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

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).