What’s the underlying principle on why you can’t know the position and momentum of a particle at the same time? Is there an explanation? I don’t have any knowledge of calculus or the math behind anything so I’m asking here, thanks!
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Let imagine we have two cars. We know the speed and initial position of one car and basically nothing about the other. We are going to assume that both drivers are going to keep their speed and direction constant and at some unknown point, they crash and we have their final positions after the crash. Now, what we would like to be able to do is figure out where the two cars crashed and how fast the other car was going. As it turns out, this is a really problem because the speed and position of the crash are interdependent. Where the crash happens would tell us what speed the other vehicle is moving at. Because the speeds and directions are consistent, we get a reasonably simple formula for describing the relationship between position and speed.
Now, lets imagine that both cars are swerving wildly across the road. This means that the vector describing their speed isn’t a constant and changes both direction and magnitude. This means even if we know the position of the crash, there is multiple possible sets of speeds & directions each car could be traveling which would produce the final positions after the crash, and the same of the crash position if we know only know the speed vectors. Knowing one of the position or speeds tells you basically nothing about the other.
Functionally, this is what is happening with particles and the uncertainty principle. We like to imagine particles moving in simple straight lines, but that isn’t really true. All particles vibrate a little tiny bit, but it’s enough to make things work like the cars swerving in the road. I also use the idea of speed as a simplification of momentum. It’s a general principle because this kind of problem whenever a property of a particle has a wave nature, and that happens for a bunch of them.
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