What I mean is that that Fourier analysis is simply a tool of human convention. Using trigonometric functions, we try to break up a waveform into it's spectral components. Analyzing duals (such as position and momentum) yields ambiguous results due to the simple fact that theyOriginally Posted byMutantJohnarecomplementary and thus non-commutative. Heisenberg saw this as the *source* of uncertainty in the universe! Who are we to say that the universe depends on Fourier transforms though? Perhaps some other mathematical construct may arise which effectively eliminates the need for Fourier analysis altogether (just as quaternions eliminate the singularities encountered when working with Euler angles).

Exactly - the latter is what we should *really* be talking about here! Mathematical operators are mere human constructs that have no place in the formulation of a physical law. It's a procedural issue, nothing more...Originally Posted byMutantJohn