Why Space Has Three Dimensions: A Derivation from Wave Intersection Physics

Why does space have three dimensions? The question has been asked since Kant, analyzed by Ehrenfest, and left unanswered by every established physical theory. General relativity, quantum field theory, and string theory all take the number of spatial dimensions as an input. None derive it.

This paper provides a derivation. In the canvas model, spacetime is a discrete voxel lattice formed from the intersections of fundamental waves. Each spatial dimension corresponds to an independent oscillator whose wave intersects the time wave. Voxels form when the combined intensity of intersecting waves exceeds a threshold.

The number of spatial dimensions is forced by the consistency of three physical quantities. The combined intensity of intersecting waves scales as the product of their amplitudes—one factor for each space oscillator plus the time oscillator. The threshold for voxel formation is a fundamental constant. The voxel density is observed to be one per Planck volume. For these three quantities to be consistent, the number of factors in the intensity product must be four. This means three space dimensions and one time dimension.

Three is not an assumption. It is not an anthropic selection. It is a theorem that follows from the physics of wave intersections. The paper is self-contained and requires only the canvas model's postulates and the observed Planck-scale voxel density. No compactification, no extra dimensions, no speculative metaphysics.