He’d be right in any classical universe. But we don’t live in a classical universe.
Our ability to perform an experiment that tells us positively that two particles are entirely identical, goes right to the heart of what distinguishes the quantum from the classical; the core of what separates the way reality actually works, from anything any pre-20th-century human ever imagined about how reality might work.
If you have a particle P1 and a particle P2, and it’s possible in the experiment for both P1 and P2 to end up in either of two possible locations L1 or L2, then the observed distribution of results will depend on whether “P1 at L1, P2 at L2” and “P1 at L2, P2 at L1” is the same configuration, or two distinct configurations. If they’re the same configuration, we add up the amplitudes flowing in, then take the squared modulus. If they’re different configurations, we keep the amplitudes separate, take the squared moduli separately, then add the resulting probabilities. As (1 + 1)2 != (12 + 12), it’s not hard to distinguish the experimental results after a few trials.
(Yes, half-integer spin changes this picture slightly. Which I’m not going into in this series of blog posts. If all epistemological confusions are resolved, half-integer spin is a difficulty of mere mathematics, so the issue doesn’t belong here. Half-integer spin doesn’t change the experimental testability of particle equivalences, or alter the fact that particles have no individual identities.)
And the flaw in Bob’s logic? It was a fundamental assumption that Bob couldn’t even see, because he had no alternative concept for contrast. Bob talked about particles P1 and P2 as if they were individually real and independently real. This turns out to assume that which is to be proven. In our universe, the individually and fundamentally real entities are configurations of multiple particles, and the amplitude flows between them. Bob failed to imagine the sequence of experimental results which established to physicists that this was, in fact, how reality worked.
Bob failed to imagine the evidence which falsified his basic and invisibly assumed ontology—the discoveries that changed the whole nature of the game; from a world that was the sum of individual particles, to a world that was the sum of amplitude flows between multi-particle configurations.
And so Bob’s careful philosophical reasoning ended up around as useful as Kant’s conclusion that space, by its very nature, was flat. Turned out, Kant was just reproducing an invisible assumption built into how his parietal cortex was modeling space. Kant’s imaginings were evidence only about his imagination—grist for cognitive science, not physics.
Be careful not to underestimate, through benefit of hindsight, how surprising it would seem, a priori, that you could perfectly identify two particles through experiment. Be careful not to underestimate how entirely and perfectly reasonable Bob’s analysis would have seemed, if you didn’t have quantum assumptions to contrast to classical ones.
Experiments tell us things about the nature of reality which you just plain wouldn’t expect from a priori reasoning. Experiments falsify assumptions we can’t even see. Experiments tell us how to do things that seem logically impossible. Experiments deliver surprises from blind spots we don’t even know exist.
Bear this in mind, the next time you’re wondering whether mere empirical science might have something totally unexpected to say about some impossible-seeming philosophical question.
