Time, as you've probably heard, is another coordinate in the 3 dimentional space we know, thus turning it into a 4D space.
I'll try to explain why is that so and by doing it I'll answer on some of your questions.
Some imagination and basic algebra lead to the following formula:
(Delta)t = (delta)t' / sqrt(1 - v^2 / c^2)
sqrt = square root.
I won't explain how to derive the formula. I can if you want, but right now I don't have the patience for that.
According to the above formula, (Delta)t (the time) depends on the speed of a moving frame (v), the speed of light (c) and a (delta)t', which I won't explain, and even if I did, you would not understand, because it can only be understood if I derive the formula step by step.
Note: I'm not sure what's the exact word for what I mean by "frame" in english, but the word in russian is sistema otchota. I'll just use the word "frame".
It's simply put a coordinate system to which things are related.
For instance, a ball thrown forward at a speed of 7 m/sec from a car moving at a speed of 25 m/sec will seem to be moving at a speed of 25+7=32 m/sec to a still observer outside the car. The person who threw the ball from inside the car will see the ball as if it was moving at the speed of 7 m/sec.
In other words, the car is another frame, moving relatively to the frame of the earth at the speed of 25 m/sec. the observer outside the car is in the frame of the earth and that is why the ball seems to be moving faster.
whenever you move, you are a frame, or a coordinate system and every part of you is in that coodinate system. Your liver, your brain, your heart, everything.
If my English vocabulary was slightly wider, perhaps I could explain better... sorry about that...
Now, take two coordinates. X and Y. Coordinates are not absolute, but relative.
The geometrical place of point A (see attachment) can be described using X and Y and also using X' an Y'.
from now on, I'll use 'D' for 'delta'.
When turning the coordinate system clockwise, from (X,Y) to (X',Y'), one coordinate (Y) becomes shorter and the other one (X) -longer. Thus, there should exist a combination of the coordinates which always remains constant.
In our case, it's:
(Dr)^2 = (DX)^2 + (DY)^2 = (DX')^2 + (DY')^2 = ... = const.
because a^2 + b^2 = c^2, the pithagorian theorem (dunno how to spell it).
Now, lets get back to our formula.
According to the formula, the higher the velocity (v), the larger the values of Dt and DX (=Dt*v).
Ok, I guess I'll have to explain how to derive the formula... but not now. Maybe tomorrow...
Anyway, now a question arises. What if there is a combination of Dx and Dt which, as in the case with the coordinates, remains constant?
There is a little problem. You can't combine time and distance.
luckily, this problem has a solution. All you have to do is to simply multiply Dt by c, which is the speed of light ~ 300000 km/sec.
The next stage requires a full understanding of the first formula plus knowing how to derive it plus it's geometrical representation.
Just in case you're familiar with it, I'll continue, but probably it won't make any sense...
Don't worry. When I have time, I'll post the explanation.
Dx/2 and c*Dt/2 are two sides of a triangle. Its' height remains constant in all frames:
DS=sqrt[(c*Dt)^2 / (Dx)^2]
If you raise the above expression to the power of two, you'll have:
(DS)^2 = (c*Dt)^2 - (DX)^2 = (c*Dt')^2 - (DX')^2 = ... = const.
Wow, this looks just like the coordinates formula!!!
And thus we have proved that time is the fourth coordinate of space.
Now, back to your questions.
Does time have to exist? Yes. It's a part of space-time, it's the fourth coordinate. Assuming that space will exist without time is like assuming that a man can live without his brain.
Your second question is basically the same as the first one...
The third question I didn't quite understand. Maybe it's my English... What do you mean by "force"? As long as I know, time has no "force"...
All written above are the basics of the special theory of relativity
and it's not guaranteed to be 100% correct. I'm not a professional, I just buy books and read them. I think it's much better than learning it in a class... dunno.
Anyway, if there are any mistakes, please let me know...