Undergrad CFD - Counterfactual Definiteness

[RUTA]

... In other words, "independent of" means "separable from and uninfluenced by", in the statement below:

The 'state of affairs' relevant to the outcome at A is independent of the setting at B, and vice versa.

NOTE: The above statement is rendered inapplicable, and therefore neither true nor false, when one asserts that

the notion of a 'state of affairs' in a spacetime region is altogether invalid.

Therefore, to say that the statement is false leaves but one alternative to "influence":

the joint-state of Alice and Bob's measuring devices is nonseparable.

What about Relational Blockworld for the but one alternative?

Explanation in RBW is adynamical, so dynamical talk about "influences" wouldn't enter the explanans. One simply says, "The distribution of spacetimesource elements in the EPR-Bell experiment is given by an adynamical global constraint, i.e., the Feynman path integral."

 

[bhobba]

[All] Bell shows [is] if you want the joint-state of Alice's ((macroscopic) measuring) instrument and Bob's ((macroscopic) measuring) instrument, in spacetime, to be separable then you need non-local influences.

No.

Its just a creelation. Thats it, that's all.

People tie themselves into all sorts of knots goimg beyond that. Dont do it.

Its real resolution is in the cluster decomposition property:
https://www.physicsforums.com/threads/cluster-decomposition-in-qft.547574/

Exclude it and all your problems disappear. Don't exclude it and you simply make a rod to break your back and create confusion. Its logically permissible but why make things harder than necessary. There is after all this thing called Occam's Razor.

Thanks
Bill

 

[zonde]

Its just a creelation. Thats it, that's all.

That's false. And repeating it over and over again won't make it true.

 

[bhobba]

That's false. And repeating it over and over again won't make it true.

You are incorrect.

If you get spin up for example the other is spin down. By definition its 100% correlated or anti correlated depending on how you look at it.

You have been posting long enough to know the facts - why you misinterpret or ignore them has me beat. Its been explained in many many threads eg in the one I gave on cluster decomposition:
'But what he's talking about is a situation in which all of the in states (α1, α2,...), (αj,αj+1,...) are known and independent. In your pion example the in states α1 and αj are correlated and dependent.'

Continue with such blatant misinformation and the mods will, correctly, censure you.

The cluster decomposition property does not make sense if you include correlated systems - it can be modified to make sense, but that complicates things somewhat. The simplest solution is simply to accept it as is and preclude correlated systems. Once you do that bell falls to pieces. I hasten to add it in no way changes the theorem ie you can't have locality and conterfactual definiteness - it simply says why bother? Why tie yourself into conceptual convolutions simply to have counterfactual definiteness and locality? Occams razor proves nothing - but it sure makes things a lot easier to understand.

Thanks
Bill

 

[zonde]

You are incorrect.

If you get spin up for example the other is spin down. By definition its 100% correlated or anti correlated depending on how you look at it.

Definition of correlation is "relationship between two things based on pattern of change". This definition implies that we can speak about two separate "things" and we can examine them independently in order to discover their relationship. Bell theorem shows limits of correlation between two such "things" that are examined independently. So if Bell type inequalities are violated it can't be "just correlation".

The cluster decomposition property does not make sense if you include correlated systems - it can be modified to make sense, but that complicates things somewhat. The simplest solution is simply to accept it as is and preclude correlated systems.

So CDP does not make sense when we are talking about entangled systems ... and so you propose that we do not talk about entangled systems in order to keep CDP as it is, right?
Hey, but this thread is about entanglement not CDP. I don't see the point in what you are saying.

 

[bhobba]

Definition of correlation is "relationship between two things based on pattern of change".

Incorrect:
http://www.bbc.co.uk/schools/gcsebitesize/maths/statistics/scatterdiagramsrev2.shtml

The correlation coefficient is positive or negative. In Bell states entangled objects are correlated or anti correlated with 100% accuracy.

I suggest you actually study some probability and statistics. Feller is a good source.

Thanks
Bill

 

[bhobba]

So CDP does not make sense when we are talking about entangled systems ... and so you propose that we do not talk about entangled systems in order to keep CDP as it is, right? Hey, but this thread is about entanglement not CDP. I don't see the point in what you are saying.

That's not what I said - 'Don't exclude it and you simply make a rod to break your back and create confusion. Its logically permissible but why make things harder than necessary. There is after all this thing called Occam's Razor.'

This thread is about CFD. If you want CFD then you can't have locality. But locality is not part of standard QM because it obeys the Galilean transformations. The concept of locality in QFT is subtle and part of CDP which naturally precludes correlations. You can keep it, but things are more complex.

Thanks
Bill

 

[stevendaryl]

This thread is about CFD. If you want CFD then you can't have locality. But locality is not part of standard QM because it obeys the Galilean transformations.

You're certainly right, that nonrelativistic quantum mechanics is nonlocal, in the same sense that Newton's mechanics is. But the quantum-mechanical prediction of weird, Bell's-inequality-violating correlations in experiments such as EPR are not an artifact of using nonrelativistic QM. Fully-relativistic QFT makes the same (or similar) predictions.

 

[bhobba]

+But the quantum-mechanical prediction of weird, Bell's-inequality-violating correlations in experiments such as EPR are not an artifact of using nonrelativistic QM. Fully-relativistic QFT makes the same (or similar) predictions.

Weirdness - now that is something different again.

All I am saying is there are a number of ways of getting to grips with Bell.

The simplest, and often forgotten one, is simply preclude them from the definition of locality from the start.

It changes nothing - its just a different interesting perspective that avoids a lot of guff and confusion.

Thanks
Bill

 

[Eye_in_the_Sky]

Do you agree that the following statement is also true?

[All] Bell shows [is] if you want the joint-state of Alice's ((macroscopic) measuring) instrument and Bob's ((macroscopic) measuring) instrument, in spacetime, to be separable then you need non-local influences.

No.

Okay.

What about statement i) below? True or false?

i) If Bob's setting had been b₂ instead of b₁, each of Alice and Bob would have obtained a definite outcome.
___________________
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i) If Bob's setting had been b₂ instead of b₁, each of Alice and Bob would have obtained a definite outcome.

 

[morrobay]

Okay.

What about statement i) below? True or false?

i) If Bob's setting had been b₂ instead of b₁, each of Alice and Bob would have obtained a definite outcome.
___________________
___________________

Maybe bhobba is allowing for non realism separability
in which case non local influences would not be required to account for inequality violations.
In your above i) CFD example + separability then non local influence would be required

 

[morrobay]

You're certainly right, that nonrelativistic quantum mechanics is nonlocal, in the same sense that Newton's mechanics is. But the quantum-mechanical prediction of weird, Bell's-inequality-violating correlations in experiments such as EPR are not an artifact of using nonrelativistic QM. Fully-relativistic QFT makes the same (or similar) predictions.

Is there a B level explanation or reference for QFT making same predictions for Bell inequality violating correlations ?

 

[zonde]

Is there a B level explanation or reference for QFT making same predictions for Bell inequality violating correlations ?

I don't have such reference but I have some B level arguments why QFT should be considered nonlocal. If you are interested I can outline them here.

 

[Simon Phoenix]

QUOTE="Eye_in_the_Sky, post: 5550830, member: 11112"]i) If Bob's setting had been b2 instead of b1, each of Alice and Bob would have obtained a definite outcome.[/QUOTE]

That statement is true, depending on what you mean by 'definite outcome'.

Alice and Bob perform measurements - they get definite outcomes

(They get a definite result - just not a predictable result)

That's true whatever spin direction they each choose. The outcomes are only perfectly correlated if they happen to choose the same spin observable to measure.

Let's suppose they decide to do the following. They decide to do the first 10,000 runs of the experiment both measuring spin-z, the next 10,000 with Alice measuring spin-z and Bob measuring spin-(z + a), and so on. As Bob keeps changing his setting progressively more towards the spin-x direction, they will see a correspondingly weaker degree of correlation between their results until when Bob reaches spin-x there is no correlation between their results whatsoever (in the limit of a very large number of experimental runs, of course - for 10,000 runs there is a very, very, very small probability that they will obtain perfectly correlated results even with spin-z and spin-x measured).

So even if we have a perfectly entangled state there will be no correlation between the observables spin-z and spin-x. So, clearly, there's something a bit more going on than just straightforward correlation between observable pre-existing 'properties'.

In my view a fundamental parameter is the mutual information (we called it the 'index of correlation' in our stuff, but it's just essentially known as the entropy of entanglement these days). This is just I = S(A) + S(B) - S, where S(A), S(B) are the entropies of the reduced systems and S is the total entropy. In effect this is the difference in information between examination of the separate systems alone and examination of their joint properties.

For classical systems this quantity is less than or equal to inf [ S(A), S(B) ]. For quantum systems this quantity is less than or equal to 2 inf [ S(A), S(B) ]. So in other words the correlation (as parameterized by the mutual information) can be twice as large as the corresponding 'equivalent' classical system. This comes about because of the Araki-Lieb inequality that yields the quantum result
| S(A) - S(B) | ≤ S. It's the possibility of pure entangled states that gives this rather surprising and beautiful relation.

In a very hand-waving kind of way it's this 'extra' information inherent in entangled states that gives rise to the various things we can do with entanglement - like dense-coding, teleportation, entanglement-swapping, etc.

 

[stevendaryl]

Is there a B level explanation or reference for QFT making same predictions for Bell inequality violating correlations ?

I don't know, but the Bell-violating predictions of QM have been experimentally verified, so if QFT fails to predict that, that would count as a falsification of QFT.

 

[morrobay]

I don't know, but the Bell-violating predictions of QM have been experimentally verified, so if QFT fails to predict that, that would count as a falsification of QFT.

Maybe a misunderstanding : Not questioning if QFT makes this prediction, rather for an explanation of how it accounts for the inequality violations while maintaining locality. Maybe this should be a new thread

 

[bhobba]

Maybe a misunderstanding : Not questioning if QFT makes this prediction, rather for an explanation of how it accounts for the inequality violations while maintaining locality. Maybe this should be a new thread

Both QFT and standard QM predict bell violations.

My point is that only QFT actually worries about locality so if locality is violated in standard QM - big deal.

In QFT locality is associated with the principle of cluster decomposition I gave a link to. Now that link correctly pointed out its a bit more subtle that what Weinberg says - but the issue is the same - simply remove correlations from it and things are a lot simpler. Once you do that - Bell - poof - gone.

Thanks
Bill

 

[bhobba]

So, clearly, there's something a bit more going on than just straightforward correlation between observable pre-existing 'properties'.

There is - its different to classical correlations such as Bell mentions in his seminal paper with Bertlmanns socks:
https://cds.cern.ch/record/142461/files/198009299.pdf

It has different statistical properties to correlations like the socks. If you want it to be like the socks and have properties regardless of observation then you must have non-locality.

But its still just that - a correlation.

Remove correlations from the definition of locality and there is no issue.

Thanks
Bill

 

[Simon Phoenix]

There is - its different to classical correlations such a bell mentions in his seminal paper with Bertlmanns socks:
https://cds.cern.ch/record/142461/files/198009299.pdf

Yes - and the Bertlmann's socks paper is still, for me, absolutely the best explanation of the various issues.

As Scotty never said to Kirk "It's correlation, Jim, but not as we know it"

 

[bhobba]

\As Scotty never said to Kirk "It's correlation, Jim, but not as we know it"

Which is why we should stop over-complicating the whole thing - IMHO anyway.

Nice posts BTW

Thanks
Bill

 

[Simon Phoenix]

Not questioning if QFT makes this prediction, rather for an explanation of how it accounts for the inequality violations while maintaining locality

I'm not at all sure that the violation of the mathematical inequality has anything to do with locality (or non-locality) in QM.

First off, I think it's important to be clear about what is meant by 'locality' because this has different meanings in different contexts. What I mean by 'locality' in the context of the Bell inequality, and in an intuitive sense, is the following : the results of experiments 'here' are not affected by the settings of devices 'there'. [Or if they are, any such influence cannot travel faster than the speed of light]

Now let's take the standard Bell set-up in which we have some source of entangled particles, one of which goes to Alice and the other to Bob. When Alice and Bob choose, at random, from 3 possible measurement settings (say 0, 60 and 120 degrees) and collect data over many runs - they will see a violation of the Bell inequality when they compare their results. Assuming all the usual caveats about ideal experiments etc.

Now suppose Alice has the source of entangled particles in her lab. She measures her particle, but prevents its partner from ever getting to Bob. Instead she uses her result to prepare a new particle in the opposite spin state and in the same basis as indicated by her measurement result. She sends this new particle off to Bob.

Bob measures as normal, not realising Alice has made this switch. If Alice and Bob meet to compare results Bob will not be able to tell whether he has really received the partner of an entangled pair or some new particle prepared by Alice.

The upshot of this is that Alice can simply prepare particles at random in the up/down eigenstates for the 3 measurement settings (without using entangled particles at all) and send them to Bob. Using the data from her state preparations she can 'fool' Bob that they have been working with entangled pairs.

In other words the mathematical inequality can be violated by single particles - the correlation tested here is, of course, that between Alice's state preparation and Bob's measurements.

This latter experiment tells us nothing about locality or non-locality - since it is explicitly a local experiment. In principle for this set up we could construct a local hidden-variable theory. I haven't constructed such a theory but I feel it wouldn't look very natural or 'classical'.

The point is that the actual violation of the mathematical inequality has precious little to do with the locality or non-locality of the set-up.

By having the measurements of Alice and Bob spacelike separated this allows us to rule out local hidden variable theories of nature. This 'extra' correlation is there in QM whether or not we test it in a non-local setting - and we don't even need entangled particles to see it in a local setting. It was Bell's genius to figure out how this quantum correlation could be tested in a way that ruled out a whole class of theories by explicitly considering a non-local setting.

 

[Heinera]

Maybe a misunderstanding : Not questioning if QFT makes this prediction, rather for an explanation of how it accounts for the inequality violations while maintaining locality. Maybe this should be a new thread

QFT accounts for this the same way that QM does. Even in QFT, there is a state that "collapses" upon observation (OK, let's not get into a discussion of what "collapse" actually means.) So, even in QFT, an observation by Alice (or Bob) will collapse the combined state of Alice and Bob. Tongue in cheek, QFT is only local until someone makes an observation and causes a collapse.

 

[Zafa Pi]

I am thinking about a single run in a typical Bell-type scenario:

A joint-measurement of an (appropriately prepared) entangled property is performed in spacetime regions A and B at spacelike separation.

Regarding the above, in conjunction with Quantum Theory, would you say the following statement is true, false, or inapplicable? Why?

The 'state of affairs' relevant to the outcome at A is independent of the setting at B.

I am particularly interested in replies which assume a single (non-branching) universe.
Nonetheless, replies from all perspectives are valued.

In your 1st bold statement A and B are both making measurements and getting pairs of 0s and 1s, like (0,0), (1,0), (0,0), (1,1), ...
For the usual set up the values that A gets are like independent coin flips (same for B). If A chooses a particular setting a and B chooses b (where a and b do not differ by 45degrees) their results are not independent (in the sense of non-independent random variables). The mystery of entanglement.

In your 2nd bold statement it seems that A is making measurements and getting data where as B is not, but merely choosing a setting. Now you are asking if A's data is independent of B's setting. How is that different than asking if her data is independent of whether B is standing or not? What does it mean? A sees a fair sequence of 0s and 1s what ever is B's setting, and B sees nothing.

Interesting that DrChinese in post #2 believes that what A gets is not independent of B's setting, and Simon Phoenix in post #8 thinks they are independent, and bhobba likes both.
So when some one tells me what it means that my fair coin flips are independent of whether Bob is standing or not then I'll get to have an opinion too.

 

[Simon Phoenix]

Now you are asking if A's data is independent of B's setting. How is that different than asking if her data is independent of whether B is standing or not? What does it mean?

Well, think about what data Alice and Bob are collecting. They do thousands of runs. If they choose (independently and at random) from 3 possible detector settings (say 0,60 and 120 degrees) then after the experiment Alice and Bob can compile the data. It will look something like :
run 1 : Alice A = 1, a = 0, Bob B = 1, b = 60
run 2 : Alice A = -1, a = 120, Bob B = 1, b = 0
run 3 : Alice A = 1 a = 0, Bob B = -1, b = 0
run 4 : Alice A = 1, a = 60, Bob B = -1, b = 120

and so on and so on. Here A stands for Alice's 'result' and a stands for Alice's 'setting' - with B and b being Bob's equivalent quantities.

From this data the joint distribution P(A,B) can be experimentally estimated. Alice and Bob might also notice that whenever they happen to choose the same setting there is a perfect correlation and a weaker (non-zero) correlation whenever they choose different settings. So they're really looking here at subsets of the data - the results given particular settings. In other words they're looking at P(A,B | a,b).

They can also determine the quantities P(A | a,b) and P(B | a,b) which are the marginal distributions. Nothing special here - just analysing the measured data. So the question is whether P(A | a,b) is a function of both a and b or just a function of a? Does Alice's result probability also depend on the setting Bob has chosen?

Theoretically we might want to make the 'locality' assumption which is to state that Alice's result probability is independent of some remote setting of Bob's. Or to state that P(A | a,b) = P( A | a).

Bell goes further - he hypothesizes that there is some 'cause' for the correlation in terms of variables that we don't know about, or don't control - and that if we only did know the values of these variables we'd be able to explain the correlation. So he assumes that what we really have is a distribution of the form
P(A,B | a,b,h) where h is a symbol that stands for this collection of 'hidden' variables - which could be just one variable, a whole collection of them, or functions etc - the actual details are irrelevant.

By 'explain' we mean that we can write P(A,B | a,b,h) = P(A | a,b,h) P(B | a,b,h)

The locality assumption means that we can reduce this further to P(A,B | a,b,h) = P(A | a, h) P(B | b,h)

Bell showed that IF we make this hidden variable assumption then the data has to satisfy an inequality. [and in the proof there's also an assumption that it's meaningful to talk about the statistics of results if we'd measured things using a different angle - the counterfactual assumption]

The amazing thing, well it's amazing to me anyway, is that Bell has reduced the entire question to simply counting 'pings and dings' and reading 'angles'. Breath taking

If you really want to understand this I strongly recommend the Bertlmann's socks paper linked to by Bhobba

There is - its different to classical correlations such a bell mentions in his seminal paper with Bertlmanns socks:
https://cds.cern.ch/record/142461/files/198009299.pdf

Bell explains it with far greater clarity and insight than I could ever achieve.

 

[bhobba]

Bell explains it with far greater clarity and insight than I could ever achieve.

That he does.

But what can you say about one of the greatest physicists ever? All you can really say is he was a future Nobel Laureate before his untimely death:
http://www.americanscientist.org/bookshelf/pub/john-bell-across-space-and-time
http://www.irishphilosophy.com/2014/11/04/john-stewart-bell/

What is the key quality that elevates the greatest from the merely great? Its best illustrated in a story. One of the greatest mathematicians ever, likely in the top 10 of all time, a man Feynman readily acknowledged as above even him, just as much a magician as Feynman was, was the truly great polymath, not just a mathematician, but something much much greater, a polymath, John Von-Neumann. His mathematical insight was simply beyond compare, technically above even many of his great contemporaries, and well above Einstein who, while a competent mathematician was not even close to the class of Von-Neumann. Even Von-Neumann reportedly admitted Einstein was greater, as well as his contemporaries like Wigner. The reason is physical insight. Von-Neumann, along with Feynman, had that in spades. They could both see to the heart of a problem with frightening ease. But against this Einstein was greater again - he was simply unsurpassed. And this is the key to making progress - not the frightening ease with the substance behind the equations possessed by Feynman and Landau but few others, not the sublime mathematical competence of Von-Neumann - all very important of course - but the ability to see to the heart of the problem.

This Bell had, just as assuredly as Einstein did. This is what elevated him above the rest and assured him of a future Nobel.

Thanks
Bill
.

 

[Zafa Pi]

Well, think about what data Alice and Bob are collecting.

It is clear to me that you you didn't understand what I was asking.
Assume for the moment that I am familiar with the various Bell theorems and inequalities as well as Bertlmann's socks (because I am).
The OP is asking whether "The 'state of affairs' relevant to the outcome at A is independent of the setting at B." is true, false. or inapplicable.
In post #8 you wrote, "The results obtained by Alice are statistically independent of the setting of Bob,". In post #2 DrChinese believes the opposite.
You will notice that Bob is not collecting data, but merely choosing a setting, as I pointed out. The results obtained by Alice are +1 or -1 with probability 1/2.
Admittedly the data collected by both Alice and Bob are correlated, i.e. not the result of independent (1,-1) valued random variables. But how does one tell if her results are independent of just Bob's setting? What does it mean?

 

[Simon Phoenix]

But how does one tell if her results are independent of just Bob's setting? What does it mean?

I don't really understand what your problem is here.

If Alice does measurements and Bob just twiddles with his equipment (so to speak) but does no measurements then the measurement data we have is simply Alice's. Conceivably Alice's results might depend on Bob's setting as well as her own - but this can easily be checked from the data. In fact it's going to be a pretty dull experiment since nothing in this experiment is correlated at all :-)

You say you're familiar with the theory - so presumably you understand the locality condition that's imposed when Bell writes
P(A,B | a,b,h) = P(A | a,b,h) P(B | a, b,h) = P(A | a,h) P(B | b,h)
So what's your problem here? This is nothing more than an explicit recognition that Alice's results are assumed not to be conditioned upon Bob's setting (and vice versa). I don't see what your issue is with results 'here' being statistically independent of settings 'there'.

What am I missing?

Also, if you read post 2 carefully - I'm pretty sure Dr Chinese does not imply that Alice's results (alone) are dependent on Bob's setting. I think he's talking about the joint results of both Alice and Bob which are, of course, dependent on the relative angle of the settings.

[edit : piece removed that I need to think about a bit more and explain better :-) ]

 

[Eye_in_the_Sky]

You will notice that Bob is not collecting data, but merely choosing a setting, as I pointed out.

I will attempt to clarify.

Go back to the statement:

A joint-measurement of an (appropriately prepared) entangled property is performed in spacetime regions A and B at spacelike separation.

This is a scenario in which both Alice and Bob collect data. It is a "joint-measurement".

Next:

The 'state of affairs' relevant to the outcome at A is independent of the setting at B.

This is a comment about that very scenario.

By symmetry (in virtue of the 'structure' of spacetime), whatever value (i.e. true, false, or inapplicable) you assign to it, you are obliged to assign the same value to its vice versa:

The 'state of affairs' relevant to the outcome at B is independent of the setting at A.

Here are both statements in more compact form:

Bob's setting is IRRELEVANT to Alice's outcome.

Alice's setting is IRRELEVANT to Bob's outcome.
__________________

Now, you might ask, "How is the term IRRELEVANT to be understood/applied in our context?"
____

One aspect is as follows:

separable & mutually non-influencing → IRRELEVANCE .

The expansion of the terms in this expression is as follows:

separable: the joint-state of Alice's (measuring) instrument and Bob's (measuring) instrument, in spacetime, is separable

mutually non-influencing: each one's instrument is uninfluenced by that of the other

IRRELEVANCE: each one's setting is IRRELEVANT to the other's outcome

So, in expanded form, the shorthand expression will read as:

IF

the joint-state of their instruments, in spacetime, is separable

AND

their instruments are mutually non-influencing

THEN

each one's setting is IRRELEVANT to the outcome of the other .

Now, go back to the original expression:

separable & mutually non-influencing → IRRELEVANCE .

This is a property of spacetime.
____

There is another aspect of how IRRELEVANCE is to be understood/applied.

This aspect is in connection with any consistent theory (purported to be about the phenomenon under consideration), as follows:

If Bob's setting is IRRELEVANT to Alice's outcome, and if the theory in question is CORRECT in this regard, then:

No contradiction can arise in the theory by supposing that Alice's outcome for (the hypothetical setting) b₂ would have been the same as that for (the actual setting) b₁.

This is a property that any consistent theory of the phenomenon is expected to have.
__________________

 

[Eye_in_the_Sky]

i) If Bob's setting had been b₂ instead of b₁, each of Alice and Bob would have obtained a definite outcome.

That statement is true, depending on what you mean by 'definite outcome'.

Simon, you have understood the statement exactly as I have meant it.

The statement is true by hypothesis. The hypothesis is that of an idealized experiment in which:

No matter what each one's setting happens to be, each one will obtain any of two possible outcomes, "YES" or "NO".

_____________________
_____________________

As Scotty never said to Kirk "It's correlation, Jim, but not as we know it"

- OR -

As Spock never did while saying, nor said:

Raising an open Hand, "Five by five," uttered the Vulcan.

_____________________
_____________________

 

[RUTA]

You may find Mermin's characterization of this experiment helpful https://www.physicsforums.com/insights/quantum-liar-experiment-instantiation-mermin-device/. [You can ignore the Quantum Liar aspect.]