Exploring Euler's Formula in First Order Chemical and Nuclear Reaction Kinetics

[GregBrown]

Has anyone ever encountered a discussion on the topic of applying Euler's formula

exp(i*x) = cos(x) + i * sin(x)

to the equation governing first order chemical (and nuclear) reaction kinetics?

d[Reactant]/dt = C*[Reactant]

 

[BvU]

Hi CJ,

No

 

[mfb]

If you set $x=-icR$ where c is a constant and R is the concentration then $e^{ix}$ is a solution to the differential equation, but this is just needlessly adding complications to the problem.

 

[GregBrown]

I’m a physician (pathologist) and wholeheartedly endorse your preference for the simpler, Real domain approach, which provides an adequate solution for all observable features of the process. It is that very preference (for the Real domain) that is the point of my post. Indulge me for a moment and consider the implications of the Complex domain solution. Exponential processes may be a “keyhole” through which we can spy a more complete understanding. The Imaginary and Complex domains enlarge the solution space of exponential processes in a way quite beyond lived experience. There simply is nothing in the physical universe that is not amenable to the enumeration and ordering process we refer to as “measurement”, while the Imaginary domain provides no comparable amenity. There are extremely compelling reasons for our preference (for the Real domain) that are reasonably self evident. [this is left as an exercise for the reader]The Complex solution, $cos{x} + i*sin{x}$ necessitates not only that the reaction products are sinusoidal, the reactants must also be sinusoidal. I’m back to where I started: there are no “particles”, only waves

 

[berkeman]

Thread closed temporarily for Moderation...

 

[berkeman]

The Complex solution, cosx+i∗sinxcos{x} + i*sin{x} necessitates not only that the reaction products are sinusoidal, the reactants must also be sinusoidal. I’m back to where I started: there are no “particles”, only waves

Personal theory development is not allowed at the PF. Please check your PMs; thread will remain closed. Thank you everyone for your contributions to the thread.