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an electron falling from one atomic shell to another
Sophie, the purpose of using the "electron falling through shells" thought experiment was exactly to show that a wave-particle duality that people are familiar with, should be extendable to all wavelengths, which people are not familiar with.
Ian, please try to be polite.I think the problems with the two slit experiment are easier to fathom when you consider reducing the number of photons (or particles) to such a low level that there is only one photon in the system at any time. The interference pattern still emerges over a suficient period of time. If you place a detector in one of the slits, it will destroy the interference pattern. If the detector is such that only some photons are detected you could consider this as the same as a 100% detector being randomly moved in and out of position. This will clearly produce a combination of single and double slit patterns according to the statistics of the detector's ability to detect. This is another way of looking at it, but is the same as Sophie's answer.
In one thought experiment photons are released one by one and a diffraction pattern is seen at the opposite end - this requires a vector summation of field so the photon must be going through both holes at once, if it is a particle.
this commentary remains absurd - from two silly slits in a piece of paper. The wave probability function "propagates" through both isn't that obvious? There is nothing hard to understand in this.
so the photon must be going through both holes at once, if it is a particle
I never can understand the obsession with the Two Slits Experiment. Diffraction happens everywhere. All the arguments rehearsed here apply in every em interaction in the Universe. People seem to want photons to be different when in a very simplified context.
The strength of the experiment is in demonstrating that whatever you're shooting at it is a wave. Since most of us would have no doubt about the wave nature of photons (they make up light waves, after all), watching them behave as waves isn't really a surprise... For photons, what is interesting is watching contexts (the photoelectric effect) there they behave as particles rather than waves.