I would just look at the Schrödinger equation. It describes how a wavefunction evolves smoothly over time. It’s a continuous function. Considering everything in the universe at the fundamental level is described most accurately by propagating quantum waves which when measured in different ways give different observables… it makes sense to me to just think of the quantum state as the smoothly evolving thing.

I got o3 to do an analogy:

Think of a weather radar map:

• The underlying atmosphere obeys smooth fluid dynamics.

• Your phone, however, refreshes the radar every 5 minutes with a bunch of colored pixels that jump across the screen.

• Nobody concludes that raindrops teleport; we just recognize the pixels are a low‑resolution sampling.

Quantum measurement is like sampling the “atmospheric pressure field” (the wavefunction) with very coarse, yes/no pixels. The smoother the waves, the more “surprising” the pixel‑to‑pixel jumps can look.