Wikipedia: Hartley transform
Weird, I get three math-related matches on the first page: [SIZE="1"] http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=272142 http://dx.doi.org/10.1109/CIC.1989.130514 http://www-hsc.usc.edu/~jadvar/CinC-Cepstrum.pdf
Interesting, but it seems to assume a priori the use of 2-dimensional quantities of some sort, though not complex numbers specifically. Has anyone devised a similar argument that rules out the reals?
The initial development of QM inherited the use of complex numbers from Fourier analysis. Had Hartley analysis been invented first, is it possible that QM might have been formulated in terms of real-valued quantities instead, or are complex numbers in some sense natural or necessary when...