Arrow of time

The arrow of time, or time's arrow is the concept positing the "one-way direction" or "asymmetry" of time. It was developed in 1927 by the British astrophysicist Arthur Eddington, and is an unsolved general physics question. This direction, according to Eddington, could be determined by studying the organization of atoms, molecules, and bodies, and might be drawn upon a four-dimensional relativistic map of the world ("a solid block of paper").[1]

Physical processes at the microscopic level are believed to be either entirely or mostly time-symmetric: if the direction of time were to reverse, the theoretical statements that describe them would remain true. Yet at the macroscopic level it often appears that this is not the case: there is an obvious direction (or flow) of time.


The symmetry of time (T-symmetry) can be understood simply as the following: if time were perfectly symmetrical, a video of real events would seem realistic whether played forwards or backwards.[2] Gravity, for example, is a time-reversible force. A ball that is tossed up, slows to a stop, and falls is a case where recordings would look equally realistic forwards and backwards. The system is T-symmetrical. However, the process of the ball bouncing and eventually coming to a stop is not time-reversible. While going forward, kinetic energy is dissipated and entropy is increased. Entropy may be one of the few processes that is not time-reversible. According to the statistical notion of increasing entropy, the "arrow" of time is identified with a decrease of free energy.[3]


In the 1928 book The Nature of the Physical World, which helped to popularize the concept, Eddington stated:

Let us draw an arrow arbitrarily. If as we follow the arrow we find more and more of the random element in the state of the world, then the arrow is pointing towards the future; if the random element decreases the arrow points towards the past. That is the only distinction known to physics. This follows at once if our fundamental contention is admitted that the introduction of randomness is the only thing which cannot be undone. I shall use the phrase 'time's arrow' to express this one-way property of time which has no analogue in space.

Eddington then gives three points to note about this arrow:

  1. It is vividly recognized by consciousness.
  2. It is equally insisted on by our reasoning faculty, which tells us that a reversal of the arrow would render the external world nonsensical.
  3. It makes no appearance in physical science except in the study of organization of a number of individuals. (By which he means that it is only observed in entropy, a statistical mechanics phenomenon arising from a system.)

According to Eddington the arrow indicates the direction of progressive increase of the random element. Following a lengthy argument upon the nature of thermodynamics he concludes that, so far as physics is concerned, time's arrow is a property of entropy alone.


Thermodynamic arrow of time

The arrow of time is the "one-way direction" or "asymmetry" of time. The thermodynamic arrow of time is provided by the second law of thermodynamics, which says that in an isolated system, entropy tends to increase with time. Entropy can be thought of as a measure of microscopic disorder; thus the second law implies that time is asymmetrical with respect to the amount of order in an isolated system: as a system advances through time, it becomes more statistically disordered. This asymmetry can be used empirically to distinguish between future and past, though measuring entropy does not accurately measure time. Also, in an open system, entropy can decrease with time.

British physicist Sir Alfred Brian Pippard wrote, "There is thus no justification for the view, often glibly repeated, that the Second Law of Thermodynamics is only statistically true, in the sense that microscopic violations repeatedly occur, but never violations of any serious magnitude. On the contrary, no evidence has ever been presented that the Second Law breaks down under any circumstances."[4] However, there are a number of paradoxes regarding violation of the second law of thermodynamics, one of them due to the Poincaré recurrence theorem.

This arrow of time seems to be related to all other arrows of time and arguably underlies some of them, with the exception of the weak arrow of time.

Harold Blum's 1951 book Time's Arrow and Evolution[5] "explored the relationship between time's arrow (the second law of thermodynamics) and organic evolution." This influential text explores "irreversibility and direction in evolution and order, negentropy, and evolution."[6] Blum argues that evolution followed specific patterns predetermined by the inorganic nature of the earth and its thermodynamic processes.[7]

Cosmological arrow of time

The cosmological arrow of time points in the direction of the universe's expansion. It may be linked to the thermodynamic arrow, with the universe heading towards a heat death (Big Chill) as the amount of usable energy becomes negligible. Alternatively, it may be an artifact of our place in the universe's evolution (see the Anthropic bias), with this arrow reversing as gravity pulls everything back into a Big Crunch.

If this arrow of time is related to the other arrows of time, then the future is by definition the direction towards which the universe becomes bigger. Thus, the universe expands—rather than shrinks—by definition.

The thermodynamic arrow of time and the second law of thermodynamics are thought to be a consequence of the initial conditions in the early universe.[8] Therefore, they ultimately result from the cosmological set-up.

Radiative arrow of time

Waves, from radio waves to sound waves to those on a pond from throwing a stone, expand outward from their source, even though the wave equations accommodate solutions of convergent waves as well as radiative ones. This arrow has been reversed in carefully worked experiments that created convergent waves,[9] so this arrow probably follows from the thermodynamic arrow in that meeting the conditions to produce a convergent wave requires more order than the conditions for a radiative wave. Put differently, the probability for initial conditions that produce a convergent wave is much lower than the probability for initial conditions that produce a radiative wave. In fact, normally a radiative wave increases entropy, while a convergent wave decreases it, making the latter contradictory to the second law of thermodynamics in usual circumstances.

Causal arrow of time

A cause precedes its effect: the causal event occurs before the event it affects. Birth, for example, follows a successful conception and not vice versa. Thus causality is intimately bound up with time's arrow.

An epistemological problem with using causality as an arrow of time is that, as David Hume maintained, the causal relation per se cannot be perceived; one only perceives sequences of events. Furthermore, it is surprisingly difficult to provide a clear explanation of what the terms cause and effect really mean, or to define the events to which they refer. However, it does seem evident that dropping a cup of water is a cause while the cup subsequently shattering and spilling the water is the effect.

Physically speaking, the perception of cause and effect in the dropped cup example is a phenomenon of the thermodynamic arrow of time, a consequence of the second law of thermodynamics.[10] Controlling the future, or causing something to happen, creates correlations between the doer and the effect,[11] and these can only be created as we move forwards in time, not backwards.

Particle physics (weak) arrow of time

Certain subatomic interactions involving the weak nuclear force violate the conservation of both parity and charge conjugation, but only very rarely. An example is the kaon decay.[12] According to the CPT theorem, this means they should also be time irreversible, and so establish an arrow of time. Such processes should be responsible for matter creation in the early universe.

That the combination of parity and charge conjugation is broken so rarely means that this arrow only "barely" points in one direction, setting it apart from the other arrows whose direction is much more obvious. This arrow had not been linked to any large scale temporal behaviour until the work of Joan Vaccaro, who showed that T violation could be responsible for conservation laws and dynamics.[13]

Quantum arrow of time

Unsolved problem in physics:
What links the quantum arrow of time to the thermodynamic arrow?
(more unsolved problems in physics)

According to the Copenhagen interpretation of quantum mechanics, quantum evolution is governed by the Schrödinger equation, which is time-symmetric, and by wave function collapse, which is time irreversible. As the mechanism of wave function collapse is philosophically obscure, it is not completely clear how this arrow links to the others. Despite the post-measurement state being entirely stochastic in formulations of quantum mechanics, a link to the thermodynamic arrow has been proposed, noting that the second law of thermodynamics amounts to an observation that nature shows a bias for collapsing wave functions into higher entropy states versus lower ones, and the claim that this is merely due to more possible states being high entropy runs afoul of Loschmidt's paradox. According to one physical view of wave function collapse, the theory of quantum decoherence, the quantum arrow of time is a consequence of the thermodynamic arrow of time.

Relational quantum mechanics proposes that there is no such thing as an absolute wave function collapse, and that what an observer sees as wave function collapse is in fact the observer becoming entangled with the measured state. The thermodynamic arrow is an increase in entanglement over time; in this way, relational quantum mechanics relates the quantum arrow to the thermodynamic arrow.

In 2019, a team of Russian scientists reported the reversal of the quantum arrow of time on an IBM quantum computer.[14] By observing the state of the quantum computer made of two and later three superconducting qubits, they found that in 85% of the cases, the two-qubit computer returned into the initial state.[15] The state's reversal was made by a special program, similarly to the random microwave background fluctuation in the case of the electron.[15] However, according to the estimations, throughout the age of the universe (13.7 billion years) such a reversal of the electron's state would only happen once, for 0.06 nanoseconds.[15] The scientists' experiment led to the possibility of a quantum algorithm that reverses a given quantum state through complex conjugation.[14]

Quantum source of time

Physicists say that quantum uncertainty gives rise to entanglement, the putative source of the arrow of time. The idea that entanglement might explain the arrow of time was proposed by Seth Lloyd in the 1980s. Lloyd argues that quantum uncertainty, and the way it spreads as particles become increasingly entangled, could replace human uncertainty in the old classical proofs as the true source of the arrow of time. According to Lloyd, "The arrow of time is an arrow of increasing correlations."[16]

Psychological/perceptual arrow of time

A related mental arrow arises because one has the sense that one's perception is a continuous movement from the known (past) to the unknown (future). Anticipating the unknown forms the psychological future, which always seems to be something one is moving towards. However, like a projection in a mirror, it makes what is actually already a part of memory, such as desires, dreams, and hopes, seem ahead of the observer.

The association of "behind ⇔ past" and "ahead ⇔ future" is itself culturally determined. For example, the Aymara language associates "ahead ⇔ past" and "behind ⇔ future".[17] Similarly, the Chinese term for "the day after tomorrow" 後天 ("hòu tiān") literally means "after (or behind) day", whereas "the day before yesterday" 前天 ("qián tiān") is literally "preceding (or in front) day."[18]

The words "yesterday" and "tomorrow" both translate to the same word in Hindi: कल ("kal"),[19] meaning "[one] day remote from today."[20] The ambiguity is resolved by verb tense. परसों ("parsoⁿ") is used for both "day before yesterday" and "day after tomorrow", or "two days from today".[21] नरसों ("narsoⁿ") is used for "three days from today."[22]

The other side of the psychological passage of time is in the realm of volition and action. We plan and often execute actions intended to affect the course of events in the future. From the Rubaiyat:

The Moving Finger writes; and, having writ,
  Moves on: nor all thy Piety nor Wit
Shall lure it back to cancel half a Line,
  Nor all thy Tears wash out a Word of it.

Omar Khayyám (translation by Edward Fitzgerald).

See also


  1. Weinert, Friedel (2005). The scientist as philosopher: philosophical consequences of great scientific discoveries. Springer. p. 143. ISBN 978-3-540-21374-1., Chapter 4, p. 143
  2. David Albert on Time and Chance
  3. Tuisku, P.; Pernu, T.K.; Annila, A. (2009). "In the light of time". Proceedings of the Royal Society A. 465 (2104): 1173–1198. Bibcode:2009RSPSA.465.1173T. doi:10.1098/rspa.2008.0494.
  4. A. B. Pippard, Elements of Chemical Thermodynamics for Advanced Students of Physics (1966), p.100.
  5. Blum, Harold F. (1951). Time's Arrow and Evolution (First ed.). ISBN 978-0-691-02354-0.
  6. Morowitz, Harold J. (September 1969). "Book review: Time's arrow and evolution: Third Edition". Icarus. 11 (2): 278–279. Bibcode:1969Icar...11..278M. doi:10.1016/0019-1035(69)90059-1. PMC 2599115.
  7. McN., W. P. (November 1951). "Book reviews: Time's Arrow and Evolution". Yale Journal of Biology and Medicine. 24 (2): 164. PMC 2599115.
  8. Susskind, Leonard. "Boltzmann and the Arrow of Time: A Recent Perspective". Cornell University. Cornell University. Retrieved June 1, 2016.
  9. Mathias Fink (30 November 1999). "Time-Reversed Acoustic" (PDF). Archived from the original (PDF) on 31 December 2005. Retrieved 27 May 2016.
  10. Physical Origins of Time Asymmetry, chapter 6
  11. Physical Origins of Time Asymmetry, pp. 109–111.
  12. "Home". Physics World.
  13. Vaccaro, Joan (2016). "Quantum asymmetry between time and space". Proceedings of the Royal Society A. 472 (2185): 20150670. arXiv:1502.04012. Bibcode:2016RSPSA.47250670V. doi:10.1098/rspa.2015.0670. PMC 4786044. PMID 26997899.
  14. G. B. Lesovik, I. A. Sadovskyy, M. V. Suslov, A. V. Lebedev, V. M. Vinokur (13 March 2019). "Arrow of time and its reversal on the IBM quantum computer". Nature. 9. arXiv:1712.10057. doi:10.1038/s41598-019-40765-6.CS1 maint: uses authors parameter (link)
  15. "Physicists reverse time using quantum computer". 13 March 2019. Retrieved 13 March 2019.
  16. Wolchover, Natalie (25 April 2014). "New Quantum Theory Could Explain the Flow of Time" via
  17. For Andes tribe, it's back to the future — accessed 2006-09-26
  18. Chinese-English Dictionary — accessed 2017-01-11
  19. Bahri, Hardev (1989). Learners' Hindi-English Dictionary. Delhi: Rajpal & Sons. p. 95. ISBN 978-81-7028-002-6.
  20. Alexiadou, Artemis (1997). Adverb placement : a case study in antisymmetric syntax. Amsterdam [u.a.]: Benjamins. p. 108. ISBN 978-90-272-2739-3.
  21. Hindi English Dictionary परसों — accessed 2017-01-11
  22. Hindi English Dictionary नरसों — accessed 2017-01-11

Further reading

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