[gus_massa]

I'm not sure about the historical part, but now the uncertainty principle is not an independent postulate. It's deduced form the non commutation of the operations to measure the position and the momentum of a particle. This can be done in the wave representation or in the matrix representation.

Moreover, similar calculations can be done with other measurements that don't conmute. One that is very important is the spin of a particle in the x, y, and z axis.

Another is the polarization of a photon in directions that are at 45°. For example, most of (all?) the experiments of the EPR paradox are done with polarization instead of position-momentum, because polarization is much easier to measure. https://en.wikipedia.org/wiki/EPR_paradox

[atomack]

It's a good point that uncertainty relations exist for all kinds of physical observables. But whether they're expressed as commutation relations or as in Heisenberg's original formulation, or whatever formulation you choose (wave mechanics, matrix mechanics, dirac representation, qft, or anything else one can think of) it's still asserted, rather than derived from an underlying set of fundamental physical objects and interactions.