Time dilations and our perspective

[bill alsept]

Sorry guys if you have already covered this subject but someone the other day mentioned time wells and different frames of reference etc. and I was wondering:

If time slows down the more massive and dense things are then how can that effect the observer's perspective? In other words when we view distant galaxies is our perspective (in relation to time) dictated by our position (in relation to density)in our own galaxy? Close to the center of a galaxy time is slower and at the far edge of a galaxy time is faster.

The subject of time is hard enough but if time dilations are true then how would that effect our view of say a distant galaxy?

If the center of a distant galaxy is in a slower time dilation (in relation to us) do we see the center section rotating slower than it actualy is and do we see the outer areas moving faster than they actually are?

If our perspective were from between galaxies or some other area where density was very low how would everything around in the distant appear to move?
Would everything be blueshifted? Would it effect the way the rotation appeared? Etc.

 

[Calimero]

Equation for gravitational time dilation is:

$$t=t_{0}\sqrt{1-\frac{2GM}{rc^{2}}}$$

This is good for spherically symmetric, non-rotating body only, but it can give you handle on values. Since G is in numerator and c^2 is in denominator, you need huge mass / radius ratio in order to get significant value.

Or you can go slightly other way. Gravitational time dilation is best understood in terms of Schwarzschild coordinates. Proper time at one Schwarzschild radius of any mass is stretched to infinite coordinate time for observer at infinity (this is what black hole actually is):

$$t=t_{0}\sqrt{1-\frac{r_{s}}{r}}$$

Schwarzschild radius of Milky Way is ~2 light years. So, even in the worst case scenario, where galaxy is approximated as a giant black hole, proper time at say 200 ly from center (remember that actual radius of Milky Way is 50000 light years, so 200 ly is very close to the center) would tick at 0.995 seconds per second of distant coordinate time.

 

[BillSaltLake]

A clock at rest (comoving rest) in the center of a galaxy will run slightly slower than a clock at rest at the edge of the galaxy, which in turn runs slightly slower than a clock far from any galaxy. This assumes all 3 clocks are measured at the same era. ("Era" is the time measured since the beginning of expansion in a comoving coordinate system that is not in a well).
These differences are slight, ~proportional to the fractional frequency shift of light climbing out of the well.