Conjugate Variables: Uncertainty Relation Explained

[spidey]

Why there is an uncertainty relation between conjugate variables?
what exactly are conjugate variables?

 

[malawi_glenn]

http://en.wikipedia.org/wiki/Canonical_conjugate

The uncertainty relation are due to the non-commuting nature of those variables. If you know how to derive HUP for x and p, it is straight forward to do it for several other pairs of conjugate variables/operators.

 

[Avodyne]

Given a lagrangian $L(q,\dot q)$, the conjugate momentum to $q$ is $p=\partial L/\partial\dot q$. There is an uncertainty relation between canonically conjugate variables because that's what quantum mechanics says, and quantum mechanics has been verified by tens of thousands of experiments (at least) to date.