# Do I see velocity decrease, when I see time slow down in special relativity?

If I would see a moving clock experience time more slowly, would then I also see its velocity decrease than its actual velocity ?

Velocity is $v=x/t$. From my view point, if it experiences more time then... $v=x/2t$. So $v$ is slower.

And if the answer is: distance also decreases, then if I saw a thing speed by me at 0.5c I should also see the path before it shrink. Length contraction only solves this problem from the object's point of view. Not from mine. And if it's velocity does decrease, then there should be no time dilation at all. But you can continue on with this circular logic to get a paradox.

Any help is appreciated. Thank you.

• You calculate an object's velocity as $\Delta x/\Delta t$ in your frame, not in the object's frame, and certainly not by calculating $\Delta x$ in your own frame and $\Delta t$ in the object's frame, which is what you appear to be suggesting. – WillO Nov 19 '16 at 3:45