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The title speaks for itself. What would be the down-to-earth meaning behind this principle beyond the incomprehensible mathematics and the abracadabrant lingo? (such as the wavefunction suddenly collapses upon observation because tee-hee! that's how reality and matter work!)

To my understanding, there are two sides to the problem: the value of the position, and that of the momentum (which has embedded within itself the speed). Mathematically, the product between the error in momentum (measured value subtracted from real value) and that in position (analogous to the previous case) must be equal or higher than a specific constant. I am deeply concerned with the "WHY?". So, why exactly this relationship between momentum and position at a quantum level? Does this happen in classical mechanics as well, but to a negligible degree?

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Without using math... The Heisenberg uncertainty principle is telling us that the more certain we are of a particle position, the more uncertain we are of its momentum. Thus if we have definitively measured a particle position, we by the uncertainty principle have total ignorance about its momentum.

Conversely, lets use the example of a free particle in all 1D space. We have definite knowledge of momentum from wavelength and wave number, and therefore have no knowledge of the particle position (it could be anywhere).

This does not happen with classical mechanics, only quantum systems, as it is within quantum mechanics where particles can be represented by wavefunctions and probability.

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