Setting aside most problems with the original, I’ve always found this interferometer example an unsatisfying introduction because it’s surprisingly ambiguous exactly what’s quantum mechanical here or what’s special about quantum mechanics.
You have superposition and interference in classical electromagnetism. That’s enough for everything until you get to the two-photon experiment (that is, for everything in “Configurations and Amplitude”). Single photons and photon counters are posited, but these are taken as given where I would sooner take as given the idea that a solution to a wave equation can be associated with a complex amplitude. Otherwise, up to that point one might as well have been talking about electromagnetic pulses and intensity detectors.
So is the interference between many-photon states the key? (“Joint Configurations”?) Not exactly. If you have classical light sources, then both quantum and classical theories give the same answer. Worse than that, really—for the quantum description, you have to posit that photons from different sources can be indistinguishable for the purposes of interference between many-photon states (“Distinct Configurations”, although it’s extra unclear about that), whereas that comes naturally if you’re just talking about electromagnetic fields as usual.
It feels somehow unfashionable in an age of quantum information to talk about wave-particle duality as the central surprise in quantum mechanics, but I think it’s right to zero in on the idea that you get superposition and interference in systems where otherwise-successful analogies from everyday experience don’t allow that.
Maybe it’s because my perspective is “electromagnetism-first”. From that direction, you’d introduce quantum mechanics by establishing the need for photons with things like the photoelectric effect. I suppose if you’re coming from the perspective that photons are only real, discrete, individual particles, then all this build-up for interferometry might make sense—did you know light can act like a wave, too? But then I think electron diffraction or spin polarization is more straightforward and doesn’t risk hammering on things that are totally fine classically.
(A marginally related suggestion—the diagrams of MZIs with lasers are going to be a little misleading for talking about experiments with photon number states, because lasers are not single photon sources. Maybe I’d be clearer about the difference between the diagram and situation in the text or just modify the figure.)
Setting aside most problems with the original, I’ve always found this interferometer example an unsatisfying introduction because it’s surprisingly ambiguous exactly what’s quantum mechanical here or what’s special about quantum mechanics.
You have superposition and interference in classical electromagnetism. That’s enough for everything until you get to the two-photon experiment (that is, for everything in “Configurations and Amplitude”). Single photons and photon counters are posited, but these are taken as given where I would sooner take as given the idea that a solution to a wave equation can be associated with a complex amplitude. Otherwise, up to that point one might as well have been talking about electromagnetic pulses and intensity detectors.
So is the interference between many-photon states the key? (“Joint Configurations”?) Not exactly. If you have classical light sources, then both quantum and classical theories give the same answer. Worse than that, really—for the quantum description, you have to posit that photons from different sources can be indistinguishable for the purposes of interference between many-photon states (“Distinct Configurations”, although it’s extra unclear about that), whereas that comes naturally if you’re just talking about electromagnetic fields as usual.
It feels somehow unfashionable in an age of quantum information to talk about wave-particle duality as the central surprise in quantum mechanics, but I think it’s right to zero in on the idea that you get superposition and interference in systems where otherwise-successful analogies from everyday experience don’t allow that.
Maybe it’s because my perspective is “electromagnetism-first”. From that direction, you’d introduce quantum mechanics by establishing the need for photons with things like the photoelectric effect. I suppose if you’re coming from the perspective that photons are only real, discrete, individual particles, then all this build-up for interferometry might make sense—did you know light can act like a wave, too? But then I think electron diffraction or spin polarization is more straightforward and doesn’t risk hammering on things that are totally fine classically.
(A marginally related suggestion—the diagrams of MZIs with lasers are going to be a little misleading for talking about experiments with photon number states, because lasers are not single photon sources. Maybe I’d be clearer about the difference between the diagram and situation in the text or just modify the figure.)