Demonstrates the stability of standing wave modes in closed spheres, indicating a necessity for 3+1 spacetime.
We classify shape-invariant standing waves on the closed sphere S^n and prove that stable fundamental modes exist only for n=3, providing a geometric derivation of 3+1 spacetime dimensionality. The analysis uses Laplacian eigenvalues on S^n and hypercube-to-sphere projection to establish dimensional selectivity.
No takes yet. Share an insight, caveat, or question.
Noriaki Kihara (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: