Space travel and elapsed time?

I am actually quite knowledgable about astronomy and space, but there's one thing I can't quite wrap my mind around. How is it that if a spacecraft were to move away from the Earth at close to the speed of light to a local star, and then return, the voyage would last only a few years for the astronauts, but several hundred (or thousand) years for inhabitants here on Earth? I just don't get the physics, can anyone explain?
Geez, Ray, get a grip. Just talking theoretical physics here, not practical application. Why? Because I find it interesting.

It's really a result of general relativity. The craft that goes to the star is accelrating and decelerating which causes the clock to slow... Here's a writeup ..

http://en.wikipedia.org/wiki/Twin_paradox

It's because time is relative. There is no constant rate of time passing.

It's not just when you go close to the speed of light. When you are traveling at any speed relative to another object then the time flowing for you slows down compared to the time flowing for the object. It's been measured with atomic clocks on the ground and on a supersonic jet. The atomic clock on the supersonic jet loses a tiny tick compared to the clock on the ground.

Well it is tricky and it took myself several years before I could fully grasp it. Space and time are linked. Think of it like this...

I'm on a boat moving, this boat has a contact speed of 20 knots. If I'm heading north then I'm going north at 20 knots. If I turn the rudder a little and start moving N by NE then I'm still moving north but not as fast because I'm also moving east. So I'm moving north at 15 knots and east by five knots. I turn the rudder a little more then I'm moving NE. I'm still moving north but not as fast because I'm also moving further east. And if I turn it a bit more I'm be moving E by NE, moving 5 knots north and 15 knots east.

Ok if you can grasp that think of this. North would be time, and East would be space. If you are completely stationary you just moving north through time. If I start moving through space I move slower through time, in fact the faster I move through space, the slower I move through time. Space and time are linked up like this. They way you move through one effects the way you move through another. Or rather more simply the faster you move through space the slower you move through time.

Now you wouldn't feel time slowing down rather if you could look out the windows of your ship moving through space then it would look like time outside is hass speed up.

I don't remember the specifics of an experiment that proved this, but here is the meat and potatoes of the experiment. There is this particle in space that will decay in a given amount of time in the atmosphere. From the calculations physicists predicted that you would be able to detect the particle from the top of mount Washington, but but the time it reached sea level it would have decayed. Well they did the experiment on mount Washington and again at sea level and they found the exact same results. Why had the particles survived past their lifetime in the atmosphere. The answer was their speed. The were moving so fast that their clocks were slowed down allowing them to survive to sea level. Had the particles been moving more slowly then they would not have survived to sea level.

Hope this helps.

~D

Part of the special theory of relativity requires that as an observer's speed approaches c the observer's perception and experience of lapsed time will slow down. This was actually tested a few years ago by a satellite bearing an atomic clock paired with an identical clock on the ground, anmd it worked as predicted.
An observer who could travel at exactly c would perceive time as standing still.
Because light travels a lot slower in water (about 130,000 mps) you get the double effect of Cerenkov radiation with subatomic particles with lengthened half lives, and in fact the calculation of half lives has to take into account speed when dealing with particles generated in a nuclear accelerator.

By the same Relativistic "Theory" the mass of the speeding object increases so actual acceleration to near light speed for REAL objects would be theoretically impossible. Thus far the only "objects" to attain light speed are photons. People get too much of their hope from Hollywood make believe and the inane mouthings from speculative theoretical cosmologists who are also paid to tell stories.
Forget light speed. Be real, nobody is going anywhere. Just do the Middle School level math starting with a one-way trip to Proxima Centauri on the fastest probe ever made, Voyager at 70,000 mph. Then crank the speed up x10, but look at what happens to the kinetic energy.
Remote space travel is in the realm of fiction writers and the blithering idiots who believe them.

It follows from the requirement that the speed of light 'c' be the same to all observers regardless of their speed relative to one another. There is an algebraic proof here: http://en.wikipedia.org/wiki/Time_dilation

Many of the other answers are correct. The one that states that an observer's observation of time slows is not correct..he sees the clock moving at what he sees as a normal rate, but if he looks out side at another clock it is slowed down.

I'm responding because your statement about not wrapping your mind around it, is the normal case. We have a hard time understanding these things because, in our world, Newtonian physics works very well. There is no need for understanding of the general or special theories, because, unless you are a nuclear physicist or other similar specialist it just doesn't matter. See if you can find Nigel Carder's (I think) book on relativity, I think the title was Einstein's Universe, or something like that. It's awesome. Or, read anything having to do with physics by Isaac Asimove.

I was going to post a rather short, easy to read writing found at http://360.yahoo.com/noddarc entitled "The Twin Paradox" but it is a few paragraphs too long for comfort to post here. I believe this will explain why physical time is relative to the system it is part of.

It's really a result of general relativity. The craft that goes to the star is accelerating and decelerating which causes the clock to slow... Here's a writeup ..