Manfred (below) posted a complete analysis of the exact setup from Joint Configurations, given in Wikipedia, but failed to put enough exclamation marks on it.
That is outstanding! My Xmas present (you decide what you want to substitue for X) from Less Wrong! I understood the prediction, the fact that the result would show up as a dip in the coincidence of arrival times, and when the veil was finally lifted the experiment had been reported in 1987 with the “HOM dip” as the signal result!
It is interesting to note that in some sense you get the opposite result if you use electrons instead of photons. Photons and other bosons give the HOM dip, a suppression of coincidence in the two detectors. Electrons and other fermions give a HOM peak: when two identical fermions pass through the beam splitter you are guaranteed to see one in each detector, they NEVER both head for the same detector! This result is documented , although I don’t know if it has been experimentally verified.
So the things that really help me understand and accept the original article are
1) The Wikipedia article, explaining the effect in standard quantum terms and citing an experiment. 2) Understanding that the result applies to Bosons and the opposite to Fermions. It feels like a Boson result, and knowing you get the opposite effect for Fermions relieves the requirement to find your mathematical treatment bulletproof, as it doesn’t apply for all particles.
Thanks to everybody who put effort in to clearing this up!
Unfortunately it is not an analysis of the math used in Joint Configurations, which would have been nice. The single-photon case of reflection off a hard boundary reversing phase is obvious from the requirements of meshing with classical physics, but where the pi/2 rotation comes from in the post is unclear.
Now—and this is a very important and fundamental idea in quantum mechanics—the amplitudes in cases 1 and 4 are flowing to the same configuration. Whether the B photon and C photon both go straight, or both are deflected, the resulting configuration is one photon going toward E and another photon going toward F.
It looks like you’re saying that the result of the experiment is one photon going each way. It took about 3-5 reads to get from that to “the outcome of cases 1 and 4 are identical: one photon going to each detector.” I’m not sure if that’s just a reading comprehension failure on my part or if there’s a way to rewrite the sentence to make it clearer (I might just strike the word “resulting”).
Manfred (below) posted a complete analysis of the exact setup from Joint Configurations, given in Wikipedia, but failed to put enough exclamation marks on it.
http://en.wikipedia.org/wiki/Hong%E2%80%93Ou%E2%80%93Mandel_effect
That is outstanding! My Xmas present (you decide what you want to substitue for X) from Less Wrong! I understood the prediction, the fact that the result would show up as a dip in the coincidence of arrival times, and when the veil was finally lifted the experiment had been reported in 1987 with the “HOM dip” as the signal result!
It is interesting to note that in some sense you get the opposite result if you use electrons instead of photons. Photons and other bosons give the HOM dip, a suppression of coincidence in the two detectors. Electrons and other fermions give a HOM peak: when two identical fermions pass through the beam splitter you are guaranteed to see one in each detector, they NEVER both head for the same detector! This result is documented , although I don’t know if it has been experimentally verified.
So the things that really help me understand and accept the original article are 1) The Wikipedia article, explaining the effect in standard quantum terms and citing an experiment.
2) Understanding that the result applies to Bosons and the opposite to Fermions. It feels like a Boson result, and knowing you get the opposite effect for Fermions relieves the requirement to find your mathematical treatment bulletproof, as it doesn’t apply for all particles.
Thanks to everybody who put effort in to clearing this up!
http://en.wikipedia.org/wiki/Hong%E2%80%93Ou%E2%80%93Mandel_effect#!!!!!!
Unfortunately it is not an analysis of the math used in Joint Configurations, which would have been nice. The single-photon case of reflection off a hard boundary reversing phase is obvious from the requirements of meshing with classical physics, but where the pi/2 rotation comes from in the post is unclear.
The following section confused me:
It looks like you’re saying that the result of the experiment is one photon going each way. It took about 3-5 reads to get from that to “the outcome of cases 1 and 4 are identical: one photon going to each detector.” I’m not sure if that’s just a reading comprehension failure on my part or if there’s a way to rewrite the sentence to make it clearer (I might just strike the word “resulting”).