Bose–Einstein Condensation: How a Billion Atoms Become One (v2)

Cooling spreads things out — so how do a billion atoms become one? A narrated, animated walk through Bose–Einstein condensation: from the paradox, through the physics, to the real 1995 experiment. Covered: • The paradox — cooling should spread atoms out, yet they collapse into a single wave • An atom is a wave, not a point: colder means wider • The thermal de Broglie wavelength λ_T = √(2πℏ²/m k_B T), grown from λ = h/p • When matter-waves overlap: interatomic spacing n^(−1/3) meets λ_T • The honest threshold: n λ_T³ = ζ(3/2) ≈ 2.612 — not just "about one" • Why everyone piles into a single quantum ground state • It's real: rubidium-87, 1995 — ~2000 atoms, ~16 million times colder than deep space • The paradox resolved, a plain-words recap, and the MERGE mnemonic Built with Manim. (v2 — a corrected re-render: typeset entirely in Computer Modern, the thermal-wavelength formulas fixed, and the narration cleaned up.)