2 ms·

Sorry, I didn't mean to imply that my comment should apply literally to all cases. I am just pointing out to parent that particles can be indistinguishable in

Sorry, I didn't mean to imply that my comment should apply literally to all cases. I am just pointing out to parent that particles can be indistinguishable in principle, and not just as a technological limitation of our measurements. Moreover, there is an experimental way to tell the difference between distinguishable and indistinguishable, roughly based on the difference between probabilities and amplitudes. To dig deeper one must look at the details, e.g. in Feynman's lectures vol. III. The statement that protons are indistinguishable is not strictly correct either, because protons have a spin. Protons with the same spin are indistinguishable, but you can tell apart protons with different spin. The spin of protons can only assume two values, so effectively there are two classes of protons, indistinguishable within the class. In your specific case, it is clearly false that the probability of having one particle in one place is 200%. However, my statement still holds for expectations, and you end up with an expected two particles in one place. In the indistinguishable case, you must compute expectations based on amplitudes, not probabilities.

db48x 5y ago
Yea, spin adds a new level of complications. You can distinguish between two otherwise–indistinguishable protons if they have opposite spin, but the spin of a proton can also change over time (usually due to interactions with other particles, such as stray radio waves passing through your experiment). Going back to the experiment that I described, you can imagine that the particles are released at A and B with opposite spins, and then the detector at A’ only detects the spin that corresponds to the particle at A. This causes you to measure yet another probability, distinct from the other two, because there are now more possibilities and there are still multiple ways to cause the detector to find something. It could detect the proton from A, but the proton from A could also have its spin flipped and thus not be detected. The particle from B could arrive at A’ with the wrong spin and not be counted, or it could have its spin flipped along the way and be counted. You still cannot tell which proton you detected! Similar complications occur with polarization of photons, which someone else mentioned in one of the comments. It’s worse though because polarization is a continuous quantity, and there are more ways to change it.

db48x 5y ago

Yea, spin adds a new level of complications. You can distinguish between two otherwise–indistinguishable protons if they have opposite spin, but the spin of a proton can also change over time (usually due to interactions with other particles, such as stray radio waves passing through your experiment). Going back to the experiment that I described, you can imagine that the particles are released at A and B with opposite spins, and then the detector at A’ only detects the spin that corresponds to the particle at A. This causes you to measure yet another probability, distinct from the other two, because there are now more possibilities and there are still multiple ways to cause the detector to find something. It could detect the proton from A, but the proton from A could also have its spin flipped and thus not be detected. The particle from B could arrive at A’ with the wrong spin and not be counted, or it could have its spin flipped along the way and be counted. You still cannot tell which proton you detected! Similar complications occur with polarization of photons, which someone else mentioned in one of the comments. It’s worse though because polarization is a continuous quantity, and there are more ways to change it.