With his work in 1916-7, Einstein was able to arrive at a “much more” quantum derivation of Planck’s Radiation Law. However, in the end he fell short, having to rely on assumptions. In 1924, Satyendra Nath Bose provided the first “fully” quantum derivation of Planck’s radiation law, which revealed the deeper nature of light that had eluded everyone else, including Einstein. With this work, he created the new area of physics known as quantum statistics.
The atoms of a Bose-Einstein fluid are in the exact same quantum state.
In 1925, Einstein predicted a very unusual phase transition that occurs for the quantum ideal gas. Einstein describes the phenomenon in a letter to Paul Ehrenfest (1880–1933):
“From a certain temperature on, the molecules ‘condense’ without attractive forces, that is, they accumulate at zero velocity.”
In other words, as the temperature is lowered, the atoms in the gas begin to “pile up” or condense into the lowest (single particle) energy state, which is the one with zero kinetic energy; there’s a critical temperature whereby a phase transition (now called (Bose-Einstein condensation) occurs. This effect becomes most pronounced as the temperature is lowered to absolute zero, at which point, all the gas atoms condense into this lowest energy state. This phenomenon is an example of quantum entanglement.
Einstein predicted a new phase transition for matter (Bose-Einstein Condensation) in 1925; it took until 1995 to verify it experimentally.
