Noticed something interesting...

For a simple spring system F= -kx so mx'' = -kx or x''+kx/m = 0. This is a homogeneous 2nd order linear DE so the solutions are:

x = e^{+/- i*sqrt(k/m)} where i = sqrt(-1). Now convention has it that there only the real solution is taken because we don't assume that the spring is also producing harmonic motion in higher dimensions.

My question is why does quantum mechanics assert that quantum complex valued wavefunctions are ontologically "real" when only real valued observations are observed in experiments? And why in contrast to this simple spring in which we make no such claims about complex valued mechanical springs?