Could classical motion be the real part of a deeper complex dynamics?

I’ve been exploring an idea about classical mechanics and time evolution:

What if classical motion—like a harmonic oscillator—is just the real part of a complex dynamical system, where the imaginary part drives the time evolution itself?

In this view, what we see as x(t) is merely the projection of a deeper, rotating complex motion. The imaginary component effectively encodes the “direction in time,” explaining why motion progresses.

This resembles the Schrödinger equation or Pilot-Wave theory, but entirely at a classical level—no separate guiding wave is needed. The time evolution is inherent in the complex structure.

I’m curious: has anyone explored this perspective before? Could this offer a novel bridge between classical and quantum viewpoints?

I’d love to hear thoughts, critiques, or related references.

Yes, I know this view really only suits rotating or oscillating classical systems; linear or accelerated systems gain no real benefit.

But it does make me wonder: could the imaginary part, as a ‘phase propagator’, offer a logical picture of decoherence? Different classical rotations with phases averaging out could illustrate why macroscopic systems appear decoherent, even if each underlying rotation is fully deterministic.