Testing a discrete model for quantum spin with two sequential Stern-Gerlach detectors and photon Fock states

Despite its unparalleled success, quantum mechanics (QM) is an incomplete theory of nature. Longstanding concerns regarding its mathematical foundations and physical interpretation persist, a full century beyond its conception. Limited by these issues, efforts to move beyond QM have struggled to gain traction within the broader physics community. One approach to progress in this direction, which is deeply rooted in the tradition of physics, is the development of new models for physical systems otherwise treated by QM. One such model is presented here, which concerns the interaction of a spin system with sequences of two Stern-Gerlach detectors that may be independently rotated. Rather than employing the traditional formalism of QM, the proposed model is supported by tools from discrete mathematics, such as finite groups, set theory, and combinatorics. Equipped with this novel toolkit, an analog of Wigner's d-matrix formula is derived and shown to deviate slightly from QM. With these results, the proposed model is extended to an optical system involving photon number states passing through a beam splitter. Leveraging recent advancements in high precision experiments on these systems, we then propose a means of testing the new model using a tabletop experiment. Hence, the proposed model not only makes clear testable predictions, but also provides valuable insight into the essential principles of quantum theory.