“The bedrock nature of space and time and the unification of cosmos and quantum are surely among science’s great ‘open frontiers.’ These are parts of the intellectual map where we’re still groping for the truth – where, in the fashion of ancient cartographers, we must still inscribe ‘here be dragons.’” –Martin Rees
Inside the nuclear furnace of the Sun, protons and other atomic nuclei are compressed together into a tiny region of space, where the incredible temperatures and energies try to overcome the repulsive forces of their electric charges. At a maximum temperature of 15 million K, and with a long-tailed (Poisson) distribution of energies at the highest end, we can compute how many protons are energetic enough to overcome the Coulomb barrier, interact with one another, and wind up in a more tightly-bound, fused state.
That number, if you do that calculation, turns out to be exactly zero. When you consider that 95% of stars are less massive and reach lower core temperatures than our Sun, the situation appears to be even more dire. If there were no quantum mechanics, nuclear fusion would be an impossibility. Yet we’re saved by a feature of quantum indeterminism, where spread-out wavefunctions can overlap, and nuclear fusion as we know it can proceed.