the nuclear glue
0.007: the sliver of mass hydrogen pays out as light. The tightest honest window in cosmology — and the reason carbon exists.
Lukasz Szramuk ·
ε is the fraction of mass hydrogen converts to energy when it fuses into helium: 0.007, seven parts in a thousand. Every sunbeam you have ever felt is that tax being collected. It is also the most precisely constrained number in the fine-tuning literature — Martin Rees's favorite example, and the Tuner's narrowest dial.
Why life cares
At 0.006, one rung of the ladder breaks. Stars climb from hydrogen to helium via deuterium, and deuterium's binding sits right at the edge: shave ε slightly and the stepping stone dissolves. Fusion stalls at step one; the sky fills with unburned hydrogen and good intentions.
At 0.008, the ladder burns instead. Protons bind to each other too eagerly in the early universe, and the entire hydrogen budget is spent before chemistry can be born. No hydrogen means no water, no hydrocarbons, no long-lived stars with fuel to spare. Between 'no fusion' and 'no hydrogen left' there is barely room for the actual value — and the actual value sits there.
And then carbon. The same 0.007 lands close enough to a resonance of carbon-12 for stars to build it three helium nuclei at a time — the coincidence Fred Hoyle predicted from our existence before anyone measured it. ε isn't just the window for fire; it's the window for ash worth having.
In the toy
The ε dial runs from 0.001 to 0.012, with the life-permitting band at the honest 0.006–0.008. Below it your universe never lights; above it the fuel is gone in the first act. Try 0.004 and watch a sky that can't catch fire.