Quantum Physics

   

Geometric Law of Quantum Mechanics and the Imaginary Unit

Authors: Se Kyun Kwon

Mathematically, the imaginary unit i has long been regarded as an algebraic generator extending the real numbers to the complex field.Yet a century after the birth of quantum mechanics (1925—2025), the answer to its oldest question is now clear: quantum mechanics is not merely a mathematical structure—it is a physical reality, and all quantities appearing in its non-commutative relations are physical.Therefore, i is not a mere algebraic extension but the universal operator demanded by the geometric completeness of non-commutative reality between position and momentum.The imaginary unit is a physical reality.The canonical relation [x, p] = i hbar is not merely algebraic—it is a geometric law, showing that the complex structure of quantum mechanics arises inevitably from physical reality itself.It stands without contradiction, without complexity. This is nature.In the (x, p) plane, i represents a 90 degree rotation and hbar quantizes the curvature of that rotation.Complex numbers thus arise as the natural geometric language of non-commutative physics, providing a geometric resolution to the century-old question of physical completeness first raised by Einstein, Podolsky and Rosen (1935).

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[v1] 2025-11-08 03:32:17

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