How does time dilation in relativity work?

[Kabu]

Wanted, Time Equation And...

Well, at the first excuse my poor english...
I would somebody to give me the time equation in the relativity.
Ie, the equatio which we can find how the timme in two objects is when both of them moving in different velocity...

Once more: There where an article written in my college magazine that when the one object moves faster than another one ie:then first one tiume is slower!

According to my "core" knowledge, I think it should be "slower"
We are talking here as if we are looking at the time in the both objects from outside of the system which they are in.

So, can anybody explain this to me,please?
Thx in advance.

 

[STAii]

Well, you can't say "from the outside".
In physics, we say that every observer is in a frame of refference.
Now in this frame of refference you measure time in a certain way.
If there is a moving object in your frame of refference (moving at any speed), the way you measure time will not change at all.
But the way you and him measure time will be different, the person that you see as moving will measure the value of anytime unit to be more than the value you measure, therefore you will feel time is slow in his frame of refference.
As far as i remember, the relation between the way you measure time, and the other moving frame measures it, is rules by the Beta factor.
That is
t'=t*[squ](1-(v²/c²))

As always, i am not really good at relativity stuff, so please people correct me if i am wrong.

 

[Mulder]

I try to remember it as that according to the observer, time for the moving object slows down. If astronauts took a clock to the moon and back, according to Earth time on it's return, it really would have slowed down, or time dilated.

 

[pi-70679]

The way i have been explained it in my courses, is the following:
Imagine a light clock (a ray of light is emitted from a bottom plate to the top one and reflected. The clock calculates the time it takes for the ray to do that). According to you, who is in the same frame of reference as the clock, light rays are only going up and down.
_______
||
UP||Down
||
-------
However, imagine the clock is on a train, what an observer outside would see is the following:

________
/\
UP / \ Down
/ \
----- -----
time=0 time=x

It is obvious that the observer outside the moving train sees it traveling a longer path, but since the speed of light is found to be constant for any frame of reference (whether you are in or outside the train), and knowing that time X speed = distance, then the time must be longer, thus dilated time phenomenon occurs.

The equation is t(dilated)=t(proper)x 1/(1-(v/c)^2)^(1/2)

The "proper" time is the time calculated by the person in the same frame of reference as the clock, i.e. the one who is in the train while it moves.

 

[pi-70679]

Sorry the ASCII art got messed up so here is an image I just made:
http://pages.infinit.net/bdufou1/time_dilation.jpg