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I am quite unsure of how phase coherence is ensured in the double slit experiment. The most typical answer that I have found is that the path length difference between the lights going in either double slit is zero, and so the phase is coherent. However, if we consider Young's experiment he used sunlight as his source which is incoherent. So in his setup, even though the diffracted light from the single slit pass through the same path length to reach the double slit, wouldn't the light still be incoherent?

I have seen explanations to this pointing out that the single slit acts as a point source for light and produces phase coherent light. If this is true, how can this be when the sunlight reaching the single slit is out of phase?

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    $\begingroup$ Sunlight is not temporally coherent, but it is spatially coherent. $\endgroup$
    – The Photon
    Commented Nov 2, 2021 at 17:19
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    $\begingroup$ May this be a duplicate to What makes the radiation behind slits coherent?? $\endgroup$ Commented Nov 4, 2021 at 4:43
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    $\begingroup$ All frequencies in sunlight are independent. Each frequency will therefor lead to its own diffraction pattern, all of which are overlaid on top of each other. A double slit with sunlight will therefor show a small amount of coloration with the red diffraction pattern being wider than the blue diffraction pattern. Unlike with much sharper optical grating patterns this dispersion is harder to notice. $\endgroup$ Commented Oct 22, 2022 at 8:24

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I am a fan of Richard Feynman and he used his path integral theory to explain much about light. He stated that every photon determines its own path .... and the corollary being that a photon will not travel a path if it cannot determine a path. The ideal path, the one of highest probability, is one that has an integer number of wavelengths, i.e. the distance between excited atom 1 and receiving atom 2 is ideally (or actually close to) this length, .... its all about probability.

How a photon determines a path is the result of transmission of forces (virtual photons) .... and real photons that transfer energy in/thru the EM field. It is the actual tight geometry of the DSE (narrow slits, pinpoint source, smooth screen) that only offers limited paths. Many photons approaching the first slit are actually reflected away ... just like hitting a mirror. The ones that pass satisfy the path integral and make the pattern.

The old classical interpretation is that photons must be in phase to cancel ... but photons never cancel as it would be a violation of conservation of energy. The classical and path integral theories have a lot of similarities mathematically and thus the classical theory is still taught today .... but you could argue its wrong to call it an "interference" pattern.

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    $\begingroup$ The semi-classical photon model is completely wrong. Photons don't have paths. They don't even exist in the free electromagnetic field. The only time we can talk about a photon is during an emission or an absorption process. "A photon" is simply the amount of energy, momentum and angular momentum that the emitting/absorbing system exchanges with the electromagnetic field. A path integral is also not the description of photon paths. It's the description of a quantum mechanical ensemble of fields. It does not describe how one field evolves but how an infinite number of fields evolve on average. $\endgroup$ Commented Oct 22, 2022 at 8:20
  • $\begingroup$ The principle of least action (or least time) is valid .... and we can time the speed of light and correlate with the distances travelled between emitter and absorber in our 3D world. Yes the EM field/path integral is infinite superpositions .... but in a DSE the geometries are well know and the PI predicts the absorption points on the screen. Paths are a great convenience in summarizing all the infinities ...... not to mention geometric optics. $\endgroup$ Commented Oct 22, 2022 at 20:38
  • $\begingroup$ We don't have a formula for the (x,y,z) coordinates where a quantum of energy will be absorbed. All we have are formulas that predict the average densities. In case of the double slit that density is identical to what Maxwell predicts. The first experiments in which field quantization really matters are something like the anomalous magnetic moment of the electron or the lifetime of positronium. One can see this fairly easily in the fact that the diffraction function of the double slit doesn't depend on Planck's constant. If it did, then Young would have noticed in 1801 already. $\endgroup$ Commented Oct 22, 2022 at 23:57

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