Starting with just a stick and basic geometry, rebuild humanity’s knowledge of cosmic scales from scratch. Learn how Eratosthenes, Galileo, Newton, and others measured Earth, the Moon, the Sun, and distant stars using ingenious observations.
The Ehrenfest theorem fails to explain how quantum mechanics becomes classical. But there is another way: when wavefunctions become sufficiently localized, they follow classical trajectories not through averaging, but through the geometry of quantum phase. Discover how the WKB approximation reveals the true classical limit—and why entanglement marks its absolute boundary.
The Ehrenfest theorem suggests quantum mechanics reduces to classical physics for average values, but this beautiful result is deeply misleading. Discover why quantum uncertainty persists even when expectation values obey classical equations.