Emergent Dimensionality (ED)

No local hidden-variable theory can reproduce all predictions of quantum mechanics. Hence, any theory must abandon at least one of: locality, definiteness of measurement outcomes, or measurement independence ('free choice').

Bell's Theorem

Observer-independent facts do not exist.

Brukner's Theorem

Shows that without a privileged set of predicates all objects are equally similar (or equally dissimilar)

Watanabe's Theorem

The only dimensionality admitting a continuum of differentiable structures — homeomorphic but not diffeomorphic to the standard ℝ4.

Exotic ℝ4

 

A living observer perceives reality momentarily as three-dimensional, but this does not imply that such three-dimensionality exists observer-independently; it emerges, for a living agent, from nature containing all unobservable dimensions.

The framework is consistent with several independent results: Bell's theorem ruling out local realism, Brukner's no-go theorem for observer-independent facts, Watanabe's ugly duckling theorem, which invalidates the identity of indiscernibles ontological principle, the holographic principle, entropic gravity, and assembly theory, in which objects are defined by the histories of their formation.

ED treats real, negative, fractional, and complex dimensions on equal footing. The distinguished role of four dimensions is tied to the existence of a continuum of exotic differentiable structures on ℝ4. This property, absent in all other dimensions, is a mathematical basis for shape preservation of memorized objects (homeomorphism) together with non-smoothness (non-diffeomorphism), as required by the first two Lewontin principles for evolutionary change.