Oppenheimer's Apocalypse Math

Before Trinity test, Manhattan Project scientists feared the extreme temperature from nuclear blast might trigger thermonuclear reaction in Earth’s atmosphere, potentially destroying the entire world.

The feared reaction would fuse nitrogen atoms (element 7) in Earth’s atmosphere into magnesium (element 12), releasing energy that propagates the reaction globally.

Oppenheimer’s team structured atmospheric ignition analysis around comparing energy produced by fusion versus energy lost from reaction region.

Without experimental data for nitrogen fusion probability, Oppenheimer’s team assumed worst-case possibility: every collision would result in fusion.

Using numerical integration, Oppenheimer’s team computed curve showing energy released per nucleus per second as function of temperature.

At fusion temperatures, electrons break free from atoms forming plasma; as electrons slow through ion interactions, they release significant radiation called bremsstrahlung (“breaking radiation”).

Comparing production and loss curves, Oppenheimer’s team found energy loss exceeded production across all temperatures—but curves became “uncomfortably close” around 10 mega electron volts with only 1.6x safety margin.

The critical temperature of 10 mega electron volts where curves nearly converge equals over 100 billion degrees Kelvin—extraordinarily high temperature providing additional safety consideration.

High-energy alpha particles released by fission explosion transfer energy to atmosphere, but low air density and small nitrogen nuclei create 57-meter average collision distance.

Heating atmospheric sphere of 57-meter radius to critical 10 MeV temperature requires approximately 100,000 times more energy than fission bombs produce.

Beyond bremsstrahlung, Oppenheimer’s team identified inverse Compton effect as another expected energy loss mechanism increasing safety confidence.

1959 American Weekly article incorrectly claimed scientists computed “slightly less than three in one million probability” that nuclear test would end the world, giving confidence to proceed.

Hans Bethe, key Manhattan Project physicist on Oppenheimer’s team, responded to 1959 misrepresentation by stating atmospheric ignition “was never a matter of probabilities” and “ignition is simply impossible.”

When Oppenheimer discovered atmospheric fusion possibility, he immediately traveled by train to meet Manhattan Project supervisor Arthur Compton—matter too sensitive to discuss by phone, and project leaders forbidden from flying.

Compton picked up Oppenheimer at train station and drove to nearby lake to discuss atmospheric ignition possibility in private.

Recalling lakeside conversation in his memoirs, Compton wrote: “This would be the ultimate catastrophe. Better to accept slavery to the Nazis than run a chance of drawing the final curtain on mankind.”