Inflativity: A Unified Framework for Relativity, Quantum Mechanics, and Cosmology

The unification of quantum mechanics and relativity remains one of the most persistent challenges in physics. Inflativity introduces a four-dimensional (4D) spatial expansion framework in which time is not fundamental but emerges from displacement through a higher spatial dimension. The study addresses the research question of whether such a 4D spatial model can reproduce the experimentally verified predictions of relativity and quantum mechanics while offering a single geometric foundation. Using two core postulates; emergent time and photon geometry, the framework derives the Lorentz transformation, gravitational redshift, and quantum wavefunction collapse directly from geometric principles. The local expansion rate ε(xᵘ) acts as a scalar field governing gravitational and temporal variation, replacing spacetime curvature with modulated 4D expansion. Within geometric algebra R₄,₀,₁, photons are represented as null multivectors that collapse to 3D events upon observation, resolving nonlocal quantum correlations as geometric intersections in 4D space. Inflativity therefore reproduces all key predictions of relativity while extending to quantum and cosmological domains. It provides a deterministic, testable, and mathematically unified model in which both relativistic and quantum phenomena emerge from the same 4D geometric mechanism.