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From another point of view, this is like the idea of a wave on a string. If the wave has a very definite wavelength, then it can’t have a very definite position, and vice versa. This is a theorem in Fourier Analysis, from what little I know.
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@Muffinshire  
It really comes down to Heisenberg. Quite simply, there is a minimum amount of uncertainty regarding any system’s position and momentum. Weird quantum shit keeps you from being able to pin down both exactly.
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@Zennistrad  
It’s more complicated than that - even doing it purely mathematically to a hypothetical electron, increasing the precision of one variable causes a decrease in the precision of another. It’s an inherent limitation of treating particles as having the properties of both particles and waves. That’s the uncertainy principle. What you’re referring to, that measuring a system changes its state, is the observer effect.