The original formulation of the 'Heisenberg Uncertainty Principle' was based on Heisenberg's observation that the accuracy of a measurement of position is limited by the wave length of light used in doing the measurement. Shorter wavelengths of light provide the opportunity for making more accurate measurements of position.
Conversely the shorter the wave length of light used, the more energetic the photon which interacts with the particle, and the more the momentum is transfered to/from the measured particle.
In Heisenberg's own words:
Today it is accepted that the Uncertainty Principle is not simply a matter of measurement error related to the limitations of our measuring devices but it is a basic limitation of physics that position and momentum are not only simultaneously unmeasureable beyond a strict limit, but they are infact unknowable beyond that limit.
The mathematical expression of this uncertainty is:
Where x is the position variable, p is the momentum and h is Planck's constant.
Another way to look at the source of this intrinsic uncertainty in the knowability of a particle's simultaneous position and momentum is to consider the deBroglie relation requirement for knowing the momentum of a particle precisely.
Precisely knowing the momentum 'p' requires a precise knowledge of the particle's probability function wave length . A solitary wavelength value for implies that must be an infinite sine wave with wave length ... In this case we could have exact knowledge of momentum 'p', but zero knowledge of the postion of the particle.
On the otherhand a precise knowledge of the position of a particle would require that be representable as a delta function. The frequency spectrum for a delta function is infinitely broad ... therefore in having exact knowledge of a particle's position would require that we had zero knowledge of the particle's momentum.