Bose–Einstein statisticsprinciple
In 1924, the young Indian physicist Satyendra Nath Bose sent Albert Einstein his derivation of Planck's radiation law, treating photons as indistinguishable particles. Einstein immediately saw the universality of the approach and in 1925 generalized it to any massive particles with integer spin. Thus Bose–Einstein statistics was born. Unlike classical physics, where particles can be labeled, in the quantum world identical bosons are fundamentally indistinguishable, and their energy distribution is described by a formula: the average number of particles in a state with a given energy depends on the ratio of the energy difference and chemical potential to the thermal energy kT. Due to the minus sign in the denominator, at low energies an avalanche effect can occur—Bose–Einstein condensation: a macroscopic number of particles accumulates on the lowest energy level.
How it works
In a laser, photons synchronously copy the same quantum state, creating a powerful narrow beam. In an MRI superconducting magnet, current flows without resistance because electrons bind into Cooper pairs, which behave as bosons, and this 'collective' does not scatter on lattice defects. In superfluid helium, boson atoms upon cooling fill the lowest energy state and move without friction.
💡 The boson is named after Bose himself, and the term was coined by Paul Dirac. The most famous boson is the photon, but a whole atom, such as rubidium-87, can also be a boson. It was on it that in 1995 the Bose–Einstein condensate—the 'fifth state of matter'—was first obtained.
n_i = \frac{1}{e^{(\varepsilon_i - \mu)/(k_B T)} - 1}
n_i — average number of particles in state i, ε_i — energy of the state, μ — chemical potential (energy of adding one particle), k_B — Boltzmann constant (k_B ≈ 1.380649×10⁻²³ J/K), T — absolute temperature)