Pressing the button to detonate the Trinity atomic bomb must have been an interesting experience. The theorists were pretty sure what was the worst (or best, if "big boom" was the goal) that could happen, but there remained the small possibility in people's minds that the explosion could be much more powerful than expected, perhaps even powerful enough to extinguish all life on earth. The thought of possibly of doing that, in a single action, has probably happened exactly twice in human history: Trinity and then Ivy Mike, the first hydrogen bomb, 1000 times more powerful than previous atomic bombs. I'm not sure if it'll ever happen again.
We can easily speculate several mechanisms that could have ended it all. We now know these don't happen, but at the time, they didn't know.
A then-unknown exothermic chemical reaction involving nitrogen, oxygen, or the materials of the earth with such high activation energy that it could only be realized inside an atomic bomb. However, once it starts, the exothermic reaction causes a chain reaction, destroying the atmosphere, or the planet.
Similarly, one could speculate a then-unknown nuclear reaction that causes a chain reaction with surrounding air or earth. For example, nitrogen wasn't predicted to favorably undergo fission, but with enough neutron flux, perhaps it does, releasing more neutrons in the process. Incidentally, the Castle Bravo H-bomb test did discover a then-unknown nuclear reaction involving lithium, causing it to explode with much more energy than expected.
Descending further, there could have been a then-unknown subatomic reaction that only occurs at high temperatures.
The general idea is, there is a limit to our knowledge of science at any given point in history. Similar doomsday predictions were raised about RHIC and LHC, though I believe those objections were addressed by known science at the time (of cosmic rays).
Fictionally illustrate a doomsday reaction triggered by Trinity spreading through the world, against the backdrop of WWII having just ended in Europe and still raging in the Pacific. Perhaps the chain reaction is slow moving. Suddenly people become no longer concerned about the war in the face of imminent extinction.
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