I Do Bob's measurement choices affect Alice's?

[zonde]

To affect (a verb I think) is to change, influence or impact something. In this case that something is Alice's measurements. An "effect" is used as a noun, a thing. In this case it would be a change in Alice's measurements "caused" (another loaded word) by Bod. Bob's measurements in no way change Alice's. Hence the card construction. I have arranged two measurement histories consistent with all known facts about QM in which Alice's entire experience, angle choice $\alpha_k$ and measurement result $a_k$, are identical whereas Bob's are not.

You are omitting one important thing. Your construction aims to show that Bob's measurements in no way change Alice's. But if you would claim that Bob's measurements in no way change Alice's and vice versa then it can be proven false.

As the reference I used is behind paywall I will try to reproduce a rough analog of Eberhard's proof for 100% efficiency.

We have to consider what we mean by statement that outcome of Alice's measurement is independent from Bob's measurement setting and at the same time Bob's measurement is independent from Alice's measurement setting.
For that we have to consider alternative possibilities where Bob hypothetically sets his measurement settings to different values, say $β_1$ and $β_2$. Then we can say that Alice's measurement is independent if it can be the same (with the same Alice's setting) for either hypothetical Bob's setting. And at the same time the reverse is true as well. And by stating that Alice's measurement outcome can be the same I mean that taking it as the same should not forbid arriving at valid predictions for experimental correlations.

So taking your approach with cards we describe results for our setup with quartets of cards
$(α_1(a_k), β_1(b_k))$
$(α_2(a_k), β_1(b_k))$
$(α_1(a_k), β_2(b_k))$
$(α_2(a_k), β_2(b_k))$
where value (either H or V) of $α_1(a_k), α_2(a_k), β_1(b_k), β_2(b_k)$ is the same based on our assumptions on all cards from k-th quartet. Angles $α_n, β_n$ are certain fixed measurement angles.
From such quartets we should be able to make sets of quartets that reproduce predictions for experimental correlations.

Now we arrange these quartets in table:

Each card from quartet falls into the larger box $α_nβ_m$ and depending on values of $α_n(a_k)$ and $β_m(b_k)$ it then appears in one of the smaller boxes. Two cards from the same quartet with the same $α_n(a_k)$ or $β_m(b_k)$ always end up in the same row or column respectively.
Now we consider all quartets where the $α_1β_1$ card falls into the box marked with "H". All $α_2β_1$ cards for these quartets fall into either "A" or "B" box. Now from initial set "H" we remove all quartets whose $α_2β_1$ card falls into box "B". So if we subtract from "H" number of cards in "B" we have removed number of these quartets and maybe more.
Similarly we remove number of cards in "D" ("H"-"B"-"D"). That way from initial set "H" we have removed all quartets whose $α_2β_2$ card falls into any box marked with "X". So all that is left in reduced set ("H"-"B"-"D") are quartets whose $α_2β_2$ cards necessarily fall into box "R". So box "R" should contain at least ("H"-"B"-"D") or more. Thus the inequality "H"-"B"-"D"=<"R"
So any violation of such inequality can be only accidental if initial assumptions hold. Predictions of QM and experimental results violate this inequality.

 

[Paul Colby]

Similarly...

Yes, if one removes cards one (may) change the card probability (frequency of occurrence) and therefore violate the predictions of QM. One could simply throw one of your four boxes away to get a nonsensical result. Every point your making is correct.

However...

Please show that Alice's measurement result statistics are altered by Bob's measurements choices where Alice's results are analyzed neglecting Bob's data.

I don't think this is possible since it would violate QM. Bob's measurements do not change the statistics of Alice's results where "change" means make numerically different. Most understand this fact very well and I'm rather certain you are one of them. I was attempting to make this point clearer and obviously have failed to do so.

When someone says Bob's measurement choices affect Alice's measurements they are making a false claim given my understanding of the word affect and my understanding of Alice's measurement results. If one insists on always assuming a composite system then Alice's measurement results include Bob's and there is clearly a modification of the joint probabilities as is predicted by QM. Blurring the meaning of words such that Bob's measurement choices affect Alice's measurement results is taken as a valid assertion only confuses a very confusing discussion.

 

[zonde]

Please show that Alice's measurement result statistics are altered by Bob's measurements choices where Alice's results are analyzed neglecting Bob's data.

I don't think this is possible since it would violate QM. Bob's measurements do not change the statistics of Alice's results where "change" means make numerically different. Most understand this fact very well and I'm rather certain you are one of them. I was attempting to make this point clearer and obviously have failed to do so.

When someone says Bob's measurement choices affect Alice's measurements they are making a false claim given my understanding of the word affect and my understanding of Alice's measurement results.

Do you understand Alice's measurement results as statistics of Alice's measurement results? If yes then I see your point. But then I would not agree that your meaning of "measurement results" is the common one. I would say that common meaning covers statistics along with more detailed data about individual clicks.

 

[Nugatory]

When someone says Bob's measurement choices affect Alice's measurements they are making a false claim given my understanding of the word affect and my understanding of Alice's measurement results.

It's not so much that they are making a false claim as that they are trying to provide a natural-language description of a phenomenon that defies such description. Your best bet may be to treat this claim as a lie-to-children - something to be outgrown rather than argued over.

 

[Paul Colby]

Do you understand Alice's measurement results as statistics of Alice's measurement results? If yes then I see your point. But then I would not agree that your meaning of "measurement results" is the common one. I would say that common meaning covers statistics along with more detailed data about individual clicks.

By Alice's measurement results I'm including all possible analyses not including knowledge of Bob's data or settings. This includes details of Alice's time history which QM says are statistically independent of one another.

 

[zonde]

By Alice's measurement results I'm including all possible analyses not including knowledge of Bob's data or settings. This includes details of Alice's time history which QM says are statistically independent of one another.

Understood

When someone says Bob's measurement choices affect Alice's measurements they are making a false claim

Yes, given our current understanding of phenomena this is false claim. Bob's measurement choices by itself can't affect Alice's measurements (otherwise it would allow FTL communication). We have to include Bob's measurement event itself and it's outcome to to say that either Bob's measurement affects Alice's measurement or Alice's measurement affects Bob's measurement.

Bob's measurements in no way change Alice's.

This statement however is not true in general. If we formulate it like "Bob's measurements in no way change Alice's and vice versa" we even can claim that this statement is false.