# Time and acceleration [duplicate]

I am confused by the explanations of time dilation and gravity vs. acceleration. The consensus (and apparently experiments) is that time dilation in a gravitational field (not free-falling) is "as if" one were accelerating. Examples given for sending light signal each way in a gravitational gradient, one sees blue shift the other red shift just as if accelerating in space due to velocity transformation. But is there a paradox? If actually accelerating, the velocity will increase and so will the time dilation relative to origin. If in a gravity field, the effect on clock time will be a constant difference relative to free-fall (e.g., orbit). Satelite clocks are apparently corrected for both velocity and gravity density which should be equivalent to acceleration. If a satelite were moving above escape velocity but held to the earth on a tether, would its time dilation only be a difference from the velocity, or would the force of the tether imply higher gravity density? Any thoughts?

## marked as duplicate by John Rennie, Jon Custer, Aaron Stevens, Kyle Kanos, sammy gerbilNov 6 '18 at 22:36

• What should be the paradox? – md2perpe Oct 20 '18 at 20:01
• – mmesser314 Oct 20 '18 at 22:38
• @JohnKineman What's the question? – N. Steinle Oct 21 '18 at 0:36
• Possible duplicate of What is time dilation really? – John Rennie Oct 21 '18 at 9:30

In both an accelerating reference frame and in a gravitational field the time dilation depends on the potential. Locally that is $$gh$$ where $$g$$ is the gravitational acceleration in the gravitational field or the acceleration of the accelerating reference frame, and $$h$$ is the height difference in the gravitational/acceleration field. I am not sure if you mean $$g$$ or $$gh$$ or something else by “gravity density”, but I would recommend avoiding that term since it is not standard terminology
• No, the potential is $gh$ in both cases. In the accelerating reference frame $g$ is the “artificial gravity” in the reference frame. – Dale Oct 21 '18 at 13:20