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# General vs Special relativity

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?

Note by Jiahai Feng
3 years, 8 months ago

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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. Staff · 3 years, 8 months ago

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 · 3 years, 8 months ago

Special 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. · 3 years, 8 months ago

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. · 3 years, 8 months ago