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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...

enter image description here

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

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marked as duplicate by Jon Custer, Yashas, sammy gerbil, peterh, heather Aug 6 '17 at 18:26

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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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  • $\begingroup$ I guess I'm having a hard time understanding what is being represented in these drawings with the waves. If we shoot a photon a a precise time at the two slits, then there isn't crest after crest of probability when the photon will hit the slits. Unless... when we talk about these crests and troughs, there are multiple crests of probability per photon, so that the different crests can interfere with each other? $\endgroup$ – J.Rockefeller Aug 4 '17 at 18:56
  • $\begingroup$ @J.Rockefeller The wavefunction is a plane wave before it enters the slits, and is a sum of two cylindrical waves when it leaves the slits (in the limit of long slit length). The diagram is meant to depict this fact. And there actually is a nontrivial probability distribution for the flight time of the photon. The photon can take different paths, which are different lengths. As such, depending on the path it takes, it will arrive at the screen after a different delay each time. $\endgroup$ – probably_someone Aug 4 '17 at 19:06
  • $\begingroup$ @J.Rockefeller The point I'm trying to make is that the wavefunction, not the photon, is the fundamental object in quantum mechanics. The behavior of measurable objects is determined by the shape of their wavefunction. $\endgroup$ – probably_someone Aug 4 '17 at 19:09
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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

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