield analogous results across different speeds, albeit on a much smaller scale due to squaring. That is, null results would be expected at the CMB and orbital speeds, while a non-null result would emerge at the scale of Earth's rotation. Specifically, interferometer experiments using optical resonators should possess sufficient resolution to verify this. This paper demonstrates that, contrary to expectations, none of the existing experiments account for Earth's rotation, as the data analysis systematically factors it out. A non-null result in first-order experiments, which involve non-inertial reference frames, can be explained by General Relativity. However, second-order experiments are conducted in inertial reference frames, where Special Relativity fails to explain a non-null result. Thus, detecting a second-order effect due to Earth's rotation could provide insights into new physics.