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Assuming that there is no gravity, currently (when both rockets are moving at a velocity of 0.5c), which rocket's time will the non-moving observer think is running slower?

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- Thread starter pavelbure9
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- #1

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Assuming that there is no gravity, currently (when both rockets are moving at a velocity of 0.5c), which rocket's time will the non-moving observer think is running slower?

- #2

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Does the time dilation formula include the acceleration anywhere?

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I was just wondering if I had to take General relativity into thought because there is an accelerationDoes the time dilation formula include the acceleration anywhere?

- #4

Ibix

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Studying accelerating reference frames (not accelerating objects) was, I gather, one of the things that led Einstein to general relativity. Also, many special relativity courses avoid accelerating objects because you have to use fairly complicated calculus almost immediately. Taken together, this can lead to the impression that you can't do acceleration in special relativity. But that is wrong - as long as you're willing to do the maths, you can.

- #5

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The transformation formulas for acceleration in special relativity are well known:

Assuming that there is no gravity, currently (when both rockets are moving at a velocity of 0.5c), which rocket's time will the non-moving observer think is running slower?

https://en.wikipedia.org/wiki/Acceleration_(special_relativity)

From that, one obtains the formulas for proper acceleration (i.e. the acceleration that a comoving observer feels):

https://en.wikipedia.org/wiki/Acceleration_(special_relativity)#Proper_acceleration

by which one finally obtains the formulas for constant proper acceleration, also known as hyperbolic motion, see

http://math.ucr.edu/home/baez/physics/Relativity/SR/Rocket/rocket.html

https://en.wikipedia.org/wiki/Hyperbolic_motion_(relativity)

https://en.wikipedia.org/wiki/Acceleration_(special_relativity)#Curved_world_lines

Using those formulas, and plugging in some numbers, you should be able to compute the time of both rockets.