At arxiv.org this week, I posted a new paper which concludes with an interesting idea for a simple kind of decisive triphoton experiment, shown in figure 3:
Zeilinger's group (quant-ph/9810035) says they have a source which can produce a wave function I would write as
1/sqrt(2) ( (|1>a)(|1>b)(|2>c)+(|2>a)(|2>b)(|1>c)).
(Ouch! Blogger uses "gt" for the greater than character, the right angle bracket. Sorry. I can't fix blogger this morning. So MANY restrictive machines in our world!)
If c is far away, and tuned to a polarization angle of zero degrees, but a and b are close and tuned to 45 degrees (a) and ninety degrees (b),
then on a first glance it seems to me that it matters which polarizer is closer to the source, a or b, even if the distance is very small,
according to Copenhagen quantum mechanics. As soon as "a" is observed (detection or not), the rest of the experiment becomes like a Bell's Theorem experiment with 90 degree difference in polarizer angles. But when "b" is observed, what remains is a Bell experiment with only 45 degree separation. I think that triple detection is absolutely impossible (zero probability) in the first case, but nonzero in the second.
If I understand what quantum mechanics predicts here, I view this as a kind of "Einstein Podolsky Rosen experiment, but at a new level."
Would quantum mechanics really fit this prediction, that a small change in timing of a and b would have a big effect? My alternative local causal model says it wouldn't. If quantum mechanics is right, I think this implies FTL communication (which Bell's Theorem experiments do not allow),
because we could put the c polarizer a meter on one side, and a and b both 90 centimeters on the other side, yielding information flow from a and b to c as if c were only 10 centimeters away. If quantum mechanics is wrong, it could be seen as "Einstein wins round two." Either way it may be a very important experiment.
At present, it is hard for me to see a way around this logic. But of course, if there is, I would be grateful for quiet guidance.
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A day later:
But of course it is important to just do the algebra on the wave function above. Hard to do, when in a state of panic, to try meet deadlines which become ever more frantic as people tighten up screws on all sides.
The difference between "M' and "M'" (defined in that arxiv paper) seems so glaring that there SHOULD be a way to find a decisive experiment, if not this way, some other way.
One would think. Would an analytic approach work? How about trying to prove
no difference ever exists between predictions based on M and predictions based on M' -- in hopes that that effort would itself help us find a counterexample. But maybe it would be proven...
Not yet resolved.
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March 9: resolved. The algebra really does seem to give a decisive experiment.
It's pretty straightforward. Have uploaded a new paper with details (the paper to
be sent to SPIE for the May Quantum Computing Conference).
======
A day later:
But of course it is important to just do the algebra on the wave function above. Hard to do, when in a state of panic, to try meet deadlines which become ever more frantic as people tighten up screws on all sides.
The difference between "M' and "M'" (defined in that arxiv paper) seems so glaring that there SHOULD be a way to find a decisive experiment, if not this way, some other way.
One would think. Would an analytic approach work? How about trying to prove
no difference ever exists between predictions based on M and predictions based on M' -- in hopes that that effort would itself help us find a counterexample. But maybe it would be proven...
Not yet resolved.
=======
March 9: resolved. The algebra really does seem to give a decisive experiment.
It's pretty straightforward. Have uploaded a new paper with details (the paper to
be sent to SPIE for the May Quantum Computing Conference).
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