40 years ago I worked in my freshman chem prof's lab measuring lots of rate constants for 1st order reactions and observed that 1st order kinetics seemed to be nearly ubiquitous - all simple chemical and nuclear processes are described by the exponential rate law. At the time I had a passing thought about the meaning of complex exponents in this setting. Of course, complex math has many useful applications, but the cosine of a mass or concentration wasn't meaningful (to me at least) so I dismissed the thought and forgot about it. In the intervening years I became a physician specializing in pathology. Chemistry and the semester I took of quantum mechanics atrophied. Recently I have been struck by the fact that we understand the physical world exclusively via measurement - the Real number system. Undoubtedly this is a consequence of our fundamental purpose as biological entities. Namely, reproduction. Another feature of life is something I call "parsimony": Life is laser focused only on phenomena that enhance reproductive success and is blind to everything else, without exception. If it were otherwise for some organism it would lose the race for survival and cease to exist. The imaginary dimension, which surely exists, does not lend itself to comparison, or measurement, that is essential to, eg, identifying edible plants, chasing down prey, selecting the optimal mating partner, etc.
Back to kinetics: A chemical reaction is a collection of molecules in space undergoing change with time. Leave the "Real" world for the Complex plane, rather than reaching some equilibrium it takes on the oscillatory character of sine and cosine functions. What this suggests to me is that my particles-in-space-time understanding of chemical reactions is an incomplete, deficient picture, and very likely "particles" are the parsimonious, biological simplification of the Real, measurable component of a process occurring in the complex dimension, while "space-time" is the Imaginary component. Have I joined the esteemed gallery of crackpots who misunderstand the weirdness of quantum mechanics? Has anyone ever explored the application of Euler's formula to first order kinetics? Is it conceivable that my idle speculating has actually unearthed some gem? My apologies if reading these two paragraphs has been a waste of your time