Personally I have almost no knowledge of momentum space. When I say almost I mean that I have heard of it, but not much more.
As to precision. You are correct. When somebody says they have made a precision measurement of anything then they are making an approximation. They may not really be aware of that fact, but scientifically you cannot make an absolutely precise measurement. And that really isn't a matter of the uncertainty principle. To make a measurement with absolute accuracy you have to have a measuring device with absolute accuracy. There is just no way to build such a device. It is obvious if you are making a measurement with something like a ruler, but even with something like a laser you still have some uncertainty. If you are measuring something with light waves then you have to observe interference between 2 waves. But you do that by eye-balling a line on a screen. Since the line will have a finite width you will have to estimate the actual position within the width of that line. So you still have an estimate, maybe a pretty good one, but still an estimate. In principle you can make finer and finer measurements, so you will have better and better estimates, but you will never be able to get absolute accuracy.
Of course once you add in the uncertainty principle you set an absolute limit as to the accuracy of any measurement. You cannot, in principle, get any better than (delta x) * (delta p) >~ h-bar. In this equation of course h-bar is h/(2*pi), that is Planck's Constant divided by 2pi. >~ represents greater than or approximately equal to.
Bill Gill
