"Quantum Mysteries for No One" Comments?

[RUTA]

TL;DR Summary

Professor Lad writes, "I provide a critical reassessment of David Mermin’s influential and misleading parable, “Quantum Mysteries for Anyone”, identifying its errors and resolving them with a complete analysis of the quantum experiment it is meant to portray. ... The errors are corrected by the recognition of functional relations embedded within the experimental conditions that have been long unnoticed."

Here is a citation with link to the paper: Lad, F. (2021) Quantum Mysteries for No One. Journal of Modern Physics, 12, 1366-1399.

I'll share my analysis when I get back online tomorrow. I'm curious to hear what the regulars here think.

 

[Grinkle]

For anyone looking for the parable itself, I think this is it ...

https://kantin.sabanciuniv.edu/sites/kantin.sabanciuniv.edu/files/makale/mermin.pdf

 

[RUTA]

For anyone looking for the parable itself, I think this is it ...

https://kantin.sabanciuniv.edu/sites/kantin.sabanciuniv.edu/files/makale/mermin.pdf

Yes, that's the version in Journal of Philosophy that Lad references. Here is the version in American Journal of Physics https://physlab.lums.edu.pk/images/e/e3/Reading2-QM2.pdf.

 

[Fra]

As my own focus and interpretation was always different then the classical objections, I just quickly skimmed it to find what "mystery" they talk about.

"While we are avowedly still to understand completely the physical details of quantum behaviour, they inhere no mysteries in themselves … for anyone."
-- https://www.scirp.org/journal/paperinformation.aspx?paperid=110797

Can someone quickly define exactly what "mystery" Land is talking about, unless it IS to understand the physicaal details of quantum behaviour?

This is the obvious "mystery" that I can see. Ie. we know the correlations are a fact, there are no FTL signalling, and the bell style causation from hidden variables does not work. Then how can we understand the causality of interactions that respect correlations? But it sounds like from the last paragraphs in Lands paper, this is not the "mystery" he talks about?

/Fredrik

 

[RUTA]

As my own focus and interpretation was always different then the classical objections, I just quickly skimmed it to find what "mystery" they talk about.

"While we are avowedly still to understand completely the physical details of quantum behaviour, they inhere no mysteries in themselves … for anyone."
-- https://www.scirp.org/journal/paperinformation.aspx?paperid=110797

Can someone quickly define exactly what "mystery" Land is talking about, unless it IS to understand the physicaal details of quantum behaviour?

This is the obvious "mystery" that I can see. Ie. we know the correlations are a fact, there are no FTL signalling, and the bell style causation from hidden variables does not work. Then how can we understand the causality of interactions that respect correlations? But it sounds like from the last paragraphs in Lands paper, this is not the "mystery" he talks about?

/Fredrik

Mermin's paper presents the mystery of Bell state entanglement for the "general reader," i.e., he did not resort to the use of any quantum formalism. The easiest way to map the "mysterious" behavior of his "device" to the outcomes predicted by QM is via a Bell spin-1/2 triplet state in its symmetry plane. In that case, the three device detector settings (1,2,3) correspond to angles (0, +120,-120) degrees in the symmetry plane for QM, and the two possible device outcomes R and G correspond to the two possible outcomes spin up and spin down for QM. In this case, QM says Alice and Bob will get the same outcomes when their detectors are set the same (Mermin's "case (a)") 100% of the time (Fact 1 about case (a)). When Alice and Bob set their detectors differently ("case (b)"), they will get the same outcomes 25% of the time. Mermin simply shows that the hidden variables seemingly necessary to explain Fact 1 do not reproduce Fact 2. He points out repeatedly that the source and two detectors are not connected in any way, so there is no information conduit allowing for information to flow (superluminally) from Alice's detector to Bob's detector (locality) and there is no information flow from the detectors to the source to reveal what settings the particles will encounter before they actually arrive at their respective detectors (no retrocausality/statistical independence). That's the mystery per Mermin and that's the mystery that Lad claims to have debunked.

Of course, you can't debunk this mystery without refuting QM, so ... where did Lad go astray?

 

[RUTA]

Here is what I have figured out regarding Lad's analysis. Why he believes this analysis debunks Mermin's version of the mystery of Bell state entanglement I cannot say. As you will see, Lad's analysis is in perfect agreement with Mermin's analysis.

I'm going to assume you have looked at one of Mermin's papers, so you are familiar with the Mermin device, its data collection method, and its mystery. I'll refer to "Quantum Mysteries for Anyone" linked above unless specifically noted otherwise.

Figure 4 shows a sample of the data collected, e.g., 13RG, 22RR, 32GG, 31GR, ... . To align the data with Lad's presentation thereof, we would need the number of data points to be divisible by 9 with each possible setting pair (11, 12, 13, 21, 22, 23, 31, 32, 33) occurring in equal number. Lad then records 13RG as 13(-1), since the outcome is different colors. Likewise, we would have 22(+1), 32(+1), 31(-1), from the example data I just gave. Now one can partition the data into 9-dim vectors (called "G9 vectors") with each component giving the +1 or -1 result for a setting pair, e.g.,

11 12 13 21 22 23 31 32 33
+1 -1 +1 -1 +1 +1 -1 -1 +1

If we organize these vectors into the rows of a table, then the first column would be all of the 11 results, the second column would be all of the 12 results, etc. Suppose we have 1,000,000 such rows, then Fact 1 about case (a) says the sum of +1 entries for columns 1, 5, and 9 would be 1,000,000 each (same outcomes occur 100% of the time for same settings). The sum of +1 entries for any other column would be ~250,000 (same outcomes occur 25% of the time for different settings, Fact 2 about case (b)).

To account for Fact 1, Mermin introduces eight possible "instruction sets" dictating the R or G outcome for Alice or Bob for any of their three settings (1,2,3). Since Alice and Bob always get the same outcome for the same settings, the instruction sets for Alice and Bob in each trial are always the same, e.g., RGG meaning they will both obtain R for setting 1, G for setting 2, and G for setting 3. Here are the four unique G9 vectors for the eight instruction sets with their names at the far right:

11 12 13 21 22 23 31 32 33
GGR RRG +1 +1 -1 +1 +1 -1 -1 -1 +1 G9-1
GRR RGG +1 -1 -1 -1 +1 +1 -1 +1 +1 G9-2
GRG RGR +1 -1 +1 -1 +1 -1 +1 -1 +1 G9-3
GGG RRR +1 +1 +1 +1 +1 +1 +1 +1 +1 G9-4

Notice that we can get pretty close to the QM results (Facts 1 and 2) if we use only G9-1, G9-2, and G9-3 in a ratio of 1:2:1. That gives us the following number of +1 results for each column: 11 12 13 21 22 23 31 32 33
1,000,000 250,000 250,000 250,000 1,000,000 500,000 250,000 500,000 1,000,000

You can see that four of the six case (b) settings reproduce QM. [Of course, all three of the case (a) settings reproduce QM by design.] This result holds for any 1:2:1 combination of these three G9 vectors with the "outliers" of 500,000 just changing columns. If you add all the case (b) results you get 2,000,000 of the +1 outcomes in 6,000,000 trials or overall agreement for case (b) of 1/3. As Mermin explains (but not using G9 vectors), the instruction sets with two R(G) and one G(R) will always produce this 1/3 agreement for case (b), regardless of their distribution. Adding any occurrences of the RRR or GGG instruction sets just increases that fraction. This "must be at least 1/3 agreement for case (b)" is the Bell inequality for the Mermin device and QM violates it (producing 1/4 agreement for case (b)).

Now Lad points out that columns 2 and 3 of our G9 table are exactly the four possible pairings of +1 and -1. If we consider those to be the domain of a function to the other seven columns, we can write that function
23 --> 1456789. There are eleven other such functions, but they're all the same idea, so let's just look at what he did with this 23 --> 1456789 (or 23 for short).

He writes a Monte-Carlo simulation generating 1,000,000 G9 vectors so that columns 2 and 3 each produce +1 outcomes with a frequency of 1/4. He obtains:

1000000 250191 250332 250191 1000000 625225 250332 625225 1000000

Let N1 denote the number of G9-1 vectors in his distribution, N2 the number of G9-2 vectors, N3 the number of G9-3 vectors, and N4 the number of G9-4 vectors. Then, we can deduce exactly what his Monte-Carlo simulation produced using the following four equations:

N1 + N4 = 250,191
N3 + N4 = 250,332
N2 + N4 = 625,225
N1 + N2 + N3 + N4 = 1,000,000

The answers are:

N1 = 187,317
N2 = 562,351
N3 = 187,458
N4 = 62,874

Notice that his case (b) outcomes exceeded the 1/3 lower limit (they give +1 outcomes in 2,251,496/6,000,000 = 0.375 of the case (b) trials). This is exactly in accord with what Mermin said, since he has added 62,874 GGG/RRR instruction sets to the distribution. The other eleven functions for all of his other Monte-Carlo simulations produce virtually the exact same distributions, so that overall each case (b) column produces like outcomes in 0.375 of the trials.

Conclusion: Contrary to his claim to have debunked Mermin's analysis, he has just substantiated it.
Question: Why does he claim otherwise?

 

[PeterDonis]

Why does he claim otherwise?

As far as I can tell (which is not a lot since I find his writing rather opaque so it's often hard for me to tell what he's saying), he seems to think that the QM prediction is actually different from what Mermin says it is, and that QM can in fact produce the same results as Mermin's model under appropriate conditions. He seems to be saying that the claim that QM predicts a probability of only 0.25 is based on a different experimental situation than the one Mermin's hidden variable model is modeling.

I'm not saying any of these claims are correct, just that those appear to me to be the claims Fan is making.

 

[Fra]

I agree the paper is a bit opaque, this is why I tried to get the overview first, to see if I am motivted to process it in depth or now. I skimmed it again quickly and now see that Lads main claim goes along these lines in short:

Mermins claimed "mystery" that the "local HV explanation" that works in special cases, does not work in the general case where detector settings are chosen at random, as it disagree with QM.

Lad seems to claim this conclude is wrong based on computing some other number, that would be "allowed" even for a the HV solution? But in the end he raises some issues on the details of his simulation. It's hard to judge this without going into detail.

----Edit:
I always felt that bell inequality is of limited vaule, as the sort of explanation I think we are looking for, are not fulfulling the assumptions in the theorem awany. If it's something like think LAd is hinting as he writes

"...
apparently no supplementary features of the experimental situation can account for the known behaviour of quantum experiments.
It is this result that is just plain wrong."
-- p31 in the Lad paper

I would actually tend to agree with this, but from skimming his paper probably for a totally different reason. The objection to the bell ansatz does quality as "supplementary features" but it does not comply with the original ideas of "local realism". But I think those old ideas are doomed - with our without this currenty mystey.
-------

Anyway, it sounds amazing and strange. Perhpas there is some explanation to this depending on the order of inferences and the details of his simulation.

In any case, it seems the real quest and mystery is neverethelss and improved understanding of the causality in interactions, that allows for this, and as I see now clues of this in the paper I feel moderately motivated to check the details. (It seems to not be in the direction I persoonally look for answers) But I will stay tuned if someone else can figure it out.

/Fredrik

 

[RUTA]

Lad writes:

Although the scheme [instruction sets] surely ensures matching light signals when the dials are set identically, [Mermin] motivates the proportion of matching lights ... deriving from such a scenario as equal to more than 1/3. It is this result, which he proposes as an instance of the supposed defiance of Bell’s inequality, that is seen to constitute the mystery of quantum behaviour: apparently no supplementary features of the experimental situation can account for the known behaviour of quantum experiments.

It is this result that is just plain wrong.

But, Lad’s analysis supports Mermin’s result! Lad shows how case (b) produces agreement with a frequency of 0.375 in his simulations, exactly as expected when mixing in some RRR and GGG instruction sets with the other six sets of two R(G) and one G(R).

Lad writes:

We have created a Monte-Carlo simulation of results of a scenario which is both wholly consistent with quantum theory and also … .

No, Lad’s simulation used G9 vectors associated with instruction sets that generates results wholly INCONSISTENT with quantum theory!

I shared my analysis with my statistician coauthor Timothy McDevitt on Answering Mermin's Challenge and he answered:

I reread everything this morning. I really don’t understand why he’s looking at those G9 vectors at all. Why is he interested in the outcomes for all possible settings for a given instruction set? That’s not how the data are collected when you run the experiment. So yes, I agree with your mathematical assessment.

I will go ahead and send an inquiry to Professor Lad himself and let you know :-)

 

[PeterDonis]

instruction sets

Lad's preoccupation with the "instruction sets" seems to be due to their use in Mermin's challenge; but he doesn't seem to grasp the fact that those "instruction sets" have nothing whatever to do with QM. They have to do with constructing a local hidden variable model. QM itself does not have anything like these "instruction sets" anywhere in its model.

 

[RUTA]

Lad's preoccupation with the "instruction sets" seems to be due to their use in Mermin's challenge; but he doesn't seem to grasp the fact that those "instruction sets" have nothing whatever to do with QM. They have to do with constructing a local hidden variable model. QM itself does not have anything like these "instruction sets" anywhere in its model.

Exactly my impression.

 

[RUTA]

I exchanged emails with Professor Lad. His email to me indicated that he misunderstood Mermin’s analysis, so I explained his mistakes and I’m waiting to hear back. I’ll keep you apprised :-)

 

[StevieTNZ]

I exchanged emails with Professor Lad. His email to me indicated that he misunderstood Mermin’s analysis, so I explained his mistakes and I’m waiting to hear back. I’ll keep you apprised :-)

Is he even a Professor? As far as I'm aware, at the University of Canterbury he is a senior lecturer.

 

[RUTA]

Is he even a Professor? As far as I'm aware, at the University of Canterbury he is a senior lecturer.

I don’t know if that is his proper title. He didn’t correct me when I addressed him as “Professor,” that’s all I can say.

Looking at his areas of expertise (self reported) and his degrees, I don’t see anything to do with physics. And it’s precisely the physics that he gets wrong in criticizing Mermin’s analysis.

 

[StevieTNZ]

I don’t know if that is his proper title. He didn’t correct me when I addressed him as “Professor,” that’s all I can say.

He might like the temporary promotion ;)

 

[StevieTNZ]

Looking at his areas of expertise (self reported) and his degrees, I don’t see anything to do with physics. And it’s precisely the physics that he gets wrong in criticizing Mermin’s analysis.

All I can say is, publish or perish. That seems the attitude of a lot of universities these days.

 

[RUTA]

I've had two lengthy email exchanges with Dr. Lad and he mistakenly thought each pair of entangled particles is measured by all nine setting pairs for the instruction sets version of the experiment. In the QM version with spin, he understands that each pair of particles is measured only once. Of course, the instruction sets version is intended to explain the actual experiment (gedanken or real), so Mermin would certainly not imply that each pair of particles with instruction sets is measured more than once. What Mermin said was that each instruction set is subject to measurement in all nine setting pairs. That's not the same as saying each pair of particles with an instruction set is measured in all nine setting pairs. Similarly, one could also say the Bell spin state is measured in all nine setting pairs, but that does not imply that each pair of particles in that Bell spin state is measured in all nine setting pairs.

Every pair of particles is in the same Bell spin state, the question is, are they also in the same (hidden) instruction set for each trial? If so, we can explain the Bell spin state outcomes in local realist fashion with the hidden, underlying instruction sets. Mermin's point is that while the instruction sets can reproduce Fact 1 about case (a), they cannot then account for Fact 2 about case (b) per the Bell spin state. Again, since Lad's G9 vectors are exclusively and exhaustively those for the eight instruction sets, his distributions of G9 vectors all violate Fact 2 exactly as Mermin explains for instruction sets (I explicitly obtained all twelve of his distributions a la my Post #6). I explained that to him as well and I'm waiting for his response.

 

[MathematicalPhysicist]

All I can say is, publish or perish. That seems the attitude of a lot of universities these days.

Hey, Michael Spivak has a publishing company by that name; so I guess "publish or perish" attitude should not only be attributed to nowadays.

P.S
I haven't read the paper, I don't have the time right now.

 

[RUTA]

I told Mermin that Lad believes Mermin’s experiment with instruction sets entailed every pair of particles being measured in all nine detector settings. This is ridiculous of course and Mermin was nice enough to write back:

I'm glad you were able to identify so clearly Frank Lad's simple misreading of my J.Phil paper. Perhaps I should have italicized "one" when I said that in each run of the experiment "the switch on each conductor is set to one of its three possible positions".

Perhaps I should also have mentioned what any physicist would know very well, that after a particle has passed through a detector its character is altered by that detector in a way that changes any information (such as an instruction set) that it might be carrying, so the hypothetical instruction set carried by a particle can specify its behavior at only a single detector. (I had thought bringing up this point would unnecessarily complicate my argument.)
Setting this last point aside, I'm surprised Lad reads the quotation from p. 404 as "very clearly" describing a single pair of particles being sent sequentially to detectors with six different settings. I am talking there about the behavior at a single one of each of the six possible case b settings that the the pair might encounter. Perhaps it would have helped him if my three uses of "will" in that paragraph were all "would"?

I do hope you can convince Lad that he has misread me. Please do keep me informed.

With that confirmation of Memin’s intent, Lad’s reason for constructing the G9 data vectors is totally without merit and his entire paper falls apart. As I showed, his G9 vectors are all equivalent to the data generated by instruction sets and his results are therefore also exactly what you would expect from instruction sets. So, contrary to his claim that his Monte-Carlo G9 data are “wholly consistent with quantum theory”, his data are rather consistent with instruction sets, which fail to reproduce Fact 2 for case (b) of the Mermin device, i.e., the locally real instruction sets fail to reproduce QM.