Time is a construct we invented to describe things. Most basically we use it to describe our sequence of experiences and memories. We feel hot and cold, but we needed to quantify hot and cold and give them operational definitions in order make definite predictions about them. So we invented temperature and thermometers. For mechanics we needed a quantified, operational definition of duration - so we invented time and clocks.

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Besides psychological time,there are at least three different possible definitions of time used in physics What they all have in common is that they assign numbers to different physical states, i.e. they index different states into some order so that this sequence of states can be compared to that sequence of states. It's this last function that makes time important in dynamical equations. We could always rewrite the equations in purely relational terms. So if we had three particles with positions X(t), Y(t), and Z(t), we could write equations Y(X) and Z(X). But the equations could be very messy if X(t) were a complicated motion. On the other hand if X(t) is a very simple motion, X(t)=t, i.e. X is a clock, then the equations are simple. In fact that's one way to define time: A variable X which can be used to parameterize equations into their simplest form. However, relativity complicates this picture a little. Clocks measure proper time along their paths, not coordinate time. But to write equations about interacting things moving relative to each other it is more convenient to define coordinate time. This is usually time as measured by a clock in some special motion, but not necessarily. All it has to be is a way of labelling space-like foliations in 3+1 space. This is a global "time" but it has no physical significance. In contrast, Zeh refers to the different times measured by clocks along world lines between foliations, as "many-fingered time". Consider the spatial analog. We could locate every city on Earth by giving its distance from every other city, i.e. the airlines miles between them. This would give an accurate picture of the globe, but a very complicated one since, for N cities we would have to give N! numbers. Instead we invented latitude and longitude, so we only have to give 2N numbers and we can figure out the distances. Coordinate time serves the same purpose in labeling events. Finally, these clock times are reversible if the underlying dynamics are reversible, as they are in most intepretations of fundamental physics. Then the arrow of time is determined by statistical properties of complex systems which are summarized by the increase of entropy. Brent Meeker Time is an illusion, lunchtime doubly so. --- Douglas Adams