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.

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

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