Why does time only move one way?

Classical mechanics, electromagnetism, general relativity and the Schrödinger equation of quantum mechanics all work the same run forwards or backwards. There is one known exception: certain weak-force interactions violate time-reversal symmetry, first evidenced indirectly through the CP violation observed in kaon decay in 1964 and reported directly by the BaBar experiment in 2012.

That violation is real but specialised, and it does not appear to be what makes coffee cool and never spontaneously reheat.

The second law of thermodynamics says entropy (roughly, a measure of how many microscopic arrangements are consistent with what you can see) tends to increase. There are vastly more ways for a glass to be broken than intact, so the transition runs one way overwhelmingly often.

This explains the arrow given a low-entropy starting point. It does not explain the starting point.

The early universe was hot and remarkably uniform: the radiation left over from it varies by about one part in 100,000 across the sky. That uniformity, in a universe with gravity, is a very low-entropy condition, which is where the arrow of time ultimately comes from on the standard account.

Assume a low-entropy beginning and the statistical account delivers the thermodynamic arrow, though how a condition on the whole universe reaches each glass and cup is still argued over. The assumption is doing all the work and is itself unexplained. Whether it needs explaining is disputed: Huw Price argues that it does, Craig Callender doubts it. We have traded a puzzle about time for a puzzle about initial conditions.

The thermodynamic arrow, the cosmological arrow of expansion, the arrow of radiation, and the psychological arrow of memory all point the same way. Whether they are one phenomenon or several that happen to align is not settled.

No accepted theory explains why the universe began in a state of such low entropy. Answering it appears to require understanding physics at the beginning, which requires a theory of quantum gravity, and no such theory has yet been tested by experiment.

The canonical approach to quantum gravity arrives at a central equation, the Wheeler-DeWitt equation, in which the state of the universe does not evolve: there is no time variable in it. Some, Julian Barbour among them, read this as a sign that time is illusory; others argue that the evolution is there and harder to find. If the first reading is right, the question is not why time flows one way but why anything like flow appears in a description that does not contain it.

Relativity describes a four-dimensional spacetime in which there is no fact about which distant events are happening now. Many philosophers read that as all times being equally real, with nothing corresponding to now moving; defenders of a real present reply that the physics does not force the reading. Whether the felt passage of time is a fact about reality or a fact about the kind of observer we are is genuinely unresolved, and sits on the boundary between physics and the study of mind.

On this view there is nothing to explain about time itself: it is symmetric, and every asymmetry we notice traces back to the universe having started in an unusual state. The question then becomes a question in cosmology.

Some proposals suggest that if the universe’s entropy were lowest in the middle of its history rather than at its beginning, and could grow without limit in both directions, observers on either side would each find entropy increasing away from that moment, so the arrow would be local rather than global. These are speculative models.

If time is not fundamental, it may emerge from entanglement between parts of the universe: in a mechanism Page and Wootters proposed in 1983, a universe that is static as a whole looks as if it evolves to an observer inside it who reads one part as a clock. The idea is mathematically serious and still controversial. A 2014 experiment reproduced the mechanism with two entangled photons, which illustrates it without testing whether our own time arises this way.