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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?

Qmechanic
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John Kineman
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1 Answers1

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You have to be very careful with statements like “The consensus (and apparently experiments) is that time dilation in a gravitational field (not free-falling) is ‘as if’ one were accelerating”. There is a grain of truth to it, but as stated it is a little problematic.

Time dilation in a gravitational field is locally the same as time dilation in a uniformly accelerating reference frame in flat spacetime. This distinction is important because it avoids your subsequent problem: “If actually accelerating, the velocity will increase”. In the accelerating reference frame the accelerating observer remains at rest.

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

Dale
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