|MadSci Network: Physics|
The effects of distorted time are only noticable for rather extreme conditions of relative velocity, gravity and the like. However, in the case of objects travelling very fast, where time is actually slowed down, communication becomes more difficult. Specifically, it seems that the other end of the line perceives time more slowly. Paradoxically, both sides will observe this effect. Very fast means that the relative velocity between the objects of interest must be a percentage of the speed of light. Extreme gravity refers to the gravitational fields available at the surface of neutron stars or near the event horizon of a black hole.
A complete answer to your question requires more time and space and talent than I have available here. You might try a book on the topic. I suggest "Understanding Relativity : A Simplified Approach to Einstein's Theories" by Leo Sartori.
Try the links in the MadSci Library for more information on Physics.