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Quantization of energy is the phenomenon discovered by Planck in 1900 that energy does not occur in the blackbody radiation emission in a continuous subset of the real line but in a discrete subset with a fixed spacing $h$.  So long as there is a Dirac-like equation for the photon, the geometric fact that on $S^4(1/h)$ the Dirac operator has a discrete spectrum with spacing $h$ implies that shape is determining quantization of energy in the actual universe.  Imagine that you return to 1900 just as Planck had explained the law of blackbody radiation using a discrete spectrum and provided him evidence that the universe is a scaled 4-sphere of radius $1/h$ and showed him that there is a Dirac-like equation for the photon and that the spectrum of the Dirac operator in this case matches the observed spectrum.  Then I think it likely that he could consider this a geometric explanation of his discovery.