October 13, 2017

Using HWPs to show that superluminal signaling cannot reasonably explain the strong correlations of quantum theory.

Hello, folks. Sorry I was away so long. This post is to quickly get an idea "out there." This is a rough draft. As far as I know, my test idea against SLS is original, although I saw some Italian physicists come close in a book about entanglement, the title not remembered. They mentioned HWPs but I don't recall details. Comments, suggestions, critiques, errors found, typos, alternatives, evidence or memories of prior or similar proposals, etc? Thank you!

Of interest to everyone who wonders about the quantum measurement problem, and especially the strange mystery of entangled correlations between distant particles. Done in simple text without special characters, and written for basic outlining and middle-brow comprehension (avoiding most tech terms like "eigenstate" etc.)
The full meaning of experimental violations of Bell inequalities is not clear, although they do confirm quantum mechanical theory versus more "realistic" alternatives that some hoped for. We don't know how to explain or conceptualize what happens when entangled photons show correlations that cannot be explained by local properties. Some just accept this situation as one of Nature's enigmas, something we can't represent realistically at all. Others want to find a way to conceptualize how these correlations happen, an "explanation" in classic terms. These realist theories should seek to "mechanize" what happens as a specific model, otherwise are they really "pictures" of Nature as opposed to the inscrutability of Copenhagen?
One prominent proposal is superluminal signaling (SLS) between the entangled particles. To avoid violation of Lorentz invariance etc, proponents typically imagine local realism (definite initial states for both particles) and a preferred frame of reference (also constructible as a "foliation.") In this PF, instantaneous influences correlate the particles, regardless of their separations. It is commonly believed that a well-constructed theory of this kind could give results fully equivalent to what we find. (Compare the advertised status of deBroglie-Bohm mechanics in general.) Hence, there would be no way to experimentally refute it.
Here I outline a conceptual argument showing that a reasonable implementation of SLS would not be fully consistent if certain detector complexes are used. First I explain how SLS would work in order to be consistent in familiar tests. Then I show that using half-wave plates in detection packages would show a discrepancy with the known outcomes predicted by unmodified quantum mechanics. The basic action of SLS is to imagine (or as equivalent to) the following process, for a case with positive correlation of polarizations. Entangled photon P1 is detected first by PF standards (maybe not in the lab frame, but the final results are the same) at D1 as being in a given state psi1. Immediately, the other photon P2 changes from its previous state psi2 into the same state psi1. We'll set the other detector D2 to the same distinction of polarization. So when P2 arrives at D2 it makes a "click" which shows the correlation, that it too is found to be in state psi1. Statistics from more trials at other settings can demonstrate the fullness of the strong correlations.
However: P2 can't always simply change into "whatever state P1 was finally detected in." That is from detection being a potentially cascaded process. We can modify a photon before it hits a simple "true detector," in a way that does not "collapse" it into a specific knowable state. For example, place an optical rotator in front of detector D1. It rotates the linear angle of polarized light by say, 20 degrees - but importantly, does not absorb or detect any light. Behind it, D1 uses a full linear polarizing filter LP set to 55 degrees. A photon that transits this second element makes for observed detection when the photocell clicks. Of course, the entering photon may have been oriented at some other angle (if there was indeed such a thing, such as from a specified preparation); but being "found" as a certain polarization makes a measurement and is the basis for the correlations of entanglement.
So: if a 10 degree linear photon enters the complex, it is rotated by OR to be at 30 degrees. This photon now has around a 82% chance of passing the LP (an effectively probabilistic situation that can't be avoided even by realist theories.) Suppose it does. D1 clicks and as far as we know, this compound system is legitimate and fully equivalent to a simpler 35 degree detector. We can say we "detected a photon at 35 degrees." Note that it shouldn't matter how widely separated the components are.
Then, apply the following reasoning to SLS under entanglement. The correlation means that we need for D2 to always click if also set for 35 degrees. Hence, P1 can't act like sending a message to P2 which says: "Whatever happened to me before, I was actually found at 55 degrees in a linear filter. So, you must now become a 55 degree photon." That would not work correctly at P2, and we would already prove that SLS was inconsistent. Instead, we note that P1 started at 10 degrees but was rotated to 30 degrees. When it hit the LP, the measurement constituted another rotation, this time by 25 degrees. So if P1 instead sends a message to "rotate 25 degrees," then P2 becomes in the correct state for full positive correlation. This process works equivalently in either direction for any photon state, as it must. This explanation can explain observed behavior through SL mediation. (The distinction between alteration by OR and the genuine measuring (and fixing) of final photon orientation may still trouble those annoyed by the special status of "measurement.")
However, for Case II suppose we replace the OR with a half-wave plate HWP. In this case, the HWP has a fast axis set at 20 degrees. This optical axis acts differently in principle from an OR. It "reflects" the angle of incoming linear polarization around itself. Hence, incoming 10 degree light becomes 30 degree light, but incoming 44 degree light exits at -4 degrees etc. We keep the LP at 55 degrees. Again, consider an entering 10 degree photon. It exits HWP at 30 degrees. If absorbed by LP, the second change angle is 25 degrees. The entering photon and both rotations are the same as before, so can we expect equivalent results for the distant D2?
Amazingly, the answer is no. The problem is that this combination of HWP and LP have a different detection setting than the previous case. An entering 35 degree photon will be rotated the wrong way, so that a 5 degree state then enters the LP. It has only 41% chance of passing LP. Hence, if D2 gets the same "rotate 25 degrees" message as from the OR + LP combination, coincidences are no longer guaranteed. (Yet if the other photon is detected first, it does send the correct message for the combo-detector!)
The implications of this are stunning: a reasonable theory about how SLS would work, cannot guarantee the proper and known results of EPR correlation experiments. Using a HWP+polarizer combination "fools" the SLS into sometimes given wrong results. We don't even need to check all possible detector correlations. We need only find a few violations of expected, complete positive correlations.
But maybe the superluminal "message" just needs adapting to the other circumstances? Maybe, but it would be difficult for various reasons. A photon in a given individual state is not supposed to have extra info attached to it like a sticky note, about where it was before etc. Entangled photons do OTOH carry a connection between them, but to change the final interactive message still requires yet more information to go along for the ride (such as having passed a HWP instead of a rotator, and even more as cascading of optical elements becomes more complex.) The transited detector elements themselves can be changed or destroyed before the final detector component is reached. Hence there are more subtleties to this lines of challenge, such as varying the timings of events in the PRF, using more complicated detector combinations, trying to catch the second photon in between optical elements when the first one is fully detected, etc. Any signaling method between photons that could handle all these complications could be critiqued as "too clever by half."


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18/8/18 00:16  

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