Here is a description of how "time changes with speed" affects physics. You can see this with a home-made spectroscope.

Spin orbit coupling

I did understand how that special relativity effect worked once (at least the Larmor precession bit). I have sat through lectures on the general relativity effect that causes the precession of the orbit of Mercury and didn't get it. It's a much more subtle effect. Thinking of it as time slowing down in the Sun's gravity well might be relevant.