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Arrow of time

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For other uses, see Time's arrow (disambiguation).
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).

In the natural sciences, arrow of time, or time’s arrow, is a term coined in 1927 by British astronomer Arthur Eddington to distinguish a direction of time on a four-dimensional relativistic map ("a solid block of paper") of the world,[1] which, according to Eddington, can be determined by a study of organizations of atoms, molecules, and bodies.

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. 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:

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.

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.

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.[2]

An obvious objection to this assertion is gravity: after all, things fall down, not up. Consider first, some bodies interacting in space. Perhaps one asteroid approaches another, loops part-way around it, and slingshots off in another direction. In this case the forward-recording and the backward-recording look equally realistic.

One could film a tossed ball as it moves up, slows gradually to a stop, and then falls back down into the catcher's hand. This is another case where the forward- and backward- recordings clearly look equally realistic. One might expect it to take the same amount of time for the ball to go up in reverse as it did for it to go up going forward, but as it turns out the film would show it taking slightly longer going forward than going backward. This is not because gravity is asymmetric but because when the ball is going forward in time it loses energy to air molecules it bumps into, but when the ball is going backwards in time the air molecules are bumping into it, giving it energy. Note that this inequality doesn't contradict the definition of time reversal because forward-up is a different leg of the trip from backward-up. So the system is strictly T-symmetrical, but we recognize that while going "forward," useful kinetic energy is dissipated into the environment: entropy is increasing. Entropy, which is a purely statistical observation, may be one of the few processes in physics that is not time-reversible. According to the statistical notion of increasing entropy, the flow of time is identified with the flow of energy that is decreasing the free energy.[3]

This kind of thinking turns out to be critical to understanding the final case of this example. What if you record somebody simply dropping a ball? It falls for a meter and stops. Certainly someone watching this recording in reverse would notice an unrealistic discrepancy: a ball falling upward! But imagine the forward-recording carefully. When the ball lands, its kinetic energy is dispersed into sound, shaking the ground, and some heat. That is what allows the ball to be moving one moment and still the next. Now think of the recording in reverse. Those sound waves, those ground vibrations, and that heat, are all rushing back into the ball, imparting just enough energy to propel it upward into the person's hand. With this understanding, the backward recording appears perfectly realistic. The only way that someone can tell the video is in reverse is by making the statistical prediction that it's unlikely that these forces could incidentally interact to propel the ball upward into your waiting hand.

See the main article for more on entropy, including another example.

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 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 and past though measuring entropy does not accurately measure time. Also in an open system entropy can locally decrease with time: living systems decrease their entropy 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."[4] 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

See also: Entropy and Entropy (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. 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. This arrow has been reversed in carefully worked experiments which have created convergent waves,[5] 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[citation needed], making the latter contradictory to the Second Law of Thermodynamics in usual circumstances.

The 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 partly a phenomenon of the thermodynamic arrow of time, a consequence of the Second law of thermodynamics.[6] Controlling the future, or causing something to happen, creates correlations between the doer and the effect,[7] 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 is 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 as, without contact, the human hand lacks the capacity to move solid 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 and charge conjugation, but only very rarely. An example is the kaon decay [1]. 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.

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.

The quantum arrow of time

Unsolved problem in physics:
What links 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 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.

The psychological/perceptual arrow of time

Main article: Sense 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".[8] 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".[citation needed]

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.
- Omar Khayyám (Fitzgerald translation)

See also

References

  1. ^ Weinert, Friedel (2005). The scientist as philosopher: philosophical consequences of great scientific discoveries. Springer. p. 143. ISBN 3540213740., 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". Proc. R. Soc. A. 465: 1173–1198. doi:10.1098/rspa.2008.0494.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  4. ^ A.B. Pippard, Elements of Chemical Thermodynamics for Advanced Students of Physics (1966), p.100.
  5. ^ http://web.archive.org/web/*/http://www4.ncsu.edu/~fouque/fink.pdf
  6. ^ Physical Origins of Time Asymmetry, chapter 6
  7. ^ Physical Origins of Time Asymmetry, pp. 109-111.
  8. ^ For Andes tribe, it's back to the future — accessed 2006-09-26

Further reading

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