I may be getting these Thread Levels wrong. I get the impression that they apply to my level of knowledge such that someone else might be able to give an answer that I might be able to understand rather than the level of knowledge required to answer the question. Rest assured I am quite stupid. Anyway. Assume I produce a bunch or gas of nominally stationary, at rest, protons but, ignoring the fact that they are going to fly apart, they have random X,Y,Z motions. Taking the X axis assume there is an uncertainty in their momentum along that axis expressed in electron volts, ueV.. Uncertainty in electron volts. I think this may be some sort of Maxwell-Boltzmann kind of thing. Let's say that they are at room temperature so about 25meV.. Milli Electron Volts. Ignore my rounding down error. Take that 25meV figure as being the uncertainty in their energy and, possibly incorrectly, extrapolated to the uncertainty in their momentum along the X axis. I am waving hands. What happens if I accelerate them to 100KeV along the X axis using a low, effectively zero noise, voltage source? Specifically have I reduced the uncertainty in their Energy/Momentum along the X axis by a factor of 100KeV/25meV or 4E6? Again I have no clue but Frames of Reference might apply. Besides being completely wrong I might also be a factor of three and a square root out.