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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Because a particle is also a wave. The Uncertainty Principle is a statement about the fundamental nature of waves.
If you have a perfect sin wave stretched infinitely far across the universe, it has a perfectly defined energy/momentum. However, it doesn’t have a well defined position because we can’t pinpoint one single locations that’s where the wave is.
One the other extreme, if you scrunched the wave down to be infinitely compact, then we know exactly where it is, but because it’s all crammed into a single point, there’s no wavelength, so we can’t say what its energy/momentum is.
The Uncertainty Principle is saying just that, as well as setting the limits for the in-between cases.
[Here’s an illustration of what I was saying above](https://pbs.twimg.com/media/D7K4UYFUIAcwQpR.jpg) The top wave has no definable position, but we can describe its wavelength (and therefore its energy or momentum). The bottom wave packet we can point to where it is, but measuring the wavelength is very hard. The middle one we can point to a rough area of where the wave is, and we can sort of measure the wavelength, but neither is perfectly precise.
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