Essay Abstract
Some theories are declared as fundamental to mathematics or to physics while they are strictly speaking rather based on semi-fundamental constructs, at best. Application of complex Fourier transform (FT) on functions of time f(t) was in the 20th century and is perhaps still considered as a if not the most fundamental mathematical method of physics and technology. Actually, FT is a tool that doesn't immediately fit to measured data of real processes. Fourier assumed f(t) to extend indefinitely to both sides, mathematically speaking from minus infinity to plus infinity. This implied taking a static view of the world. The alternative dynamic view has proved the more appropriate basis: In reality, in contrast to closed models of processes, the future is more or less open to erratic influences and evades therefore complete prediction. Causality means: Only the past is absolutely closed in the sense it cannot be changed. This essay reminds of how a trick adapted the FT on real conditions where future data are not yet available and asks: Is complex FT with analytic continuation indeed a primary and indispensable fundament? There is a surprising but compelling counterargument: Instead of using complex calculus, any analysis of measured data may, in principle, be based on the real-valued cosine transform (CT). Real time audio technology benefits from CT. The missing in CT imaginary part is obviously a redundant copy. CT and FT are equivalent to each other except for an arbitrarily added to the latter point of reference, and subjectively chosen references are definitely less fundamental than non-arbitrary ones. Therefore, some putative pillars of science are suspected to be just semi-fundamental constructs on a shaky basis. Judge yourself.
Author Bio
See http://www.fqxi.org/community/forum/topic/369 . The author would like to appreciate FQXi contests and discussions guiding him in his ongoing critical and self-critical search for correct basics. His last boss had refused to comment on his IEEE paper [4] because he considered the matter as too ("so was von") fundamental.