I have the following conceptual problem with the quantum effects of (in)distinguishability of particles:(adsbygoogle = window.adsbygoogle || []).push({});

Imagine the following experimental setup. I have two pairs of entangled electrons, A1, A2, B1, B2 (i.e. A1 is maximally entangled with A2, and so is B1 with B2). The spins of all electrons are random and I don't know them. I keep A1 and B1 and send A2, B2 to my partner.

My partner makes a measurement on his particles, say, measures the spin z-component of A2 and B2, but keeps the results to himself. So, for example, if he gets +1 on A2, he knows that A1 is now in the -1 eigenstate, since these particles were entangled, and likewise for the -1 result. Suppose that A2 and B2 now have opposite spins (if not, I simply repeat the experiment from the start).

Now imagine two experiments:

a) I collide A1 with B1, without knowing the results of my partner's measurements; since, to my knowledge, the particles are indistinguishable (I don't know anything about their spins before the collision), I get a "fermion-like" collision, i.e. interference of two possible collision scenarios; I assume that the interaction during the collision is such that no spin exchange occurs

b) I phone my partner to get the results of his measurements; now I know which of my electrons is which (beacuse I know that A1 has spin +1 and B1 has -1 or vice versa); the particles are therefore distinguishable, so the collision I'll get is the "distinguishalbe particles collsion", with no interference

The only difference between a) and b) is my telephone call, i.e. acquiring information about the identity of electrons A1 and B1. So, it seems that either my information can affect the physical collision, which is nonsense, or I don't get interference in a) (i.e. electrons are indistinguishable to me, but collide like distinguishable particles), becausein principleI could know their identity.

Now, my question is: how, in this example, can you formalize the notion of "knowing in principle" or "being able, in principle, to acquire information about the system"? Maybe this can be done under the information-theoretic framework? Does it matter that the information about my particles is physically "encoded" somewhere (in this case, in my partner's measurement results) and so affects (how?) the outcome of my experiment? I know that questions like "how does the electron know whether you have the information or not?" are silly nonsense, however, I think that the notions of "information" and "in principle" here needs clarifying.

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# (In)distinguishable particles

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