"How does time stop?"

"I heard that Einstein's Relativity said it is possible to stop time. Is that true and, if it is, how do you do it and what do you experience when time stops?"

The simple answer is, "Yes, it is possible to stop time. All you need to do is travel at light speed."

The practice is, admittedly, a bit more difficult.

Addressing this issue requires a more thorough exposition on Special Relativity, the first of Einstein's two Relativity Theories. (Special - 1905; General - 1916). Special Relativity pertains specifically to light. The fundamental tenet is that light speed is constant in all inertial reference frames, hence the denotation of "c" in reference to light. To phrase this tenet in a more friendly manner, it means that a light beam's speed remains unchanged even if the observer moves relative to it. This consistency is wholly foreign to us macroscopic world dwellers, because an automobile's speed appears to increase if one is moving toward it and seems to decrease if one moves away from it. Light's behavior is different.

We know that an object, or a light beam's, speed measures the distance traversed over time. How can we reconcile this relationship with the fact that a light beam's measured speed remains constant for all observers, moving or stationary? Time dilation affects this reconciliation.

Time dilates on moving vessels: the greater the speed, the greater the time dilation. Only when such velocities* approach light speed do such effects become significant. If, and this one of those extreme IF's, a vessel could attain light speed, time aboard the vessel would cease altogether. Any person on that vessel would experience nothing at all. Though Spock and Kirk are able to trade barbs and witticisms at warp, in the real world, they would experience no time at all. Let's say, to play with this fantasy world a bit, that a vessel moves at light speed from now (2014) to 2214. For us, two hundreds years would elapse. No time would pass at all on the vessel. What would be two centuries on Earth would be instantaneous on the ship.

Extremely strange, but, theoretically true.

Now, we ruin the moment when some pragmatism: accelerating a ship to such a velocity is not possible, at least not with our technology.  The problem is that a vessel's mass also increases with increasing speed. A vessel at light speed would have infinite mass! Special Relativity indicates that a vessel's mass increases, length contracts with increasing velocity. Time dilation is not the only effect.

The fastest human made vessels, the Helios Probes I and II, established heliocentric orbits that were closer to the Sun than Mercury. Consequently, they attained speeds of more than 170,000 mph. Here, we extend as much credit to the Sun as to the engineers, for these impressive speeds. However, even the Helios probes moved at less than 1/3600th light speed: not particularly impressive by Starfleet standards.

Will we ever construct starships capable of light speed? (In so doing, we could send people to remote locations without worrying about them aging to dust or getting on each others' nerves.) We can't today, but who knows what humans will eventually accomplish? We certainly hope so.

*Using the terms 'speed' and 'velocity' interchangeably is not precisely an excommunication offense, but should be avoided. Speed is a scalar quantity: 100 mph or 90 kilometers per second are both speeds: values without direction. Whereas 100 mph east of the police barracks is a  measure of velocity, as it includes a direction. We use them synonymously out of sheer laziness.