Their “false” idea of time

Aristotle believed in a preferred state of rest, which any body would take up if it were not driven by some force or impulse. but it follows from newton's laws that there is no unique standard of rest. All netwon's experiment would still work on a train moving on the earth. So there is no way to tell whether it is the train or the earth that is moving. 

The lack of an absolute standard of rest meant that one could not determine whether two events that took place at different times occured in the same position in space. 

Both Aristotle and Newton believed in absolute time. Time was completely separate from and independent of space. 

We had to change our ideas of space and time. Although our appearently common sense notions work well when dealing with thinks like apples or planets that travel comparatively slowly, they don't work at all for things moving at or near the speed of light.