Does wave superposition consume time?

[LarryS]

In Classical Mechanics, waves produced in linear systems, like EM waves, obey the Superposition Principle in which the wave amplitudes of, say two input waves, “add up” to create one output wave whose varying amplitude is the sum of the two input waves. One example would be Young’s Double Slit experiment, the two waves being the waves emerging from the two slits.

In QM, systems are also linear and wave functions also obey the Superposition Principle. The Double-Slit experiment is also a good example of superposition in QM. The two waves emerging from the two slits superpose and create the interference pattern.

I’m not sure if this should be two questions, one for CM and one for QM.

Question: In wave superposition, does the “adding up” of wave amplitudes constitute a genuine physical process that consumes time, or is it more of a mathematical phenomenon that is immediate?

Thank you in advance.

 

[hilbert2]

It doesn't consume any time. You can always write a function $A(x,t)$ describing wave motion as a sum of two (or as many as you want) components, like in

$A(x,t) = \sin(2x - t) = \left(\sin (2x-t) + \sin(3x-t)\right) - \sin(3x -t)$,

where the $\left(\sin (2x-t) + \sin(3x-t)\right)$ and $- \sin(3x -t)$ are the two components. The only thing done here is adding and subtracting the same term.