Paper 32 Recasting Quantum Mechanics Without Imaginary Numbers: A Real-Valued Framework Based on Angular Coherence in Holosphere Theory

Quantum mechanics traditionally employs complex-valued wavefunctions to model phase, interference, and unitary time evolution. However, in Holosphere Theory—a discrete, coherencebased lattice of spinning, nested Planck-scale spheres—these features emerge naturally from real-valued angular strain within the lattice. In this framework, the imaginary unit i is replaced by a 90-degree coherence rotation operator R90, encoding physically real phase deviation. We demonstrate that this real-valued formalism reproduces all standard quantum phenomena, including interference, energy quantization, and probability current, while providing a concrete ontological foundation for phase rotation. This reinterpretation is further supported by independent analyses showing that complex quantum mechanics can be reformulated using coupled real-valued systems, as well as by critiques of unphysical abstraction in quantum theory [10, 11, 7, 8]. Holosphere Theory offers a realist, testable alternative to the conventional use of imaginary numbers in quantum mechanics