- Chosen by Voters \\How can you possibly know the speed of something if you have no idea where it is?//The Heisenberg Uncertainty Principle arises from the fact that particles exhibit wave-like behavior, so it's harder to visualize these things if you think of the particles as a rigid sphere.It requires fourier analysis to show that ?k?x?1/2, where k is the wavenumber. Multiply both sides by ? to get the familiar form of the HUP ?p?x??/2 (because p=?k). As noted by another answer, a particles momentum isn't typically derived by first measuring ?x/?t as you might with a massive object like a car, but by things like conservation of momentum, analyzing the radius of the trajectory of a particle in a magnetic field, or solving the Schrodinger Equation (SE) for the particle with a given set of boundary conditions. If you can determine a well-defined wavenumber k from the SE, then you can determine a well-defined momentum (again, p=?k). However, a perfectly well-defined wavenumber can only arise from a plane wave, and so, there can be no definite position. On the other hand, if you can determine an exact position of a particle, then the particle's wave function exists as a single pulse, which according to fourier analysis, is made up of an infinite sum of sines and cosines without a well-defined wavenumber k.\\Even measuring say a soundwave, we can measure the speed and we know where the wave originates from.//Knowing where the wave originates from and knowing where it currently is are two different things. Think of a sine wave on the interval (-2?, 2?) like the one linked below, and now imagine that function represents a particle. Can you give me the exact position of that particle? That is a function with a well-defined wavenumber k (and thus momentum), but no well-defined position. Source(s): http://radarproblems.com/chapters/ch05.d… 6 days ago 100% 2 Votes