There seem to be a bunch of physics questions about sooo… bandwagon, me, jump.
Can someone, in layman language :), explain to me why time moves slower for objects closer to massive objects? Is it a gravitational effect?
To give the extremely simplified version, any massive object will distort time and space around itself. Sort of like a dimple. Gravity is just an “observed” effect. You get weird things happening. Objects orbit around it - from their point of view, they are travelling in a straight line; that straight line is in a distorted space, so from our perspective it is going around and around. Time gets distorted too - frame dragging. I’m not an astrophysicist, so my understanding is primitive (to say the least).
Hoo man, am I jumping off the deep end here, simply because I am a complete layman. But I thought it would be fun to relate an analogy that made it much easier for me to understand General Relativaty.
And remember, IANAP. So… salt, grain, take.
analogy
Think of all objects traveling at the speed of light through spacetime. When an object is at rest (not undergoing accelerated motion) it will be traveling at 100% the SOL through time. As soon as the object starts undergoing accelerated motion, it has to trade some of its speed through spacetime in order to travel through space, resulting in the object, say, going 5% the SOL in space and now 95% the SOL through time. In essence, it’s a trade off. The faster you move through space, the slower you move through time in order to compensate. Now, you ask: What does this have to do with gravity? I’ll tell you. Gravity happens to have the identical effect on an object that accelerated motion does, and vice versa.
/analogy
I hope this comes close to forming an answer in your mind. I think the Key will be to understand how accelerated motion and gravity are similar. Now that i’ve made myself vulnerable to higher intellect of those that understand this stuff better, I’ll duck out.
I’m waiting to see if E = mc[sup]2[/sup] comes up with a good answer to this one. 
Very siplified answer.
Think of space as a piece of rubber with grid marks. A dense object will distort space (think bowling ball on trampoline) around it. As the grid stretches, the distance between gridlines grows, taking longer to traverse, sense of time slowing down.
You’re actually pretty close, but you’re leaving out the one thing that (inexplicably) everyone seems to leave out: what do “time” and “space” mean. As someone (I think Minkowski) said: time and space will pass away and only a mixture of the two will survive.
To be more explicit, the tradeoff you’re describing really has nothing to do with acceleration, but just motion, and is a special-relativistic effect. Remember that splitting spacetime into “space” and “time” is only relevant to a given observer. When an object is at rest relative to a given observer, the 4-velocity is 100% in the “time” direction of that observer.
As for the OP: the notion of stretching out spacetime coordinates is pretty good. Again, though, it must be emphasized that this effect is only sensibly stated relative to a given observer “far from the gravitational source”.
I do not get the “far from the gravitation” part. Scientists have put super accurate clocks at the bottom and top of a water tower and measured the difference in the passing of time between the two clocks (the clock at the top of the tower is further from the gravitational source…earth…so runs at a different speed). Granted the effect at the water tower is very, very small but it is there nontheless.
The upper clock is far(ther) from the source. Remember, physicists play fast and loose with “far”. For this application, that’s far enough. For others, and to prove the statement in general, they generally to assume the canonical observer be far enough from the source that spacetime is pretty much flat around it.
sooo if I’m getting this right, the clock at the top moves faster because the spacetime it inhabits is less warped then the spacetime at the bottom?
It’s a bit of an oversimplification, but yes. Remember that technically you can only compare clocks when they’re at the same point in spacetime. The clocks start at the same point, are moved to two places with different spacetime curvature, are left there for a while and are moved back to the same point. Each one has been ticking along at the exact same rate relative to itself, but the two paths between the start and end points in spacetime have different lengths, largely determined by the curvature of spacetime where they sat in the interim.
Yup, that’s it. Some people might put it as the clock on the bottom moves slower because it’s spacetime is more warped, but same thing.
Thank you to all of you! I actually got it; it’s been bothering me for some time. Much appreciated - Mathochist’s last post makes perfect sense to me.
Time is an incurable rubbernecker.
/me blinks.
Wow. that’s a first.
A couple of points:
Frame dragging is a phenomena associated with rotating massive objects. For the most part, its influence is subtle, though the implications are startling; it is actually possible to travel through “dragged space” faster than light moving through unwarped space. (Essentially, you add the velocity of space to the velocity of your moving object.) This isn’t quite all that useful when you consider that, between the enormous mass required, the rotational velocity it must have, and the “shearing” action it has on the surrounding space, you’d need an object several magnitudes larger than the galaxy in order to made the gravitational gradients moderate enough to allow a person to fly a path about the object without being rendered to component atoms, but it’s a neat mathematical trick. You can also create closed timelike paths through space, theoretically allowing you to travel “backward” in time (to a previous point in space-time), although this creates an information paradox that is irresolvable, and although it is an unsupported hypothesis, most relativity physicists seem to believe that some kind of “Law of Cosmic Censorship” prevents such paths from actually occuring lest they undermine the structure of causality. (Larry Niven has an amusing story about this, in which anyone trying to develop a time machine is befallen by some kind of accident, though I can’t remember the title offhand.)
Also, talking of object in an orbit moving in a “straight line” is a bit misleading; the object does experience outside forces and undergoes acceleration and change of velocity, even if it maintains a constant speed. It is better to say that the object acts in such a way as to maintain a equilibrium of forces.
Stranger
If it’s feeling outside forces and accelerating, then it’s not really in orbit. An object in orbit is one which is only subject to gravity. But gravity is not really a “force” like the others; it’s a distortion of space. An object affected only by gravity will follow a straight-line path, or rather the closest thing to a straight line one can have in distorted space.
Yes. We’re definitely talking GR here, and so talking about “forces” is what’s misleading here. The objects that aren’t travelling in straight lines are those sitting on the surface of the Earth, which pushes them off their straight-line paths.
The way I learned this concept was like this.
The speed of light is CONSTANT. It is the same no matter what.
How does one measure the speed of light. Basically with a clock and a ruler.
Now when the Apollo spacecraft got far away from earth and got going really fast, the pysical size of it changed, slightly smaller. Now if you think of the apollo spacecraft as a ruler than when you measure the speed of light you should get a different reading. The ruler is different. But you don’t get a different reading because the speed of light is CONSTANT. So then TIME must also change. It changes when you go really fast.
So if the speed of light is constant, how fast is it going if it can’t escape a black hole? It is still going the same speed because the speed of light is CONSTANT. If the light never get to 186,000 miles (roughly) away from the black hole, then the second hand never gets to one.
No, no, no, a thousand times no!
This is the biggest mistake that everyone keeps making in relativity: that something actually changes. All that changes about the object is it’s appearance.
Look, if I look at you head on and then turn and look at you from the side, you look a lot different. Have you changed? No. It’s just my perspective. An object in constant motion (with respect to me) is just like an object at rest (w.r.t. me), but “rotated” in spacetime. Nothing about it has actually changed.
A nonrotating object in free fall (or a person within) doesn’t “feel” a force, but it is subject to the influence of gravity, and although an internal observer can’t measure acceleration, from an “objective” viewpoint (yeah, I know, no observer is objective) the object in orbit is certainly accelerating as it changes position during its orbit. Of course, from a special relativistic point of view, forces due to gravity are abstractions of distorted space (and assuming someone puts together a valid GU theory someday, we’ll say the same about the other forces as well) but from a traditional Newtonian view it is under acceleration.
As for the semantics of what constitutes a “straight line” in distorted space, I’m just kind of troubled by the unqualified nomenclature; the path is “straight” in that it represents a net balance of forces, or that the curvature of space and the velocity of the object in orbit maintain a constant relationship, but it isn’t geometrically straight, even from the point of view of the object, as it sees space rotate about it. The use of the term “straight” here just strikes me as ambiguous and subject to interpretation; I’d rather state it in terms of a path that maintains a constant sum of kinetic and potential energy, or speaks to the relationship between curvature of space and the velocity of the object.
Stranger