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

Question

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 04 '15 at 17:07
The mass is uncertain. Relativity links mass to energy and energy has an uncertainty with time. — CuriousOne, Jun 04 '15 at 17:07

score 9 · Accepted Answer · answered Jun 04 '15 at 16:48

There is no uncertainty for velocity because velocity is not a well-defined quantum observable.

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.

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

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