If time does not exist, then what of the saying that 'no two objects can occupy the same space at the same time'. The obverse of this is that 'two objects can occupy the same space, but only at different times'. We know what happens if we try to force this state of existence--an explosion! If time does not exist, how can we make sense of this observable fact?
It seems to me that time exists because events do not occur instantaneously. An occurrence of any kind depends on the transfer of energy from one object to another or from one point in space to another. The fact that energy transfer is not instantaneous is not only based on scientific measurement, but also by inference--the universe would not exist if energy transferred instantaneously. All there would have been was a Big Bang, then a Big Snuff.
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