Observing a Quantum particle changes its state because we are smacking it with a Photon or interacting with it in some other way such that it loses its original state.
Angular Momentum
For example angular momentum would be changed through observation. We can only know the z component. However, which direction we call z is arbitrary. What happens if we call some direction z and then redefine z to be our old x? Redefining the z as the old x and remeasuring affects the particle in its measurement, rendering the original z measurement no longer correct. Unless
Spin
Same as angular momentum, just the quantum version.