In this video we get our first glimpse of the Heisenberg uncertainty principal. This arises when you get two or more observables that share the same vector space but don’t share the same eigenvectors. So a definite state for one is a mixed state for the other, making the other’s value uncertain.
In my humble opinion, this fact, born out by numerous experiments, that a system can exist in a superposition of states, together with the Plank-Einstein hypothesis: E = hf, are the cornerstones of quantum theory. All the maths that I’m going through are really just our way of modelling this. Those who understand the physics better, which is probably just about every physicist on the planet, are free to explain to me why I’m wrong.