Time does move slower in space but only to the outside observer. This is due to the effects of Time Dilation (see http://nishlaverz.hubpages.com/hub/Time-Dilation.)
However the idea of time running slower in space is contradicted by gravitational time dilation. This shows that time runs slower the closer to a gravity source you are. So a clock on the ground should run slower than on suspended in the air. See link above.
It is a confusing subject as you have to look at all the different forms of time dilation and factor in all the objects and velocities travelled to get the answer.