Arrow of time

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 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.

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:

It is vividly recognized by consciousness.
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.

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.

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.

An example of 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. With no barrier between the two liquids, the random jostling of their molecules will result in them becoming more mixed as time passes. 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. However, for a large numbers of molecules it is so unlikely that one would have to wait, on average, 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.

Arrows

The thermodynamic 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 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.

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). 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

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, 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 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. 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. 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.

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

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. 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 (also see Entropy (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 unknown (Future) to the known (Past). 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).^[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.
- 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. 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).

References

^ For Andes tribe, it's back to the future — accessed 2006-09-26

External links

The Ritz-Einstein Agreement to Disagree Electrodynamic arrow of time, origin of second law of thermodynamics.

[1] For Andes tribe, it's back to the future — accessed 2006-09-26

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