Gourt Home::Gourt :: Arrow of time
- Time's Arrow redirects here. For the novel, see Time's Arrow (novel).
Physical processes at the microscopic level are 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.
Introduction
The symmetry of time can be understood by a simple analogy: if time were perfectly symmetric, then it would be possible to watch a length of film from a movie, and everything that happens in it would make sense whether the film was run backwards or forwards.
For example, a movie of a cup falling off a table would make sense run forwards, but would seem laughable when run backwards. On the other hand, a movie of the planets orbiting the sun would have the orbits following paths that obey the laws of gravity, regardless of which direction of time it was run in. This is because gravity is time-symmetric.
Another example that shows that gravity is time-symmetric is a movie of an object in vertical motion near the moon. If the movie were played in one direction, the object would be moving upward and slowing down. If it were played in the other direction, it would be falling towards the moon and speeding up. At first there might appear to be an asymmetry, as in one direction the object is speeding up while in the other it is slowing down. However, in either case the object is accelerating towards the moon (the object slowing down as it moves away is an acceleration in the opposite direction of travel) and so the gravity remains time symmetric.
As stated above, most physical laws follow this concept, however the arrow of time concept does not.
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, once they have mixed you would not expect the dye and water to separate out again simply by being left to themselves.Now imagine that the experiment is repeated, but this time with a very small container with only a few molecules (perhaps only 10). Given a relatively short period of time, one can imagine that – by chance alone – the molecules would eventually become separated for an instant, with all dye molecules on one side and all water molecules on the other. This is formalized in the fluctuation theorem.
It is not impossible for the molecules in the large container to separate out, just so very unlikely as to never actually happen – even if given the lifetime of the Universe to do so. The liquids start out in a highly-ordered state and their entropy (a word that is sometimes defined as "disorder") increases with time.
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.
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 as time increases; it will not decrease over time. Entropy can be thought of as a measure of disorder, such that the Second Law implies that time is asymmetrical with respect to the amount of order in an isolated system (i.e. as time increases, a system will always become more disordered). This asymmetry can be used empirically to distinguish between future and past. In other words, an isolated system will become less and less ordered towards the future.
While any isolated system becomes more and more disordered with time, correlations are formed between different parts of the system. A simple example is the breaking of a glass: the final state (a broken glass) is less ordered than the initial state (a whole glass), but there are now a correlation between its different parts - the breaking lines of the different parts fit each other. Thus, any isolated system is ordered and its parts uncorrelated in the past, and it is (relatively) disordered and its parts correlated in the future.
The second law does not hold precisely; any system can fluctuate to a state of lower entropy (see the Poincaré recurrence theorem). Rather, the Second Law describes the overall trend of the system to a state of higher entropy.
This arrow of time seems to be highly related to all other arrows of time (usually it is their reason), with the exceptions of the (unrelated) 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 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. Some have argued that this does not actually supply a distinct arrow. If the thermodynamic arrow were reversed then we would regard scattering shards on the floor to be the cause and the plate jumping up into our hands to be the effect. Indeed, according to the Second Law of Thermodynamics, initial conditions are always simpler (more ordered and less self-correlated) than final conditions, and therefore it is easier to view the former as the reason for what happens in between.
The psychological arrow of time is also interconnected with the causal arrow of time, because we remember the past and can affect the future (but not vice versa), and therefore we view the past as the reason for the future.
The weak arrow of time
Certain subatomic interactions involving the weak nuclear force violate the conservation of parity, but only very rarely. 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 parity 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
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 still obscure, it's not known 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 theory of quantum decoherence, and assuming that the wave function collapse is merely apparent, 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
This is the most obvious arrow in human experience: We feel as if we are travelling from the past to the future; we perceive and remember the past and not the future (although sometimes these are treated as two different phenomena). However, because the workings of the mind are so complex and little understood, it is not obvious how the physical arrows of time contribute to this perception. It may be that learning to generate the causes needed to produce desired effects embedded the causal arrow in our perception.
It has also been argued that the arrow of time as we perceive it results from the influence of the second law of thermodynamics on the evolution of the brain, so that the psychological arrow follows from the thermodynamic. To remember something, our memory goes from a disordered state to a more ordered one, or from one ordered state to another. To ensure that the new state is the correct one, energy must be used to perform the work and this increases the disorder in the rest of the universe. There is always a greater increase in disorder than the amount of order gained in our memory, thus the arrow of time in which we remember things is in the same direction as that in which the disorder of the universe increases.
The link between this arrow of time and the thermodynamic arrow of time is best understood if we remember that the Second Law of Thermodynamics dictates that correlations between different parts of a system will be increased towards the future (rather than towards the past). Since memory is correlations between our brain cells (or computer bits) and the outer world, it is obvious why memory should be created as time passes (towards the future) rather than vice versa (towards the past). Additionally, our deeds may affect the future but not the past because affecting the outer world means to create correlations between ourselves (our bodies or brains) and the outer world.
See also
Further reading
- (technical).
- Translated from the original German by Stephen G. Brush. Originally published 1896/1898.
- Section 3.8.
- Chapter 5.
- Chapter 7.
- Chapter 27.
- Website
- Official website for the book
External links
- The Ritz-Einstein Agreement to Disagree Electrodynamic arrow of time, origin of second law of thermodynamics.
Time | Philosophy of thermal and statistical physics | Non-equilibrium thermodynamics
"Arrow of time"