Gravity vs. Velocity time-dilation

Question

Is there any difference in effects from time dilation of that due to gravity vs. that due to velocity?

Answer 1

I assume you mean by "the effects of time dilation...due to gravity vs. ... due to velocity" you mean can we tell the difference between the relativistic time dilation

$$t=\frac{t_0}{\sqrt{1-\frac{v^2}{c^2}}}$$

and the gravitational time dilation

$$t=\frac{t_0}{\sqrt{1-\frac{2GM}{rc^2}}}$$

where $t_0$ is the proper time in both cases. The answer is yes--the different time dilations are slightly different. If I am in a space ship and going past you at near light speed (and not accelerating), I will see your clock slowed down and you will see my clock slowed down. However, if you are on the International Space Station, you will see my clock tick slower and I will agree that my clock is ticking slower than your clock. In that sense, the different time dilations are different--see the wikipedia article on time dilation for more.