This paper introduces a new tool for analyzing quantum mechanics, adding new insight into the nature of spin and amplitudes. Instead of restricting states to discrete spin, we model the physical state of an individual particle using a continuous, phase-coherent directional amplitude. We have successfully derived a mathematical distribution for the vector sum of these individual amplitudes.

​

By keeping this enriched amplitude information intact and tracking its geometric phase, the framework naturally reproduces Malus’ law for single photons. More importantly, when we apply this tool to entangled photon pairs, we demonstrate that preserving the information about the local state of the photons exactly saturates the Tsirelson Bound (). Ultimately, this proves that the complex correlations usually attributed to "non-local" entanglement can be fully generated by strictly local interactions, provided we do not prematurely discard the system's underlying amplitude information.

​

We demonstrate that the rules of quantum mechanics must incorporate such underlying properties, and therefore we arrive at the same endpoint. But the method of QM hides some of the underlying dynamical principles, while our framework utilize these principles openly for reaching the same end goal. We benchmark our discovery by testing it on entangled photons proving that we can preserve the information from their common origine, and by calculating probabilities from amplitudes before analyzers, we achieve the same results as CHSH tests without any non-local influences.