system
Given the following post, respond as if you're commenting on Reddit:
human
The Heisenberg Uncertainty Principle.

I've been reading a lot of physics books recently out of curiosity and interest in physics (I'm a compsci major). I was wondering if anyone could explain to me the Heisenberg Uncertainty Principle. I get what it's saying about how if one property is measured to high precision the others can't be. I'm confused as to why this is true.   

**Edit: Thanks for all the explanations. They have made things clearer for me.**
gpt
There are multiple ways to approach this.  

The most intuitive approach is you ask how you would simultaneously measure both for some quantum system (where this principle becomes important).  E.g., if you want to measure an electron's position, how do you do it?  You bounce photons off of it and measure the photons locations in a detector.  Well to measure its location to a very high precision, you need photons with very short wavelengths, and those impart higher energy/momentum to the the electron (for a photon shorter wavelength means higher energy), making you uncertain of its momentum.

Now, the physicist approach is that the mathematical underpinnings of quantum mechanics have it as such that position and momentum are conjugate variables of each other.  E.g., there's position space and its Fourier transform is momentum space.  From this foundation you can derive the uncertainty principle (e.g., momentum is equal to the derivative the wavefunction in position space with respect to position (p ~ d/dx); and position is a equal to the derivative of the wavefunction in momentum space with respect to momentum x ~ d/dp; hence they don't commute and in the minimum uncertainty they can have (sigma_x sigma_px = hbar/2 is if the wavefunction is Gaussian shaped).).

Now that may sound nonsensical if you don't have the math background, but that's how physicists think of it (in the framework of QM which explains lots of phenomena and has been very well tested).  To simplify to non-mathematical language, when we have a particle (like an electron), before measuring its position or momentum, it doesn't have a definite position or momentum.  It has a continuous probability function for both that are related by a transformation (e.g., the function might tell us it has a 10% chance of having a position between x=1cm and x=1.1cm, and and 20% chance of having a momentum if measured between p=0 kg m/s and 0.1 kg m/s).  These transformation will take particles with very narrow probability range for having a momentum in a small range and make it so they have a wide range of position.