Arrow of time

The arrow of time is the observed asymmetry between past and future: eggs scramble but never unscramble, glasses shatter but never reassemble, heat flows from hot to cold and not back. The puzzle is that the fundamental laws of motion — Newtonian, electromagnetic, quantum — are invariant under time reversal t → −t, so they single out no preferred direction. The asymmetry must therefore come from somewhere other than the dynamics.

The thermodynamic answer is that the arrow is statistical, not dynamical. A system evolves toward macrostates of higher multiplicity simply because there are overwhelmingly more of them, so entropy S = k_B ln Ω increases. The reverse process is not forbidden, merely so improbable — by factors like one in 10 raised to 10²⁴ — that it never occurs on any observable timescale. The direction in which entropy increases is what we call 'the future.'

Why the arrow points the way it does ultimately traces to the low-entropy initial state of the universe (the past hypothesis), since the dynamics alone cannot prefer one direction.

The English astrophysicist Arthur Eddington coined the phrase 'time's arrow' in his 1928 book 'The Nature of the Physical World,' identifying it with the increase of entropy. The underlying statistical account is Boltzmann's, defended against Loschmidt's and Zermelo's objections in the 1870s–1890s.