A scientific realization and verification of Yin-Yang theory: Complex-valued mechanics

Mathematically, the philosophy of Tai Chi advocates that the nature (the Tao) is a complex-valued world containing two parts: yang is the observable (real) part and yin is the unobservable (imaginary) part. What we have sensed and measured is only the real part of the world, which is the physical world that we experience in daily life. However, this Yin-Yang concept has remained an issue of pure philosophy for a very long time; no mathematical or physical principles had ever been developed exclusively for Yin-Yang theory to justify its scientific truth. The proposed complex-valued mechanics is the first scientific realization of the Yin-Yang theory following the same kind of philosophy that physical phenomena happen in complex space and what we customarily consider as the physical reality is merely the projections of the physical phenomena into the real space. Complex mechanics successfully demonstrates the evolution of a physical phenomenon in the complex space and verifies the consistence of its projection into the real space with the measurement data. The aim of this paper is to introduce complex mechanics as a bridge between Yin-Yang theory and quantum mechanics by pointing out that the unique features of quantum motions, such as tunneling, spin, quantization, uncertainty principle, multiple paths and wave-particle duality, all originate from the Yin-Yang entanglement, i.e., the interaction between real and imaginary motions in complex space.