Take a Heisenberg uncertainty principle. It originates from the fact that on a microscopic level everything (electron, proton, photon,graviton, etc)is a wave. What is the POSITION of a wave? If the wave has DEFINITE momentum (=definite wave number k = definite energy = definite frequency), then its LENGTH (which is Fourie - image of momentum) is INFINITE. (Not the wavelength, but a length of a wave packet). And what is the position of infinite wave? Infinitely uncertain. So it is MATHEMATICAL RELATIONSHIP (Fourie-transformations) between entangled properties of a wave: momentum and the length of wave train.

You can make a wave train shorter simply by putting electron in a small box (say, in electric field of a proton)- but short wave train will now have different Fourie-transform-defined momentum (and a wave number k, and energy, and frequency too): no longer as a sharp infinitely narrow delta-function, but as a blurry band spread around some average number. The smaller the "box" (the stronger the field) - the less certain is momentum - therefore, the more "violent" is electron "motion" in an atom with 2,3,... protons.

Same Fourie relationships between energy and time (of pass of a wave via certain point in space).

So, the Heizenberg uncertainty principle (which is central to quantum mechanics and which makes world unpredictable on a quantum level) is simply a mathematical Fourie-relationship of various properties of a wave. By the way, because energy and time (or momentum and position) are Fourie images of each other, we call them ENTANGLED properties - modifying one immediately results in change of the other.