Imagine a spatial frame of reference attached to a point-like particle. It has x=0 since it is at the origin and p=0 since it is at rest. Having definite position and momentum is normally considered a violation of the uncertainty principle. How would you resolve this paradox? 1. Position frames and momentum frames are not the same. I.e. there is no such thing as a common "spatial" frame, because such a frame would imply a common eigenstate for both position and momentum representations in the frame indicated above. 2. This special case is an exception. 3. The uncertainty principle applies only to actual measurements. 4. There is no such thing as a point particle. 5. Other. I have my own resolution of this paradox, centered on (3), but the implications are many and complex and would probably be considered speculative (though I think they are obvious and focused on the distinction between translations and boosts and their unitary representations*) so I won't relate it here, but I'd love to hear what others think. *If anyone wants to know my resolution, pm me.