Does time actually slow down in space?

The answer

Yes, time dilation is a real and measured phenomenon. Einstein's special relativity shows that time passes more slowly for objects moving at high speeds relative to a stationary observer, while general relativity shows that time passes more slowly in stronger gravitational fields. GPS satellites, orbiting at high speed but in weaker gravity than Earth's surface, experience both effects. Without correcting for time dilation (about 38 microseconds per day), GPS positions would drift by roughly 10 kilometers daily. Astronaut Scott Kelly, after a year on the ISS, aged about 5 milliseconds less than his twin brother Mark on Earth.