How Does Gravitational Time Dilation Work?

[Blingles]

I have to learn about general relativity and to understand that, I need to know gravitational time dilation.

I heard that time on Earth and time in space is different by few nanoseconds.
How can time be different? Why does time go slowly in certain gravitational fields?

Also, how can time be infinite in black holes? I was searching for the easiest answer possible online but I can't find anything, so I decided to post here.

I'm not advanced, so I would appreciate the easiest answers that I can understand.

 

[twofish-quant]

Why does time go slowly in certain gravitational fields?

One way of thinking about it is that being in a graviational field is the same thing as accelerating and if you are accelerating it causes some time dilation.

Also, how can time be infinite in black holes? I was searching for the easiest answer possible online but I can't find anything, so I decided to post here.

Suppose you have a flashing light that goes off at one pulse per second. You have a friend that is far away, and he will see the flashing lights arrive at one pulse per second.

Now let's do this experiment on earth. You have your flashing light going off at one pulse per second, but your friend that is far away will see the pulses going at a little more than one pulse per second. It's a few microseconds, but it is something that you can actually measure with GPS satellites.

Now let's go into the black hole. As you get nearer to the event horizon, your friend will see the pulses flash at slower and slower speed. Once you cross the event horizon, your friend will no longer see the pulses at all. You could sort of say that time is slowing down for you. However, even if as you fall into the black hole, you'll see your flashing light flash at one pulse per second, and you won't notice anything odd.

 

[Entropee]

Hypothetically speaking, someone could be standing on star X looking at star Y while the person standing on star Y is looking at star X and both people could time the life of each others stars with a stopwatch. Maybe star X is much more massive, so it will die faster, but it also will dilate time and cause the person standing on it to perceive time slower. It is then possible for both people to claim that each others stars lived for the same amount of time, while a third observer can exclaim that one star died much faster than the other. (sorry that was just an example not an explanation)

Also twofish I would greatly appreciate any help coming up with a mathematical example of this, I am having trouble calculating time dilation.

 

[Drakkith]

The exact WHY of your question isn't explainable without knowing some things about Spacetime and such, but we can explain WHAT it is easily.

Put simply, time WILL be slower for an observer inside a greater gravitational field compared to an observer in a lesser gravitational field. (All gravitational fields, not just certain ones) This means that if I am in space in orbit around the earth, then my clock will be ticking faster to you than your own clock is down on the ground. This is only talking about Gravitational Time Dilation, and not dilation due to velocity. In reality it is the sum of both the satellites speed and the effect of gravity that make the actual amount of time dilation what it is.

Now, the key here is that to the observer in orbit (Me), I will not experience ANY difference in time for myself. My clock still ticks exactly as it should to me. From my point of view it is YOUR clock that has been altered and is now running SLOWER than mine is.

If you take that situation and apply it to a Black Hole, then you will see that in any frame that is falling into a black hole an observer in that frame will not have any change in their perception of time. They keep falling into the black hole at an increasing speed.

However, if you were watching me fall towards a Black Hole, then to you it would look like time got slower and slower for me as I got closer and closer to it.

The key to all this, in my opinion, is to understand that if you look at ANY individual frame of reference, time for that frame is always normal. It is only when you compare one frame to another frame that the effect happens. This is what we mean when we say that time is Relative.