Editing Angular momentum (section)

=== Uncertainty ===
In the definition <math>\mathbf{L}=\mathbf{r}\times\mathbf{p}</math>, six operators are involved: The [[position operator]]s <math>r_x</math>, <math>r_y</math>, <math>r_z</math>, and the [[momentum operator]]s <math>p_x</math>, <math>p_y</math>, <math>p_z</math>. However, the [[uncertainty principle|Heisenberg uncertainty principle]] tells us that it is not possible for all six of these quantities to be known simultaneously with arbitrary precision. Therefore, there are limits to what can be known or measured about a particle's angular momentum. It turns out that the best that one can do is to simultaneously measure both the angular momentum vector's [[magnitude (vector)|magnitude]] and its component along one axis.

The uncertainty is closely related to the fact that different components of an angular momentum operator do not [[commutator|commute]], for example <math>L_xL_y \neq L_yL_x</math>. (For the precise [[commutation relation]]s, see [[angular momentum operator]].)