This article is horrible.
"The Heisenberg uncertainty principle is in part an embodiment of the idea that in the quantum world, the mere act of observing an event changes it."
That's not the Heisenberg uncertainty principle. That's just the observer effect, and it's not something peculiar to quantum mechanics. You want to measure the temperature of a system, so you stick a thermometer in there. Okay, the mercury in the thermometer absorbs a bit of heat from the system, providing you with a temperature measurement at the same time it changes the temperature of the system. If you want to measure the parameters of a particle, you stick a bubble chamber in the way, and as the particle flies through the chamber it smacks into hydrogen molecules, showing you what it's doing but also taking a different path than it would have if none of those hydrogen molecules were in the way. Big fat hairy deal.
The HUP doesn't just say that you can't simultaneously measure the position and momentum of a particle, it says that a particle *does not simultaneously possess* a well-defined position and momentum. If the particle's doing something in a system and is interacting in such a way that you can define its position to arbitrary precision, then it *does not have* a well-defined momentum for you to measure, and vice versa. Position and momentum are what are called quantum conjugate variables, and the HUP says that when you have a pair of those variables, then the product of their uncertainties is greater than or equal to a constant. There is *no state* in which that particle is even *allowed* to exist in which it possesses both a well-defined position and well-defined momentum.
A signal processing analogy, for any analog people. A particle's wavefunction carries information about its position and its momentum. Where the wave exists is where the particle actually is, and the wavelength is the particle's momentum. Take a particle whose momentum you know to the utmost precision, and graph that. Range of momentums on the x axis, probability of the particle having that momentum on the y axis. You'll get a graph that looks like a Dirac function, a value of 0 everywhere except for a single spike corresponding to the particle momentum, area under the curve of 1.
Now switch domains, change from the momentum to the position domain, this is mathmatically the same thing as changing from a time domain to a frequency domain, which means you can use your old friend the Fourier Transform.
What do you get when you do an FT of a Dirac function? You get a constant value everywhere, from -infinity to +infinity. If you know exactly where that particle is, you have no idea *where* it is, and it's not because you disturbed it in measuring it, it's because *it* has no idea where it is, a well-defined position does not exist; since the uncertainty in the momentum measurement approaches zero than the uncertainty in the position measurement has to approach infinity so that the product of those uncertainties remains greater than a constant.
The "you change the system by measuring it" is an analogy, and it's one that Heisenberg himself used to explain the HUP, but *that is not what it says*. The HUP is not a statement about the process of measuring things, it is a statement about the nature of the universe, and finding a way to improve a measuring system to reduce the disturbance it creates in the system it's measuring has nothing to do with the HUP.