# Unstable equilibrium

#### Pencil on tip

A pencil sits on its point in an unstable equilibrium. The pencil is 18 cm long and has a mass  of 7 grams.  From a quantum mechanical perspective this pencil has to fall. Classically it could remain in unstable equilibrium.  Please estimate the time necessary for the pencil to land on the table, from its initial upright unstable position on its point.

Small oscillations about all positions exist in quantum mechanics. . The uncertainty principle states this. Because of this, an unstable equilibrium position in quantum mechanics can not be maintained. After a certain time, a pencil that sits on its tip is going to fall on the table, on all cases after a certain time.