Actually, it's not such a bad idea. I'm not saying it will work, but
take a look at the following performed experiment:
"Experimental realization of Popper's Experiment: Violation of the
Uncertainty Principle?"
http://arxiv.org/PS_cache/quant-ph/pdf/9905/9905039.pdf
where the authors use entangled photons to measure DxDp<h, in apparent
contradiction to Heisenberg.
First they produce a position/momentum entangled pair of photons. They
align the system by putting an aperture in the path of each photon,
and arranging it so that whenever a photon goes through one, its
partner photon goes through the other aperture. So they prove that the
momenta are correlated within the uncertainty given by the aperture
width and path length. Then they remove the slit from one path, and
measure the position spread for those photons. So now whenever they
get coincidence, they know the momentum (from one) and the position
(from the other), and build up a statistic in Fig 5 where DxDp<h.
They make it clear that this is entirely within QM, and is only true
for entangled photons, not individual photons.
However, it is not clear to me what would happen in a double-slit
case. First block one slit each of the double slits, and align
according to the above experiment. In reference to Fig 5 of the above
paper, have the second slit at 1.5 mm from the first slit. This is at
a distance which is "within" the spread of the individual photons, but
"outside" the spread of the correlated photons. What would you get? It
seems too good to be true that the visibility of the fringes at B
would change, so they probably don't. My guess is that the visibility
cannot approach 1 for the fringes at B, so there is always some
component of interference, and some component of non-interference. By
correlating B with A, you can pick out the non-interference component,
but unless you know the result at A you cannot do this and you don't
have a FTL system. However, what is to stop the visibility at B from
approaching 1??? I would have thought it possible for the photons to
be as close to monochromatic and from a point source as you like. But
there may be a problem there.
I suggest you email Kim and/or Shih and get their view. I have emailed
Kim before, and he answered my questions, so if he replies please let
me know the answer!
There must be something which goes wrong, but I for one like the
question.
BR
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