Arrow of time

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The arrow of time is the phenomenon by which, for macroscopic action, time flows in only one direction; it can't be reversed. This is in contrast with the dimensions of space, which are all reversible. In the early days of home movies, people would sometimes make a movie of some everyday phenomenon such as a person eating a piece of pie, and then play it backwards to show how incongruous it looked. This irreversibility is ubiquitous in real life—one would never expect to "shuffle" a deck of cards that had been random, and get a result in which all the suits were in sequence.

This irreversibility is actually a phenomenon of statistical mechanics, not fundamental physics per se. The fundamental molecular interactions that make up the phenomena of the Second Law of Thermodynamics are actually reversible. It is the statistical behavior of enormous aggregates of particles that leads to the Second Law. The Second Law is the branch of science where statistical mechanics and macroscopic physics meet, so it is the branch where irreversibility shows up.

The particular aspect of statistical mechanics that drives this irreversibility is entropy, which is basically a measure of disorder. The principle is that entropy never decreases, but can (and in normal macroscopic phenomena, usual does) increase. On the statistical mechanics side, this is just an overall increase in disorder. The shuffling of cards illustrates it. On the macroscopic physics side, this is the actual "classical" Second Law of Thermodynamics, which states that heat never flows from a colder body to a warmer one.

The term was coined in 1927 by astronomer Sir Arthur Eddington.[1][2]

Time-symmetric systems

Physical systems with a few degrees of freedom usually are time-symmetric; for example, analysing the breakup of a binary asteroid with the capture of one of them as a planet's satellite yields equations where the time can be reversed: the analysis can be made for the event where a rogue asteroid captures a planet's satellite. Also, Kepler's laws of planetary motion describe a very simple, and reversible, situation.

When the freedom degrees increase, it becomes improbable that the time can be reversed: a rogue star that passes close to a solar system and disrupts the nice orbits of the planets might be seen as the inverse process where a rogue star "fixes" the disrupted orbits, but this scenario is very improbable.

Fundamental physics

It's usually believed (and backed by experiments) that most "forces" in nature (gravitation, electromagnetism, strong nuclear force) are time-symmetric, at least in the microscropic level. The possible exception is the weak nuclear force, that is not time-symmetric but has CPT symmetry (CPT stands for "charge", "parity" and "time") If we reverse time, the only way to have a realistic process is by reversing charge (swapping particles with their antiparticles) or parity (reversing the particles' intrinsic spin).


  1. Edgar Anrews (2010). Who made God? Searching for a theory of everything.. Carlisle, PA, USA: EP Books, 112. ISBN 978-0-85234-707-2. 
  2. Arthur Eddington (1927, 2012). The Nature of the Physical World: Gifford Lectures. Cambridge University Press, 80, 295. ISBN 9781107663855.