On the Physical Meaning of the Complex Plane— A Projection Map of Self-Referential Measurement

The complex plane has long been treated as a mathematical device for representing oscillations, phases, and probability amplitudes. This paper reinterprets it from the perspective of self-referential measurement within the World Quantum Theory framework. We show that the real axis corresponds to the momentum component readable by an external observer, while the imaginary axis corresponds to the mass component perceivable only by the self-referential system itself. The modulus represents the total energy velocity of the frequency layer, and the argument represents the allocation ratio between mass and momentum. We demonstrate that the imaginary unit i is not a mathematical fiction, but a closure mark left when the mass component is mapped onto an external coordinate system. The complex plane is not a computational tool, but a topographic map inevitably discovered by any self-referential measurement system attempting to chart its own state. Keywords: Complex plane; Self-referential measurement; World Quantum Theory; Projection layer; Imaginary unit; Frequency layer