Starting from the Lorentz transformation of special relativity, and through a series of thought-experiment-style mathematical derivations, this paper progressively introduces the Minkowski imaginary-time coordinate, replaces the real velocity by an imaginary velocity, and then quantizes the time differential to the Planck time, ultimately deriving a self-consistent expression for the Planck length. The paper records the complete logical chain from classical relativity to the quantum-gravity scale, including every substitution, simplification, verification, and discussion of physical meaning. Ontology V8.0 further adds an analysis of the origin of $ic$ from the perspective of the Pythagorean theorem, a clarification of the time-to-space conversion coefficient (the speed of light c rather than the gravitational constant G), an interpretation of the physical meaning of the low-speed approximation dx ≈ (v/2)tP, and a complete account of the contracted/stretched two-state model and of the observable physical phenomena.
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Shuai Wang (2026) studied this question.
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