Arrow of time

From Academic Kids

Time flies like an arrow; fruit flies like a banana.Groucho Marx

The arrow of time is a concept used because almost all of the processes of physics at the microscopic level are time symmetric, meaning that the equations used to describe them are the same if the direction of time were reversed, yet when we describe things at the macroscopic level, there is an obvious direction of time.

At the macroscopic level there is the second law of thermodynamics, or law of entropy, which roughly speaking is the principle that the amount of disorder in a system will increase with time. To use a homely example, a plate gains entropy if it breaks. So entropy can be used as an "arrow" to point in the direction time is moving. This is not unique. For example, at the macroscopic level, we see things like friction, viscosity, and dissipation of energy, which produce an arrow of time, while all of these things appear to be absent at the microscopic level.

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The thermodynamic arrow of time

Template:Unsolved It has been argued that the arrow of time as we perceive it – giving a distinct past and future – results from the influence of the second law of thermodynamics on the evolution of the brain. 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.

According to the prevailing scientific Big Bang theory, the Universe was initially very hot with energy distributed uniformly. As the Universe grows its temperature drops, which leaves less energy available to perform useful work in the future than was available in the past. Thus the Universe itself has a well-defined thermodynamic arrow of time.

The electromagnetic arrow of time

The fact that electromagnetic waves are mostly seen diverging rather than converging creates another arrow of time. It has many similarities with the thermodynamic one.

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. The liquids start out in a highly-ordered state and their entropy, or their 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.

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