Heisenberg Uncertainty Principle

The HUP is perhaps one of the top most popular relations in physics. In QM it is even more popular, and far more celebrated, but what does it mean?

What the equation states: the uncertainties in position (Δx) multiplied by the uncertainties in momentum (Δp) is greater than half the reduced Planck constant (ℏ).

What that means: we can not precisely know the position and the momentum no matter how accurate our measuring abilities are. 

The most important thing about this relation is that the uncertainty in variables is not due to a flaw in technology. The uncertainties in position and momentum are intrinsic to the quantum world.

To make the concept even easier to understand in terms of experimentation, we can precisely measure an electron’s position, but can not accurately determine it’s momentum at that position. Likewise, we can measure its momentum, but not precisely measure it’s location at the same time. These inaccuracies are often referred to as blurs.

The derivation of the HUP is quite mathematical involved, albeit fun, but is something for another post.