The Uncertainty Principle falls out of a the porobablistic nature of QM. Momentum and position, for example, are conjugate variables (as are energy and time). They are described by a wave function and are Fourier transforms of each other, so there is a limit to how well you can determine each value. If you know one exactly, it means you have a delta function; the FT of that function is a constant, meaning that all values are possible.

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