Dimensional Transition from Quantum to Spacetime: A Deformation-Energy Threshold Framework

This study introduces a theoretical and numerically verified model that describes a dimensional transition from quantum-scale deformation to macroscopic spacetime manifestations. The model hinges on the relation B = de / t, where de is a quantum deformation constant and t is the characteristic transition time. The transition produces a dynamically evolving temporal dimension τ(t) = Ae^t + Be^{-t}, and in an advanced formulation, τ(t) = e^{e^t B} ψ₀. These equations are confirmed via symbolic differentiation and evaluated against real experimental data from the Dynamic Casimir Effect and LIGO.The author acknowledges the use of OpenAI’s language model for assistance in drafting certain sections of this work.