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So, I heard that all speed is relative. And that nothing can travel faster than light.

Then I guess it is OK for a spaceship to leave Earth at 0.6c constant speed. And what if an other spaceship were to leave Earth at 0.6c in the opposite spacial direction.

Then the relative speed between the two ships would be 1.2c, which is greater than c. How would that work out? Maybe something with time dilation?

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marked as duplicate by dmckee Apr 9 '16 at 23:59

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Galilean relativity and Special relativity use different identities to find the relative velocity of different objects. In classical mechanics, velocity addition formula of Galilean relativity can be used($v=v_1+v_2$). However, this doesn't apply to objects travelling at speeds close to $c$. At these conditions, relativistic addition formula gives much more accurate results. For inertial frames, this can be explained via Lorentz transformation.(Simply, each frame has different distance and time measures.) Therefore, the relativistic velocity-addition formula becomes; $$ v=\frac{v_1+v_2}{1+\frac {v_1v_2}{c^{^{2}}}} $$ Overall, you can say that special relativity gives us a more generalized equation to calculate the relative velocity.

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It does indeed have something to do with time dilation. You can use the formula $$s=\frac{v+u}{1+(uv/c^{^{2}})}$$ where s is the speed of one spaceship relative to the other while u and v are their speeds relative to the Earth. I think you will find whatever values of u and v you use s will always be smaller than c.

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  • $\begingroup$ Where can I read more about this formula? (about where it comes from and how it works) $\endgroup$ – nc404 Apr 9 '16 at 15:21
  • $\begingroup$ Maybe start at University of Pittsburghand the Eistein for Everybody. If you want something a bit more mathematically check out University of New South Wales $\endgroup$ – M. Enns Apr 9 '16 at 16:12

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