A 4D Oscillatory Model incorporating Floquet states: Quantum Mechanics embracing Special Relativity

ABSTRACT This paper enhances the Theory of Space, originally proposed by Mazzini, which unifies quantum mechanics and special relativity through a quantum system oscillating between three-dimensional (3D) space and an energy-dependent fourth dimension, defined as λp = cτ, where τ = h/E is Planck’s periodic time. By incorporating Floquet theory, it describes the oscillatory dynamics using time-periodic Floquet states and quasi-energies, providing a rigorous mathematical framework for phenomena such as superposition, wave function collapse, entanglement, and quantum tunneling. The model eliminates the need for observer-induced collapse or many-worlds interpretations by treating wave function collapse as random 3D projections from a 4D superposition, modulated by Floquet-driven dynamics. Bell’s inequality violations are resolved via 4D locality (existence outside the observable 3D), and the wave-particle duality is reconciled by coexisting oscillating quantum space and compact entities. It proposes experimental validations, including a photon tunneling experiment with sinusoidal probability variations and time resolved interference patterns, leveraging Floquet spectroscopic techniques. A hypothesis of time dilation invariance in free fall is introduced, with a proposed test using atomic clocks. The framework offers a unified, realistic, and testable description of quantum and relativistic phenomena, with implications for quantum optics, topological phases, and gravitational physics. Keywords: Floquet states, Quantum mechanics, measurement problem, double slit experiment, entanglement, quantum spin