Does Time Flow Differently in Distant Galaxies Due to Speed?

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Wykydtron
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Ok if these two facts are true
1. The faster you go time slows down
2. The galaxies farther away are traveling faster
Does this mean the flow of time would be different in different galaxies?

Ill do my best to explain what I am thinking
If the milky way is traveling at a speed of X we see 1 second as 1 second
But in a galaxy traveling 2X would 1 second = something like 0.8 seconds because time is slower the faster you are going?
 
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I believe you are correct. I would like to make sure you understand that time dilation is simply an effect of transforming one frame of reference to another. A person traveling at 90% the speed of light relative to you and I would NOT experience time any differently in their own frame of reference. It is only when you compare two different frames that time dilation is observed.

Another thing; from our point of view the milky way is not moving in any direction and we are not experiencing any time dilation at all because of this, just like an observer would experience in their own galaxies.
 
Just to reinforce what Drakkith said, all of that's going to be relative. Any clocks in other galaxies which we can see will appear to be ticking more slowly than clocks with rest with respect to us, but any observers in that other galaxy will see our clocks ticking slower than theirs. Very odd, but welcome to Special Relativity.
 
Ok if these two facts are true
1. The faster you go time slows down
2. The galaxies farther away are traveling faster

more accurate to say:
1. The faster you go relative to someone else, the more your local time appears to slow to them.
2. more distant galaxies are separating faster than neaby galaxies.

The relationships you describe are not quite the same as special relativity because cosmological spacetime is curved while SR spacetime is flat. How you describe that curvature affects your calculated measures and is dependent on the model you use. The standard model used by cosmologists is the FRW model with lambda cdm parameters that make the general model a close fit to our universe.

A good reference from which to begin to think about cosmological comparisons from relativity are these ideas:

Locally, light travels the same speed for everybody: So light in a distant galaxy whizzes by local observers there at 'c', just like it does here locally for us.

Locally, everybody's clocks tick at the same rate [absent gravitational potential differences such as those near black holes].