# Interfering alternatives and identical particles in Feynman and Hibbs

I am currently self-studying Feynman and Hibbs, and in his first chapter, Feynman talked about 'alternatives' like the various possibilities or paths an experiment can take. He defined two different types of 'alternatives'- interfering alternatives and exclusive alternatives. He then used this concept to explain Identical Particles in Quantum Mechanics (page 17), but I can't seem to understand his explanation for identical electrons using scattering experiments. I have linked the screenshot at the end of the page.

In summary, I'm confused with the following. Feynman argues that if two particles are "approximately identical", we can do a scattering experiment, starting from positions A and B, and then determine by close scrutiny if the particle reaching the position 1 was from A or B. Since this act of scrutiny occurs after the scattering event, our measurement can't affect the scattering process. If we can possibly resolve the difference between the two particles, and if the measurement to determine the particle doesn't affect the scattering process, that means that these alternatives are exclusive (particle from A reaches 1, and particle from B reaches 1) and there should be no interference between the probability amplitudes of these alternatives. I understand his arguments till now, but I start to get confused after this.

Now he says, that we can conclude from the uncertainty relation that there is no way to distinguish these possibilities. (particle from A reaches 1, and particle from B reaches 1), which sounds like a contradiction since we just discussed that they can be distinguished. And thus he concludes that identical electrons can't be distinguished.

I don't really understand the leap that he took from the inference of non-interfering amplitudes, to uncertainty relation and then to identity of electrons, neither was I able to find any other explanation on the internet about this. If someone could clarify it, that would make it a whole lot easier.

• This part was indeed confusing for me too. I'll be happy if someone answers this. Commented Dec 29, 2020 at 15:38
• I am currently reading from the book and trying to figure this out as well. Unfortunately I can't get myself convinced, even reading the answer below. Did you eventually understand it? Commented Oct 3, 2021 at 6:48