"Time is what a clock measures." -
I am sure we are all familiar with Einstein's famous definition of time; but what does it mean?
Every clock measures some sort of change, whether it is a clock’s movement(pendulum/subatomic changes) or part of the clock’s environment(sundial).
In an environment that is totally inert - (In which nothing is changing, even at the subatomic level) would any time pass? If nothing is changing, there is nothing for a clock to measure, so any clock would be 'stopped' or 'frozen in time'.
Place a clock in such an environment and time would pass because of the changes taking place within the clock - the clock's 'movement'. It will measure time generated by the changes that are part of the clock.
So is time generated by change?
All changes are governed by scientific laws; therefore time must be generated at the same rate in identical clocks subject to the same environmental conditions, (Einstein's first postulate)
and, based upon the constancy of the speed of light c, (Einstein's second postulate) the time measured for identical changes, in identical conditions, obeying identical scientific laws, must be the same in any inertial frame of reference. So how does a clock moving inertially run slow?
Because of Relativity.
Relativity, the viewing and measuring of mechanical processes in system, K', moving relative to observers in system K.
It is because of the motion of the clock's System, K', relative to the observer's system, K. A clock at rest in its own frame measures proper time when read from its frame, while an observer in another frame relative to which the clock is moving, measures coordinate time for that moving clock.
There are then two measures of the time read on the clock in a system. Proper time measured by the system’s own, local, clock at rest in that system, K', and Coordinate time measured against the local clock in an observer’s system, K, relative to which the system K’ is moving.
The Spacetime, or Invariant, Interval between two events is the same for all observers. It is the proper interval, read objectively by an observer for whom the clock is moving using the 'rods and clocks' of the moving system; or, by using the 'rods and clocks' from the observer's own system, they may read the moving clock subjectively - adding (by vector addition) the transit time of the measured System K', relative to the observer's System K, to give the coordinate time.
Coordinate Time is a Subjective measure made from another system, K, using the clock in system K.
Proper Time is an Objective measure that can be made remotely from anywhere, by any observer, using the rods and clocks of the measured system, K’. An objective measure takes no account of the location, nor the motion, of the observer.
Surely one of the main reasons for Einstein’s Theories of Relativity, was to recognize that measurements are fundamentally Subjective.
Definition of Time
Time is generated by intervals in processes of change.
Time is a measure of the duration of change. Time is generated by any process of change.