Do Bob's measurement choices affect Alice's?

[Paul Colby]

Theory often affords multiple viewpoints or interpretations of phenomena. Not all of these need provide one with a feeling that they are sensible. For example, we could choose to view the classical trajectory of say a baseball as being “caused” or due to some future position and velocity and by convention simply integrate the equation of motion in time reverse order obtaining what we normally refer to as the initial conditions. That we can do this doesn’t in itself recommend it.

I would like to layout a view of the classic EPR style experiment in which the decay of an S=0 state particle pair is measure by our friends Bob and Alice. My intent in doing so is to address in part what I feel is a common miss use of terms like “cause” and “effect” in regard to Alice and Bob’s measurement choices. It is clear that choice of measurement apparatus in QM very much is effects measurements, it’s the nature of the beast. It is also clear that Bell’s arguments are an important aspect of the phenomena. But, I’m left wondering in what sense does Alice’s measurements effect Bob’s? Well, there is a view point where Alice’s measurements simply are unaffected by Bob’s.

Because QM measurements involve random events beyond our control things are complicated experimentally. No observation in this type of work is comprised of a single event. In this case what is a single event? We define a single event as a measurement on a single entangled pair of particles. This event, say event $i$, is Alice’s measurement angle, $\alpha_i$ with her up or down result, $a_i$ obtained. Each of these are paired with Bob’s chosen angle, $\beta_i$, and his up or down result, $b_i$. We suppose that Alice and Bob dance around wildly choosing measurement angles at random (or not, it matters not) and we let them do so for a very long time. In this time we collect each event outcome on a card. This gives us a set of measurements, $(\alpha_i,a_i,\beta_i,b_i)$ which we put in a big deck. Now, since each event is independent of every other even, we may shuffle the deck freely. No matter how the deck is shuffled we will always have a potential time sequence of event which is completely consistent with QM and whatever Bell has to say. Each time the deck is shuffled we get a physically reasonable potential outcome of an experiment. Now, we could also choose any subset of cards and we will still have a consistent potential time sequence or outcome for an experiment.

Now, I’m going to choose two sequences of events of identical in length, say $N$, from our much bigger deck. The first is simply the first $N$ cards of the big deck. The second I am going to choose card $k$ such that $(\alpha_k,a_k)$ is the same as Alice’s results for the $k$-th card in the first deck. What this does is it gives us two experiments in which Alice’s event sequence is identical in both decks. Both of these experiments could happen even though arranging it real time is not possible (well, very very unlikely at best). Both experiment time sequences are completely consistent with QM. At this point I ask; can we really claim that Bob’s measurements have effected Alice’s? How is such a claim made since both Alice’s results are identical between the two time sequences while Bob's are completely different?

Now, Bob certainly does see a dependence on his choice of relative measurement angle to Alice’s. But this is to be expected since all Bob’s measurements depend on Bob’s choices in QM.

 

[shiva mahadeva]

This is not that easy like card games. First you need to know how polarizers works.
We have a Malus-law for polarizer.
https://en.wikipedia.org/wiki/Polarizer#Malus.27_law_and_other_properties
Second important detail the independency of events.
"Two events A and B are independent (often written as {\displaystyle A\perp B}https://wikimedia.org/api/rest_v1/media/math/render/svg/6522d65c3a0cf823fff40501a93b74e877a96f1e or {\displaystyle A\perp \!\!\!\perp B}[PLAIN]https://wikimedia.org/api/rest_v1/media/math/render/svg/92e1d46c72b6742b13c8a88a72090534bd60c06f) if their joint probability equals the product of their probabilities:"
https://en.wikipedia.org/wiki/Independence_(probability_theory)
Now we can start make "science"
Suppose that there are two independent random events on both side of measurement. We can write up the probalility of common detection of photons.
P=cos2(p-a)*cos2(p-b)
p is the polarization of photon and a,b are the orientation of polarizers.
Let a=0 b=90 p=45 the probability of common detection will be nonzero.
The problem starting here because the equation of entangled photon of type1 is
P=0.5*cos2(a-b)
When a=0 and b=90 the probability will be ZERO.
Well the detections of entangled photon are not INDEPENDENT events.

 

[shiva mahadeva]

Its works by classical Malus-law when p=a or p=b only.
/This called "spooky action at the distance" because you can rotate both polarizers freely./
But the result will be symmetrical only if half of sample will be p=a another half will be p=b.
Its looks like case of one photon and two polarizers but the lightsource alternately bounce between the two sides.
Surprizely the equation is same as entanglement.
P=0.5*cos2(a-b) when initial light is unpolarized.

 

[Paul Colby]

This is not that easy like card games. First you need to know how polarizers works.
We have a Malus-law for polarizer.

The cards contain a record of actual data clicks of detectors and angle settings that have happened. All the QM is done by the time one has the cards filled out. Shuffling the deck and selecting subsets is allowed because the events are independent of one another. One may construct[1] two plausible measurement histories that are consistent with QM in every way and in which Alice has identical results between the two while Bob's differ between the two. This argument doesn't resolve anything and says nothing new. It does, however, provide a view in which Alice's measurements are unaffected by Bob's. The reverse also holds if Bob and Alice roles are reversed.

[1] one may also construct statistical outliers. For example flipping two coins and always choosing Bob's to be heads. One may also with the simple picking scheme yield two very plausible measurement histories that are consistent with the expected statistics in every way.

 

[Paul Colby]

I notice that a large section of my original post does not appear, however, when I attempt to edit the post the missing bits jump into existence as if by magic. I hate these web based things. Okay, I've restored the missing section. Sorry.

 

[Paul Colby]

Well the detections of entangled photon are not INDEPENDENT events

Nor have I ever claimed such. Each of the cards contains the results that occurred for a single entangled pair. The results are obtained from an actual measurement.

 

[shiva mahadeva]

I get it. The big different between cards and entanglement is the randomness. Better you think that there are two dice.
If you roll a six with one the other dice has six also. This randomness is very important.
In this metaphore east to see that is impossible to send message with it.

 

[Strilanc]

So you record two runs of experiments, then re-arrange the list of results from the second run so that it matches up with the first run? And this is somehow an analogy for what happens during Bell tests? I don't see how they're equivalent in any relevant way.

Yes you can create correlations by cherry-picking and splinching data. But then the data isn't going to be representative of what you measured anymore. Why are you even doing the experiment, if you're just going to ruin the data like that? Even just looking at subsets of the data can create apparent superpowers (e.g. post-selecting away wrong guesses to create the appearance of communication).

The thing that makes Bell tests interesting is that you get the surprisingly-strong correlations in the raw data. It's due to the physics, instead of due to cherry-picking and editing.

 

[Paul Colby]

So you record two runs of experiments, then re-arrange the list of results from the second run so that it matches up with the first run? And this is somehow an analogy for what happens during Bell tests? I don't see how they're equivalent in any relevant way.

I often encounter the statement that Alice's measurements are "affected" by Bob's choice. The construct I used produces two measurement histories that could actually happen and are not, when taken by themselves, statistical outliers. In them Bob's measurements depend on his choices of measurement angle relative to Alice's just as QM predicts, yet Alice's measurement angle choices and measured results are identical between the two experiments. My construction is required because the chance of two successive measurements of this kind, while not physically disallowed, are very very unlikely to occur in a real unedited measurement.

The thing that makes Bell tests interesting is that you get the surprisingly-strong correlations in the raw data. It's due to the physics, instead of due to cherry-picking and editing.

I have in no way changed the statistics in either measurement. One certainly can by choice of cards, but I'm not in this case. All correlations predicted by QM are evident in both data sets.

 

[Strilanc]

The construct I used produces two measurement histories that could actually happen

Yes, but you made them more likely by discarding data where they didn't happen. You're cherry picking. It's not enough that "it could happen".

Basically you're describing an experiment where Alice picks a list of random settings, then uses it twice. Post-selecting doesn't avoid the consequences of using random data twice, because knowing that post-selection is going to happen can be used to gain the same advantage as knowing the same list of settings would be used twice.

 

[Nugatory]

I often encounter the statement that Alice's measurements are "affected" by Bob's choice.

You will often hear this, but it's not an accurate statement of the physics involved, it's one of those things that you'll find in popularizations that try to explain the physics without demanding excessive rigor. (The only place it shows up in serious discussions is in the context of collapse interpretations, and there the conclusion is that collapse doesn't work well in analyzing spacelike-separated measurements on a quantum system). Thus, it is something of a strawman and there's only so much to be gained by refuting it instead of replacing it with a more correct and complete statement of the problem.

One cup of coffee into my morning, I do find the question @Strilanc raises to be interesting: Is your procedure in fact statistically valid? Any approach that filters the raw data should be presumed bogus until proven otherwise requires a fair amount of justification. Gimme another cup of coffee and I may find this question less interesting, but I'm pretty sure that it will take more than handwaving to justify the approach.

 

[Paul Colby]

Yes, but you made them more likely by discarding data where they didn't happen. You're cherry picking. It's not enough that "it could happen".

Totally true. One (meaning me) must show that the statistics of each experiment taken in isolation is consistent (likely) given QM. The first experiment is taken directly from the first N cards and has no cherry picking and therefore can't be questioned. The second "cherry picked" experiment is constructed from the remaining cards not used in the first set. It is completely obvious that this cherry picking can be done to make anything happen. That's not the intent. The intent is to get a consistent history that isn't a statistical outlier when taken in isolation. This is what is meant by "could happen". Have I shown this, no. Is it possible, yes (he asserts without proof). I'm with Nugatory in that the question is likely not sufficiently of interest to people to warrant the effort. The reason to bring this up at all is the hope that this provides yet another way to look at the problem that might help others think about it.

 

[shiva mahadeva]

The dice metaphore is not really good because there is no measurement. Now I try another one.
Now we have two coin. The coin has two state: heads or tails . It is like up and down spin of electron.
The angle of measurement will be the tilt axis between coin and top of the table.
If you drop like zero degrees then we got same state as initial state was. It is clear.
But when you let fail into edge of coin /90 degrees/ then you can not tell the final state. The chance is 50-50 percent.
This is works perfectly like
https://en.wikipedia.org/wiki/Stern–Gerlach_experiment
with entangled electrons.
When you have two entangled coin then and drop it in 90 degress both, the result will be suprising:
If one coin become tail the other will be head always.

 

[Strilanc]

Now I try another [metaphor]. [...]When you have two entangled coin then and drop it in 90 degress both, the result will be suprising:
If one coin become tail the other will be head always.

Drop two coins on their side, and you could get any of HH, TH, HT, or TT. They don't always disagree. The coin system has two output states and a continuous measurement angle, but doesn't work as an analogy because the coin outcome doesn't behave the way the quantum outcome does.

 

[stevendaryl]

It seems to me that whether Alice's measurement choice has an effect on Bob's particle depends on whether quantum probabilities are objective or subjective. According to Alice, Bob initially has a 50/50 chance of observing spin-up or spin-down along the $z$ axis. If Alice measures the spin of her particle along the $z$ axis, then Bob's chances change to either $0/100$ or $100/0$. From Alice's point of view, Bob's probabilities changed drastically and instantaneously. If probabilities are viewed as a subjective property (it reflects Alice's knowledge about Bob, rather than reflecting something directly about Bob), then maybe nothing objectively has changed in Bob's neighborhood. If probabilities are viewed as something objective, then it seems as if Bob's situation was changed by Alice's choices.

 

[shiva mahadeva]

you do not say?lol
try to read again
"If one coin become tail the other will be head always."
This is kind of magical coins. Entangled. The essense is not what you get.
The essence how magical coins behave randomess but connected. This works perfectly like real entanglement.

 

[shiva mahadeva]

Okay change the situation.
Suppose that the coins are a little magnets
and the table has hidden uniform magnetic field.
Then its works perfectly.
Quantum entanglement is solved.

 

[Nugatory]

Okay change the situation.
Suppose that the coins are a little magnets
and the table has hidden uniform magnetic field.
Then its works perfectly.
Quantum entanglement is solved.

That doesn't work - in fact, it is impossible to construct any mechanism for manipulating the two objects (coins, dice, subatomic particles) that will reproduce all the correlations predicted by quantum mechanics. This is Bell's theorem: http://www.drchinese.com/Bells_Theorem.htm

 

[bhobba]

I get it. The big different between cards and entanglement is the randomness.

No.

The difference is cards are the same whether observed or not, but QM is silent on if things are the same regardless of observation - its very interpretation dependent.

This is the rock bottom cause of Bell inequalities.

There is a view, one I agree with but to be clear its simply a view, that entanglement is the the rock bottom essence of QM:
https://arxiv.org/abs/0911.0695

You need to read the above in conjunction with Hardy's seminal paper (and again I believe it is part of the essence of QM - but it's just a view which like any interpretation is no better or worse than any other - it simply reveals what I find elegant and beautiful but in an objective sense means Jack shite):
http://arxiv.org/pdf/quant-ph/0101012.pdf

Thanks
Bill

 

[zonde]

Now, I’m going to choose two sequences of events of identical in length, say $N$, from our much bigger deck. The first is simply the first $N$ cards of the big deck. The second I am going to choose card $k$ such that $(\alpha_k,a_k)$ is the same as Alice’s results for the $k$-th card in the first deck. What this does is it gives us two experiments in which Alice’s event sequence is identical in both decks. Both of these experiments could happen even though arranging it real time is not possible (well, very very unlikely at best). Both experiment time sequences are completely consistent with QM. At this point I ask; can we really claim that Bob’s measurements have effected Alice’s? How is such a claim made since both Alice’s results are identical between the two time sequences while Bob's are completely different?

There are carefully chosen angles $\alpha_k$ and $\beta_k$ for which you can't carry out that procedure for several steps (same subset for Alice -> different subsets for Bob -> same subset for Alice for both Bob's subsets but different as a first Alice's subset) even if you allow arbitrary cherry picking. That is basis for Eberhard's version of Bell inequalities.

 

[Paul Colby]

There are carefully chosen angles $\alpha_k$ and $\beta_k$ for which you can't carry out that procedure

If I was looking for or claiming a loophole you'd have a good point. I'm not looking for or believe I require one to make the point I'm attempting to make[1]. The cards are produced by measurements and must obey QM at every level. They are simply records of Alice and Bobs angle settings and measurement results. The probability of each event is $P(\alpha_k-\beta_k,a_k,b_k)$ just as QM predicts. The cards are originally taken in a the order in which the measurements were made. The events are independent of each other. The order in which the events occur does not enter into a calculation of the correlation, only the frequency of the events is used. The first set of cards is taken as the first $N$. The second is in very large measure just a permutation of remaining cards. The reason exactly $2N$ cards is insufficient is due to the statistical fluctuations in the numbers cards produced.

[1] A point which is basically that no messages may be sent because there is no "effect" Bob can make on Alice's measurements. A point which is well understood by many but not by all.

 

[zonde]

A point which is basically that no messages may be sent because there is no "effect" Bob can make on Alice's measurements.

Sorry if I misunderstood you but to me it seemed like you are trying to make a point that because no message can be sent between Alice and Bob by making measurements at different angles there is no effect of Bob's (or Alice's) measurement angle on Alice's (Bob's) measurement. Here:

At this point I ask; can we really claim that Bob’s measurements have effected Alice’s? How is such a claim made since both Alice’s results are identical between the two time sequences while Bob's are completely different?

 

[Paul Colby]

Sorry if I misunderstood you but to me it seemed like you are trying to make a point that because no message can be sent between Alice and Bob by making measurements at different angles there is no effect of Bob's (or Alice's) measurement angle on Alice's (Bob's) measurement.

What I struggle with is peoples frequent use of the word "effect". Yes, the mutual probabilities are functions of the experimenters angle choices and therefore effected by them. But, in what sense are Bob's choices "effecting" Alice's results. What my (arguably lame) construction does is provide two histories in which Alice's results are identical where Bob's differ in detail. So the question is; how is Bob effecting Alice. The answer would seem to be not at all.

 

[DrChinese]

I often encounter the statement that Alice's measurements are "affected" by Bob's choice.

This has already been addressed by Nugatory and Strilanc and bhobba. I will add a couple of comments:

1. No one can say if Alice affects Bob - or vice versa.
2. No one can say if anything affects anything in the examples. The results may be correlated to a 3rd something.
3. No one can say if causation is even present.

So your difficulty starts with the statement you are chasing, which must be taken with a grain of salt.

 

[zonde]

What I struggle with is peoples frequent use of the word "effect". Yes, the mutual probabilities are functions of the experimenters angle choices and therefore effected by them. But, in what sense are Bob's choices "effecting" Alice's results. What my (arguably lame) construction does is provide two histories in which Alice's results are identical where Bob's differ in detail. So the question is; how is Bob effecting Alice. The answer would seem to be not at all.

English is not my native language so can you explain meaning of the word "effecting"? Does it mean that Bob's choices determine Alice's results completely? Or does it allow meaning that Alice's results are partially influenced by Bob's choices?

 

[Paul Colby]

English is not my native language

English is my first and only language, a fact that doesn't help me very much.

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. There have been valid sounding objections to the card construction but they seem easy to counter.

Does it mean that Bob's choices determine Alice's results completely? Or does it allow meaning that Alice's results are partially influenced by Bob's choices?

If one claims Bob's measurements change (affect) Alice's measurements, then I believe one is in error.

Now, the entire conversation changes (is affected) when discussing correlations between Alice and Bob's measurements. The correlation between Alice and Bob's measurements is a function of the measurement choice (selection of angles in this case).

 

[DrChinese]

If one claims Bob's measurements change (affect) Alice's measurements, then I believe one is in error.

I don't think it is fair to say Bob's measurements change Alice's results in some usages of the word "change"; but I don't think it is fair to say that they are independent either. It's a single system, which includes the nature of the observation(s).

 

[Paul Colby]

I found zonde's question [#25] very helpful in articulating the point of the original post. I hope my reply helps him to better understand what was being said.

I don't think it is fair to say Bob's measurements change Alice's results in some usages of the word "change"

So, if I may ask, is there a usage of the word "change" which makes it fair[1] to say "Bob's measurements change Alice's results"?

[1] I would say correct rather than fair.

 

[DrChinese]

I found zonde's question [#25] very helpful in articulating the point of the original post. I hope my reply helps him to better understand what was being said. ... So, if I may ask, is there a usage of the word "change" which makes it fair[1] to say "Bob's measurements change Alice's results"?

Yes, that's the kind of usage of "change" where it is meant: "Participates In" or "Partially Influences". When part of a system, it is not possible to isolate one individual element being responsible for the outcome.

 

[Paul Colby]

Yes, that's the kind of usage of "change" where it is meant: "Participates In" or "Partially Influences". When part of a system, it is not possible to isolate one individual element being responsible for the outcome.

Ah, I see, the usage of "change" which removes it from one sentence and putting it in an entirely different one. We completely agree there is a correlation in the two person system formed by Alice and Bob and their particles that is wonderful and mysterious. What I find questionable is the use of words like change in sentences such as "Bob's measurement choices change Alice's measurement results". It's a fine point I know, but doing so makes the subject even more mysterious by including statements that are false in the discussion.

 

[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.