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

Question

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.

Answer 1

The speed you see it moving vs. the speed it is moving at isn't a factor of relativity it's a factor of light taking time to reach you.

Answer 2

You measure velocity and time dilation in your own reference frame, or "rest frame". If you are alone, you cannot measure moving clock rate. Measuring procedure looks like that: You hire an assistant and give him a clock. Then you stay at certain spatial position, for example in origin (0,0). Your assistant has to go into another spatial position, (X,0) at x axis. Then your assistant and you synchronize your clocks by beam of light. Now your clocks show the same time. Then a moving clock passes by you and you compare readings of your clock and moving clock in immediate vicinity.Let's say, both clock show 12. Then,some later moving clock passes by your assistant. He compares his clock with moving clock in immediate vicinity. Assistant's clock show 5 pm and moving clock shows 3 PM. Hence, moving clock dilates. It is important to note, that in Special Relativity "an observer" is not a physical person, who "looks by eyes". It is rather a team of persons and each of them possesses a clock. https://en.wikipedia.org/wiki/Observer_(special_relativity)