Sai -
These are wonderful questions and your own observations are excellent.
I guess the practical reason that we consider time to be an
independent quantity is because our perception is that we have no
control over it. Our understanding of quantities we deal with in
everyday live certainly has this as an implicit assumption. As a simple
example, take velocity... velocity is the change in position over the
change time, with time as the independent variable. If time were
actually a dependent quantity, then velocity could no longer be
described in such a simple fashion.
But yes, we certainly
could describe time as being
dependent. Perhaps you're right and it is just a figment of our
perception. But this would imply that all of the other rules of the
universe are significantly more complex than we currently view them as
being. And since we know of nothing else on which to suggest that time
depends, we follow Occam's Razor, which says that the simplest
explanation must be the true one.
As a more general statement, we base our scientific progress on the
assumption that we can draw conclusions about the world around us
beyond just our perception. This is because we have seen that in the
past, the things that we have observed could be predicted according to
certain rules. Then we use these rules to predict what will happen in
the future. Certainly, we can not be 100% confident that the future
will continue to follow the rules of the past. But in the end, we have
two possibilities: either the future does not obey the rules
established by the past, in which case modeling them would be useless
but not harmful, or the future will continue to obey the rules
established by the past, in which case our assumptions will have
practical benefit.
-Tamara
(published on 10/22/2007)