The Principle of Time Orthogonality: Spacetime Geometric Reconstruction Based on Relativistic Imaginary Solutions and Photon Eigen-events

This paper identifies profound contradictions between the conventional view of time (collinear past and future) and the mathematical structure of special relativity as well as quantum observational facts. By analyzing the imaginary time solutions generated when the velocity exceeds the speed of light (v>c) in the Lorentz transformation, this paper proposes that such imaginary numbers are not mathematical artifacts, but represent a physical dimension strictly orthogonal to the real time axis — the imaginary future time axis. Supported by a proof by contradiction based on the observational fact that photons have an absolute generation moment, this paper proves that the real past time axis and the imaginary future time axis satisfy a strict orthogonality relation (zero inner product) at the nodal point "the present". This model provides a geometric interpretation for quantum randomness via directional degrees of freedom in a high-dimensional orthogonal hyperplane, and clarifies the fundamental reason why imaginary time cannot be directly measured.