# Time and Symmetry

When people first hear that time is considered to be a fourth "dimension" akin to the three dimensions of space, they often get confused and think that because it is useful to consider time and space together that they're the same. In fact, there are many differences between time and space, and perhaps the most important is that time is not symmetrical and has a very definite directionality. What I mean is this: if you look at a picture it's impossible to know if the image you see is the original or if it's been reversed.

Space is symmetric in that if you consider any of its dimensions in reverse it doesn't affect the rationality of your perceptions. Space appears to be symmetric in every way. A car that gets 30 mpg driving north will get 30 mpg driving south, east, or west. A box two feet long, three feet wide, and four feet tall has the same volume as a box three feet tall, two feet wide, and four feet long.

Time is different in that it is directional, a property commonly referred to as time's arrow. The Second Law of Thermodynamics says that some events are irreversible in that once they have occured the universe cannot be put back to the way it was before. (In fact, almost every event is irreversible.)

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. ...

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.

If you had two complete snapshots of the universe it would be possible to determine which was taken before the other by calculating the amount of entropy in each snapshot; the shot with less entropy was taken first. Thus, time is not symmetric, and traveling forward through time (as we all do) is very different from traveling backward.