# Why does the uncertainty principle relate position and momentum when mass is always certain?

Why do physicists relate $x$ and $p$, instead of $x$ and $v$ since mass is well known and is not uncertain?

• Photons has momentum but no mass. We use x and p because it is more generally applicable – Jim Jun 4 '15 at 17:07
• The mass is uncertain. Relativity links mass to energy and energy has an uncertainty with time. – CuriousOne Jun 4 '15 at 17:07

Quantum observables are obtained through canonical quantization from classical observables, which are functions on the classical phase space of Hamiltonian mechanics, whose coordinates are generalized positions and momenta. In particular, $v = \frac{\mathrm{d}x(t)}{\mathrm{d}t}$ is not such a classical phase space observable, since it is not a function of the coordinates on the phase space, but of a particular trajectory $(x(t),p(t))$. Hence, canonical quantization does not yield a quantum notion of velocity.