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 is the only quantity in the physical sciences that "picks" a particular direction for time sometimes called an Arrow of time.

In the natural sciences, arrow of time, or time’s arrow, is a term coined in 1927 by British astronomer Arthur Eddington used to distinguish a direction of time on a four-dimensional relativistic map of the world; which, according to Eddington, can be determined by a study of organizations of atoms, molecules, and bodies. In Science, the term natural science refers to a naturalistic approach to the study of the Universe, which is understood as obeying rules or law of Sir Arthur Stanley Eddington, OM (28 December 1882 – 22 November 1944 was an English Astrophysicist of the early 20th century

Physical processes at the microscopic level are believed to be either entirely or mostly time symmetric, meaning that the theoretical statements that describe them remain true if the direction of time is reversed; yet when we describe things at the macroscopic level it often appears that this is not the case: there is an obvious direction (or flow) of time. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. Microscopic is a term 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 T Symmetry is the symmetry of physical laws under a Time reversal transformation &mdash T t \mapsto -t Macroscopic is commonly used to describe physical objects that are measurable and observable by the Naked eye. For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of An arrow of time is anything that exhibits such time-asymmetry.

History of term

From the 1928 book The Nature of the Physical World, which helped to popularize the term, Eddington states:

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.

Here, according to Eddington, the arrow indicates the direction of progressive increase of the random element. Following a lengthy argument into the nature of thermodynamics, Eddington concludes that in so far as physics is concerned time's arrow is a property of entropy alone. In Physics, thermodynamics (from the Greek θερμη therme meaning " Heat " and δυναμις dynamis meaning " In Thermodynamics (a branch of Physics) entropy, symbolized by S, is a measure of the unavailability of a system ’s Energy

Overview

The symmetry of time (T-symmetry) can be understood by a simple analogy: if time were perfectly symmetric then it would be possible to watch a movie taken of real events and everything that happens in the movie would seem realistic whether it was played forwards or backwards. T Symmetry is the symmetry of physical laws under a Time reversal transformation &mdash T t \mapsto -t

For example, a movie showing a cup falling off a table seems realistic when run forwards, but seems unrealistic if run backwards. On the other hand, a movie of the planets orbiting the sun would look equally realistic run forwards or backwards; either way the orbital motions would appear to conform to physical laws. The Solar System consists of the Sun and those celestial objects bound to it by Gravity. The Sun (Sol is the Star at the center of the Solar System.

An example of irreversibility

Main article: irreversibility

Consider the situation in which a large container is filled with two separated liquids, for example a dye on one side and water on the other. In science a Process that is not reversible is called irreversible. Liquid is one of the principal States of matter. A liquid is a Fluid that has the particles loose and can freely form a distinct surface at the boundaries of With no barrier between the two liquids, the random jostling of their molecules will result in them becoming more mixed as time passes. In Chemistry, a molecule is defined as a sufficiently stable electrically neutral group of at least two Atoms in a definite arrangement held together by However, if the dye and water are mixed then one does not expect them to separate out again when left to themselves. A movie of the mixing would seem realistic when played forwards, but unrealistic when played backwards.

If the large container is observed early on in the mixing process, it might be found to be only partially mixed. It would be reasonable to conclude that, without outside intervention, the liquid reached this state because it was more ordered in the past, when there was greater separation, and will be more disordered, or mixed, in the future.

Now imagine that the experiment is repeated, this time with only a few molecules, perhaps ten, in a very small container. One can easily imagine that by watching the random jostling of the molecules it might occur — by chance alone — that the molecules became neatly segregated, with all dye molecules on one side and all water molecules on the other. That this can be expected to occur from time to time can be concluded from the fluctuation theorem; thus it is not impossible for the molecules to segregate themselves. The fluctuation theorem (FT is a theorem from Statistical mechanics dealing with the relative probability that the Entropy of a system which is currently away from However, for a large numbers of molecules it is so unlikely that one would have to wait, on average, many times longer than the age of the universe for it to occur. Thus a movie that showed a large number of molecules segregating themselves as described above would appear unrealistic and one would be inclined to say that the movie was being played in reverse.

See also another example. Entropy is the only quantity in the physical sciences that "picks" a particular direction for time sometimes called an Arrow of time.

Arrows

The thermodynamic arrow of time

Main article: Entropy (arrow of time)

The thermodynamic arrow of time is provided by the Second Law of Thermodynamics, which says that in an isolated system, entropy will only increase with time; it will not decrease with time. Entropy is the only quantity in the physical sciences that "picks" a particular direction for time sometimes called an Arrow of time. The second law of Thermodynamics is an expression of the universal law of increasing Entropy, stating that the entropy of an Isolated system which In the Natural sciences an isolated system, as contrasted with a open system, is a Physical system that does not interact with its Surroundings In Thermodynamics (a branch of Physics) entropy, symbolized by S, is a measure of the unavailability of a system ’s Energy Entropy can be thought of as a measure of disorder; thus the Second Law implies that time is asymmetrical with respect to the amount of order in an isolated system: as time increases, a system will always become more disordered. This asymmetry can be used empirically to distinguish between future and past. A central concept in Science and the Scientific method is that all Evidence must be empirical, or empirically based that is dependent on evidence The future is commonly understood to contain all events that have yet to occur PAST (short for Polska Akcyjna Spółka Telefoniczna, Polish Telephone Joint-stock Company) was a Polish telephone operator in the period between World War I

Since the Second Law is statistical, it does not hold with strict universality: any system can fluctuate to a state of lower entropy (see the Poincaré recurrence theorem). In Mathematics, the Poincaré recurrence theorem states that certain systems will after a sufficiently long time return to a state very close to the initial state However, the Second Law 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

See also: Entropy and Entropy (arrow of time)

The cosmological arrow of time points in the direction of the universe's expansion. In Thermodynamics (a branch of Physics) entropy, symbolized by S, is a measure of the unavailability of a system ’s Energy Entropy is the only quantity in the physical sciences that "picks" a particular direction for time sometimes called an Arrow of time. 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. The heat death is a possible final state of the universe, in which it has " run down " to a state of no Thermodynamic free energy to sustain 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. In Physics and Cosmology, the anthropic principle states that humans should take into account the constraints that human existence imposes on the kind of theoretical Gravitation is a natural Phenomenon by which objects with Mass attract one another 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

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. The second law of Thermodynamics is an expression of the universal law of increasing Entropy, stating that the entropy of an Isolated system which In Mathematics, in the field of Differential equations an initial value problem is an Ordinary differential equation together with specified value called Therefore they ultimately result from the cosmological set-up.

The 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 allow for solutions of convergent waves as well as radiative ones. Radio waves are electromagnetic waves occurring on the Radio frequency portion of the Electromagnetic spectrum. Sound' is Vibration transmitted through a Solid, Liquid, or Gas; particularly sound means those vibrations composed of Frequencies The wave equation is an important second-order linear Partial differential equation that describes the propagation of a variety of Waves such as Sound waves 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 in usual circumstances. The second law of Thermodynamics is an expression of the universal law of increasing Entropy, stating that the entropy of an Isolated system which

The causal arrow of time

Causes are ordinarily thought to precede effects. The future can be controlled, but not the past.

A problem with using causality as an arrow of time is that, as David Hume pointed out, the causal relation per se cannot be perceived; one only perceives sequences of events. David Hume (26 April 1711 25 August 1776 Scottish Philosopher, Economist, and Historian is an important figure in Western philosophy Furthermore it is surprisingly difficult to provide a clear explanation of what the terms "cause" and "effect" really mean. It does seem evident that dropping the plate is the cause, the plate shattering is the effect.

Physically speaking, this is another manifestation of the thermodynamic arrow of time, and is a consequence of the Second law of thermodynamics. The second law of Thermodynamics is an expression of the universal law of increasing Entropy, stating that the entropy of an Isolated system which 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. Entropy is the only quantity in the physical sciences that "picks" a particular direction for time sometimes called an Arrow of time.

The 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. The weak interaction (often called the weak force or sometimes the weak nuclear force) is one of the four Fundamental interactions of nature In Physics, a parity transformation (also called parity inversion) is the flip in the sign of one Spatial Coordinate. In Physics, C-symmetry means the symmetry of physical laws under a charge -conjugation transformation. An example is the kaon decay [1]. In Particle physics, a kaon (/ˈkeɪɒn/ also called K-meson and denoted) is any one of a group of four Mesons distinguished by the fact that they According to the CPT Theorem, this means they should also be time irreversible, and so establish an arrow of time. CPT symmetry is a fundamental symmetry of Physical laws under transformations that involve the inversions of charge, parity and Such processes should be responsible for matter creation in the early universe. In Physical cosmology, baryogenesis is the generic term for hypothetical physical processes that produced an asymmetry between Baryons and anti-baryons in

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 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. In Physics, a parity transformation (also called parity inversion) is the flip in the sign of one Spatial Coordinate. In Physics, C-symmetry means the symmetry of physical laws under a charge -conjugation transformation.

The quantum arrow of time

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. The Copenhagen interpretation is an interpretation of Quantum mechanics. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons In Physics, especially Quantum mechanics, the Schrödinger equation is an equation that describes how the Quantum state of a Physical system In certain interpretations of quantum mechanics, wave function collapse is one of two processes by which Quantum systems apparently evolve according to the laws of As the mechanism of wave function collapse is philosophically obscure, it is not completely clear how this arrow links to the others. An interpretation of quantum mechanics is a statement which attempts to explain how Quantum mechanics informs our Understanding of Nature. While at the microscopic level, collapse seems to show no favor to increasing or decreasing entropy, some believe there is a bias which shows up on macroscopic scales as the thermodynamic arrow. According to the modern 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. In certain interpretations of quantum mechanics, wave function collapse is one of two processes by which Quantum systems apparently evolve according to the laws of In Quantum mechanics, quantum decoherence is the mechanism by which quantum systems interact with their environments to exhibit probabilistically additive behavior Entropy is the only quantity in the physical sciences that "picks" a particular direction for time sometimes called an Arrow of time.

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 one mental arrow of time. Another 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). The Aymara are a native Ethnic group in the Andes and Altiplano regions of South America; about 1 ^[1] 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".

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 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. Rubaiyat of Omar Khayyam ( Persian: رباعیات عمر خیام The Rubáiyát ( Arabic: رباعیات is a collection of Poems
- Omar Khayyám (Fitzgerald translation)

The psychological arrow of time is thought to be reducible to the thermodynamic arrow: it has deep connections with Maxwell's demon and the physics of information; In fact, it is easy to understand its link to the Second Law of Thermodynamics if we view memory as correlation between brain cells (or computer bits) and the outer world. For the Thoroughbred racehorse see Omar Khayyam (horse Ghiyās od-Dīn Abol-Fath Omār ibn Ebrāhīm Khayyām Neyshābūri (غیاث الدین Edward Marlborough FitzGerald ( 31 March 1809 &ndash 14 June 1883) was an English Writer, best known as the Poet Entropy is the only quantity in the physical sciences that "picks" a particular direction for time sometimes called an Arrow of time. The second law of Thermodynamics is an expression of the universal law of increasing Entropy, stating that the entropy of an Isolated system which Since the Second Law of Thermodynamics is equivalent to the growth with time of such correlations, then it states that memory will be created as we move towards the future (rather than towards the past). Entropy is the only quantity in the physical sciences that "picks" a particular direction for time sometimes called an Arrow of time.

See also

• Anthropic bias
• Loschmidt's paradox
• Maxwell's demon
• T-symmetry
• Royal Institution Christmas Lectures 1999

References

Further reading

• Halliwell, J. In Physics and Cosmology, the anthropic principle states that humans should take into account the constraints that human existence imposes on the kind of theoretical 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 was an 1867 Thought experiment by the Scottish Physicist James Clerk Maxwell, meant to raise questions about the possibility T Symmetry is the symmetry of physical laws under a Time reversal transformation &mdash T t \mapsto -t The Royal Institution Christmas Lectures have been held in London annually since 1825 Year 2006 ( MMVI) was a Common year starting on Sunday of the Gregorian calendar. Events 46 BC - Julius Caesar dedicates a J. et. al. (1994). Physical Origins of Time Asymmetry. Cambridge. ISBN 0-521-56837-4.   (technical).
• Boltzmann, Ludwig (1964). Ludwig Eduard Boltzmann ( February 20, 1844 &ndash September 5, 1906) was an Austrian Physicist famous for his founding Lectures On Gas Theory. University Of California Press.   Translated from the original German by Stephen G. Brush. Originally published 1896/1898.
• Peierls, R (1979). Surprises in Theoretical Physics. Princeton.   Section 3. 8.
• Feynman, Richard (1965). Richard Phillips Feynman (ˈfaɪnmən May 11 1918 – February 15 1988 was an American Physicist known for the Path integral formulation of quantum The Character of Physical Law. BBC Publications.   Chapter 5.
• Penrose, Roger (1989). Sir Roger Penrose, PhD, OM, FRS (born 8 August 1931) is an English Mathematical physicist and Emeritus The Emperor's New Mind. Oxford University Press. ISBN 0-19-851973-7.   Chapter 7.
• Penrose, Roger (2004). Sir Roger Penrose, PhD, OM, FRS (born 8 August 1931) is an English Mathematical physicist and Emeritus The Road to Reality. Jonathan Cape. ISBN 0-224-04447-8.   Chapter 27.
• Price, Huw (1996). Time's Arrow and Archimedes' Point. ISBN 0-19-510095-6.   Website
• Zeh, H. D (2001). The Physical Basis of The Direction of Time. ISBN 3-540-42081-9.   Official website for the book

External links

• The Ritz-Einstein Agreement to Disagree Electrodynamic arrow of time, origin of second law of thermodynamics.
• The Thermodynamic Arrow: Puzzles and Pseudo-Puzzles Huw Price on Time's Arrow
• The Arrow of Time