Brian Bi

If someone could film the process of radioactive decay and play it back fast, what would the movie look like?

You can't, really. There is a lot of intrinsic uncertainty at the subatomic level in accordance with the Heisenberg uncertainty principle. The particles involved in the decay have neither particular positions or particular momenta, just a wave function that sort-of describes both (incompletely) at the same time. You can measure one or the other at some given point in time (just not both accurately at the same time). If you measure a particle's position at two times, you can't know exactly what path it took between those two points (according to the path integral formulation of QM, it actually takes all possible paths). If you observe it "continuously", then you also disturb it continuously, because you cannot observe anything without interacting with it somehow (for example, in a dark room, we must fire photons at something before we can observe it); so you won't see "what is really happening" (which has no well-defined meaning, anyway).

A common model of alpha decay found in undergraduate textbooks involves imagining that there is already an alpha particle trapped inside the nucleus that has to quantum-tunnel through the strong-interaction barrier in order to escape. One moment it's inside the nucleus; the next, it's outside. You can't observe what's "actually happening" when quantum tunnelling takes place; the only correct description in QM is that part of the alpha particle's wave function is already outside the nucleus, which means it has a nonzero probability of ending up there during any given interval of time.

Meanwhile, for beta decay, we can draw Feynman diagrams (e.g., up quark emits W+ particle and changes into down quark; proton changes into neutron; W+ particle decays to positron and neutrino) but the W+ particle involved in this process is "virtual" and cannot be directly observed (unlike the "real" W particles produced in some of the world's most powerful particle accelerators). Thus, all we can observe is that in one moment there's a proton and in the next there's a neutron, an electron, and a neutrino. Electron capture is similar.