Dean Mamas writes: "From the trivial geometry of classical optics, this component of the photon’s electric field varies as the cosine of the angle through which the filter is rotated, which is in agreement with the observed cosine dependence in the correlation data. Note that the observed cosine dependence is seen in the dichotomic Bell test data which when averaged into statistical correlations exhibit this same cosine dependence that is expected from the geometry of classical optics."
If we would only look at photons arriving at the filter with one given polarization, we would see the cosine as we varied the orientation of the filter. The detectors however are actually counting measurement outcomes of photons which previously had all possible polarizations. What we actually get to see is the addition of many curves. The physical picture which Mamas describes generates lots of curves which together might add up to anything.
His mistake is his assumption that the cosine dependence at the filters would lead to a cosine dependence in the aggregated data - the final correlation curve.
It turns out, when one does the math (or implements it in a computer simulation), that the curves do add up to a cosine curve, but not a full amplitude cosine curve. Mamas' informal description of what goes on (two particles which immediately lose their entanglement after they are separated) actually defines a local hidden variables model in the sense defined mathematically by John Bell. Hence the Bell inequalities must be satisfied. They are satisfied. A full amplitude cosine curve cannot be reproduced, even approximately. Instead, Mamas' physical intuition tells us to expect a shrunk, shifted, cosine curve. Satisfying the Bell inequalities. But that is not what the latest experiments show.
Here's the proof: https://rpubs.com/gill1109/mamas3
Here's another simulation with a slight variation. Now a centered cosine
Richard Gill is not a physicist and has no degrees in Physics. His computer program does not represent the mechanism described in the article, which he does not understand. For one, the article uses a minimalist Statistical Ensemble interpretation, which Gill confuses with a Copenhagen interpretation. He is very obviously not a physicist.
Gill uses the minimalist statistical ensemble interpretation. Mamas is very obviously not a mathematician, though one’s undergraduate degree should be pretty irrelevant
On the contrary, Gill's computer program does represent the mechanism described in the article, which he does understand. One does not need to talk about interpretations since the comparison is between the statistical predictions of quantum mechanics, and the statistical predictions of Mamas' mechanism. If they do not agree, they do not agree.
Mamas is a PhD in Physics from UCLA.
Thanks for the correction. DL Mamas published three papers in high energy physics (plasma physics) in the mid 70’s.
Mamas seems to be unaware of the mathematical content of Bell’s theorem. If two particles leave a source, and by doing so are no longer in an entangled state, they can obviously still be in correlated states. A standard QM description of what happens to them at polarizers and photo detectors can always be expressed as a local hidden variables model. Hence measured correlations must satisfy Bell inequalities. Mamas seems not to realize this.
His intuition that the Malus law could lead to cosine shaped correlation functions is absolutely correct. But it cannot lead to a full amplitude cosine curve.
Bell gave an example of a similar LHV model which led to the sawtooth curve or triangle wave. Some popular accounts of Bell’s theorem might lead one to imagine that that’s the only possibility for LHV. Actually, I like Mamas’ model better. It seems to be new. Thus he is onto something interesting, but without realizing what.
The article does not use Malus' law at all as Gill mistakenly states above. He does not understand the mechanism in the article and so misrepresents it in his simulation. In addition, no simulation is necessary if one understands the article. Gill and also Larsson need understand it is simply trigonometry and a strict Ensemble Interpretation that immediately dictates a perfect full cosine.
Pub Peer is just a forum where people can attack each other's articles without any peer review. The correct way to criticize an article is to publish an opposing article, instead of taking cheap shots on a forum with no peer review.
[Moderator: it is true that previous discussions of quantum phenomena have rarely reached a consensus. But, as always, readers can make up their own mind. The usual commenting guidelines apply - no insults, factual/logical comments, etc.]
First, the two first sentences of Mamas' Section "II. ANALYSIS" essentially contain Malus' law.
Second, the same sentences tell us that Mamas model has photon polarization as a realist property. He then explains that pairs of polarized photons gives the same cosine shape of the correlation as is obtained from quantum mechanics. That the shape is the same is well known, but not enough. More is required.
Quantum mechanics also predicts equal measurement outcomes with probability 1 if the filters (using Mamas' terminology) are equally oriented. In Mamas' model, using pairs of polarized photons, this only occurs if the filters have the same angle as the polarization of the photons in the pair, or 90 degree shifted. Which is not always the case.
Furthermore, if the photon pairs always have the same polarization, or shifts between say horizontal and vertical polarization randomly, the correlation will not only depend on the difference of the filter angles, but also on their sum. The only way (in this model) to obtain a correlation that only depends on the difference of the two filter angles and has no dependence on the sum of the two filter angles (as quantum mechanics predicts) is to have a uniform distribution of the angle of the photon pair polarization. This is what Gill uses.
Gill then obtains a cosine form of the correlation from this model. But the probability to have equal outcomes at equal angles will be 50%, not 100% as quantum mechanics predicts. Gill expresses this as "not a full amplitude cosine curve". To violate the Bell-CHSH inequality you will need more than 70.7%. Mamas model does not reach this.
My criticisms aren’t “cheap shots”. I attempted to understand the physical picture which Mamas has in mind. I converted it as best I could (in two different ways) into a computer simulation. The simulations confirmed Mamas’ idea that after breakdown of entanglement, Malus law could still lead to the emergence of a cosine-shaped correlation function. However, according to Bell’s theorem, it can not lead to a full amplitude cosine. Mamas has a PhD in plasma physics so he surely is able to write his own computer simulation, or do the necessary calculus and trigonometry, to show that Bell’s theorem is not true, and hence that the 2022 Nobel prize for physics should be returned by the recipients Clauser, Aspect and Zeilinger. Probably, Mamas should have it instead.
I’ll write up my findings as a short paper. I posted my critique here to warn other readers of Mamas’ paper that there might be some problems with his heuristic arguments (his paper is a short essay, it does not contain any math formulas or other supporting details).
I agree with the above comment that "Pub Peer is just a forum where people can attack each other's articles without any peer review. The correct way to criticize an article is to publish an opposing article, instead of taking cheap shots on a forum with no peer review."
However, to be fair to the statistician Richard D. Gill, he does occasionally publish peer-reviewed responses to papers he disagrees with. Unfortunately, whenever he does go through that official and respectable path, his misconceptions about physics and elementary mathematical mistakes are exposed in equally respectable peer-reviewed responses. I myself have done this on several occasions. One recent example is my following response, which is published in IEEE Access:
https://ieeexplore.ieee.org/document/9693502
The full list of my peer-reviewed responses to Richard D. Gill's critiques can be found by Googling my name, or from the list of my papers published on the physics arXiv.
It is not exactly Malus' law as Gill stated, because Malus is cosine squared. Note, in the usual interpretation of Bell tests the particles can instantly affect each other at arbitrarily great distances which, frankly, is absurd. Mamas' solution is to respect a strict Ensemble Interpretation where there is then no superposition, no mixed states, no wave function collapse, and therefore, no entanglement. There is a uniform distribution of the angle of the photon pair polarization. Each pair of particles is in a completely fixed state where the particles are of course opposite, by symmetry. In this interpretation the probability to have equal outcomes at equal angles is assured to be 100%, by symmetry. Gill's attempt at simulation therefore does not correctly reflect the article.
I answered Dr. Larsson point by point and somehow Pubpeer lost it.
Let me just say that Dr. Larsson is not reading the article in the way it is intended.
No simulation is needed.
In a strict Ensemble Interpretation there is no superposition, no wave function collapse, and therefore no entanglement.
the twin particles are symmetric and so have 100% equal outcomes at equal angles.
The article is correct.
Mamas' model does give 100% equal outcomes at equal angles by symmetry. And why does Pubpeer block my responses ?
Mamas' model does not give 100% equal outcomes at equal angles.
Mamas' model gives 100% equal outcomes at equal angles if the photon polarizations are equal (or 90 degree shifted) to the measurement angles. If the angles differ from the photon polarization, there is a nonzero probability that the outcomes are different.
Bell's inequality uses several angles, with smaller shifts than 90 degrees. So Mamas' model will not work. It simply cannot reproduce the quantum predictions. Or the experimental results we obtain from an actual experiment.
This model was first studied (and ruled out) in Bohm, D. & Aharonov, Y. Discussion of Experimental Proof for the Paradox of Einstein, Rosen, and Podolsky. Phys. Rev. 108, 1070–1076 (1957) https://doi.org/10.1103/PhysRev.108.1070
#15 (Ostorhinchus luteus ) wrote “Gill's attempt at simulation therefore does not correctly reflect the article”. My simulations showed that a cosine shaped correlation need be no surprise. The problem is that Mamas’ article contains no formulas, no explicit description of what the author has in mind. It expresses some opinions. They are not new, they are held by a few other physicists. For instance, Al Kraklauer has published numerous papers exploring Mamas’ idea; see for instance A F Kracklauer 2004 J. Opt. B: Quantum Semiclass. Opt. 6 S544. However, the 2022 Nobel prize in physics is quite some endorsement of the work of John Bell. In #16, the author DL Mamas himself wrote that his critics are not reading his article as he intended. He says “no simulation is needed”. But extraordinary claims do require extraordinary evidence. (Even Kraklauer provided a computer simulation, and so did another Bell critic, Joy Christian, who has also joined this PubPeer discussion). I hope that Mamas will follow up his Essay with a full length physics paper with formulas, calculus and trigonometry, and a mathematical proof; and maybe even a Monte Carlo simulation - or at least some pseudo-code describing his physical picture in enough detail that anyone who can write computer code can check his claims. Unfortunately for him, it has very long been well known that Bell’s theorem can be formulated as a theorem in computer science, saying that a certain distributed computer task is impossible with classical computers and network connections, see for instance https://doi.org/10.3390/e24050679. So in fact, no simulation is possible - at least, not if it respects the constraints proposed by Bell in his 1981 paper “Bertlmann’s socks and the nature of reality” and imposed in the 2015+ ‘loophole-free Bell experiments’ in Delft, Munich, NIST and Vienna.
#15 Ostorhinchus luteus wrote "Malus is cosine squared", which is of course true. The graph of cosine squared is a cosine curve since cos(2 theta) = 2 cos^2(theta) - 1.
He went on to say that " in the usual interpretation of Bell tests the particles can instantly affect each other at arbitrarily great distances which, frankly, is absurd."
Many would agree with him. As a mathematician, not a physicist nor a philosopher of science, I do not take any position on that issue.
He went on to say "Mamas' solution is to respect a strict Ensemble Interpretation where there is then no superposition, no mixed states, no wave function collapse, and therefore, no entanglement. There is a uniform distribution of the angle of the photon pair polarization. Each pair of particles is in a completely fixed state where the particles are of course opposite, by symmetry. "
Actually, having each pair of particles in a completely fixed state of equal and opposite polarization, uniformly distributed over the unit circle, is by definition a mixed state. In a strict ensemble interpretation, using only the Born rule to derive probability distributions of outcomes of measurements, there is no wave function collapse. One can see an entangled state as a computational device to derive probability distributions of outcomes of measurements, and experiment shows that this very minimal interpretation works just fine. If we trust in quantum mechanics (as Mamas does), then Tsirelson's theorem shows that the full amplitude cosine observed in state of the art Bell experiments, see for instance Wei Zhang et al. Nature 609, 687 (2022), can only occur with the singlet state and the usual spin measurements (up to mathematical isomorphism).
Jan-Åke, Bohm and Aharanov assume equal and opposite polarizations are generated uniformly at random from the surface of the sphere S^2. They state that this scenario leads to different correlations from the ones obtained when one assumes the joint state of the two particles is still entangled when they arrive at the detectors, but they do not do the calculations. Mamas wants equal and opposite polarizations generated uniformly at random from the circle S^1. He does not do the computations.
Of course, both B&A's model, and Mamas's model, can be modelled by LHV (the particle's actual polarizations are the hidden variable and the detectors work according to Malus's law with probabilities cos-squared and sin-squared of the two outcomes. By Bell's theorem, we won't get the 100% cosine correlations.
I have redone my simulations with cos-squared and sin-squared (probabilities adding to one) instead of abs cos and abs sin (normalised to add to one), which Mamas had suggested to me. The result is 0.5 times cosine, as you say. https://rpubs.com/gill1109/mamas5
Bohm's 1957 treatment is not for the exact scenario in Mamas' article and does not start from Mamas' modern postulates. Bohm writes ''we shall cite the scattering cross section of a single photon from an electron''. Mamas' article is simply classical EM. There is no interaction like Bohm goes into.
I've written a "Comment" on Mamas' paper. Two pages, and a computer simulation. https://arxiv.org/abs/2211.01068
As in Mamas' article, in the clear case of Alice turning her polarizer 90 degrees or even 180 degrees for a full perfect cosine, why does Gill's program not show a perfect cosine ? Gill's program is clearly wrong and does not correspond to Mamas' article. Larsson should not be citing Gill.
I wish Mamas would stop talking about himself in third person.
Not much of a cosine if you can only turn the polarizer by 90 degree steps. Try having your photons polarized at 0 degrees and both filters at 45 degrees. The outcomes should be equal. But in Mamas' model the outcomes are random, since each filter receives a 0 degree polarized photon and is rotated 45 degrees with respect to that, the outputs are probability 1/2 to exit the filter and probability 1/2 to be absorbed. These events are independent, locally at Alice and Bob, so we have: i) probability 1/4 to have both photons exit the filter ii) probability 1/4 to have Alice's photon exit the filter but not Bob's iii) probability 1/4 to have Bob's photon exit the filter but not Alice's iv) and probability 1/4 to have no photon exit either filter. This is not going to give the correct predictions, ever.
The answer to this question is easy. Suppose Alice and Bob set their polarisers both to, say, 0 degrees. Pairs of photons arrive there with any polarizations from 0 to 180, always differing by 90. If the photons’ polarisation pair is (0, 90) then the outcomes are certain: +1, -1. If they are (90, 180) then the outcomes are certain: -1, +1. However, in between, they can be anything. For instance, if the pair is (45, 135) then all four possible pairs of outcomes have the same probability 1/4. The final correlation of 50% is the result of averaging different correlations varying between +1 and 0.
The writer of this comment needs to read Bohm and Aharanov more carefully. Those authors discuss the situation in which a pair of spin half particles in the singlet state arrive at the two detectors in two separate states of equal and opposite spin, uniformly distributed over the unit sphere. Mamas instead has the states uniformly distributed over the unit circle. Indeed, Bohm has something different in mind from Mamas. But the results will be similar. A lower amplitude negative cosine. Correlations satisfying Bell inequalities. In both cases, the physical luchtruim can be represented by local hidden variables. One might imagine the hidden variables to be associated with the source (the separate states of the two particles, transmitted to the detectors) and with the detectors (the random response of the detector, set at a given direction, to the arriving particle).
Larsson is using a result that comes from a Malus' law interpretation for great numbers of photons in mixed states in a beam. Mamas is using an ensemble interpretation where each individual pair of photons is in a fixed state, in which case Alice's photon exits the polarizer in measure of the cosine, as also does Bob's photon, there remains a correlation between the two photons. Malus' law does not apply to an individual pair of ''entangled'' particles.
Dr. Mamas, could you be more specific in what you mean with “in measure of the Cosine”? The cosine can be negative. Suppose it is -1. What does it mean to say that an amount -1 of one photon goes through the filter?
On the other hand, Malus law gives us a probability of cosine squared for each photon. In an ensemble of photons with the same polarisation, that fraction of them passes the filter.
As an example, suppose Alice and Bob set their polarizers to 45 degrees. Suppose Alice and Bob's photons are polarized in the opposite directions of 0 degrees and 90 degrees respectively. Each then passes its polarizer with probability one half. Cos^2(pi/4) = 1/2. Do you agree?
Mamas’ paper makes a number of vague assertions. He does not specify exactly what he means, and he does not verify mathematically (or by simulation) that they lead to the result he claims.
No, I am using "an ensemble interpretation where each individual pair of photons is in a fixed state, in which case Alice's photon exits the polarizer in measure of the cosine, as also does Bob's photon, there remains a correlation between the two photons." If you use this for a large amount of individual pairs of photons with the same polarization, the output power from the filters will obey Malus' law.
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