The way my inner child handwaves it away: you have the electron wavefunction spread out, say, it’s equally likely to be in one of 2 points in space. If you only look at one of these 2 points, you are likely to measure only half an electron.. until an adult (say, you) corrects me (using the Feynman Dirac hand/belt trick)
That explains having a 50% chance of seeing an electron somewhere, not seeing an entity of charge 1/2. It's like a weather report saying there's a 50% chance of rain doesn't mean you're going to see little raindrops cut in half.
If you look at the experiments, they don’t mention observing a single entity of fractional charge, it is always in terms of aggregate behavior under EM fields: conductance(1) inferred from shot noise (2), or density (3)
Personally, I find it curious that people talk about detecting single photons, but in these fractional charge experiments, nobody mentions detecting a single quasiparticle.
As for the math, nobody says it outright, or even in a single paragraph, but a fractional charge (“filling fraction”) of p/q does correspond to p “normal” charges distributed over q degenerate states (q=2 equivalent locations I used in the naive example)
> Personally, I find it curious that people talk about detecting single photons, but in these fractional charge experiments, nobody mentions detecting a single quasiparticle.
You detect a single photon when it perturbs an apparatus like a photon multiplier; you detect a single quasiparticle when it perturbs a split stream of electrons.
The apparent difference is that photons can travel through free space and strike such an apparatus from afar; while quasiparticles definitionally cannot. However, I’ve read about experiments that measure a single anyon on a dot by wrapping electron interferometry around it, which is measuring the lone quasiparticle on that dot.
I still think my point, originally about 1 electron split into 2 locations, or “ends” of string (but devolving to a complaint about casual ignorance of the central issue in publications) hasn’t been completely destroyed, because here you are measuring interference of 2 anyons, somewhat like measuring the interference of a photon “with itself” in a double split experiment.
The broader point could be that the effect of a single photon is “localized”, but here to see the effect, you have to move 1 anyon in a “complete path” around the other, recalling the Feynman/Dirac belt in my top level comment, a trick I said an adult should try to correct me with :)
