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alex2718 comments on Feynman Paths - Less Wrong
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When we sum over all paths some paths are longer than others. The argument says that the phase arrow will move further round because the time is longer. If the time is longer the the path won't end at the destination at the right time to coincide with the other paths. So how can this work?
The amplitudes don't coincide at the end. In fact some are pointing oppositely to each other and so cancel out. The final amplitude for a photon at P is the sum of the configurations coming into P. The amplitudes don't equal each other, but they can be added together to yield the amplitude for a photon at P.