The Inability to Collapse Three Dimensions Into Two Dimensions Physically

This investigation evaluates the physical viability of a literal, mathematical dimensional reduction within the universe, specifically addressing the question: ”Can a three-dimensional world create a pure two-dimensional plane?” While lower-dimensional spaces serve as effective
mathematical models, forcing a spatial coordinate metric to compress entirely to absolute zero breaches the foundational boundaries of classical and modern physics. This inquiry evaluates the structural breakdown across three physical frameworks. First, macroscopic geometric metrics analyzed through epsilon-delta limits and Lebesgue measures prove that collapsing the z-axis boundary to a singular region reduces three-dimensional volume to exactly zero, forcing physical density to diverge to infinity or necessitating a non-physical mass of zero. Second, evaluating a constrained quantum system through the time-independent Schrodinger equation shows that as the confinement wall length approaches zero, the localized energy states diverge to infinity, demanding infinite energy or collapsing the system into a gravitational singularity. Finally, evaluating Einstein’s field equations in general relativity under these metric constraints transforms the energy density component of the stress-energy tensor into an impossible zero-denominator fraction. This forces the tensor to blow up to infinity, yielding an infinite local curvature of spacetime. Ultimately, these multi-disciplinary mathematical failures confirm that a pure two-dimensional plane cannot physically exist as a structural product of a three-dimensional universe.