I have this doubt about general and special relativity.

Under general relativity, the time dilation experienced an accelerating body would be the constant, but under special relativity, the time dilation experienced by an inertial body would be constant, but time dilation experienced by an accelerating body would be varying.

Correct me if I'm wrong, but is this a paradox?

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## Comments

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TopNewestSpecial Relativity doesn't really account for the time dilation caused due to acceleration. Although the Lorentz Factor (and so does the time dilation) varies during acceleration, but that effect is negligible. By differentiating Lorentz Factor with respect to time, you will see that the rate at which the Lorentz Factor changes with acceleration is almost zero. This means that the change in time dilation due to acceleration is negligible. dl/dt = (1-(v/c))^3/2 * (-2av/c^2) where l is Lorentz Factor, a is acceleration, c is the speed of light and v is the instantaneous velocity. The right side is almost zero. Hence, time dilation experienced by an accelerating body doesn't vary much (in SR) unless the acceleration is of very high order.

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But acceleration does in fact make a difference in special relativity, however small?

To consider special relativity at all a person need to accelerate something to relativistic speeds. Integrate the change in lorentz factor over time, and the difference should be noticeable.

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My apologies... I went totally wrong up there. I thought that Special relativity is not for accelerated objects and there is some other reason that causes time dilation for accelerated objects and that is dealt with General Relativity but I was wrong. I did a little research and found out that Special relativity handles acceleration just fine, as long as you are working in an inertial reference frame (and space-time is flat, or at least can be reasonably approximated as flat). However, special relativity only lets you do calculations in an inertial frame of reference, and not an accelerating one. So the calculations of time dilation are made from two different frames(In case of SR it is made from inertial frame and in case of GR it is made from non-inertial frame) and this shouldn't come as a surprise that in one the time dilation is varying but not in the other.

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You can treat accelerating objects and their corresponding coordinates without much difficulty in special relativity. For example, consider Rindler coordinates, which is a very important coordinate system adapted to uniformly accelerating observers. You need general relativity to describe gravity, not acceleration.

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special relativity does not account for acceleration and is made according to the assumption of flat space time whereas general relativity accounts for curved space and accelerated systems

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