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When discussing the interference pattern of a double slit, it is often described as two sets of concentric circles rippling out towards the wall and interfering with each other. In truth, each circle beyond the initial two propagating towards the wall represents a FOLLOWING wave (or particle)--one that happens slightly later in time than the wave crest before it. So how can these following waves interfere with the first wave if the photon is shot one at a time?

I must be understanding these diagrams wrong, but I don't understand how...

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Here's another way of looking at the question: enter image description here

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Your misunderstanding is based on what's interfering here. Individual photons aren't interfering with each other; rather, the portion of the wavefunction coming from one slit interferes with the portion of the wavefunction coming from the other slit. The path of any individual photon that is unaltered by any in-flight measurement is random, with a probability distribution determined by the squared magnitude of the wave function.

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I guess it was easy for me to conceptualize this interference pattern, but it requires a (pair of) stationary source(s) for ripple after ripple over time to create the radiating interference pattern:

enter image description here

Whereas this interference pattern is more true to what you (@probably_someone) are saying (I think), which is a local wavefunction traveling through time:

enter image description here