The Heisenberg Uncertainty Principle states that both the exact (as near as we can get to thusfar) position AND momentum of a particle cannot be obtained because in learning its exact position we alter its momentum and vice versa. Does this mean we only have rough measurements of particles produced in particle accelerators? If so, why can't two particles be produced from a collision and the momentum of one measured and the position of the other measured thereby giving exact measurements of both position and momentum for each (albeit after the measurements were taken both variables would have changed, but at least exact measurements at the point of collision could be obtained). Can this be done? Has it? Is there some basic physics principle I've forgotten about? Thanks for your replies in advance.