I may be wrong from the start here, but for this problem I've been treating the uncertainty of position of my small but massive particle (may as well be a proton) as a perfect mathematical sphere, whose centre is a measurement of position I made of the proton, i.e it is somewhere in the sphere but we'll be damned if we know where.

Now for potentially false assumption two: If we were to accelerate the proton to a large percentage of the speed of light and continued to measure it's position while it orbitted around us, (I have been assuming) the uncertainty of the proton would contract in a Lorentz-like way, reducing the volume of the sphere to the observer.

As (delta)position(delta)momentum>h/4pi;

would the uncertainty of position increase as a reaction to the loss of volume of the imaginary sphere? That is assuming that everything that I've assumed is true.

I am fairly sure that things just don't work like this, with any of the assumptions I've made. Hopefully you guys and gals can put my on the right track?