  Defining the observable ${\bf \phi}$ canonically conjugate to the number
observable ${\bf N}$ has long been an open problem in quantum theory. The
problem stems from the fact that ${\bf N}$ is bounded from below. In a previous
work we have shown how to define the absolute phase observable ${\bf
\Phi}\equiv |{\bf\phi}|$ by suitably restricting the Hilbert space of $x$ and
$p$ like variables. Here we show that also from the classical point of view,
there is no rigorous definition for the phase even though it's absolute value
is well defined.
