Joy Christian's disproof of Bell

[harrylin]

[..] if local hidden variables are required to describe an entangled state, then from that you can formulate an inequality that will be violated by qm and experimental results -- none of which contradicts the possibility or assumption of the existence of local hidden variables or the assumption that nature is locally causal (and wrt to this it helps to keep in mind that Bell showed that qm is quite compatible with a local hidden variable account of individual results) [..].

"none of which contradicts [..] the assumption that nature is locally causal", isn't that exactly what the BI is supposed to contradict? Or did you simply mean that nature can be also locally causal?

 

[yoda jedi]

For Christian, the output values of the function A (the measured "spin" components) are only +1 and -1.*
A is function of hidden variable L and detector angle a. His beef is with Bell's statement that A (L , a ) = +1 or -1, it should be A ( L , a ) = +1 or -1 *about* a, as the output is relative to the chosen detector position. It is completely unclear to me if, as he suggests, that makes any difference for the calculation.

So, his analysis (it's not a theory!) may certainly be erroneous and a waste of time; but clearly, it does concern hidden variable theories.

*Personal communication, Sep 2009

the modal approach is another example of hidden variables.

Dickson
http://www.science.uva.nl/~seop/entries/qm-modal/

..."aware of the nonlocality inherent in standard quantum theory. It arises most dramatically in the context of the projection postulate, which asserts that upon measurement of a physical system, its state will ‘collapse’ (or be ‘projected’) to a state corresponding to the value found in the measurement. This postulate is difficult to accept in any case (what effects this discontinuous change in the physical state of a system? what exactly is a ‘measurement’ as opposed to an ordinary physical interaction?), but it is especially worrying when applied to entangled compound systems whose components are well-separated in space. The classic example is the Einstein-Podolsky-Rosen experiment, in which two particles which have interacted in the past are separated. Their quantum-mechanical state is ‘entangled’, which means, for our purposes, that there exist strict correlations between the two systems, in spite of the fact that the correlated quantities are not sharply defined in the individual systems. This correlation has the effect that the collapse resulting from a measurement on one of the systems simultaneously (and instantaneously) affects the other...
..A possible way clear of this problem was noticed by van Fraassen (1972, 1974, 1991), who proposed to eliminate the projection postulate from the theory. Of course, others had made this proposal before. Bohm's (1952) theory (itself preceded by de Broglie's proposals from the 1920s) eliminates the projection postulate, as do the various many-worlds (and relative-state) interpretations. Van Fraassen's elaboration of the proposal to do without the projection postulate was, however, different from these other approaches. It relied, in particular, on a distinction between what van Fraassen called the ‘value state’ of a system, and the ‘dynamical state’ of a system. The value state at any instant represents the system's physical properties at that instant, in the sense that it specifies the values of all physical quantities that are sharply defined for the system at the point in time in question. By contrast, the dynamical state determines the evolution of the system. It determines which properties the system might have at later times. In other words, the dynamical state is what we need to make predictions about future value states...
...and of modal interpretations in general, is that physical systems at all times possesses a number of well-defined physical properties, i.e. definite values of physical quantities, and that these properties are represented by the system's value state...
...Healey's main concern was the apparent nonlocality of quantum theory. Healey's intuition about the way a modal interpretation based on the biorthogonal decomposition theorem would be applied to, say, an EPR experiment is to implement the idea that an EPR pair possesses a 'holistic' property; this can then explain why the apparatus on one side of the experiment acquires a property that is correlated to the result on the other side...
...a hidden-variables theory, in which value states are added as hidden variables to the original formalism in order to obtain a full description of the physical situation"...



---------------------
Dieks
http://arxiv.org/PS_cache/quant-ph/pdf/0703/0703020v1.pdf

..quantum mechanics as an objective, man-independent description of physical reality...

 

[ThomasT]

About the exchange of signals, does he state that somewhere? I must have overlooked it...

In the last paragraph, after equation 30.

"none of which contradicts [..] the assumption that nature is locally causal", isn't that exactly what the BI is supposed to contradict?

That's the view of many, and maybe it was Bell's intention, but that isn't what BI violations, definitively and unarguably, indicate -- which is that the LR formulation on which the formally and experimentally violated BI is based is incompatible with standard qm and the experimental preparation. No more, no less. This is what I meant by the minimalist interpretation and unarguable applicability of Bell's theorem.

As I mentioned in a previous post, BIs are based on the requirement that entanglement be modeled by (local hidden) variables which are irrelevant (even in an exclusively locally causal world) wrt entanglement (which depends exclusively on global properties and measurement parameters), and that if lhv's are required in the model of entanglement, then the predictions of such a model will necessarily be skewed.

Or did you simply mean that nature can be also locally causal?

No, I meant that BI violations don't contradict the assumption that nature is exclusively local.

 

[Avodyne]

For Christian, the output values of the function A (the measured "spin" components) are only +1 and -1.

Sure, but he also says that the values don't commute. So they're not just numbers. In fact, all he is doing is attaching a different set of words to the usual quantum operators, and then declaring that these operators are actually elements of "local reality".

Which makes the whole thing pretty silly.

 

[JesseM]

As I mentioned in a previous post, BIs are based on the requirement that entanglement be modeled by (local hidden) variables which are irrelevant (even in an exclusively locally causal world) wrt entanglement (which depends exclusively on global properties and measurement parameters), and that if lhv's are required in the model of entanglement, then the predictions of such a model will necessarily be skewed.

Not clear what you're saying here--are you distinguishing between 1) a "locally causal world" and 2) the idea that all observable measurements are determined by local variables (hidden or measurable) whose values are only causally influenced by events in their past light cones? If you don't consider 1) and 2) to be synonymous, can you explain more about what alternative type of "locally causal world" you are considering? For example, are you considering the possibility that measurements don't have unique outcomes, as in the MWI?

 

[yoda jedi]

Not clear what you're saying here-----

me two

 

[Gordon Watson]

It is not clear to me why Admins, or empowered others, do not correct obvious spelling errors in thread TITLES?

Is there an explanation for this?

The person's name is JOY CHRISTIAN.

Without correction, it seems to me, future searches on the subject may this thread.

 

[ThomasT]

Not clear what you're saying here ...

The outcomes of Bell tests are determined by global, not local, properties and parameters. The term global here isn't synonymous with ftl or action at a distance. It refers to relationships. Wrt, say, Aspect 1982 there's the relationship (presumably produced via the emission process) between the photons and the relationship between the polarizer settings, and the experiment is measuring the correlation (another relationship) between those two relationships. Local hidden variables, eg. optical vector(s) of the incident photons, are irrelevant in this context.

Given that, then if a model of Aspect 1982 is required to include those irrelevant hidden variables, then the predictions get skewed accordingly (which has been amply demonstrated ). Then, if you make a Bell inequality based on that sort of model, then of course the qm predictions and the experimental results will violate it.

Given that, then what do BI violations reveal about the deep reality? Nothing, I think. So that's why I said that even in a world in which local hidden variables exist and which is exclusively locally causal (ie., in which ftl and action at a distance don't exist), then viably modelling Aspect 1982 in terms of local hidden variables would still be impossible -- because it isn't local properties that are being correlated, it's global ones (relationships).

I should add that it's because of this way of thinking about it that Christian's Bell stuff was potentially interesting.

 

[JesseM]

The outcomes of Bell tests are determined by global, not local, properties and parameters. The term global here isn't synonymous with ftl or action at a distance. It refers to relationships.

Huh? In a local realist universe of the type I described in 2), you can still talk about statistical relationships between measurements at different locations, is that all you're talking about here?

Wrt, say, Aspect 1982 there's the relationship (presumably produced via the emission process) between the photons and the relationship between the polarizer settings, and the experiment is measuring the correlation (another relationship) between those two relationships. Local hidden variables, eg. optical vector(s) of the incident photons, are irrelevant in this context.

In a local realist universe like I described in 2), how could the "emission process" create a relationship between measurements at different locations except by inducing a correlation in local variables which each particle "carries with them" from the location of the emission to the location of the measurement? For example, if an emitter repeatedly sends out pairs of boxes with coins inside them, and on each trial we find that the coin I find in my box is of the same type as the coin you find in yours, then the natural conclusion would be that the emitter was putting identical coins into each box, and as the boxes traveled the hidden variable "coin-inside-the-box" remained the same for each box.

So that's why I said that even in a world in which local hidden variables exist and which is exclusively locally causal (ie., in which ftl and action at a distance don't exist), then viably modelling Aspect 1982 in terms of local hidden variables would still be impossible -- because it isn't local properties that are being correlated, it's global ones (relationships).

Again, huh? The relationship is just a relationship between local facts, namely the result of each measurement at a discrete location in space and time (analogous to the relationship between the result of opening the box at one location and the result of opening the box at another location in my analogy above). If you think Bell's reasoning somehow forbids you from talking about such relationships then you are really completely confused. Bell's assumption is not that there can't be statistical relationships between local events, it's just that each local event is causally influenced only by other events in its past light cone (like the idea that each measurement result was influenced by properties the particles were assigned at the moment they were emitted from a common location).

 

[ThomasT]

The relationship is just a relationship between local facts ...

There's the relationship between the photons, and the relationship between the polarizers, both of which are relationships between local facts, and then there's the relationship between those relationships (which is the relationship that the experiment is measuring) and that relationship is not a relationship between local facts. If you require your account to be in terms of local facts, ie. local hidden variables (instead of, as qm does, solely in terms of those relationships -- which do not, and don't need to, specify definite values), then you get skewed predictions (basically showing the qm-predicted angular dependence in a reduced range of joint detection frequency).

 

[JesseM]

There's the relationship between the photons, and the relationship between the polarizers, both of which are relationships between local facts, and then there's the relationship between those relationships (which is the relationship that the experiment is measuring) and that relationship is not a relationship between local facts.

It is in a local realist universe that matches my definition 2):

the idea that all observable measurements are determined by local variables (hidden or measurable) whose values are only causally influenced by events in their past light cones?

The only measurable facts that Bell's argument concerns itself with are the fact I set my polarizer to some angle, and then see a pointer on my detector give either result +1 or -1, and you do likewise. The statistical relationship between these specific facts on each trial--for example, the observation that any trial where both of us choose the same detector angle, we both get the same result--is a relationship between local facts. Do you disagree? If not, then the question remaining is what the physical explanation for this relationship might be, and Bell's work successfully rules out a broad class of theories where each local fact (like whether my pointer gave result +1 or -1 on a particular trial) is only causally influenced by other local facts in its past light cone (classical electromagnetism would be an example of such a theory where local facts at each point in spacetime, specifically electric and magnetic field vectors, are only influenced by other local facts in their past light cone). That's a pretty big result! I can't quite tell if you understand and agree that Bell's work successfully rules out this class of theories, or just don't consider the result very interesting.

In any case, based on Avodyne's comment in post #30 it sounds like Joy Christian's model just ignores the real-world observation that the experimenter always sees one of two discrete results (pointer going to +1 or -1), and instead posits a sort of hypothetical universe where the results are elements of Clifford algebra. I don't know if the idea is like a MWI scenario (as vanesch suggested) where the experimenters themselves are supposed to remain in a superposition of states which involve different measurement results, or what. As you said in post #31, it would be interesting to quiz Christian about what he thinks the physical significance of his analysis is supposed to be.

 

[ThomasT]

The only measurable facts that Bell's argument concerns itself with are the fact I set my polarizer to some angle, and then see a pointer on my detector give either result +1 or -1, and you do likewise. The statistical relationship between these specific facts on each trial--for example, the observation that any trial where both of us choose the same detector angle, we both get the same result--is a relationship between local facts. Do you disagree?

There's no statistical relationship between individual detections or data streams, afaik. The relationship that's being measured in Aspect 1982 is between the relationship between the polarizer settings and the relationship between the polarizer-incident photons vis joint detection attributes (and while each of those is a relationship between local facts, the relationship between those relationships is not a relationship between local facts, because the relationships between local facts are not themselves local facts). It's a relationship between a global measurement parameter (the angular difference in the polarizer settings) and a global property (the relationship between the polarizer-incident photons which doesn't vary from pair to pair). There's no local hidden variable(s) involved in modelling this. Just the global measurement parameter and the global property (vis the application of the law of conservation of angular momentum). The local hidden variables determine individual results. For the individual measurement situation qm can be supplemented with (that is, it's compatible with) lhv's. But, not so strangely, where lhv's are irrelevant, as in the joint context, then qm isn't amenable to lhv supplementation.

If not, then the question remaining is what the physical explanation for this relationship might be ...

Wrt Aspect 1982 the explanation is that the entangled photons have been emitted by the same atom during the same transition interval. For other preparations there are other physical explanations for the relationship between entangled quanta.

... and Bell's work successfully rules out a broad class of theories where each local fact (like whether my pointer gave result +1 or -1 on a particular trial) is only causally influenced by other local facts in its past light cone (classical electromagnetism would be an example of such a theory where local facts at each point in spacetime, specifically electric and magnetic field vectors, are only influenced by other local facts in their past light cone). That's a pretty big result! I can't quite tell if you understand and agree that Bell's work successfully rules out this class of theories, or just don't consider the result very interesting.

I agree that Bell's work successfully, and forever, rules out the application of any and all local hidden variable theories to entanglement preparations. And, even given my view on why LHV's aren't applicable to entanglement preparations, Bell's work is nonetheless interesting and important because it quantified the question and precipitated a lot of important experimental and theoretical research.

 

[vanesch]

It is not clear to me why Admins, or empowered others, do not correct obvious spelling errors in thread TITLES?

Is there an explanation for this?

The person's name is JOY CHRISTIAN.

Without correction, it seems to me, future searches on the subject may this thread.

Ok, noted and done.

 

[JesseM]

There's no statistical relationship between individual detections or data streams, afaik. The relationship that's being measured in Aspect 1982 is between the relationship between the polarizer settings and the relationship between the polarizer-incident photons vis joint detection attributes (and while each of those is a relationship between local facts, the relationship between those relationships is not a relationship between local facts, because the relationships between local facts are not themselves local facts). It's a relationship between a global measurement parameter (the angular difference in the polarizer settings) and a global property (the relationship between the polarizer-incident photons which doesn't vary from pair to pair).

This sounds like the kind of ill-defined not even wrong claims that people often make when they try to "explain" physics results using purely verbal arguments with no clearly-defined notion of how to translate the words into math (which is all that really counts in physics)--if that's unfair, can you define what "relationship between relationship" means in mathematical, not verbal, terms? To me, in this context "relationship" just means "statistical correlation", which just means that we can assign probabilities to each possible combination of the possible values of each of the 4 variables (polarizer setting at location #1, measurement result at location #1, polarizer setting at location #2, measurement result at location #2). To say there's a statistical correlation between the 4 variables just means the following:

P(polarizer setting #1=W AND measurement result #1=X AND polarizer setting #2=Y AND measurement setting #2=Z) is not equal to P(polarizer setting #1=W) * P(measurement result #1=X) * P(polarizer setting #2=Y) * P(measurement setting #2=Z)

Where W, X, Y, and Z represent any given combination of values (for example, we might have W=60 degrees, X=+1, Y=120 degrees, and Z=-1). So, if the two sides are not equal, that means there's a statistical correlation between the 4 variables, each of which tell you about purely local facts. That's all that any Aspect-type experiment looks at, the statistical correlations between the values of some number of variables representing local facts. If we have a chart showing the values of each variable over a large number of trials, it's a simple matter to use the relative frequencies of different combinations of values to estimate both joint probabilities like P(polarizer setting #1=W AND measurement result #1=X AND polarizer setting #2=Y AND measurement setting #2=Z) and individual probabilities like P(measurement result #1=X) so you can check whether a statistical correlation is found. And Bell showed that it's impossible to explain the combinations of probabilities predicted by QM if we assume the probability of any given local fact can only be causally influenced by other local facts in its past light cone.

Wrt Aspect 1982 the explanation is that the entangled photons have been emitted by the same atom during the same transition interval.

What do you mean by "explanation"? It's just an empirical observation that photons emitted by the same atom are correlated in this way, but it doesn't tell you, for example, whether they are correlated because they were each assigned identical hidden variables at the moment they were created and they just carried the variables with them as they traveled, or whether the fact that they were created together gives them an FTL connection which allows a measurement on one to instantly affect the behavior of the other, or some other picture of what's going on "behind the scenes". Of course you can say that you're not interested in any behind-the-scenes picture and are only concerned with finding the correct mathematical relationships between observable measurements, in that case you just have ordinary orthodox QM (the 'shut up and calculate' version), but all these interpretational issues and ideas about hidden variables are discussed exactly because many physicists think there should be more of a physical "explanation" for the observed mathematical relationships.

And, even given my view on why LHV's aren't applicable to entanglement preparations

I don't understand what you mean by "aren't applicable". Do you think they somehow wouldn't be applicable even if we were dealing with the same sort of experiment involving polarized light in purely classical electromagnetism, where no violations of Bell inequalities would be seen? Because as I said, the structure of classical electromagnetism definitely matches the definition of a local realistic theory (although obviously all variables in classical EM are in principle measurable, not hidden), so any statistical relationships seen in such an experiment, even ones involving what you might call a "relationship between relationships", would be fully explainable in local realist terms.

 

[ThomasT]

This sounds like the kind of ill-defined not even wrong claims that people often make when they try to "explain" physics results using purely verbal arguments with no clearly-defined notion of how to translate the words into math (which is all that really counts in physics)--if that's unfair, can you define what "relationship between relationship" means in mathematical, not verbal, terms?

This is a conceptual consideration, so if it isn't clear in it's verbal version, then putting it into shorthand isn't going to help.

The relationship between the polarizers isn't a local fact, and the relationship between the photons isn't a local fact. Wrt the polarizers this relationship just refers to their angular difference ( θ). Wrt the photons, things aren't so simple. What the polarizers are jointly physically measuring during any coincidence interval is the relationship between two optical disturbances emitted by the same atom -- a relationship that's expressed vis the applicable conservation law. What the experiment is correlating to θ is the rate of generation of identical detection attributes. The joint detection attribute, (A,B), is also not a local fact. E(A,B) isn't, effectively, determined by local hidden variables. Wrt the two photon scenarios, the hidden variable, λ, is typically taken to refer to the optical vector of the polarizer-incident photons. I hope it's become clear(er) that E(A,B) = Cos²θ is effectively determined independently of λ.

It's just an empirical observation that photons emitted by the same atom are correlated in this way, but it doesn't tell you, for example, whether they are correlated because they were each assigned identical hidden variables at the moment they were created and they just carried the variables with them as they traveled, or whether the fact that they were created together gives them an FTL connection which allows a measurement on one to instantly affect the behavior of the other, or some other picture of what's going on "behind the scenes".

The assumption that the relationship between their motional properties is due to their being emitted in opposite directions from the same atom during the same transition seems to me to be the most reasonable assumption. Isn't this what qm's application of the law of conservation of angular momentum in Aspect 1982 is based on?

I don't understand what you mean by "aren't applicable".

As in irrelevant. See above. BIs are violated because they're based on a formulation of joint detection (entanglement) preparations which requires the inclusion of a variable which is irrelevant wrt those contexts. It's possible to understand these experiments in local realist terms without requiring that the mathematical model include any local hidden variables.

Edit: Isn't what qm does is define the relevant relationships and then relate those relationships accordingly?

 

[Gordon Watson]

Ok, noted and done.

Thank you vanesch.

Can you also fix each page header?

It would give PF a better look if its page-headers were error-free.

 

[JesseM]

The relationship between the polarizers isn't a local fact, and the relationship between the photons isn't a local fact.

No, but both involve a statistical correlation between a collection local facts. Clearly the assumption of local realism does not rule out the existence of such correlations between local facts, and whether you call them "relationships between local facts" or "relationships between relationships", we could find the same kind of relationships in classical electromagnetism which is a local realist theory, do you disagree?

Wrt the polarizers this relationship just refers to their angular difference ( θ). Wrt the photons, things aren't so simple. What the polarizers are jointly physically measuring during any coincidence interval is the relationship between two optical disturbances emitted by the same atom -- a relationship that's expressed vis the applicable conservation law.

And couldn't we find relationships between two electromagnetic waves generated by the same source in classical electromagnetism?

What the experiment is correlating to θ is the rate of generation of identical detection attributes. The joint detection attribute, (A,B), is also not a local fact. E(A,B) isn't, effectively, determined by local hidden variables.

But E(A,B) for any joint detection attributes we could come up with in a classical EM experiment would be determined solely by local variables in the region of each measurement, do you disagree?

It almost sounds like you're arguing that by the very nature of the experiment Bell's assumptions about local realist are wrong, but that clearly isn't the case, if you did the same type of experiment but the statistical results were a little different, then it might be fully explainable by a local realist theory just as would be true for an experiment in classical EM.

Wrt the two photon scenarios, the hidden variable, λ, is typically taken to refer to the optical vector of the polarizer-incident photons.

No it isn't, this is an idea I've seen you refer to before, but if you think this is the way physicists conceive of it then that's a misconception. The hidden variable is sometimes imagined to be, not any sort of "vector", but simply a function that assigns a + or - to every possible detection angle in advance...but one of the points of Bell's proof is that it requires no understanding of what the local hidden variables would actually be or exactly how they would determine the measurement results.

It's just an empirical observation that photons emitted by the same atom are correlated in this way, but it doesn't tell you, for example, whether they are correlated because they were each assigned identical hidden variables at the moment they were created and they just carried the variables with them as they traveled, or whether the fact that they were created together gives them an FTL connection which allows a measurement on one to instantly affect the behavior of the other, or some other picture of what's going on "behind the scenes".

The assumption that the relationship between their motional properties is due to their being emitted in opposite directions from the same atom during the same transition seems to me to be the most reasonable assumption. Isn't this what qm's application of the law of conservation of angular momentum in Aspect 1982 is based on?

But "relationship between their motional properties is due to their being emitted in opposite directions from the same atom during the same transition" is still very vague, it doesn't tell me what this "due to" consists of--for example, whether you are imagining that "due to their being emitted in opposite directions" they were assigned the same properties at birth and just carried these unchanging properties with them to the location of the measurements (which of course would mean the properties were local hidden variables, so that's ruled out by Bell), or if "due to their being emitted in opposite directions" they were given an FTL connection that causes any measurement on one to instantly affect the other, or some other picture of exactly how their common emission explains later correlations.

I don't understand what you mean by "aren't applicable".

As in irrelevant. See above.

Doesn't help me either--and here you snipped out the questions about classical EM which were meant to specifically probe my confusion about what you mean by terms like "aren't applicable" and "irrelevant", which is why I repeat them again in this post, please actually address these questions this time. Again, I'm confused about whether you think that the nature of the experiment and what sort of correlations are being measured (ignoring the detailed statistics of the results) invalidates Bell's local realist assumptions, or whether you agree that with slightly different results Bell's assumptions might indeed by applicable.

BIs are violated because they're based on a formulation of joint detection (entanglement) preparations which requires the inclusion of a variable which is irrelevant wrt those contexts.

It doesn't "require" the inclusion of the hidden variable. If I say that in general z can be a function of w,x,y and write this as z=f(w,x,y), this doesn't rule out the possibility that y is irrelevant and the correct function is z=w^2 + 2x, since you could always rewrite this as z=w^2 + 2x + 0y. Bell's proof is general, it totally rules out the possibility that the QM measurement statistics could be explained by any local realist theory, including one where the only local variables that influenced the measurement results were non-hidden ones.

It's possible to understand these experiments in local realist terms without requiring that the mathematical model include any local hidden variables.

No, it's definitely not possible to understand the experiments in local realist terms, if you think it is you're fundamentally misunderstanding Bell's proof. If you assume there are no hidden variables and simply redefine λ to refer to the state of all non-hidden local variables in the immediate region of the each measurement (including variables whose state may represent properties of the electron that it was assigned at birth and that it just "carried with it", unchanging, to the region of the measurement, so that the states of these variables could be correlated for the two particles in the region of each measurement) then the proof would still work fine and would show that you can't explain the violation of BI in a local realist theory where the measurement results are determined by local non-hidden variables in the region of the measurement.

Edit: Isn't what qm does is define the relevant relationships and then relate those relationships accordingly?

I don't know what you mean by "relate those relationships" as separate from "define the relevant relationships". QM just gives mathematical functions which tell you the probability of some measurement result(s) given knowledge of some other measurement result(s).

 

[Gordon Watson]

... <SNIP> ...

QM just gives mathematical functions which tell you the probability of some measurement result(s) given knowledge of some other measurement result(s).

Dear JesseM and vanesch, I agree with Jesse's point above.

Earlier in this thread, vanesch cited Sakurai and http://en.wikipedia.org/wiki/Sakurai%27s_Bell_inequality

I'd be pleased to see the QM probabilities for the eight (8) probabilities (P1-P8) in the cited text.

Can you provide them, please?

Thank you, JenniT

 

[JesseM]

Dear JesseM and vanesch, I agree with Jesse's point above.

Earlier in this thread, vanesch cited Sakurai and http://en.wikipedia.org/wiki/Sakurai%27s_Bell_inequality

I'd be pleased to see the QM probabilities for the eight (8) probabilities (P1-P8) in the cited text.

Can you provide them, please?

Thank you, JenniT

Those probabilities are for the various hidden-variable states, not for measurable outcomes (you can't measure more than one angle a, b, or c for a given particle). Since QM doesn't say anything about hidden-variable states which may or may not exist, only about measurable outcomes, QM does not assign probabilities to P1-P8. But what Bell shows is that we can imagine any possible combination of probabilities for P1-P8 in a hidden-variable theory (with the probabilities being in the range 0 ≤ Pn ≤ 1 and adding up to 1, of course), and the theory will always predict that the inequality P(a+, b+) ≤ P(a+, c+) + P(c+, b+) will be respected, but QM predicts this inequality is violated.

 

[Gordon Watson]

Those probabilities are for the various hidden-variable states, not for measurable outcomes (you can't measure more than one angle a, b, or c for a given particle). Since QM doesn't say anything about hidden-variable states which may or may not exist, only about measurable outcomes, QM does not assign probabilities to P1-P8. But what Bell shows is that we can imagine any possible combination of probabilities for P1-P8 in a hidden-variable theory (with the probabilities being in the range 0 ≤ Pn ≤ 1 and adding up to 1, of course), and the theory will always predict that the inequality P(a+, b+) ≤ P(a+, c+) + P(c+, b+) will be respected, but QM predicts this inequality is violated.

Thanks Jesse,

So: Would it be OK if I post, for discussion, a local realistic hidden-variable theory under this heading: What's wrong with this local realistic counter-example to Bell's theorem?

The OP will:

A: Deliver P1-P8.

B: Have them summing to unity.

C: Have them fully compatible with QM-style experiments.

D: Have them recognizing topology associated with the spherical symmetry of the singlet state.

E: Have them breaching Bell's inequality.

F: Have them based on nothing more than high-school maths and logic.

PS: I'm an engineer, I'm here to learn, and I could be mistaken -- which is not the same as being crackpot.

Thanks again,

JenniT

 

[JesseM]

Thanks Jesse,

So: Would it be OK if I post, for discussion, a local realistic hidden-variable theory under this heading: What's wrong with this local realistic counter-example to Bell's theorem?

The OP will:

A: Deliver P1-P8.

B: Have them summing to unity.

C: Have them fully compatible with QM-style experiments.

D: Have them recognizing topology associated with the spherical symmetry of the singlet state.

E: Have them breaching Bell's inequality.

F: Have them based on nothing more than high-school maths and logic.

PS: I'm an engineer, I'm here to learn, and I could be mistaken -- which is not the same as being crackpot.

Thanks again,

JenniT

I think as long as you are willing to listen to arguments as to why your argument might be flawed, it should be OK to post. Keep in mind though, the idea is that on each trial the experimenters choose randomly which of the 3 angles a, b, c to use, in a way that's uncorrelated with which of the 8 hidden states occur on that trial, and that it must be true that whenever they pick the same angle, they get the same result (which is guaranteed as long as you assume the possible hidden states of the particle pair must be one of the 8 listed in the wikipedia article, rather than other possibilities where not all the hidden states are opposite for Alice and Bob, like if Alice's state was +++ while Bob's was +--) And do you understand that if Alice chooses angle a and Bob chooses angle b, it must be true that P(a+, b+) is equal to P3 + P4 since those are the only probabilities corresponding to hidden states which have + in the a-column of Alice's particle and + in the b-column of Bob's particle? Likewise if Alice chooses a and Bob chooses c, then P(a+, c+) = P2 + P4, and if Alice chooses c and Bob chooses b, then P(c+, b+) = P3 + P7. If all the probabilities have non-negative values, it should be obvious that you can't come up with any values for the probabilities that don't satisfy P3 + P4 ≤ (P2 + P4) + (P3 + P7), since this can be rearranged as (P3 + P4) ≤ (P3 + P4) + P2 + P7 and neither P2 nor P7 can be negative.

edit: another option would be to just say what part of this argument isn't making sense to you...presumably you are not claiming you can find non-negative values for P2, P3, P4, P7 which fail to satisfy (P3 + P4) ≤ (P3 + P4) + P2 + P7 so there must be some earlier point in this argument, like maybe the step that says P(a+, b+) = P3 + P4 and P(a+, c+) = P2 + P4 and P(c+, b+) = P3 + P7, that's different from what you had when you were analyzing the problem.

 

[vanesch]

Thanks Jesse,

So: Would it be OK if I post, for discussion, a local realistic hidden-variable theory under this heading: What's wrong with this local realistic counter-example to Bell's theorem?

The OP will:

A: Deliver P1-P8.

B: Have them summing to unity.

C: Have them fully compatible with QM-style experiments.

D: Have them recognizing topology associated with the spherical symmetry of the singlet state.

E: Have them breaching Bell's inequality.

F: Have them based on nothing more than high-school maths and logic.

PS: I'm an engineer, I'm here to learn, and I could be mistaken -- which is not the same as being crackpot.

Thanks again,

JenniT

We're walking on a thin line here, I'm not entirely sure that all my co-mentors will agree.

But for sake of pedagogy, be my guest. It is clear to me (and to Jesse I think) that you have a misunderstanding of what is claimed, what is going on and what all this is about, so as it is always pedagogically interesting to see a wrong argument developed in order to pinpoint the misunderstanding, go ahead.

However, I have to warn you: you are attempting to find numbers which have to satisfy mutually incompatible inequalities.

You are trying the equivalent of something like the following: find 2 numbers x and y such that x > 0, y > 0 and x + y < x - 1 and x + y < y - 1 or something.

So "good luck"

 

[harrylin]

In the last paragraph, after equation 30.[/QUOTE

There he writes that "one can exchange signals" as the proper-time τ elapsed for each of the particles is unequal to zero...
To me that sounds as if it can have to do with the entangled particles exchanging signals at speeds less than light.

(About "none of which contradicts [..] the assumption that nature is locally causal": - see also my PS below!)

That's the view of many, and maybe it was Bell's intention, but that isn't what BI violations, definitively and unarguably, indicate -- which is that the LR formulation on which the formally and experimentally violated BI is based is incompatible with standard qm and the experimental preparation. No more, no less. This is what I meant by the minimalist interpretation and unarguable applicability of Bell's theorem. [..] BI violations don't contradict the assumption that nature is exclusively local.

"LR" stands for local realism I suppose... Thus you hold that the class of LR theories that the Bell Inequality disproves is incompatible with the experimental preparation??

As I mentioned in a previous post, BIs are based on the requirement that entanglement be modeled by (local hidden) variables which are irrelevant (even in an exclusively locally causal world) wrt entanglement (which depends exclusively on global properties and measurement parameters), and that if lhv's are required in the model of entanglement, then the predictions of such a model will necessarily be skewed.

Then according to you, Bell's theorem (BI => "no local deterministic hidden-variable theory can reproduce all the experimental predictions of quantum mechanics") is basically wrong or misunderstood?
For it does not make sense to require a theory to model an effect by means of irrelevant variables - that is a false requirement! :uhh:

PS: I now see that my questions here above about "none of which contradicts the assumption that nature is locally causal" have already largely been answered - apparently both with "yes".

 

[JesseM]

ThomasT, I can't edit the post any more, but when I wrote this:

But "relationship between their motional properties is due to their being emitted in opposite directions from the same atom during the same transition" is still very vague, it doesn't tell me what this "due to" consists of--for example, whether you are imagining that "due to their being emitted in opposite directions" they were assigned the same properties at birth and just carried these unchanging properties with them to the location of the measurements (which of course would mean the properties were local hidden variables, so that's ruled out by Bell), or if "due to their being emitted in opposite directions" they were given an FTL connection that causes any measurement on one to instantly affect the other, or some other picture of exactly how their common emission explains later correlations.

...I should have said "which of course would mean the properties were local variables, so that's ruled out by Bell", as the properties that each particle carries with them may not necessarily be hidden ones, and as I explained Bell's proof rules out all local realist explanations regardless of whether they involve hidden or non-hidden variables.

 

[harrylin]

[..]In any case, based on Avodyne's comment in post #30 it sounds like Joy Christian's model just ignores the real-world observation that the experimenter always sees one of two discrete results (pointer going to +1 or -1), and instead posits a sort of hypothetical universe where the results are elements of Clifford algebra.[..]

That is not the case, see my comment in post #34.

 

[JesseM]

That is not the case, see my comment in post #34.

OK, if the communication was by email, do you still have the emails? I'd be interested to see his exact words...

 

[vanesch]

Thank you vanesch.

Can you also fix each page header?

It would give PF a better look if its page-headers were error-free.

I could, but it is too much work. I'd have to edit each individual post.
:yuck:

 

[Gordon Watson]

I could, but it is too much work. I'd have to edit each individual post.
:yuck:

OK; thanks; no worries. I thought that the page header, that occurs once every 16 pages or so, was automatically derived from the OP's opening header.

 

[Gordon Watson]

We're walking on a thin line here, I'm not entirely sure that all my co-mentors will agree.

But for sake of pedagogy, be my guest. It is clear to me (and to Jesse I think) that you have a misunderstanding of what is claimed, what is going on and what all this is about, so as it is always pedagogically interesting to see a wrong argument developed in order to pinpoint the misunderstanding, go ahead.

However, I have to warn you: you are attempting to find numbers which have to satisfy mutually incompatible inequalities.

You are trying the equivalent of something like the following: find 2 numbers x and y such that x > 0, y > 0 and x + y < x - 1 and x + y < y - 1 or something.

[Emphasis added by JenniT.]

So "good luck"

1. OK; let me sleep on it. I'm time-poor at the moment -- and I would want to be readily available for such a thread.

2. In the interim, could you elaborate, please, on the "equivalent" that you think I am addressing?

JesseM provided helpful additional remarks, reinforcing issues to be addressed.

So I would certainly want to ensure, and explain why, I am not falling into the apparent conundrum that you have in mind.

Thank you,

JenniT

 

[ThomasT]

There he writes that "one can exchange signals" as the proper-time τ elapsed for each of the particles is unequal to zero...
To me that sounds as if it can have to do with the entangled particles exchanging signals at speeds less than light.

Yes, but this has to do with what "amounts to a null-like condition on the spin bi-vector", and that "despite that the addition of two momenta in ordinary spacetime remains timelike and the difference of the momenta is spacelike, consistent with the spacelike separation of the two particles 1, 2 moving along the z-axis in opposite directions, the addition laws of the poly-momentum in C-space is null-like". So, "since the interval in C-space (X₁ − X₂)² is null one can exchange signals from the locations 1, 2 in C-space".

An LR description of the sort that Einstein and Bell (and most everybody else I would guess) would consider an LR description wouldn't have the entangled particles exchanging signals in order to account for the correlation between θ and the rate of coincidental detection. Rather, it would identify some sort of common cause as being the determiner of the entanglement between the particles.

Maybe Christian's C-space formulation can be translated into a bona fide LR account, but I don't know how that might be done. Maybe you can give it a try.

"LR" stands for local realism I suppose...

Yes LR stands for Local Realism or Local Realistic.

Thus you hold that the class of LR theories that the Bell Inequality disproves is incompatible with the experimental preparation??

Yes. At least that much follows from the fact of experimental violations of BIs.

My current way of thinking about it is that all bona fide LR or LHV theories of entanglement are ruled out.

As I mentioned in a previous post, BIs are based on the requirement that entanglement be modeled by (local hidden) variables which are irrelevant (even in an exclusively locally causal world) wrt entanglement (which depends exclusively on global properties and measurement parameters), and that if lhv's are required in the model of entanglement, then the predictions of such a model will necessarily be skewed.

Then according to you, Bell's theorem (BI => "no local deterministic hidden-variable theory can reproduce all the experimental predictions of quantum mechanics") is basically wrong or misunderstood?

I think that it's been thoroughly demonstrated, that "no local deterministic hidden-variable theory can reproduce all the experimental predictions of quantum mechanics" wrt entanglement preparations. But many (most?) people take violations of BIs to be indicating that either nature is nonlocal or that local hidden variables don't exist. I just currently think that there's a more parsimonious explanation for why BIs are violated.

Anyway, this isn't the thread to get into that, and I apologize for temporarily derailing it. It appears that the thread is back on topic talking about Christian's stuff.

Ok, just one more ...

... it does not make sense to require a theory to model an effect by means of irrelevant variables - that is a false requirement!

The lhv's aren't irrelevant physically wrt the individual data streams, but they're irrelevant or superfluous wrt an accurate statistical accounting of the correlation between θ and rate of coincidental detection. My current line of thinking about it might be wrong, but I just have this nagging feeling that the effective reason why BIs are violated, and the correct interpretation of Bell's work, has to do with something much more mundane than that nature is nonlocal or that lhv's don't exist.

 

[ThomasT]

ThomasT, I can't edit the post any more, but when I wrote this:

But "relationship between their motional properties is due to their being emitted in opposite directions from the same atom during the same transition" is still very vague, it doesn't tell me what this "due to" consists of--for example, whether you are imagining that "due to their being emitted in opposite directions" they were assigned the same properties at birth and just carried these unchanging properties with them to the location of the measurements (which of course would mean the properties were local hidden variables, so that's ruled out by Bell), or if "due to their being emitted in opposite directions" they were given an FTL connection that causes any measurement on one to instantly affect the other, or some other picture of exactly how their common emission explains later correlations.

...I should have said "which of course would mean the properties were local variables, so that's ruled out by Bell", as the properties that each particle carries with them may not necessarily be hidden ones, and as I explained Bell's proof rules out all local realist explanations regardless of whether they involve hidden or non-hidden variables.

Ok, thanks for your comments, JesseM. Not wanting to derail this thread any more, I'm going to go over our discussion in this thread and will probably start a new thread on it, but this will take longer than I originally thought it would.

 

[Gordon Watson]

I think as long as you are willing to listen to arguments as to why your argument might be flawed, it should be OK to post. Keep in mind though, the idea is that on each trial the experimenters choose randomly which of the 3 angles a, b, c to use, in a way that's uncorrelated with which of the 8 hidden states occur on that trial, and that it must be true that whenever they pick the same angle, they get the same result (which is guaranteed as long as you assume the possible hidden states of the particle pair must be one of the 8 listed in the wikipedia article, rather than other possibilities where not all the hidden states are opposite for Alice and Bob, like if Alice's state was +++ while Bob's was +--) And do you understand that if Alice chooses angle a and Bob chooses angle b, it must be true that P(a+, b+) is equal to P3 + P4 since those are the only probabilities corresponding to hidden states which have + in the a-column of Alice's particle and + in the b-column of Bob's particle? Likewise if Alice chooses a and Bob chooses c, then P(a+, c+) = P2 + P4, and if Alice chooses c and Bob chooses b, then P(c+, b+) = P3 + P7. If all the probabilities have non-negative values, it should be obvious that you can't come up with any values for the probabilities that don't satisfy P3 + P4 ≤ (P2 + P4) + (P3 + P7), since this can be rearranged as

(A) (P3 + P4) ≤ (P3 + P4) + P2 + P7 and neither P2 nor P7 can be negative. [Emphasis and identifier added by JenniT.]

edit: another option would be to just say what part of this argument isn't making sense to you...presumably you are not claiming you can find non-negative values for P2, P3, P4, P7 which fail to satisfy (P3 + P4) ≤ (P3 + P4) + P2 + P7 so there must be some earlier point in this argument, like maybe the step that says P(a+, b+) = P3 + P4 and P(a+, c+) = P2 + P4 and P(c+, b+) = P3 + P7, that's different from what you had when you were analyzing the problem.

Thanks Jesse, your attention to explanatory detail is to be applauded. It is much appreciated. (A) is the very point that I planned to address -- a very clear impossibility.

My idea is to show that (A), an impossibility, is not mandated by all local realistic hidden-variable theories.

I personally do not require LHV's to do the impossible, going beyond QM. I seek LHV's which are explanatory -- requiring neither recourse nor inference to FTL or NL (non-locality).

PS: In my view, the remarkable spherical symmetry of the singlet state seems not much addressed in this connection. But I'll sleep on it, and triple-check the idea, until I have more time for involvement.

Thanks again, JT.

 

[JesseM]

Thanks Jesse, your attention to explanatory detail is to be applauded. It is much appreciated. (A) is the very point that I planned to address -- a very clear impossibility.

My idea is to show that (A), an impossibility, is not mandated by all local realistic hidden-variable theories.

OK, but do you agree that in a LHV theory, in order to explain how the two experimenters always get the opposite results when they pick the same angle (and they are picking angles at random), it must be true that each time the source sends out a particle pair, it must create them with LHV that predetermine what their results will be for any possible angle, in such a way that they each are guaranteed to have opposite predetermined results for every angle?

If that's the case, then whatever the hidden variables may be, if we are only interested in the predetermined results for three possible angles a, b, and c, every combination of hidden variables should fall into one of the following 8 categories:

1. Particle 1: a+ b+ c+ / Particle 2: a- b- c-
2. Particle 1: a+ b+ c- / Particle 2: a- b- c+
3. Particle 1: a+ b- c+ / Particle 2: a- b+ c-
4. Particle 1: a+ b- c- / Particle 2: a- b+ c+
5. Particle 1: a- b+ c+ / Particle 2: a+ b- c-
6. Particle 1: a- b+ c- / Particle 2: a+ b- c+
7. Particle 1: a- b- c+ / Particle 2: a+ b+ c-
8. Particle 1: a- b- c- / Particle 2: a+ b+ c+

...where, for example, if the hidden variables fall into category #4 that means they predetermine that particle 1 will give + if angle a is chosen, - if angle b is chosen, and - if angle c is chosen, while particle 2 is predetermined to give the opposite result for each angle. Of course the hidden variables can be much more complicated than this, so just knowing that they fall into category #4 doesn't tell you the full value of all hidden variables (for example it doesn't tell you what the predetermined result would be for some different angle d), but even if there are an infinite number of distinct possible hidden-variable states, each one must fall into one of the eight categories above depending on its predetermined results for angles a, b, and c.

If you don't see why this would necessarily be true in a LHV theory, please explain the specific point you would dispute--for example, do you disagree that the hidden variables must give a predetermined result for each possible angle in order to explain how the experimenters always get opposite results whenever they pick the same angle?

 

[Gordon Watson]

OK, but do you agree that in a LHV theory, in order to explain how the two experimenters always get the opposite results when they pick the same angle (and they are picking angles at random), it must be true that each time the source sends out a particle pair, it must create them with LHV that predetermine what their results will be for any possible angle, in such a way that they each are guaranteed to have opposite predetermined results for every angle?

If that's the case, then whatever the hidden variables may be, if we are only interested in the predetermined results for three possible angles a, b, and c, every combination of hidden variables should fall into one of the following 8 categories:

1. Particle 1: a+ b+ c+ / Particle 2: a- b- c-
2. Particle 1: a+ b+ c- / Particle 2: a- b- c+
3. Particle 1: a+ b- c+ / Particle 2: a- b+ c-
4. Particle 1: a+ b- c- / Particle 2: a- b+ c+
5. Particle 1: a- b+ c+ / Particle 2: a+ b- c-
6. Particle 1: a- b+ c- / Particle 2: a+ b- c+
7. Particle 1: a- b- c+ / Particle 2: a+ b+ c-
8. Particle 1: a- b- c- / Particle 2: a+ b+ c+

...where, for example, if the hidden variables fall into category #4 that means they predetermine that particle 1 will give + if angle a is chosen, - if angle b is chosen, and - if angle c is chosen, while particle 2 is predetermined to give the opposite result for each angle. Of course the hidden variables can be much more complicated than this, so just knowing that they fall into category #4 doesn't tell you the full value of all hidden variables (for example it doesn't tell you what the predetermined result would be for some different angle d), but even if there are an infinite number of distinct possible hidden-variable states, each one must fall into one of the eight categories above depending on its predetermined results for angles a, b, and c.

If you don't see why this would necessarily be true in a LHV theory, please explain the specific point you would dispute--for example, do you disagree that the hidden variables must give a predetermined result for each possible angle in order to explain how the experimenters always get opposite results whenever they pick the same angle?

I'm about to lose power for 6+ hours; will get back to you.

 

[Gordon Watson]

I'm about to lose power for 6+ hours; will get back to you.

Jesse, sorry for delay. My general answer to your concerns is YES; for I'm familiar with many of the Bell fundamentals. But there's a subtlety, associated with my understanding Bohr's attitude to EPR -- which I'm at present attributing to "topology" -- which questions the impossibility equation.

So the earlier points raised remain valid. Most of my case is based on simple maths -- so errors can be easily spotted and agreed, such errors perhaps having important lessons about BT, as vanesch points out.

The OP will:

A: Deliver P1-P8.

B: Have them summing to unity.

C: Have them fully compatible with QM-style experiments; delivering accepted QM results.

D: Have them recognizing a topology [for want of a better word] associated with the spherical symmetry of the singlet state and measuring-device settings.

E: Have them challenging the basis of Bell's inequality.

F: Have them based on nothing more than high-school maths and logic; so no fancy maneuvers are involved -- and the discussion should be understood by most everyone.

PS: It would be good to have vanesch's concern [above; re, x, y, etc.] spelt out -- to minimize the chance of blunder.

JenniT