It is actually conceivable to me this morning that a high school student who learns a little MatLab

could do the crucial experiment, in simulation, which would open up FTL communication. Or, failing that, force us to revise our understanding of quantum mechanics, or at least create a useful tool for exploring design ideas in quantum computing.

You can see the key idea in a couple of images:

images of two experiments with links to detail

See also:

Matlab task a high school student could do

Notice that this specification does not require that you know any physics; in a way, it EXPLAINS the physics at a high school level.

So what I owe you is a bit of explanation and background. (The background is a lot trickier than the

task itself!)

Lots and lots of people have proposed that you could produce faster than light communication (or even backwards time communication) by exploiting the weird properties of Bell's Theorem experiments, the kind of experiment shown on the first image. It has been shown that changing the angle of the polarizer on the left will change the probabilities of what you observe on the right, instantaneously or even backwards in time. But a careful mathematical analysis shows that you can't use that kind of experiment for that purpose. However -- what if we could entangle THREE photons together, as in the bottom figure? THE BOTTOM FIGURE is just a kind of inspiration; it's isn't real. But it reminds me of how the magic of measurement is supposed to work, in standard quantum mechanics. If measurements are carried out in different orders... FTL communication might be possible. I have seen a lot of abstract theoretical debate about that, but nothing really decisive that I know of. (I have seen debates of people who claimed they knew that literature well.. but of course, there could be something simple and clear that answers this that none of us knew about.) In any case, it's nice to be able to predict and design new experiments in this space.

By the way, I wanted to give you the URL for the NSF award to Yanhua Shih on his proposal for a "backwards time telegraph." But due to the government shutdown, I can't find it. It would be easy for anyone to find, by clicking on awards->search at www.nsf.gov -- after the web site comes back up. Shih is one the very top experimenters in this area.

After I read Keller's thesis, I looked to see what three photon experiments have actually been done, that would be relevant. I found many key papers, such as the paper by Greenberger, Horne Shimony and Zeilinger (GHSZ) which started this whole line of research. On the web, I found a PhD thesis by Michael Reck under Dr. Anton Zeilinger from 1996. In section 1.4, he says: "This dramatic result (GHSZ) has led to the search for sources of entangled triples. However, no sufficiently bright source has yet been realized." I downloaded a dozen papers by Zeilinger (of Austria), the real leader in this area. It seems he shifted his attention over time to another types of experiment, which could illustrate the same general ideas, which he could actually implement. A key paper, right from the beginning of real experiments, is posted at:

http://arxiv.org/abs/quant-ph/0201134

What would it takes to do a simple model of experiments like what he shows in Figure 2 in that paper? Originally, I was thinking of doing a repeat of my own quant-ph paper, showing how we can use a kind of classical stochastic model of this type of experiment. That does not look hard. But first, I needed to extract exactly what standard quantum mechanics actually says here. The student MatLab specification does exactly that. It is a bit idealized, but that's fine for now; the qualitative predictions are what matter.

In the specification, I talk about what happens if we do the same operations in a different order.

If changing the order of measurements on the left changes what we can actually observe on the right, that's FTL. Of course, we can choose the angles to be anything we like; if we get FTL at any choice of angles, that's pretty radical.

Of course, someone with more math background could prove interesting theorems about this system. A lot of Zeilinger's resecnt work on this kind of system proves theorems about "local, causal hiudden variable theory," which aren't relevant to the questions we are asking here.

If any of the predictions look strange -- well, that would be interesting, since they could be tested.

Even in the worst case, this might be a useful step towards low-cost simulators for quantum optics circuits, as I discussed in my own recent arxiv paper (see the figures).

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But as a matter of honesty... I should confess what my expectations really are here.

I think that the probability is about 50-50 that experiments with this system can show how a different order of the same operations leads to different observable outcomes (different values for the array psi). (The order of calling procedures simply reflects which object the photons reach first. That can be controlled simply by moving some objects further from the source.) Even if it leads to different results, I feel it is only 50% likely (or less?) that the differences could lead to a scheme for FTL communication.

BUT: I also don't believe that the order of operations would really matter, in the real world,

in physical experiments. It is quite possible that we need to revise the standard

formulation of quantum mechanics, to correctly predict this kind of experiment. Maybe; maybe not. In a way, all of this started with Einstein, who proposed a simple experiment (EPR), where he didn't really believe the real world could be as strange as what standard quantum mechanics predicts.

I don't believe the real world would be so strange that the order of measurements would really matter here... but IF STANDARD QUANTUM MECHANICS predicts that it is that strange, we need to know, and we need to follow up by doing the experiment. And maybe I would be surprised, just as Einstein would have been surprised at what happened to his simple idea. If so... well, maybe FTL communication might be possible after all, even without invoking things like bending space and nuclear energy. Maybe. I hope someone finds out... even as I switch to the world produced by government shutdowns and other things. But if I am right in my guess about the real world... well, we need to revise our models before we have any hope of doing things which would use the trickier forces we would have to use for FTL or backwards time technology.

But: a clarification: OF COURSE the outcome changes if a single photon passes through TWO polarizaers, and the order of the polarizer along its path is swapped. The question is: does it ever change the results when the timing of DIFFERENT photons reach in different objects IN PARALLEL is switched? In standard quantum mechanics, it is assumed that an act of measurement on one photon "condenses the wave function of the entire universe" at exactly that moment in time.

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Just to be complete... as I look at Figure 2 in the paper 0201134, I do notice that TIMING is really crucial in these experiments. This simple model specification assumes that the timing is all set up correctly, as intended, as in their experiment. But how would we generate a more general model, able to address failures of the initial pulse timing and such? Keller's PhD thesis under Morton Rubin of UMBC says a lot about the more complicated and tricky mathematics required for that. In essence, one would have to pay the price of going to simulations of partial differential equations (PDE) to really cover those phenomena. There are very subtle issues involved, in the foundations of quantum theory, which I am sorry I did not appreciate back when Shih gave me a copy of Keller's thesis. (But then again, I don't think anyone else on earth understood those issues then either.) One of these days I may update and make public some new thoughts I have on how to address those issues... but not this week. Too many other things going on... and besides, the simpler cases can help get us all better prepared for the hard stuff anyway.

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