It is entirely likely that the 201 physics class I had in 1990 is both dated, and not as sophisticated as your (or current) understanding of how very small particles exist, move, and are observed. IANAP :)
Well there is the underlying unobservable quantum state that seems to be evolving smoothly, just because observations decohere the state into seemingly discrete observables… you might think this means that it’s looks like particles are evolving discontinuously.
The true reality of everything *is* the quantum state, so i don’t think it’s true to say that just because you observe discrete outcomes that particles don’t move continuously, unless you are referring to some other mechanism i have never heard about.
There is even evidence (yale 2019, quanta article here[1]) that quantum decoherence is more of a smooth phenomenon vs an instantaneous, discrete jump.
[1] https://www.quantamagazine.org/quantum-leaps-long-assumed-to-be-instantaneous-take-time-20190605/
Discussion
I'm really not that much more enlightened after reading your link and this:
https://www.physicsforums.com/threads/particle-movement-in-quantum-mechanics.1054807/
The combination reminds me that observation has a resolution, and this is a separate issue and equally weird for multiple reasons. I do remember at the time that I cycled around that point of particle movement, and went back to my professor, as it disturbed me.
I'll remember going forward that I know longer *know* that small particles move in a discontinuous way. (I also remember the professor saying something like the particles are only statistically there.)
I kind of like that way... slowly realizing that nothing you thought you knew is still valid, until you just... disappear...
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.
In your quantum measurement tho, who is the observer? And why should I trust them?