How does Heisenberg’s uncertainty principle work?

Question

(Sorry if my wording is bad and sorry for no formatting I’m on mobile)

Why is it that two people can’t observe the same object and one measures momentum and the other the position of something.

Also, why can’t we use the momentum to calculate its future position, and then since we already have the momentum we can then have the position at the same time

(disclaimer: I know that the example I provided was wrong, I just want to know why it’s wrong)

In: Physics

Answer 1

This is a really complex concept. I’ll first give a short text explanation that probably will be insufficient to explain it, afterwards I’ll refer you to a video that in my opinion explains the concept very well.

Every particle can be represented as a quantum wave. One way to represent this wave is to use the wave’s amplitude for the particle’s position and the wave’s rotation for the particle’s momentum. Another way to represent the wave is to use the amplitude for the momentum and the rotation for the position. If you have one of these representations, you can get the other by applying a mathematical transformation called a Fourier transform.

The uncertainty is a fundamental property of the Fourier transform. This means that if both representations are valid, then you can’t exactly know both position and momentum at the same time. As far as we can tell, both representations are in fact valid, which lets us conclude that Heisenberg uncertainty is real.

This probably hasn’t been sufficient to explain the concept. After all, it’s a really complex idea to understand. I strongly recommend you to watch [this video](https://www.youtube.com/watch?v=p7bzE1E5PMY), which does a relatively good job of explaining the basics of quantum waves. Around the 10 minute mark, it explains how you cannot know both position and momentum exactly. The video doesn’t explicitely refer to Heisenberg uncertainty, but that’s essentially what it’s explaining there.

There’s another explanation that argues that in order to measure either position or momentum, you have to somehow interact with the particle, which inevitably changes it. While this does effectively mean that you can’t exactly know both position and momentum, I don’t think it properly captures the fundamentality of Heisenberg uncertainty.