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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."

Demonstration of necessity of the Born Rule

The Born Rule in quantum mechanics states that probability of detection of a particle etc. is proportional to the square of the absolute value of the net wavefunction at that place and time. Despite inviting comparison to energy density being proportional to field amplitude squared, the BR is often presented as mysterious--as if it were a free parameter of nature rather than something that makes logical sense. I came up with a simple way to show that the known form of the BR is necessary, if we neglect complicated and unusual alternatives. We also reasonably assume simple additive superposition of amplitudes, basic linearity (e.g. of filter response), and that exponents must be positive or zero (to avoid the zero-amplitude crisis.)

My proof derives from the need to conserve the total number of particles transiting a Mach-Zehnder interferometer with asymmetrical beamsplitters. The total is normalized as unity. An ABS splits an incoming beam into unequal outputs. Hence a ≠ b, where a is transmitted amplitude and b is reflected amplitude. These may have different phases and thus complex values, but the proof can proceed because of the equal phases that combine for the fully constructive output from the relevant channel. This demonstration may not show universal applicability of squared moduli, but it does rule out alternatives.

We know from the BR that the corresponding intensities equal a² and b², and hence in the idealized case of no absorption used for modeling: a² +  b² = 1 . But did that have to be true, instead of say,  cubed amplitudes; such that a³ +  b³ = 1? If we simplify by considering one-term exponent laws, then consistency says "yes." (Further exploration is welcome, but the case implies any alternative would be contrived.) So, consider an MZI with asymmetrical BS at each end. The first, ABS₁, has transmitting amplitude a, and reflecting as b. Considering simple exponents (which don't have to be integers), we need aⁿ + bⁿ = 1. So far, we have no way to narrow that. These beams are recombined in ABS₂. This latter follows typical practice of outputting maximum constructive interference (no phase difference) in the lower, "A" Channel. However, it reverses transmission/reflection amplitudes relative to ABS₁. So: the originally transmitted beam is reflected at ABS₂ into Ch. A for a final output amplitude there of a². The originally reflected beam is transmitted at ABS₂ into Ch. A for a final output amplitude there of b². Superposition gives the total as a² +  b².

That already looks promising but we aren't done yet. First, we have to ensure that the output at Channel B must be zero. We can: since the Ch. A output is already the maximum output, pairing it with other than zero amplitude would be a contradiction. Suppose zero output was paired with less than the maximum possible amplitude. If so, then pairing the maximum with any value zero or over, would produce a larger total than before. But the totals must always be the same, so zero and maximum are paired. (It may seem obvious, but it's good to show the formal necessity.)

Now, we can proceed to satisfy the following equation:

(a² +  b²)ⁿ  =  1

a² +  b²  =  1⁻ⁿ  =  1

That is basically it. If the rule had been say, the amplitude itself or the cube; it could not be so that
 a³ +  b³  =  1 and a² +  b²  =  1, as well. Note: this whole argument only makes sense if we assume or accept, that there really is a number of particles output according to some rule, and not just two "branches" of arbitrary relative amplitudes. The whole idea of probability falls apart in the latter case, despite awkward attempts by MWI supporters to contrive an equivalence.

Is this an electromagnetic paradox?

Because of relative motion of sources of B (regardless of how one imagines their source), there should be an E field near the poles of magnets spinning around their polar axes. (Compare to separate magnets held in a rotating cylinder and their relative motions.) It would be a similar configuration to the B field from a solenoid (even more so if we used a hollow cylindrical magnet to isolate magnetization as close to the rim.) It seems rather obscure.

  This seems rather prosaic until you start thinking about "sources of E" in terms of what projects potential and magnetic vector potential A. The usual view of sourcing E is to write, such as from Feynamn Lectures II:
E = -Del phi - dA/dt,
and the source of phi is retarded 1/r^2 from dV of rho, and source of A is 1/r projection from current density j.

   There is a problem here
  1. Because this is a stable configuration there can't be a continuing dA/dt, and
  2. magnets aren't really current loops (most of the B comes from axial electron quantum spin, not orbital motion anyway) so there isn't really a shifting of current density to project the changed phi.
We need to treat the spinning magnet poles as actual "pole currents" since it is misleading to pretend there are actual little loops with increased relativistically altered current densities in them. Yeah, amazing this wouldn't have been hashed out before, but there it is. Your thoughts?

Discussion thread for "The Light of Paradox"

This is the post for discussing "The Light of Paradox."

Greetings, readers of Analog Science Fiction and Fact Magazine, and others interested in the unexpectedly paradoxical physics of "wigglers" and undulators. This is my blog post dedicated to discussing issues raised in my [proposed, waiting on updates] Analog article "The Light of Paradox." I presume it is acceptable to pre-publish the Abstract for the article, (which may or may not appear in the published version if Analog accepts the article.)

We discuss three paradoxes deriving from interactions in devices (such as undulators) that simulate illumination by electromagnetic radiation. The major cause of the paradoxes is the lack of actual photons striking the targets exposed to this simulated light (SL.) The first paradox develops from the problematical nature of the additional momentum correction required when energy from SL is absorbed in a compound target. The second paradox concerns the light pressure from SL differing from that exerted by ordinary light. The third paradox concerns the difficulty of accounting for all momentum and energy when SL interferes with ordinary light. Attractive solutions are not evident.

As readers here can imagine, I can't provide or send you the whole article until finding out whether my submission was accepted. Best.

My new FQXi essay is available

My new FQXi essay is online. Sorry for delay, I've had technical problems here for awhile. The FQXi contest (their fifth) was titled "It from Bit or Bit from It?" (per John Wheeler and related thinking such as MUH, modal realism etc.) My essay is titled "New Pathways to Quantum Spring: Can Information About States Be Made More Democratic?" (Yes, the political analogy is deliberate and pertinent, if perhaps too trendy.) Abstract and link below:

Quantum theory curiously implies that preparers of states can know the complete initial specification of the state, but uninformed observers (UOs) are limited in what they can discover. UOs must currently use projective tests that typically destroy the original information. There is thus more to "it" than democratically available as "bit." Previous attempts to empower UOs include weak measurements and using repeated interactions between detector and one particle. A novel theoretical perspective and thought experiment are introduced to distinguish between supposedly equivalent mixtures of states. The original-spin hypothesis postulates that actual spin transfers from photon interactions remain based on the original expectation value, instead of the final apparent detection. The proposal itself uses mechanical spin transfer by statistical "runs" of same-type detections, as analyzed by the OSH, to expand what UOs can find out. It would not be practical, but stimulates theoretical insight. A supportive asymmetry claim about detection [measurement] is currently testable.

http://fqxi.org/community/forum/topic/1610.

To not boldly go anywhere?

This piece is depressing yet very well thought out and well put. I want to believe it's better, but at least consider the apt arguments. The author could have put some attention to advanced details like ion propulsion, not just classical rocket exhaust, but this is thought-provoking:

The Recline and Fall: To not boldly go anywhere.: I wrote this some time back after reading Tom Murphy's blog. I'll publish this as is because it is still worth saying even though it...

How about this, for some simple and reasonably fair Social Security reform:

Remove the cap on earnings subject to FICA, but don't institute any "means testing" other than just making SS benefits taxable by combination with other income. That would get some of the money back from the more wealthy folks, and in a simple way (ie, by not adding a new complex formula to decide how much one is paid SS to start with), without "messing with the system" by changing overall payment protocols, or switching to the odious chained CPI, etc.

My new FQXi essay is available

My entry for the latest FQXi Essay Contest is finally in, it was delayed due to some IT issues. The Contest orienting topic was:

Questioning the Foundations

Which of Our Basic Physical Assumptions Are Wrong?

Well here it is:
Can Repeated Interactions Show More About a Photon Than Current Theory Allows?

Essay Abstract

We explore whether it is possible in principle to find the "circularity" (amount of circular polarization) of a single photon to a degree not allowed in conventional quantum theory. The thought experiment involves passing the same photon many times through a half-wave plate (with intermediate correction) so the tiny "spin" interaction of the photon is amplified enough to transfer measurable angular momentum to the detector HWP. HWPs invert coefficients for RH and LH states instead of "collapsing" the photon into a circular basis. Because passing one photon many times through a HWP should be like passing many photons once each though the plate, the transferred angular momentum would be revealed on a continuum. Such a measurement would violate the projection postulate (which says that only yes/no answers to probabilistic detection questions can be found for a single particle).

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Folks, I need your votes as much as anybody else "running" for some accomplishment that depends on them. Check out the proposal, remember it doesn't have to prove the point, just to be a thought-provoking attempt and exploration. All I ask is for what you think is fair. Thanks.

Older and why-sore ...

A Facebook Friend asked me awhile ago if I felt any wiser on my birthday ("fifty-something" will suffice.) I told him:
Well, somehow both wiser and more foolish. Certainly, I am why-sore: worn out from asking "why" so much!
Heh, any of you other seekers, delvers (I love that word) and paradoxers feel why-sore? Let us know.