I’ve got the world on my wrist, swinging on a rainbow

It’s simple, Doc. If I don’t wind my watch, the world stops.
My mother told me that. And since I was five, I’ve kept this watch wound up.
I’ve gone through so many wristbands, but the watch itself just keeps on ticking.
Never overwound, mind you. That makes time go by too fast. It’s hard enough keeping up as it is.
Once, some guy stole my watch on the subway, but I got it back before the world stopped.
I planned on giving it to my daughter, but Sarah took her. No forwarding address.
So, now will you clone me?