Well, I am not a physicist, but I can fake it well enough for HN :-) Before I say anything, if you have never heard of amplitudes before, you should read the F

Well, I am not a physicist, but I can fake it well enough for HN :-) Before I say anything, if you have never heard of amplitudes before, you should read the Feynman lectures on physics vol. III, which you can find here: https://www.feynmanlectures.caltech.edu/III_toc.html https://www.feynmanlectures.caltech.edu/III_toc.html Specifically read chapter 1 and chapter 3. The specific situation about distinguishable/indistinguishable particles is described in section 3-4. Your question is kind of phrased backwards. Probabilities and amplitudes are human inventions to describe Nature's behavior, so by themselves they don't imply anything about Nature. The implication is the other way around: Nature has decided that some particle pairs are indistinguishable (proton vs. proton) and some are distinguishable (proton vs. neutron). Different rules apply to the two cases. This indistinguishability is a pure quantum phenomenon. In a classical world, all objects are distinguishable---you can in principle label all protons and know which is which. But Nature does not work like that, and there exists this peculiar notion that you cannot tell two protons apart not even in principle. There is no deeper explanation of this phenomenon AFAIK---it is what it is. You can tell experimentally whether two particles are or are not distinguishable by running the experiment as in Feynman 3-4. If you observe a distribution consistent with the add-amplitude rule, then the particles are indistinguishable. Any attempt to distinguish them leads to the contradictions explained in Chapter 1. There is an even more peculiar phenomenon. Despite being indistinguishable, swapping two indistinguishable particles is not a no-op because it changes the amplitudes. You must still add amplitudes, but the amplitudes are different, yet different in such a subtle way that you still cannot tell the particles apart. Feynman 3-4 tells you how the amplitudes change during the swap, with a deeper explanation in chapter 4.