bort said:
If an object is located at the exact center of the universe, would time pass by infinitely fast for this object? An object at the exact center of the universe would not move at all. It would be independent of inflation. Using Einstein's time dilation equations (as I understand them) basically state that the faster an object moves, the slower time passes for it. Therefore a competely stationary object should have the exact opposite properties. or no...?
Well, for starters, we don't think there's any center to the universe. That doesn't seem to be the primary misconception here, however. It is true that time dilation implies that a moving clock runs slower, but it is not true that a stationary object's clock runs infinitely fast.
Imagine you have two observers, one that is stationary and one that is passing by at a speed, v, and that the stationary observer claps his hands twice. The increment of time between these claps, as measured by the moving observer, is
\Delta t' = \gamma \Delta t = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}\Delta t
where \Delta t refers to the corresponding increment of time on the stationary observer's clock and c is the speed of light. Since 0 \leq v < c, this will always give \Delta t' \geq \Delta t. The important thing is that this expression is relative, not absolute. It can compare the amount of time that passes from one clock to the next, but it does not give a sense of
absolute time.
So what, then, is a stationary object? In special relativity, the basic answer is that it's an object moving with the same velocity as your frame of reference. To find the interval of time on a clock that's stationary with respect to yourself, you just plug v=0 into the above equation. Not surprisingly, you just get
\Delta t = \Delta t'
meaning that the stationary object's clock runs at the same rate as yours.
However, when describing gravity (and thus, the evolution of the universe), we need to use
general relativity. In this theory, the passage of time between two observers depends not just on their relative velocity, but also on the curvature of spacetime. Thus, the above expression for time dilation will not be sufficient to describe the passage of time for a "stationary" observer.
). If the surface of the Earth were suddenly twice the size, there's still no apparent center of the expansion. Of course, when you add the third dimension, the center becomes clear...but there is no 4th dimension of space (at least not according to the cosmological model from Relativity).
