  The paper reassesses the old dilemma "compact vs. extended phase" in the
quantum theory of the rotator and the Josephson junction and the analogy of
these two systems with the a particle moving in a periodic potential. This
dilemma is in fact the dilemma whether the states with the phases $\varphi$ and
$\varphi+2\pi$ are distinguishable, or not. In the past it was widely accepted
that in the Josephson junction these states are distinguishable like for a
particle moving in a periodic potential. This paper argues that the states with
the phases $\varphi$ and $\varphi+2\pi$ are indistinguishable as in a pendulum
(a particular example of the quantum rotator). However, this does not lead to
revision of the conclusions of the conventional theory predicting the
transition from the superconducting to the insulating state in the small
Josephson junction.
