When measuring position the Compton wavelength is believed to be a limit on the precision of the result. If we shine light of a too high frequency on the particle then we will see particle creation and it will not longer be obvious which particle we have measured.
Now what about measuring the direction of particle spin? I am thinking of an experimental setup which first produces particles with spin-up along a known axis. Next we measure spin by a Stern-Gerlach type of experiment or by a polarization filter (along the identical or a different axis). We test a large number of particles and every single experiment provides us with a tiny bit more of precision.
In this setup: Will there be a limit to the precision of spin direction measurement?
I am looking for an effect in this thought experiment which limits spin precision measurements. The same question comes up for measurements of momentum. It boils down to my initial issue: Which effects provide a limit in precision measurements of quantum physics?