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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It’s less that you can’t know, and more that the particle doesn’t have a well defined position and momentum at the same time.
The uncertainty principle applies to more than just position/momentum and fundamental particles. It’s really a property of waves and it makes a bit more intuitive sense to take about them.
If someone strums a string and let’s it vibrate then it’s very easy to define the frequency at which it’s vibrating, but pinpointing the exact point in time when it was played doesn’t make sense, it was played over a whole range of time. Going the other way if they pluck a string but then hold onto it, defining what single frequency it vibrates at doesn’t make sense, but the time range is much shorter.
This relationship between time and frequency (really energy) is also an uncertainty relation.
So when you take a fundamental particle and constrain it’s position, it’s momentum is really a wide range and not a single value. And if you pin down it’s momentum then it’s position is a wide range
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