(adsbygoogle = window.adsbygoogle || []).push({}); FTL Signaling with Dopfer - Why Won't This Work?

I think at the outset we will all agree that the following will not work, but the more interesting question will be why.

Take the Dopfer experiment described at:

http://www.quantum.univie.ac.at/publications/thesis/bddiss.pdf [Broken]

On page 36, Dopfer shows an apparatus consisting of an "upper half" and a "lower half", each corresponding to one of two entangled photons. The "upper photon" is sent to a Heisenberg lens which focuses parallel photons to a single point on the focal plane. The detector D1 is placed fixed at the focal point. Photons in the "lower half" are sent through a double slit and then to a detector D2 which scans the x-axis. An interference pattern emerges when the photons are correlated with those in the upper half that have been detected at the focal point. The detection at the focal point results in position information being utterly destroyed, thereby allowing the interference pattern in the lower half to emerge.

JesseM and I have discussed extnesively why the coincidence circuitry is necessary and the conclusion we both reached is that with each position of D1, only a subset of photons is detected with position information destroyed; for the rest, it is possible, at least in principle, to detect position information. The only way to correlated that subset in the upper half with image-generating photons in the lower half is with slower-than-light coincidence circuitry.

And so I asked, what would happen if we destroyed position information for ALL the upper half photons corresponding to lower half photons that went through the slits? Would ALL of the lower-half photons going through the slits therefore generate an interference pattern? If so, could this not be used as the coveted switch to send a binary FTL signal?

So the means I thought of to destroy the position information in the upper half photons is as follows. In points in space in the upper half corresponding to the slits in the lower half, place two small biconvex lenses such that the focal point of those lenses is placed exactly where the slits would be in the lower half. All photons passing through those focal points will emerge parallel from the lenses. Then when those photons reach the Heisenberg lens shown on page 36 of Dopfer's thesis, ALL of them will strike the detector D1, thereby destroying position informaiton.

The question is: will an interference pattern then emerge from ALL photons striking detector D2, eliminating the need for coincidence counting? If not, why not?

Jesse suggested that placing the small converging lenses in the upper half might be problematic due to the HUP, that by isolating the photons to two small points in space, there is too much uncertainty in their momentum to ensure that they reach the correct lens and emerge parallel. However, the radius of the lenses could be large enough to account for the uncertainty, since the focal points would be quite small (5 mm or so).

So, why won't this work?

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# Variation on Dopfer Experiment - Why Won't This Work?

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