The arrow of time, also called time's arrow, is the concept positing the "one-way direction" or " asymmetry" of

time Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, ...

. 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

atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, ...

molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioche ...

s, and

bodies Bodies may refer to: * The plural of body * ''Bodies'' (2004 TV series), BBC television programme * Bodies (upcoming TV series), an upcoming British crime thriller limited series * "Bodies" (''Law & Order''), 2003 episode of ''Law & Order'' * ...

, and might be drawn upon a

four-dimensional A four-dimensional space (4D) is a mathematical extension of the concept of three-dimensional or 3D space. Three-dimensional space is the simplest possible abstraction of the observation that one only needs three numbers, called ''dimensions'', ...

relativistic map of the world ("a solid block of paper"). Physical processes at the

microscopic The microscopic scale () is the scale of objects and events smaller than those that can easily be seen by the naked eye, requiring a lens or microscope to see them clearly. In physics, the microscopic scale is sometimes regarded as the scale be ...

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 The macroscopic scale is the length scale on which objects or phenomena are large enough to be visible with the naked eye, without magnifying optical instruments. It is the opposite of microscopic. Overview When applied to physical phenomena a ...

level it often appears that this is not the case: there is an obvious direction (or ''flow'') of time.

Overview

The symmetry of time (

T-symmetry T-symmetry or time reversal symmetry is the theoretical symmetry of physical laws under the transformation of time reversal, : T: t \mapsto -t. Since the second law of thermodynamics states that entropy increases as time flows toward the futur ...

) 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.

Gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...

, 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 In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acc ...

is dissipated and

entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...

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. In his book The Big Picture, physicist

Sean M. Carroll Sean Michael Carroll (born October 5, 1966) is an American theoretical physicist and philosopher who specializes in quantum mechanics, gravity, and cosmology. He is (formerly) a research professor in the Walter Burke Institute for Theoretical ...

has compared the asymmetry of time to the asymmetry of space: While physical laws are in general isotropic, near Earth there is an obvious distinction between "up" and "down", due to proximity to this huge body, which breaks the symmetry of space. Similarly, physical laws are in general symmetric to the flipping of time direction, but near the Big Bang (i.e. in the first many trillions of years following it) there is an obvious distinction between "forward" and "backward" in time, due to relative proximity to this special event, which breaks the symmetry of time. Under this view, all the arrows of time are a result of our relative proximity in time to the Big Bang, and the special circumstances that existed then. (Strictly speaking, the

weak interaction In nuclear physics and particle physics, the weak interaction, which is also often called the weak force or weak nuclear force, is one of the four known fundamental interactions, with the others being electromagnetism, the strong interaction ...

s are asymmetric to both spatial reflection and to flipping of the time direction. However, they do obey a more complicated symmetry that includes both.)

Conception by Eddington

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 Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
. 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: # It is vividly recognized by

consciousness Consciousness, at its simplest, is sentience and awareness of internal and external existence. However, the lack of definitions has led to millennia of analyses, explanations and debates by philosophers, theologians, linguisticians, and scien ...

. # It is equally insisted on by our reasoning faculty, which tells us that a reversal of the arrow would render the external world nonsensical. # 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.)

Arrows

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 The second law of thermodynamics is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects (or "downhill"), unles ...

, 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." 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'' "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 In information theory and statistics, negentropy is used as a measure of distance to normality. The concept and phrase "negative entropy" was introduced by Erwin Schrödinger in his 1944 popular-science book ''What is Life?'' Later, Léon Brillo ...

, and

evolution Evolution is change in the heritable characteristics of biological populations over successive generations. These characteristics are the expressions of genes, which are passed on from parent to offspring during reproduction. Variation ...

." Blum argues that evolution followed specific patterns predetermined by the inorganic nature of the earth and its thermodynamic processes.

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 Heat death may refer to: *Heat death of the universe, a proposed cosmological event ** Heat death paradox, a philosophical examination of the cosmological event *Hyperthermia, injury up to and including death, from excessive heat *Thermal shock ...

''(Big Chill)'' as the amount of

Thermodynamic free energy The thermodynamic free energy is a concept useful in the thermodynamics of chemical or thermal processes in engineering and science. The change in the free energy is the maximum amount of work that a thermodynamic system can perform in a process ...

becomes negligible. Alternatively, it may be an artifact of our place in the universe's evolution (see the

Anthropic bias The anthropic principle, also known as the "observation selection effect", is the hypothesis, first proposed in 1957 by Robert Dicke, that there is a restrictive lower bound on how statistically probable our observations of the universe are, beca ...

), 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 mathematics and particularly in dynamic systems, an initial condition, in some contexts called a seed value, is a value of an evolving variable at some point in time designated as the initial time (typically denoted ''t'' = 0). For ...

in the early universe. Therefore, they ultimately result from the cosmological set-up.

Radiative arrow of time

Waves, from

radio waves Radio waves are a type of electromagnetic radiation with the longest wavelengths in the electromagnetic spectrum, typically with frequencies of 300 gigahertz ( GHz) and below. At 300 GHz, the corresponding wavelength is 1 mm (s ...

sound waves In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the ...

to those on a pond from throwing a stone, expand outward from their source, even though the

wave equation The (two-way) wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields — as they occur in classical physics — such as mechanical waves (e.g. water waves, sound waves and seism ...

s accommodate solutions of convergent waves as well as radiative ones. This arrow has been reversed in carefully worked experiments that created convergent waves, 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 causes or 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 David Hume (; born David Home; 7 May 1711 NS (26 April 1711 OS) – 25 August 1776) Cranston, Maurice, and Thomas Edmund Jessop. 2020 999br>David Hume" ''Encyclopædia Britannica''. Retrieved 18 May 2020. was a Scottish Enlightenment phil ...

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, correlations between a system and its surrounding are thought to increase with entropy, and have been shown to be equivalent to it in a simplified case of a finite system interacting with the environment.Esposito, M., Lindenberg, K., & Van den Broeck, C. (2010). Entropy production as correlation between system and reservoir. New Journal of Physics, 12(1), 013013. The assumption of low initial entropy is indeed equivalent to assuming no initial correlations in the system; thus correlations can only be created as we move forward in time, not backwards. Controlling the future, or causing something to happen, creates

correlations In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics ...

between the doer and the effect, and therefore the relation between cause and effect is a result of the

thermodynamic Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of the ...

arrow of time, a consequence of the second law of thermodynamics. Indeed, in the above example of the cup dropping, the initial conditions have high order and low entropy, while the final state has high correlations between relatively distant parts of the system - the shattered pieces of the cup, as well as the spilled drops of water, and the object that caused the cup to drop.

Particle physics (weak) arrow of time

Certain subatomic interactions involving the

weak nuclear force In nuclear physics and particle physics, the weak interaction, which is also often called the weak force or weak nuclear force, is one of the four known fundamental interactions, with the others being electromagnetism, the strong interaction ...

violate the conservation of both parity and

charge conjugation In physics, charge conjugation is a transformation that switches all particles with their corresponding antiparticles, thus changing the sign of all charges: not only electric charge but also the charges relevant to other forces. The term C-sy ...

, but only very rarely. An example is the

kaon KAON (Karlsruhe ontology) is an ontology infrastructure developed by the University of Karlsruhe and the Research Center for Information Technologies in Karlsruhe. Its first incarnation was developed in 2002 and supported an enhanced version of ...

decay Decay may refer to: Science and technology * Bit decay, in computing * Software decay, in computing * Distance decay, in geography * Decay time (fall time), in electronics Biology * Decomposition of organic matter * Tooth decay (dental caries ...

. According to the

CPT theorem Charge, parity, and time reversal symmetry is a fundamental symmetry of physical laws under the simultaneous transformations of charge conjugation (C), parity transformation (P), and time reversal (T). CPT is the only combination of C, P, and ...

, 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.

Quantum arrow of time

Quantum evolution is governed by equations of motions that are time-symmetric (such as

Schrödinger equation The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of th ...

in the non-relativistic approximation), and by

wave function collapse In quantum mechanics, wave function collapse occurs when a wave function—initially in a quantum superposition, superposition of several eigenstates—reduces to a single eigenstate due to interaction with the external world. This interaction is ...

, which is a time-irreversible process, and is either real (by the

Copenhagen interpretation The Copenhagen interpretation is a collection of views about the meaning of quantum mechanics, principally attributed to Niels Bohr and Werner Heisenberg. It is one of the oldest of numerous proposed interpretations of quantum mechanics, as feat ...

quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistr ...

) or apparent only (by the

many-worlds interpretation The many-worlds interpretation (MWI) is an interpretation of quantum mechanics that asserts that the universal wavefunction is objectively real, and that there is no wave function collapse. This implies that all possible outcomes of quantum ...

and relational quantum mechanics interpretation). The theory of quantum decoherence explains why wave function collapse happens in a time-asymmetric fashion due to the second law of thermodynamics, thus deriving the quantum arrow of time from the thermodynamic arrow of time. In essence, following any particle scattering or interaction between two larger systems, the relative phases of the two systems are at first orderly related, but subsequent interactions (with additional particles or systems) make them less so, so that the two systems become decoherent. Thus decoherence is a form of increase in microscopic disorder in short, decoherence increases entropy. Two decoherent systems can no longer interact via quantum superposition, unless they become coherent again, which is normally impossible, by the second law of thermodynamics.Schlosshauer, M. (2005). Decoherence, the measurement problem, and interpretations of quantum mechanics. Reviews of Modern physics, 76(4), 1267. In the language of relational quantum mechanics, the observer becomes entangled with the measured state, where this entanglement increases entropy. As stated by

Seth Lloyd Seth Lloyd (born August 2, 1960) is a professor of mechanical engineering and physics at the Massachusetts Institute of Technology. His research area is the interplay of information with complex systems, especially quantum systems. He has perform ...

, "the arrow of time is an arrow of increasing correlations".Univ of Bristo
(26 Nov 2021) Time-Reversal Phenomenon: In the Quantum Realm, Not Even Time Flows As You Might Expect
Lead: Professor Caslav Brukner: "quantum systems can simultaneously evolve along two opposite time arrows — both forward and backward in time". However, under special circumstances, one can prepare initial conditions that will cause a decrease in decoherence and in entropy. This has been shown experimentally in 2019, when a team of Russian scientists reported the reversal of the quantum arrow of time on an IBM quantum computer, in an experiment supporting the understanding of the quantum arrow of time as emerging from the thermodynamic one. 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. The state's reversal was made by a special program, similarly to the random

microwave background In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all spac ...

fluctuation in the case of the

electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no ...

. However, according to the estimations, throughout the

age of the universe In physical cosmology, the age of the universe is the time elapsed since the Big Bang. Astronomers have derived two different measurements of the age of the universe: a measurement based on direct observations of an early state of the universe, ...

(13.7 billion years) such a reversal of the electron's state would only happen once, for 0.06

nanoseconds A nanosecond (ns) is a unit of time in the International System of Units (SI) equal to one billionth of a second, that is, of a second, or 10 seconds. The term combines the SI prefix ''nano-'' indicating a 1 billionth submultiple of an SI unit ( ...

. The scientists' experiment led to the possibility of a quantum algorithm that reverses a given

quantum state In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the quantum state together with the rules for the system's evolution i ...

through complex conjugation of the state. Note that quantum decoherence merely allows the process of quantum wave collapse; it is a matter of dispute whether the collapse itself actually takes place or is redundant and apparent only. However, since the theory of quantum decoherence is now widely accepted and has been supported experimentally, this dispute can no longer be considered as related to the arrow of time question.

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. This phenomenon has two aspects: Memory - we remember the past and not the future; and volition - we feel we can influence the future but not the past. The two aspects are a consequence of the causal arrow of time: past events (but not future events) are the cause of our present memories, as more and more correlations are formed between the outer world and our brain (see correlations and the arrow of time); and our present volitions and actions are causes of future events. This is because the increase of entropy is thought to be related to increase of both correlations between a system and its surroundings and of the overall complexity, under an appropriate definition, thus all increase together with time. Past and future are also psychologically associated with additional notions.

English English usually refers to: * English language * English people English may also refer to: Peoples, culture, and language * ''English'', an adjective for something of, from, or related to England ** English national ide ...

, along with other languages, tends to associate the past with "behind" and the future with "ahead", with expressions such as "to look forward to welcoming you", "to look back to the good old times", or "to be years ahead". However, this association of "behind ⇔ past" and "ahead ⇔ future" is culturally determined. For example, the

Aymara language Aymara (; also ) is an Aymaran language spoken by the Aymara people of the Bolivian Andes. It is one of only a handful of Native American languages with over one million speakers.The other native American languages with more than one millio ...

associates "ahead ⇔ past" and "behind ⇔ future" both in terms of terminology and gestures, corresponding to the past being observed and the future being unobserved. Similarly, the

Chinese Chinese can refer to: * Something related to China * Chinese people, people of Chinese nationality, citizenship, and/or ethnicity **''Zhonghua minzu'', the supra-ethnic concept of the Chinese nation ** List of ethnic groups in China, people of ...

term for "the day after tomorrow" 後天 ("hòutiān") literally means "after (or behind) day", whereas "the day before yesterday" 前天 ("qiántiān") is literally "preceding (or in front) day", and Chinese speakers spontaneously gesture in front for the past and behind for the future, although there are conflicting findings on whether they perceive the ego to be in front of or behind the past. There are no languages that place the past and future on a left–right axis (e.g., there is no expression in English such as ''*the meeting was moved to the left''), although at least English speakers associate the past with the left and the future with the right. The words "yesterday" and "tomorrow" both translate to the same word in

Hindi Hindi ( Devanāgarī: or , ), or more precisely Modern Standard Hindi (Devanagari: ), is an Indo-Aryan language spoken chiefly in the Hindi Belt region encompassing parts of northern, central, eastern, and western India. Hindi has been ...

: कल ("kal"), meaning " neday remote from today." 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".Hindi-English.org Hindi English Dictionary परसों
— accessed 2017-01-11 तरसों ("tarson") is used for "three days from today

and नरसों ("narson") is used for "four days from today". 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 of Omar Khayyam, 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).

In June 2022, researchers reportedthe local arrow of time in interacting systems
Christopher W. Lynn, Caroline M. Holmes, William Bialek, and David J. Schwab,

Physical Review Letters ''Physical Review Letters'' (''PRL''), established in 1958, is a peer-reviewed, scientific journal that is published 52 times per year by the American Physical Society. As also confirmed by various measurement standards, which include the ''Journa ...

, accepted 2022-06-21 in

finding that

salamander Salamanders are a group of amphibians typically characterized by their lizard-like appearance, with slender bodies, blunt snouts, short limbs projecting at right angles to the body, and the presence of a tail in both larvae and adults. All t ...

s were demonstrating

counter-intuitive A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically u ...

responses to the arrow of time in how their eyes perceived different stimuli.

References

External links

a review of historical perspectives of the subject, prior to the evolvement of quantum field theory.
The Thermodynamic Arrow: Puzzles and Pseudo-Puzzles
Huw Price on Time's Arrow
Arrow of time in a discrete toy model

The Arrow of Time

Why Does Time Run Only Forwards
by Adam Becker, bbc.com. {{Time Topics Asymmetry Non-equilibrium thermodynamics Philosophical analogies Philosophy of thermal and statistical physics Philosophy of time Time in physics