Arrow of time

Arrow of time

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This article is an overview of the subject. For a more technical discussion and for information related to current research, see Entropy (arrow of time)
Entropy (arrow of time)
Entropy is the only quantity in the physical sciences that requires a particular direction for time, sometimes called an arrow of time. As one goes "forward" in time, the second law of thermodynamics says, the entropy of an isolated system will increase...

.


The arrow of time, or time’s arrow, is a term coined in 1927 by the British astronomer Arthur Eddington to describe the "one-way direction" or "asymmetry" of time. This direction, which can be determined, according to Eddington, by studying the organization of atoms, molecules and bodies, might be drawn upon a four-dimensional relativistic map of the world ("a solid block of paper").

Physical
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

 processes at the microscopic
Microscopic
The microscopic scale is the scale of size or length used to describe objects smaller than those that can easily be seen by the naked eye and which require a lens or microscope to see them clearly.-History:...

 level are believed to be either entirely or mostly time-symmetric
T-symmetry
T Symmetry is the symmetry of physical laws under a time reversal transformation: T: t \mapsto -t.Although in restricted contexts one may find this symmetry, the observable universe itself does not show symmetry under time reversal, primarily due to the second law of thermodynamics.Time asymmetries...

: if the direction of time were to reverse, the theoretical statements that describe them would remain true. Yet at the macroscopic
Macroscopic
The macroscopic scale is the length scale on which objects or processes are of a size which is measurable and observable by the naked eye.When applied to phenomena and abstract objects, the macroscopic scale describes existence in the world as we perceive it, often in contrast to experiences or...

 level it often appears that this is not the case: there is an obvious direction (or flow) of time
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....

.

Eddington


In the 1928 book The Nature of the Physical World, which helped to popularize the term, 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
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

. 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
    Consciousness
    Consciousness is a term that refers to the relationship between the mind and the world with which it interacts. It has been defined as: subjectivity, awareness, the ability to experience or to feel, wakefulness, having a sense of selfhood, and the executive control system of the mind...

    .
  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.


According to Eddington the arrow indicates the direction of progressive increase of the random element. Following a lengthy argument upon the nature of thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...

 he concludes that, so far as physics is concerned, time's arrow is a property of entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

 alone.

Overview


The symmetry of time (T-symmetry
T-symmetry
T Symmetry is the symmetry of physical laws under a time reversal transformation: T: t \mapsto -t.Although in restricted contexts one may find this symmetry, the observable universe itself does not show symmetry under time reversal, primarily due to the second law of thermodynamics.Time asymmetries...

) can be understood by a simple analogy: if time were perfectly symmetrical a video of real events would seem realistic whether played forwards or backwards. An obvious objection to this notion is gravity: things fall down, not up. Yet a ball that is tossed up, slows to a stop and falls into the hand is a case where recordings would look equally realistic forwards and backwards. The system is T-symmetrical
T-symmetry
T Symmetry is the symmetry of physical laws under a time reversal transformation: T: t \mapsto -t.Although in restricted contexts one may find this symmetry, the observable universe itself does not show symmetry under time reversal, primarily due to the second law of thermodynamics.Time asymmetries...

 but while going "forward" kinetic energy
Kinetic energy
The kinetic energy of an object is the energy which 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 acceleration, the body maintains this kinetic energy unless its speed changes...

 is dissipated and entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

 is increased. Entropy may be one of the few processes that is not time-reversible
Irreversibility
In science, a process that is not reversible is called irreversible. This concept arises most frequently in thermodynamics, as applied to processes....

. According to the statistical notion of increasing entropy the "arrow" of time is identified with a decrease of free energy.

If we record somebody dropping a ball that falls for a meter and stops, in reverse we will notice an unrealistic discrepancy: a ball falling upward! But when the ball lands its kinetic energy is dispersed into sound, shock-waves and heat. In reverse those sound waves, ground vibrations and heat will rush back into the ball, imparting enough energy to propel it upward one meter into the person's hand. The only unrealism lies in the statistical unlikelihood that such forces could coincide to propel a ball upward into a waiting hand.

The thermodynamic arrow of time



The thermodynamic arrow of time is provided by the Second Law of Thermodynamics
Second law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...

, which says that in an isolated system
Isolated system
In the natural sciences an isolated system, as contrasted with an open system, is a physical system without any external exchange. If it has any surroundings, it does not interact with them. It obeys in particular the first of the conservation laws: its total energy - mass stays constant...

, entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

 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 will statistically become more disordered. This asymmetry can be used empirically to distinguish between future
Future
The future is the indefinite time period after the present. Its arrival is considered inevitable due to the existence of time and the laws of physics. Due to the nature of the reality and the unavoidability of the future, everything that currently exists and will exist is temporary and will come...

 and past
Past
Most generally, the past is a term used to indicate the totality of events which occurred before a given point in time. The past is contrasted with and defined by the present and the future. The concept of the past is derived from the linear fashion in which human observers experience time, and is...

 though measuring entropy does not accurately measure time. Also in an open system entropy can locally decrease with time: living systems decrease their entropy
Entropy and life
Research concerning the relationship between the thermodynamic quantity entropy and the evolution of life began in around the turn of the 20th century...

 by expenditure of energy at the expense of environmental entropy increase.

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." The Second Law is universal and seems to accurately describe the overall trend in real systems toward higher entropy.

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.

The 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
Big Crunch
In physical cosmology, the Big Crunch is one possible scenario for the ultimate fate of the universe, in which the metric expansion of space eventually reverses and the universe recollapses, ultimately ending as a black hole singularity.- Overview :...

.

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
Second law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...

 are thought to be a consequence of the initial conditions in the early universe. Therefore they ultimately result from the cosmological set-up.

The radiative arrow of time


Waves, from radio waves
Radio waves
Radio waves are a type of electromagnetic radiation with wavelengths in the electromagnetic spectrum longer than infrared light. Radio waves have frequencies from 300 GHz to as low as 3 kHz, and corresponding wavelengths from 1 millimeter to 100 kilometers. Like all other electromagnetic waves,...

 to sound waves to those on a pond from throwing a stone, expand outward from their source, even though the wave equation
Wave equation
The wave equation is an important second-order linear partial differential equation for the description of waves – as they occur in physics – such as sound waves, light waves and water waves. It arises in fields like acoustics, electromagnetics, and fluid dynamics...

s allow for solutions of convergent waves as well as radiative ones. This arrow has been reversed in carefully worked experiments which have 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
Second law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...

 in usual circumstances.

The causal arrow of time


A cause
Causality
Causality is the relationship between an event and a second event , where the second event is understood as a consequence of the first....

 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
David Hume
David Hume was a Scottish philosopher, historian, economist, and essayist, known especially for his philosophical empiricism and skepticism. He was one of the most important figures in the history of Western philosophy and the Scottish Enlightenment...

 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 partly a phenomenon of the thermodynamic arrow of time, a consequence of the Second law of thermodynamics
Second law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...

. Controlling the future, or causing something to happen, creates correlations between the doer and the effect, and these can only be created as we move forwards in time, not backwards. However, it is also partly a phenomenon of the relation of physical form and functionality to the attributes and functional capacities of physical agents. For example, the causes of the resultant pattern of cup fragments and water spill are easily attributable in terms of the loss of manual grip, gravity, trajectory of the cup and contents, irregularities in its structure, angle of its impact on the floor, etc. However, applying the same event in reverse, it is difficult to explain how the various pieces of the cup come to possess exactly the nature and number of a cup before assembling, how they could assemble (as neither floors nor hands can create china cups unaided), why they should assemble precisely into the shape of a cup and fly up into the human hand (as immobile floors cannot throw and, without contact, the human hand lacks the capacity to move objects unaided) and why the water should position itself entirely within the cup.

The particle physics (weak) arrow of time


Certain subatomic interactions involving the weak nuclear force violate the conservation of both parity
Parity (physics)
In physics, a parity transformation is the flip in the sign of one spatial coordinate. In three dimensions, it is also commonly described by the simultaneous flip in the sign of all three spatial coordinates:...

 and charge conjugation, but only very rarely. An example is the kaon
Kaon
In particle physics, a kaon is any one of a group of four mesons distinguished by the fact that they carry a quantum number called strangeness...

 decay
Particle decay
Particle decay is the spontaneous process of one elementary particle transforming into other elementary particles. During this process, an elementary particle becomes a different particle with less mass and an intermediate particle such as W boson in muon decay. The intermediate particle then...

 http://physicsweb.org/articles/world/11/12/3. According to the CPT Theorem
CPT symmetry
CPT symmetry is a fundamental symmetry of physical laws under transformations that involve the inversions of charge, parity, and time simultaneously.-History:...

, this means they should also be time irreversible, and so establish an arrow of time. Such processes should be responsible for matter creation
Baryogenesis
In physical cosmology, baryogenesis is the generic term for hypothetical physical processes that produced an asymmetry between baryons and antibaryons in the very early universe, resulting in the substantial amounts of residual matter that make up the universe today.Baryogenesis theories employ...

 in the early universe.

This arrow is not linked to any other arrow by any proposed mechanism, and if it would have pointed to the opposite time direction, the only difference would have been that our universe would be made of anti-matter rather than from matter. More accurately, the definitions of matter and anti-matter would just be reversed.

That the combination of parity
Parity (physics)
In physics, a parity transformation is the flip in the sign of one spatial coordinate. In three dimensions, it is also commonly described by the simultaneous flip in the sign of all three spatial coordinates:...

 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.

The quantum arrow of time



According to the Copenhagen interpretation
Copenhagen interpretation
The Copenhagen interpretation is one of the earliest and most commonly taught interpretations of quantum mechanics. It holds that quantum mechanics does not yield a description of an objective reality but deals only with probabilities of observing, or measuring, various aspects of energy quanta,...

 of quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

, quantum evolution is governed by the Schrödinger equation
Schrödinger equation
The Schrödinger equation was formulated in 1926 by Austrian physicist Erwin Schrödinger. Used in physics , it is an equation that describes how the quantum state of a physical system changes in time....

, which is time-symmetric, and by wave function collapse, which is time irreversible. As the mechanism of wave function collapse is philosophically obscure
Interpretation of quantum mechanics
An interpretation of quantum mechanics is a set of statements which attempt to explain how quantum mechanics informs our understanding of nature. Although quantum mechanics has held up to rigorous and thorough experimental testing, many of these experiments are open to different interpretations...

, 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
Loschmidt's paradox
Loschmidt's paradox, also known as the reversibility paradox, is the objection that it should not be possible to deduce an irreversible process from time-symmetric dynamics...

.
According to the modern physical view of wave function collapse, the theory of quantum decoherence
Quantum decoherence
In quantum mechanics, quantum decoherence is the loss of coherence or ordering of the phase angles between the components of a system in a quantum superposition. A consequence of this dephasing leads to classical or probabilistically additive behavior...

, the quantum arrow of time is a consequence of the thermodynamic arrow of time
Entropy (arrow of time)
Entropy is the only quantity in the physical sciences that requires a particular direction for time, sometimes called an arrow of time. As one goes "forward" in time, the second law of thermodynamics says, the entropy of an isolated system will increase...

.

The psychological/perceptual arrow of time



Psychological time is, in part, the cataloguing of ever increasing items of memory from continuous changes in perception. In other words, things we remember make up the past, while the future consists of those events that cannot be remembered. The ancient method of comparing unique events to generalized repeating events such as the apparent movement of the sun, moon, and stars provided a convenient grid work to accomplish this. The consistent increase in memory volume creates a mental arrow of time. Storing a memory, from an information theoretic perspective, requires an increase in entropy, thus the perceptual arrow ultimately follows from the thermodynamic arrow.

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, but, 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 Chinese and the Aymara people both associate "ahead = past" and "behind = future". In Chinese, for instance, the term "the day after tomorrow" literally means "behind day" while "the day before yesterday" is referred to as "front day" and in Hindi (an Indian language), the term used for "tomorrow" and "yesterday" is the same.

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. Hardly anyone tries to change past events. Indeed, in the Rubaiyat
Rubaiyat of Omar Khayyam
The Rubáiyát of Omar Khayyám is the title that Edward FitzGerald gave to his translation of a selection of poems, originally written in Persian and of which there are about a thousand, attributed to Omar Khayyám , a Persian poet, mathematician and astronomer...

 it is written (sic):


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
Omar Khayyám
Omar Khayyám was aPersian polymath: philosopher, mathematician, astronomer and poet. He also wrote treatises on mechanics, geography, mineralogy, music, climatology and theology....

 (translation by Edward Fitzgerald
Edward FitzGerald (poet)
Edward FitzGerald was an English writer, best known as the poet of the first and most famous English translation of The Rubaiyat of Omar Khayyam. The spelling of his name as both FitzGerald and Fitzgerald is seen...

).

See also

  • Anthropic bias
  • Ilya Prigogine
    Ilya Prigogine
    Ilya, Viscount Prigogine was a Russian-born naturalized Belgian physical chemist and Nobel Laureate noted for his work on dissipative structures, complex systems, and irreversibility.-Biography :...

  • Loschmidt's paradox
    Loschmidt's paradox
    Loschmidt's paradox, also known as the reversibility paradox, is the objection that it should not be possible to deduce an irreversible process from time-symmetric dynamics...

  • Maxwell's demon
    Maxwell's demon
    In the philosophy of thermal and statistical physics, Maxwell's demon is a thought experiment created by the Scottish physicist James Clerk Maxwell to "show that the Second Law of Thermodynamics has only a statistical certainty." It demonstrates Maxwell's point by hypothetically describing how to...

  • Philosophy of space and time
    Philosophy of space and time
    Philosophy of space and time is the branch of philosophy concerned with the issues surrounding the ontology, epistemology, and character of space and time. While such ideas have been central to philosophy from its inception, the philosophy of space and time was both an inspiration for and a...

  • Royal Institution Christmas Lectures 1999
    Royal Institution Christmas Lectures
    The Royal Institution Christmas Lectures are a series of lectures on a single topic, which have been held at the Royal Institution in London each year since 1825. The lectures present scientific subjects to a general audience, including young people, in an informative and entertaining manner....

  • Time Reversal Signal Processing
    Time Reversal Signal Processing
    Time Reversal Signal Processing is a technique for focusing waves. A Time Reversal Mirror is a device that can focus waves using the time reversal method. TRMs are also known as time reversal mirror arrays, as they are usually arrays of transducers, but they do not have to be arrays...


Further reading

Translated from the original German by Stephen G. Brush. Originally published 1896/1898. Website Chapter 5. (technical). Section 3.8. Chapter 7. Chapter 27. Website Official website for the book

External links