Yes of course it's hand wavey, all analogies are hand wavey. That's why they're called analogies and not lectures. You don't devise an analogy to deliver all th

Yes of course it's hand wavey, all analogies are hand wavey. That's why they're called analogies and not lectures. You don't devise an analogy to deliver all the academic rigor of a topic, you devise it to ground something back into the realm of the intuitive and familiar. Not all analogies are useful, but the reason this one is useful is because it captures the heart of why this isn't meaningfully "time reversal." If you have all information about a linear system, yes you can transform it back into its previous state. That's not at all mysterious or unintuitive even if it's a technical achievement. Obviously reality is nonlinear, which is precisely the point the analogy is trying to capture. We're not trying to teach quantum mechanics here, we're trying to make sure people don't come away from the article thinking the second law of thermodynamics is (non-locally) violated or that time travel at the macro level is plausible. The basic idea is that you did a reversible thing, then reversed it.