I like to try and derive little things by myself if I think it is manageable. One such thing is the addition of velocities. I gave it a stab, got an answer, and it turned out to be wrong. So tell me where my logic messes up.(adsbygoogle = window.adsbygoogle || []).push({});

There's a spaceship moving at velocityu. A man in the spaceship throws a ball, which from his POV is thrown at velocity_{1}uin the same direction of the ship. Let's look at the man in the spaceship's POV:_{2}

In 1 unit of time, the ball will moveuunits of distance._{2}

Now, from a man outside of the spaceship, any of distancedin the spaceship is observed to have a distance of_{0}d√(1-u_{0}_{1}^{2}/c^{2})

Also, any event that takes a time oftin the spaceship is observed take the time of_{0}t/√(1-u_{0}_{1}^{2}/c^{2})

So, in the space ship the ball travelsd/_{0}t_{0}

But outside the spaceship, I would think that it would taked/_{0}t* (1-u_{0}_{1}^{2}/c^{2})

But that's not it... What's wrong with my reasoning?

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# Why is this idea on addition of velocities in SR wrong?

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