  In quantum theory, physical systems are usually assumed to evolve relative to
a c-number time. This c-number time is unphysical and has turned out to be
unnecessary for explaining dynamics: in the timeless approach to quantum theory
developed by Page & Wootters (1983), subsystems of a stationary universe can
instead evolve relative to a 'clock', which is a quantum system with a q-number
time observable. Page & Wootters formulated their construction in the
Schr\"odinger picture and left open the possibility that the c-number time
still plays an explanatory role in the Heisenberg picture. I formulate their
construction in the Heisenberg picture and demonstrate that c-number time is
completely unnecessary in that picture, too. When the Page-Wootters
construction is formulated in the Heisenberg picture, the descriptors of
physical systems are functions of the clock's q-number time, and derivatives
with respect to this q-number time can be defined in terms of the clock's
algebra of observables, resulting in a calculus for q-numbers.
