wespe said:
What is your exact definition of time?
I don't have an exact definition of time. However, the universe is composed of two fundamental entities, time and space. The Big Bang caused time and space to interact, in the form of space-time. All of time is bound up in space, and all of space is bound up in time, as space-time.
Clocks can measure time. However, such usage of time is quite limiting, as each unit of space, such as the observer of a clock, relates to his own time in a unique way. His space is bound up with his time, not with the clock's time.
To say that time is what a clock measures is to ignore the significance of space-time.
wespe said:
ok let's think of a light clock: light continually bouncing back and forth between two parallel mirrors. If I am stationary wrt the mirrors, what would be the error in the measurement of this clock?
You ask about the error in the measurement of the clock. I ask about the value of it.
As far as clocks are concerned, yours is an excellent example. Let us consider two observers, you and me. You body is in motion through space. Consider that chemical processes are going on within your body, metabolism, etc. My body is in motion through space, in the same way. They are not moving through space at the same rate of time. How is it relevant that we can use some objective third object to measure time? My rate of motion through time is different from your motion through time, as my body interacts with space in a manner different from yours. Using a light clock, or a mechanical clock, or watching the sun rise and set is very useful to create an objective time for us to share. However, how can you consider it completely applicable to either of us, let alone to both of us? Where is the effect of the interaction of space-time? If you are searching for a close approximation, as close as is possible given that you must use a clock, then I accept your example as close, forgiving the fact that you must use a clock.
If you use a clock as an objective way to relate your motion through space-time with mine, then you are ignoring the fact that each object has a unique relationship to space-time.
How can you compare two unique objects in space-time by relating them to a third, irrelevant object in space-time? What is the value of your comparsion. It does have value, I admit. Do you recognize its limitation?