How small of a scale or vector I guess can science currently detect the effects of or realities of relativity be it general or special?

I know there have been experiments detecting the effects of GR on the scale of ~10km. I don't know whether there have been any more precise than that.

How small of a scale or vector I guess can science currently detect the effects of or realities of relativity be it general or special?

 

Magnetism would be an effect of special, would it not?

Magnetism would be an effect of special, would it not?

It can probably be seen as an effect of the SR transformations, yes.

 

Considering an electron is an elementary particle and that an electron with an energy of 1 MeV does not move at [math]v = \sqrt{2E/m} = \sqrt{2c^2 \text{ MeV}/ 0.5 \text{ MeV}} = 2 c[/math] but at ~c, I would say "pretty arbitrarily small for SR".