Can we all agree on the following about QM correlations?

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

Re: Can we all agree on the following about QM correlations?

Postby Heinera » Sun Jun 09, 2019 8:01 am

Yablon wrote:This is actually a fairly broad definition. I am perfectly content to regard this "vital assumption" as a minimal necessary requirement for a "hidden variable" used in connection with QM correlations between A and B. Also I would even consider more restrictive requirements which tighten this definition, i.e., to entertain the possibility that this definition is insufficiently restrictive, as to how something acquires status as a "hidden variable" to begin with.

[...]

Jay


The point of Bell's definition being broad, is that the hidden variable must include everything that is relevant for the prediction of the outcome, with the exception of the angle setting in the detector, and the mechanism of the detectors (which are encoded in the functions and ). In Bell's setup, the outcome at Alice is a function of two things only: and . If your variable is not this all-inclusive, it is not a hidden variable in the sense of Bell.
Last edited by Heinera on Sun Jun 09, 2019 8:35 am, edited 1 time in total.
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Re: Can we all agree on the following about QM correlations?

Postby Yablon » Sun Jun 09, 2019 8:20 am

Heinera wrote:The point of Bell's definition being broad, is that the hidden variable must include everything that is relevant for the prediction of the outcome, with the exception of the angle setting in the detector. In Bell's setup, the outcome at Alice is a function of two things only: and . If your variable is not this all-inclusive, it is not a hidden variable in the sense of Bell.


I agree with this, assuming by "prediction of the outcome" you mean explaining how the singlet correlation comes to be .
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Re: Can we all agree on the following about QM correlations?

Postby Heinera » Sun Jun 09, 2019 8:39 am

Yablon wrote:
Heinera wrote:The point of Bell's definition being broad, is that the hidden variable must include everything that is relevant for the prediction of the outcome, with the exception of the angle setting in the detector. In Bell's setup, the outcome at Alice is a function of two things only: and . If your variable is not this all-inclusive, it is not a hidden variable in the sense of Bell.


I agree with this, assuming by "prediction of the outcome" you mean explaining how the singlet correlation comes to be .


No, I do not mean that, because the correlations are already very well explained by QM. With "outcome" I (and Bell) meant -1 or +1.
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Re: Can we all agree on the following about QM correlations?

Postby Yablon » Sun Jun 09, 2019 8:55 am

Heinera wrote:
Yablon wrote:
Heinera wrote:The point of Bell's definition being broad, is that the hidden variable must include everything that is relevant for the prediction of the outcome, with the exception of the angle setting in the detector. In Bell's setup, the outcome at Alice is a function of two things only: and . If your variable is not this all-inclusive, it is not a hidden variable in the sense of Bell.


I agree with this, assuming by "prediction of the outcome" you mean explaining how the singlet correlation comes to be .


No, I do not mean that, because the correlations are already very well explained by QM. With "outcome" I (and Bell) meant -1 or +1.

Fair enough, I agree.
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Re: Can we all agree on the following about QM correlations?

Postby FrediFizzx » Sun Jun 09, 2019 9:03 am

FYI: Bell's original paper is available direct from the publisher now for free.

https://journals.aps.org/ppf/abstract/1 ... zika.1.195
.
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Re: Can we all agree on the following about QM correlations?

Postby Yablon » Sun Jun 09, 2019 9:35 am

OK, following some exchanges with Richard and Heinera, I think we have reached agreement with regard to the matters in rounds I and II. So let's move on to round III. I will start using the "round numbers" for future reference. References below are still to equation numbers in https://jayryablon.files.wordpress.com/ ... -4.1-1.pdf. Here, I'd like to talk about intrinsic spins as an example of the uncertainty principle.

III:1) Does everyone agree that the Pauli matrices have the following non-zero commutator:

(1.4)

III: 2) If so, do all agree that we can define an operator to represent intrinsic spin, and that this will have the following commutator?

unnumbered, paragraph before (3.1)

III: 3) Does everyone agree that if all three of the are for a single particle or locally-interacting system which we shall call system (A), then the commutator will have an Uncertainty Principle relationship which is a consequence of this non-commutation?

III: 4) Does everyone agree that the Robertson uncertainty relation (https://en.wikipedia.org/wiki/Uncertain ... _relations) in general is where and are the standard deviations of these operators and ? And that when these operators are constant, the Robertson relation loses the expectation value and simplifies to ?

III: 5) Does everyone agree that when applied to the intrinsic spin operators from point 2) above, that there are three uncertainty relations for the spin of a single particle, one for each space dimension, which are the following?


(3.1)


Note: In the standard deviations have used the eigenvalues of these operators obtained via , because the standard deviations of the operators are calculated to be equal to the standard deviations of their eigenvalues. So do you agree with that also?

III: 6) Does everyone agree that one way to represent that "act of observing" one of these eigenvalues is to set its standard deviation to zero? And that, say, if we observe while setting , the second and third equations in point 5 lead to a result which contradicts any possibility of simultaneously observing and ? And that this is the origin of the so-called "spin cone" for uncertainty / indeterminacy in the spin azimuth which I diagram in Figure 1 on page 19, also shown right below? And of the common view that spin cannot be simultaneously measured along more than a single axis at a time?

Image

III: 7) Does everyone agree that we can thereby represent the intrinsic spin vector using spherical coordinates with a magnitude based on the Casimir operator for , a polar descent angle for z spin up and for z spin down, and an entirely unobservable-in-principle azimuth ?

III: 8) Finally, with two of the three spherical coordinates and being observable but the third coordinate being unobservable-in-principle, does everyone agree that there is a good discussion to be had regarding the EPR status of as an "element of reality"? (We are not having that discussion yet, I just want to see if everyone can get this far on the same page).

Jay
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Re: Can we all agree on the following about QM correlations?

Postby FrediFizzx » Sun Jun 09, 2019 12:36 pm

I agree. It is all pretty standard.
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Re: Can we all agree on the following about QM correlations?

Postby gill1109 » Sun Jun 09, 2019 9:47 pm

Yablon wrote:III: 8) Finally, with two of the three spherical coordinates and being observable but the third coordinate being unobservable-in-principle, does everyone agree that there is a good discussion to be had regarding the EPR status of as an "element of reality"? (We are not having that discussion yet, I just want to see if everyone can get this far on the same page).

By the way, I do not think we settled the question of what is a correlation. Theories talk about correlations. Experimenters gather date and calculate things which they call correlations. We have to discuss sooner or later what we take as axiom or definition, what we take as heuristic principle, what we mean by chance.

Now here too something is being slipped in which we are going to have to grapple by the horns. Why should something be "unobservable-in-principle"? A theory may assert that there are no experiments which can directly access certain variables in the theoretical model. But if the theory itself is in question, we can't take that assertion and raise it to the level of dogma.

I recall that Inge Helland (he's a guy, from Norway) has attempted to rewrite and fuse quantum mechanics and statistics through introduction of a new kind of variables. He calls them e-variables ("epistemic conceptual variables"). Get his book, and read it:"Epistemic Processes (A Basis for Statistics and Quantum Theory)" https://www.springer.com/gp/book/9783319950679 which came out very recently.
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Re: Can we all agree on the following about QM correlations?

Postby Yablon » Mon Jun 10, 2019 10:53 am

gill1109 wrote:By the way, I do not think we settled the question of what is a correlation. Theories talk about correlations. Experimenters gather date and calculate things which they call correlations. We have to discuss sooner or later what we take as axiom or definition, what we take as heuristic principle, what we mean by chance.

Well, lets go back to viewtopic.php?f=6&t=383#p8702. I just want to know whether the calcuation

(1.17a)

with the standard deviations:


(1.17b)

to derive:

(1.19)

is a mathematically correct calculation? Yes or no? And if no, why?

Now, for want of better technical language I would call this a theoretical correlation. And I would agree that there is a second very important calculation to be done which goes event by event, emits a singlet at each event which then splits, which then has a binary value detected by Alice and another one by Bob, and which also arrives at as an expectation value from an average as the number of events approaches infinity. And, if locality is to stand a chance, that second calculation would have show also, that there is no non-local signalling. But we have to walk before we run, so I all want right now is your agreement that there is nothing mathematically amiss in the above calculation.


gill1109 wrote:
Yablon wrote:III: 8) Finally, with two of the three spherical coordinates and being observable but the third coordinate being unobservable-in-principle, does everyone agree that there is a good discussion to be had regarding the EPR status of as an "element of reality"? (We are not having that discussion yet, I just want to see if everyone can get this far on the same page).

...
Now here too something is being slipped in which we are going to have to grapple by the horns. Why should something be "unobservable-in-principle"? A theory may assert that there are no experiments which can directly access certain variables in the theoretical model. But if the theory itself is in question, we can't take that assertion and raise it to the level of dogma.

I recall that Inge Helland (he's a guy, from Norway) has attempted to rewrite and fuse quantum mechanics and statistics through introduction of a new kind of variables. He calls them e-variables ("epistemic conceptual variables"). Get his book, and read it:"Epistemic Processes (A Basis for Statistics and Quantum Theory)" https://www.springer.com/gp/book/9783319950679 which came out very recently.

I took a look at whatever I could see from the online reference, and it does look interesting. But again, let keep the rubber on the road. So I have a few questions, and I will try to stay as mathematical as possible and not use words or phrases (such as "uncertainty principle") which carry too much weighty baggage:

1) From my question III: 4), Do you agree with Robertson that for constant non-commuting operators and , the standard deviations for those operators have an inequality with the commutator for those operators which is given by:

?

2) For the "same particle," do you agree that if which means that two operators do not commute, that the equation of point 1) above simplifies to:

?

3) Do you agree that it is important to differentiate between whether and are operators for two different particles or for the same particle?

4) Do you agree that for the "same particle," when we actually observe a state value of and therefore acquire a known result, that the a priori non-zero standard deviation, after the observation, goes from ? "Before we know to after we know."

5) And here is the main point for critics of "uncertainty" which is really better called "impossibility of simultaneous measurement" (and this is what EPR confine themselves to). Do you agree with the following disproof-by-contradiction?

a) Postulate that . So we have observed a result from the X operator, and the point 2 equation is now:

?

b) Also postulate that . So we have also simultaneously observed a result from the Y operator.

c) Now the 5)a) equation becomes:

.

d) So as a result of 5)c) we have falsified the postulate 5)b) that we observed something from Y simultaneously with X. And so, we cannot simultaneously observe both.

Call it uncertainty, or don't. But unless you care to argue that Robertson's 1) is wrong, we are stuck with the fact that some quantities pertaining to the same particle or interacting system simply cannot be simultaneously measured, when there are non-commuting operators involved.

Anything else, or can we start to talk about how to best understand the "reality" of those quantities which cannot be observed because some other quantity for the same particle or system has already been observed and a second observation would raise a contradiction in the nature of 5)c)?

Jay
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Re: Can we all agree on the following about QM correlations?

Postby gill1109 » Mon Jun 10, 2019 9:45 pm

I'm not very interested in the conventional dogmas of conventional QM. Things have progressed a lot in the last 50 years. There are more things you can measure. Even conventional QM gives you more options. For instance, what you can also do is ... bring in an independent ancillary system in a fixed state. Let it interact in unitary way with the system of interest. Now measure an observable of the ancillary system. You can also randomise. Toss classical coins or dice and perform different measurements according to the outcome of the randomisation. Nowadays experimenters do routinely simultaneously "measure" non-commuting observables on one and the same system. There are many many more uncertainty relations/uncertainty principles than the original.

By all means lets start to talk about the "reality" of those quantities which according to your interpretation of conventional QM "cannot be observed". I'm right now at a conference where 60 people are talking full time a whole week exactly on the question what "realism" should mean and what "locality" should mean and what "randomness" is. There are very very exciting new developments. And it seems as though there are more interpretations around than every before.
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Re: Can we all agree on the following about QM correlations?

Postby Yablon » Tue Jun 11, 2019 5:35 am

gill1109 wrote:Nowadays experimenters do routinely simultaneously "measure" non-commuting observables on one and the same system.

I'd be interested in understanding what it means to simultaneously "measure" values of non-commuting operators. And since the "example" I am starting with is intrinsic spin, I'd like to see whether someone can really measure spin up or down along the z axis, and simultaneously measure the spin vector azimuth in the xy plane, i.e., the angle around the spin cone illustrated in viewtopic.php?f=6&t=383#p8723.
gill1109 wrote:By all means lets start to talk about the "reality" of those quantities which according to your interpretation of conventional QM "cannot be observed". I'm right now at a conference where 60 people are talking full time a whole week exactly on the question what "realism" should mean and what "locality" should mean and what "randomness" is. There are very very exciting new developments. And it seems as though there are more interpretations around than every before.

Good! This is where I wanted to get to. I think we should start with "reality," but far from end there. Also on the table should be completeness, observability, uncertainty, predictability with certainty, locality, and hidden variable (which several of us argued about yesterday). And of course, the intertwining of all of these. I think I will start a separate, new thread devoted to "definitions" of these key concepts and how they are interrelated, and the underlying principles we use to fashion these definitions.
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