This is a linkpost for https://www.wired.com/2014/06/the-new-quantum-reality/
So, does the bouncing oil droplet also tunnel through barriers, spontaneously arise or annihilate, and occupy discrete energy levels?
Because to me this seems like merely an analogy that works in some aspects, but fails in other aspects.
Yes and yes and yes (those are all examples mentioned in the article). If you have a specific example of a quantum phenomenon that pilot wave theory doesn't exhibit, I'd like to know. Pilot wave advocates claim that pilot wave theory results in the same predictions, although I haven't had time to chase down sources or work this out for myself.