# How does Heisenberg’s uncertainty principle work?

(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

Share

To measure something you need to interact with it. In other words you affect the next state of a system by interacting with the current state.

So when it comes to say, measuring the position of a particle. You can’t do that without physically interacting with it, touching it in a sense. That means you’ll affect the momentum. Conversely, you can’t measure the momentum without affecting its position.

The uncertainty principle isn’t binary, meaning it’s that really you know either one thing or another. The name itself is a clue, it means the *more* certain you are of one property, the *less* certain you are of another.

The really cool thing about the uncertainty principle is that it pops up everywhere. For example, in information theory the more certain you are of how information behaves in terms of frequency (e.g. an audio signal, or speech) the *less* certain you are of how it behaves in time.

The problem arises because the particles being measured are small relative to the photons we used to observe them.

Let’s imagine we’re attempting to measure an object shaped like one of [these](https://www.youtube.com/watch?v=fRqwYsfiME8) rolling through a dark room (we can’t see or hear the object or collisions all we can observe are the paths of the balls we shoot at the object). We have a devise that shoots a huge number of balls to bounce off to measure it (but we only get two options pool balls or Styrofoam balls).

If we use pool balls, we’ll be able to figure out where our pool ball bounced and get some information, but because our pool balls have a lot of momentum we won’t know whether the unknown object ever completes a rolling cycle.

If we use Styrofoam balls, we can see the cycle the object takes, but we’ll have a hard time accurately measuring it’s weight because it’s hard to tell whether something else affected the path of the very light foam balls.

The uncertainty principle describes something similar that affects observation of particles that are very small compared to the photos we use to observe them (photons scatter randomly unlike colliding objects). If you use a high energy photon, you get a good measure of the particles position, but you add lots of momentum from the collision. If you use a low energy photon you don’t add momentum in the collisions, but you get a fuzzy answer on position. You don’t have anything else to measure with, so you’re stuck choosing which error term you want to have (because removing one gives you more of the other).

The basic idea is that you can’t know the position and the wavelength of a thing, because ideal waves don’t have a well defined position yet particles do. The problem is that real particles behave both like a particle and a wave. So when I measure the wavelength of a particle, I’m forcing it to behave more like a wave and less like a particle and so it’s position becomes more uncertain. Likewise when measuring the position, I’m making the particle act like a particle and so I lose it’s wavelike behaviour. It can’t act like an ideal particle and an ideal wave at the same time. You can get clever and get it to act kind of like both (don’t measure the exact position but instead measure if it’s in a particular region or not), but never exactly.

The momentum only comes in later due to the fact that the momentum of any real particle is directly related to it’s wavelength, thus knowing somethings momentum means that you know it’s wavelength and so the particle is more wave than particle and therefore doesn’t have a well defined position.

If you want to dive deeper, I’d recommend looking into some videos regarding the Fourier transform, since that is the actual math that relates position and wavelength.

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.