Why are Bell's inequalities violated?

[DrChinese]

I never realized that, and will have to check it out - thanks!

Yes, and note that this is the very first equation with a, b and c in it. Without all 3, of course, you don't have realism expressed as a testable assumption.

 

[bohm2]

I don't know. I don't understand the Wood and Spekkens article. Maybe you can explain it?

If one argues that something is local, realism is implied as above posts, I think. Analogously, if non-realism, then the issue of locality vs non-locality is kind of pointless since there's no ontological issues. I mean what ontological difference would there be between local vs non-local non-realism? Anyway, that's how I understood it. I think Gisin argues similarily here:

What is surprising is that so many good physicists interpret the violation of Bell’s inequality as an argument against realism. Apparently their hope is to thus save locality, though I have no idea what locality of a non-real world could mean? It might be interesting to remember that no physicist before the advent of relativity interpreted the instantaneous action at a distance of Newton’s gravity as a sign of non-realism (although Newton’s nonlocality is even more radical than quantum nonlocality, as it allowed instantaneous signaling).

Is realism compatible with true randomness?
http://arxiv.org/pdf/1012.2536v1.pdf

 

[harrylin]

Yes, and note that this is the very first equation with a, b and c in it. Without all 3, of course, you don't have realism expressed as a testable assumption.

I certainly recall that point, which was the subject of many discussions... I just never interpreted it in the sense as expressed in that paper!

Their clarification ("assign a property to a system (e.g. the position of an electron)") plus your explanation allows me to make sense of Neumaier's claim (which he did not prove and with which you probably disagree). He holds that:
"all proofs of Bell type results [..] become invalid when particles have a temporal and spatial extension, with an internal structure that is modified when interacting in a beam splitter."
- http://arnold-neumaier.at/ms/lightslides.pdf

So, he suggests that that is why Bell's inequalities are violated.

 

[DrChinese]

I certainly recall that point, which was the subject of many discussions... I just never interpreted it in the sense as expressed in that paper!

Their clarification ("assign a property to a system (e.g. the position of an electron)") plus your explanation allows me to make sense of Neumaier's claim (which he did not prove and with which you probably disagree). He holds that:
"all proofs of Bell type results [..] become invalid when particles have a temporal and spatial extension, with an internal structure that is modified when interacting in a beam splitter."
- http://arnold-neumaier.at/ms/lightslides.pdf

So, he suggests that that is why Bell's inequalities are violated.

He makes several statements like this that are difficult for me to place in a suitable context. Photons have both temporal and spatial extension in my view. Not sure if they do to a local realist though. And I do not follow his reasoning on how that connects to Bell. So I guess I would say that I disagree. If you are enforcing strict Einsteinian locality as is done in Weihs et al (1998), the spatial extent of a photon is already accounted for.

 

[harrylin]

[..] I do not follow his reasoning on how that connects to Bell. [..]

Neither did I follow his reasoning until you explained it to me! Now I guess that I can follow it, for the first time.

Assuming that light is a wave and not a collection of photon particles, then the photon positions are undefined or non-existent until they are measured - and the same for some other properties. If so, then Bell's theorem may not apply because the existence of such unmeasured properties is required for that theorem - is that correct? It should be, following our posts #49 and #50 here above.

 

[DrChinese]

Assuming that light is a wave and not a collection of photon particles, then the photon positions are undefined or non-existent until they are measured - and the same for some other properties. If so, then Bell's theorem may not apply because the existence of such unmeasured properties is required for that theorem - is that correct?

I keep saying that you have it backwards. QM does not assert photons have well-defined values for non-commuting operators - realists do!

EPR asserts that there is an element of reality IF Alice can predict Bob's outcome with certainty. Because this is experimentally demonstrated, you must accept EPR's key challenge. Which is that if QM is complete (read accurate in this instance), the reality of Bob's measurement is a function of Alice's choice of what to observe. Therefore if QM predicts correctly, we live in an observer dependent universe. This is directly from EPR. It does require the assumption of SIMULTANEOUS elements of reality (anything else is an unreasonable definition of reality, they say) and the assumption that there is no spooky action at a distance.

Bell simply takes those one step forward in his proof. So sure, Bell doesn't "apply" in the sense that one of the local realists' (and EPR's) 2 assumptions is invalid (much as you say: "the existence of such unmeasured properties"). But that is simply agreeing with Bell, disagreeing with EPR and denying local realism in one breath.

 

[akhmeteli]

I certainly recall that point, which was the subject of many discussions... I just never interpreted it in the sense as expressed in that paper!

Their clarification ("assign a property to a system (e.g. the position of an electron)") plus your explanation allows me to make sense of Neumaier's claim (which he did not prove and with which you probably disagree). He holds that:
"all proofs of Bell type results [..] become invalid when particles have a temporal and spatial extension, with an internal structure that is modified when interacting in a beam splitter."
- http://arnold-neumaier.at/ms/lightslides.pdf

So, he suggests that that is why Bell's inequalities are violated.

I don't know, maybe A. Neumaier has revised his text since you looked at it, but I find a slightly different phrase there: "All proofs of Bell type results (including the present argument) become invalid when "particles" have a temporal and spatial extension over the whole experimental domain, with an internal structure that is modified when interacting in a beam splitter."

These extra words ("over the whole experimental domain") make me wonder if what he had in mind might be pretty much the same as the locality loophole.

 

[DrChinese]

I don't know, maybe A. Neumaier has revised his text since you looked at it, but I find a slightly different phrase there: "All proofs of Bell type results (including the present argument) become invalid when "particles" have a temporal and spatial extension over the whole experimental domain, with an internal structure that is modified when interacting in a beam splitter."

These extra words ("over the whole experimental domain") make me wonder if what he had in mind might be pretty much the same as the locality loophole.

I saw that too, couldn't figure out what he meant. Does he mean: non-local? Obviously the locality loophole itself was closed a while back.

 

[akhmeteli]

I saw that too, couldn't figure out what he meant. Does he mean: non-local? Obviously the locality loophole itself was closed a while back.

Only separately:-)

 

[DrChinese]

Only separately:-)

I would expect no less!

 

[JK423]

In a previous post i wrote down the CHSH inequality that any hidden variable model satisfies

S_j = A_j\left( {{a_1}} \right)B_j\left( {{b_1}} \right) + A_j\left( {{a_1}} \right)B_j\left( {{b_2}} \right) + A_j\left( {{a_2}} \right)B_j\left( {{b_1}} \right) - A_j\left( {{a_2}} \right)B_j\left( {{b_2}} \right),
where A_j\left( {{a_i}} \right) = \pm 1 and B_j\left( {{b_i}} \right) = \pm 1, and j denoting a particular photon pair,
is always {S_j} = \pm 2, for any measurement result A and B.
When we take the mean value over all photon pairs, \,\left\langle S \right\rangle = \frac{1}{N}\sum\limits_{i = 1}^N {{S_j}} we find it to be bounded, i.e.
- 2 \le \,\left\langle S \right\rangle \le 2.

I have understood quite well why every photon pair should satisfy this inequality (if local realism holds). Consequently, the mean value \left\langle S \right\rangle, over all photon pairs, should satisfy it as well. However, this quantity is unmeasurable in a real experiment, due to the fact that it involves unmeasurable quantities in each run, e.g. the covariances in different angles.
Now my problem is to express the CHSH inequality in an equivalent way, so that it involves only measurable quantities, like the number of pairs detected anti-correlated when measured in the angle \theta_1, and consequently will be applicable in a real experiment. But i want to do this completely equivalently! For example, the fact that in the quoted post i have written down the inequality satisfied by the mean value of S, i.e.
- 2 \le \,\left\langle S \right\rangle \le 2,
it doesn't mean that this inequality would also be satisfied by the mean value of the measurements! The mean value of S (including all unmeasurable quantities), that satisfies the above inequality, and the mean value of S which includes only experimental mean values (that don't include the unmeasurable quantities) are not equivalent! They are not equivalent because, in the first case the mean value of each quantity \left\langle {A\left( {{a_1}} \right)B\left( {{b_2}} \right)} \right\rangle involves all photon pairs in the experiment, while in a real experiment the corresponding mean value would include only 1/4 of the total photon pairs (if we suppose that the four angles are chosen with the same probability), since with each photon pair we can measure only one of the 4 observables. The two quantities are totally different.

So, what i am looking for is an equivalent but measurable expression. Does anyone have any idea of how to do this?
Note: The above CHSH inequality holds for every initial preparation of the photons, so in the proposed derivation we should not include any condition on the initial state in order to have a more general result.

 

[DrChinese]

In a previous post i wrote down the CHSH inequality that any hidden variable model satisfiesI have understood quite well why every photon pair should satisfy this inequality (if local realism holds). Consequently, the mean value \left\langle S \right\rangle, over all photon pairs, should satisfy it as well. However, this quantity is unmeasurable in a real experiment, due to the fact that it involves unmeasurable quantities in each run, e.g. the covariances in different angles.
Now my problem is to express the CHSH inequality in an equivalent way, so that it involves only measurable quantities, like the number of pairs detected anti-correlated when measured in the angle \theta_1, and consequently will be applicable in a real experiment. But i want to do this completely equivalently! For example, the fact that in the quoted post i have written down the inequality satisfied by the mean value of S, i.e.
- 2 \le \,\left\langle S \right\rangle \le 2,
it doesn't mean that this inequality would also be satisfied by the mean value of the measurements! The mean value of S (including all unmeasurable quantities), that satisfies the above inequality, and the mean value of S which includes only experimental mean values (that don't include the unmeasurable quantities) are not equivalent! They are not equivalent because, in the first case the mean value of each quantity \left\langle {A\left( {{a_1}} \right)B\left( {{b_2}} \right)} \right\rangle involves all photon pairs in the experiment, while in a real experiment the corresponding mean value would include only 1/4 of the total photon pairs (if we suppose that the four angles are chosen with the same probability), since with each photon pair we can measure only one of the 4 observables. The two quantities are totally different.

So, what i am looking for is an equivalent but measurable expression. Does anyone have any idea of how to do this?
Note: The above CHSH inequality holds for every initial preparation of the photons, so in the proposed derivation we should not include any condition on the initial state in order to have a more general result.

This is a point that is so confusing, I would say most folks reason do not understand at all. S is a derived formula, and to a certain extent, an arbitrary expression. There is absolutely NO need to be able to measure this in a single experiment.

What you are really attempting to do is to verify the QM prediction of cos^2(theta) for matches. That is experimentally verifiable. If QM predicts accurately (with cos^2), then Bell tells us that LR is violated. There is then no need to have the CHSH inequality. And if you look at a lot of the Bell tests, they graph the QM predicted value against the experimental results to show this. (The LR function would need to be a straight line, in contrast.)

However, it is possible to look at the graphed results and say, "hmmm, maybe a straight line as close to the observed results as the QM prediction". This is where CHSH comes in. It is a concrete way to determine that LR is rejected while QM is confirmed.

So specifically: the coincidence prediction for 60 degrees for QM is .25 and for LR is .33 or higher. All you have to do is measure that, it is directly measurable exactly as you hope! Then you see that the measured value is quite close to .25 and far away from .33 (by perhaps 30+ standard deviations). And you rule out LR because its prediction is flat out wrong.

 

[JK423]

Thank you both, DrChinese and Gordon Watson, for your feedback.
Let me restate where my doubts are specifically located, so that my point will become more clear and you will be able to give me more "targeted" help. First, let me repeat the necessary formulas:

S_j = A_j\left( {{a_1}} \right)B_j\left( {{b_1}} \right) + A_j\left( {{a_1}} \right)B_j\left( {{b_2}} \right) + A_j\left( {{a_2}} \right)B_j\left( {{b_1}} \right) - A_j\left( {{a_2}} \right)B_j\left( {{b_2}} \right),
where A_j\left( {{a_i}} \right) = \pm 1 and B_j\left( {{b_i}} \right) = \pm 1, and j denoting a particular photon pair,
is always {S_j} = \pm 2, for any measurement result A and B.
When we take the mean value over all photon pairs, \,\left\langle S \right\rangle = \frac{1}{N}\sum\limits_{i = 1}^N {{S_j}} we find it to be bounded, i.e.
- 2 \le \,\left\langle S \right\rangle \le 2.
This quantity is bounded whatever the values of A and B for the photon pairs.

Now, the reason why the CHSH inequality holds is because S_j is always S_j=±2 for every photon pair separately. And this is due to the locality assumption, i.e. that the outcome in Alice's side does not depend on what Bob measures, etc. Mathematically this assumption is expressed by the fact that {A_j}\left( {{a_1}} \right) is the same in both {A_j}\left( {{a_1}} \right) \cdot {B_j}\left( {{\beta _1}} \right) and {A_j}\left( {{a_1}} \right) \cdot {B_j}\left( {{\beta _2}} \right), i.e. whether Bob measures \beta_1 or \beta_2 is irrelevant, the outcome {A_j}\left( {{a_1}} \right) will be the same. The same reasoning applies to {A_j}\left( {{a_2}} \right).
The important thing here is that this is always true because {A_j}\left( {{a_1}} \right) corresponds to the same photon in these two expressions {A_j}\left( {{a_1}} \right) \cdot {B_j}\left( {{\beta _1}} \right) and {A_j}\left( {{a_1}} \right) \cdot {B_j}\left( {{\beta _2}} \right), so it cannot be different if locality is assumed.

Now, look what happens if you consider the measureable edition of \left\langle S \right\rangle, where each of the quantities \left\langle {A\left( {{a_i}} \right)B\left( {{b_j}} \right)} \right\rangle are mean values over the measurements. For simplicity let me consider only one of the measured values (instead of the whole mean value) in order to make my point clear. So assume just one run:
\left\langle {A\left( {{a_1}} \right)B\left( {{b_1}} \right)} \right\rangle = {A_1}\left( {{a_1}} \right){B_1}\left( {{b_1}} \right) , corresponding to the measured value of the photon pair "1",
\left\langle {A\left( {{a_1}} \right)B\left( {{b_2}} \right)} \right\rangle = {A_2}\left( {{a_1}} \right){B_2}\left( {{b_2}} \right), corresponding to the measured value of the photon pair "2".
Now take the sum of these in order to form the first half part of the quantity S:
\left\langle {A\left( {{a_1}} \right)B\left( {{b_1}} \right)} \right\rangle + \left\langle {A\left( {{a_1}} \right)B\left( {{b_2}} \right)} \right\rangle = {A_1}\left( {{a_1}} \right){B_1}\left( {{b_1}} \right) + {A_2}\left( {{a_1}} \right){B_2}\left( {{b_2}} \right). (1)

I told you previously that CHSH holds because {A_j}\left( {{a_1}} \right) has the same value in these two quantities, since it corresponds to the same photon. But now that we have considered the mean values over measurements, {A_1}\left( {{a_1}} \right) and {A_2}\left( {{a_1}} \right) are, generally, different since they correspond to different photons "1" and "2", and that way they could be mimicking non-locality, since it looks as if {A}\left( {{a_1}} \right) depends on what Bob measures.
You can generalize (1) for N photon pairs and take a more appropriate mean value. The moral in this story is that the photons are different in each quantity, so there is no obvious reason why CHSH would not be violated.

I hope that i made my point clear..
I'm looking forward to your feedback!

Giannis

 

[nanosiborg]

If one argues that something is local, realism is implied as above posts, I think. Analogously, if non-realism, then the issue of locality vs non-locality is kind of pointless since there's no ontological issues. I mean what ontological difference would there be between local vs non-local non-realism? Anyway, that's how I understood it. I think Gisin argues similarily here:

Is realism compatible with true randomness?
http://arxiv.org/pdf/1012.2536v1.pdf

Thanks for helping me wade through this bohm2.

If one argues that something is local, realism is implied as above posts, I think.

What about, eg., QFT?

We're (as Bell was) concerned with lhv formalism as it relates to qm and quantum entanglement experiments ... and not with how lhv formalism relates to the ontology of the world.
Can we agree that realism, for our purposes, means the formal expression of hidden variables?

We see by dBB that hidden variables and therefore hv formalisms aren't ruled out. But lhv (at least Bell lhv) formalisms are. So, it seems to come down to something to do with the formal expression of locality in terms of hidden variables ... and I'm reminded again of Jarrett's (and similar) treatment(s) of this which say that BI violation might be ruling out Bell type lhv models without also ruling out the possibility that nature is exclusively local.

 

[harrylin]

[...] if QM is complete (read accurate in this instance), the reality of Bob's measurement is a function of Alice's choice of what to observe. [..]
It does require the assumption of SIMULTANEOUS elements of reality (anything else is an unreasonable definition of reality, they say) and the assumption that there is no spooky action at a distance.

As I just discovered and clarified, it's exactly the meaning of those "simultaneous elements of reality" that appears to be an unreasonable requirement if that means "counterfactual" in the sense as cited in post #49. So, I guess that we now discovered in two parallel threads (and for different reasons) that it may be useful to focus more on Bell's "realist" criteria.

[..] But that is simply agreeing with Bell, disagreeing with EPR and denying local realism in one breath.[/b]

Once more: thanks for pointing out that Bell-realism is only a particular form of realism, different from that of Neumaier and myself. I will have to read again EPR to verify if their formulation of "realism" was as limited as Bell's.

I don't know, maybe A. Neumaier has revised his text since you looked at it, but I find a slightly different phrase there: "All proofs of Bell type results (including the present argument) become invalid when "particles" have a temporal and spatial extension over the whole experimental domain, with an internal structure that is modified when interacting in a beam splitter."

These extra words ("over the whole experimental domain") make me wonder if what he had in mind might be pretty much the same as the locality loophole.

I did a copy-paste so that's puzzling... I forgot what is meant with "locality loophole", but I'm pretty sure that he refers to his interpretation of QFT [EDIT:"Photons are intrinsically nonlocal objects"] which I think differs from the kind of spatial extension that DrChinese has in mind.

 

[morrobay]

In this very basic table of the 2³ possible cases of a spin 1/2 system with 3
axis settings, x,y,z ;

A _________ B
x y z ______ x y z
+++ _______ ---
++- _______ --+
+-+ _______ -+-
+-- _______ -++
-++ _______ +--
-+- _______ +-+
--+ _______ ++-
--- _______ +++

P(x⁺y⁺) < P(x⁺z⁺)+P(z⁺y⁺)
In the above inequality what are the exact counts that violate it ? And if the magnetic
field in the detector not only alters the spin on y-axis when detecting spin on x but also
alters the spin on the axis being measured, x , then how is this violation valid ?

 

[DrChinese]

In this very basic table of the 2³ possible cases of a spin 1/2 system with 3
axis settings, x,y,z ;

A _________ B
x y z ______ x y z
+++ _______ ---
++- _______ --+
+-+ _______ -+-
+-- _______ -++
-++ _______ +--
-+- _______ +-+
--+ _______ ++-
--- _______ +++

P(x⁺y⁺) < P(x⁺z⁺)+P(z⁺y⁺)
In the above inequality what are the exact counts that violate it ? And if the magnetic
field in the detector not only alters the spin on y-axis when detecting spin on x but also
alters the spin on the axis being measured, x , then how is this violation valid ?

The cases you show assume a realistic/hidden variable perspective. OK, that is fine for a starting point for a Bell Inequality. Are you thinking that x, y and z are 3 perpendicular spatial axes (not clear to me from the example) ? Because if so you can't get a Bell Inequality from those. Instead, you need something like:

x=0
y=135
z=90

Assuming this is fine with you, and these angles are on the same plane:

xz= theta of 90 degrees
yz= theta of 45 degrees
xy= theta of 135 degrees

The quantum mechanical prediction for Matches (M) when anti-correlated is: 1 - cos^2(theta/2) or simply sin^2(theta/2). Your realistic requirement is M(xy) < M(xz) + M(yz) which is the same as saying: 0 < M(xz) + M(yz) - M(xy). Substituting the right hand side, you get something like:

M(xz)* + M(yz) - M(xy) =

sin^2(90/2) + sin^2(45/2) - sin^2(135/2) =

.5 + .1465 - .8535 =

-.2070**

Oops, this was supposed to be greater than zero per your realism requirement! So the realism requirement is flat out inconsistent with the predictions of QM. So here are the specific values that lead to a violation.

*There was a minor issue in your formula that became immaterial because of the angle settings I selected.
** And this is reduced by half to -.1035 if we only look at the ++ match cases, not that it really matters. The QM prediction is still less than zero and realism requires it be non-negative.

 

[morrobay]

The quantum mechanical prediction for Matches (M) when anti-correlated is: 1 - cos^2(theta/2) or simply sin^2(theta/2). Your realistic requirement is M(xy) < M(xz) + M(yz) which is the same as saying: 0 < M(xz) + M(yz) - M(xy). Substituting the right hand side, you get something like:

M(xz)* + M(yz) - M(xy) =

sin^2(90/2) + sin^2(45/2) - sin^2(135/2) =

.5 + .1465 - .8535 =

-.2070**

Oops, this was supposed to be greater than zero per your realism requirement! So the realism requirement is flat out inconsistent with the predictions of QM. So here are the specific values that lead to a violation.

The question on the above ( as an outsider to QM ) I have is that you are applying QM predictions to negate the realism requirement. That would be like using realism predictions
to negate the QM requirement. That is why I asked what the actual data is that violates
the inequality. Having said that, I could give up realism in all these discussions for
saving locality. Especially when Bell/EPR experiments are done with photons.

 

[DrChinese]

The question on the above ( as an outsider to QM ) I have is that you are applying QM predictions to negate the realism requirement. That would be like using realism predictions to negate the QM requirement.

Having said that, I could give up realism in all these discussions for
saving locality.

That is what we are doing, and it makes perfect sense. QM is incompatible with local realism, predictions as defined above, and that was Bell's discovery. It is not often that such clear disagreements occur with such fundamental ideas.

Giving up realism for QM + locality is a good trade, in my opinion.

 

[nanosiborg]

As regards Bell's theorem, locality or localism refers to the particular form in which Bell has expressed it in his lhv model of quantum entanglement. Since that form is necessarily realistic (ie., expressed in terms of hidden variables), then BI violation can't entail the option of keeping either locality or realism in a model of quantum entanglement. As far as Bell's lhv formulation is concerned locality and realism are inseparable.
Keeping in mind that it's only locality and realism as formalized by Bell in his lhv model of quantum entanglement that are relevant.

 

[morrobay]

As regards Bell's theorem, locality or localism refers to the particular form in which Bell has expressed it in his lhv model of quantum entanglement. Since that form is necessarily realistic (ie., expressed in terms of hidden variables), then BI violation can't entail the option of keeping either locality or realism in a model of quantum entanglement. As far as Bell's lhv formulation is concerned locality and realism are inseparable.
Keeping in mind that it's only locality and realism as formalized by Bell in his lhv model of quantum entanglement that are relevant.

According to this PDF paper : Resolution of the nonlocality puzzel in the EPR paradox.

The definition of Bell/EPR realism is the problem:
Realism defined by observers in the classical world requires outcomes before measurement.
But there are physical systems that are beyond the scope of the EPR definition of reality.
Their realism ( for spin 1/2 particles ) is a system with phases associated with spin rotations
( a geometric phase ). With no objective reality to the outcomes before measurement.
The actual outcome is related to the phase varible.

 

[nanosiborg]

According to this PDF paper : Resolution of the nonlocality puzzel in the EPR paradox.
The definition of Bell/EPR realism is the problem:

We're only concerned with realism as formalized in Bell-type hidden variable models of quantum entanglement. Bell writes A(a,λ)=±1, B(b,λ)=±1 , denoting that individual results are determined by unit vectors, a and b, and an underlying parameter, λ. That's Bell realism.

 

[Nugatory]

We're only concerned with realism as formalized in Bell-type hidden variable models of quantum entanglement. Bell writes A(a,λ)=±1, B(b,λ)=±1 , denoting that individual results are determined by unit vectors, a and b, and an underlying parameter, λ. That's Bell realism.

That is very true.

At first glance, this might appear to be a limitation of Bell's model, but in fact these models do cover just about anything that an intuitive layman (and probably Einstein, Podolosky, Rosen and kindred spirits) would accept as "non-weird".

Thus, the real importance of Bell's inequality and its observed violations is that we're stuck with quantum weirdness. Post-Bell, we don't talk about whether the world is weird, we talk about how to deal with that weirdness.

 

[nanosiborg]

That is very true.

At first glance, this might appear to be a limitation of Bell's model, but in fact these models do cover just about anything that an intuitive layman (and probably Einstein, Podolosky, Rosen and kindred spirits) would accept as "non-weird".

Thus, the real importance of Bell's inequality and its observed violations is that we're stuck with quantum weirdness. Post-Bell, we don't talk about whether the world is weird, we talk about how to deal with that weirdness.

I don't think I'd use weird to describe Bell tests, though they are incompletely understood. I think the real importance of Bell's theorem is the experimental and interpretational innovation that's happened because of it.

 

[bohm2]

I don't think I'd use weird to describe Bell tests, though they are incompletely understood. I think the real importance of Bell's theorem is the experimental and interpretational innovation that's happened because of it.

It is interesting to read Bell's thoughts on this issue:

For me then this is the real problem with quantum theory: the apparently essential conflict between any sharp formulation and relativity. That is, to say we have an apparent incompatibility, at the deepest level, between the two fundamental pillars of contemporary theory...

Speakable and Unspeakable in quantum mechanics
http://www.futuretg.com/FTHumanEvolutionCourse/FTFreeLearningKits/03-PH-Physics,%20Chemistry%20and%20Free%20Energy/040-PH04-UN02-03-Quantum%20Mechanics/J.%20S.%20Bell%20-%20Speakable%20And%20Unspeakable%20In%20Quantum%20Mechanics.pdf

 

[morrobay]

Its been close to 50 years and why Bells inequalities are violated has not been explained.
So first , is it possible to have ' spin rotations ' and ' geometric phase' as taken from the PDF paper I referenced ? If not then Admin can delete this post.
But if so then A(aλ)=±1 where λ is a phase variable related to entangled two photon spins
from a Calcium atoms' 6_s level can be considered. And this table:
A________B
xyz______xyz
+++______---
++-______--+
+-+______-+-
+--______-++
-++______+--
-+-______+-+
--+______++-
---______+++

And this P[x-z+]≤ P[y+x-] + [x+z+] being violated could be explained by the above table not having fixed values but with ' rotating spins ' and it would be like an 8 level slot
machine set in motion. The challenge would be to explain why the spins at two equal angular settings are always opposite.
Im only taking the initiative here because the question is not being answered when limited
to EPR/Bell realism

 

[nanosiborg]

Its been close to 50 years and why Bells inequalities are violated has not been explained.

...

Im only taking the initiative here because the question is not being answered when limited
to EPR/Bell realism

As I mentioned above, we're only concerned with realism as formalized in Bell-type hidden variable models of quantum entanglement.

BIs are based on a linear correlation between θ and rate of coincidental detection, which is due to the form that Bell's locality condition requires his lhv-supplemented qm expectation value formulation to take, ie., that the probability distribution be factorizable into the functions that determine individual detection.

I mentioned in an earlier post that A(a,λ)=±1, B(b,λ)=±1 are Bell realism. A(a,λ) and B(b,λ) are also explicitly local. As opposed to the explicitly nonlocal A(a,b,λ) and B(a,b,λ), A(a,λ) and B(b,λ) specify that A doesn't depend on b, and B doesn't depend on a.

The intensity of light (or photon flux) transmitted by the analyzing (or second) polarizer in sequenced two polarizer (local) setups is always a nonlnear function of the angular difference of the polarizer settings. (In the two polarizer Bell test setups both polarizers are the analyzer, and rate of coincidental detection is intensity.)

BIs are (must be) violated because a necessarily linear correlation expectation is being applied to a setup that must necessarily (even if nothing nonlocal is happening, as in local sequenced setups) produce nonlinear correlations.

 

[nanosiborg]

It is interesting to read Bell's thoughts on this issue:

Speakable and Unspeakable in quantum mechanics
http://www.futuretg.com/FTHumanEvolutionCourse/FTFreeLearningKits/03-PH-Physics,%20Chemistry%20and%20Free%20Energy/040-PH04-UN02-03-Quantum%20Mechanics/J.%20S.%20Bell%20-%20Speakable%20And%20Unspeakable%20In%20Quantum%20Mechanics.pdf

Thank you bohm2.

 

[ZealScience]

I don't quite understand your question. Because Bell's equation follows from Hidden variable and statistics which is orthogonal to QM prediction.

And it is later EXPERIMENTALLY proven to be violated. Maybe the only thing we could ask is the validity of the experiment rather than the reason...

Personal opinion

 

[DrChinese]

Its been close to 50 years and why Bells inequalities are violated has not been explained.
So first , is it possible to have ' spin rotations ' and ' geometric phase' as taken from the PDF paper I referenced ? If not then Admin can delete this post.
But if so then A(aλ)=±1 where λ is a phase variable related to entangled two photon spins
from a Calcium atoms' 6_s level can be considered. And this table:
A________B
xyz______xyz
+++______---
++-______--+
+-+______-+-
+--______-++
-++______+--
-+-______+-+
--+______++-
---______+++

And this P[x-z+]≤ P[y+x-] + [x+z+] being violated could be explained by the above table not having fixed values but with ' rotating spins ' and it would be like an 8 level slot
machine set in motion. The challenge would be to explain why the spins at two equal angular settings are always opposite.
Im only taking the initiative here because the question is not being answered when limited
to EPR/Bell realism

Asked and answered, morrobay. They are violated because local realism is untenable. And no one knows the answer to that any more than anyone can answer why c is the specific value it is. Further, QM explains why spins are opposite as mentioned.

 

[bohm2]

There seems to be only 3 options based on assumptions made by Bell:

1. Non-locality
2. Anti-realism
3. Superdeterminism (no freedom of choice)

I just realized that these are not the only options. Another possibility is backward causation, where future apparatus settings can affect system in past. I think the Transactional Interpretation and Aharonov presented such models. I'm guessing that neither non-locality or anti-realism is required. And of course, the MWI, which denies that the results of measurements have definite outcomes (e.g. measurement outcomes are relative to a branch).

 

[DrChinese]

I just realized that these are not the only options. Another possibility is backward causation, where future apparatus settings can affect system in past. I think the Transactional Interpretation and Aharonov presented such models. I'm guessing that neither non-locality or anti-realism is required. And of course, the MWI, which denies that the results of measurements have definite outcomes (e.g. measurement outcomes are relative to a branch).

I think of retro-causal as being non-realistic. That is because realistic implies PRE-existing hidden variables. If the hidden variables are in the future, then it is not realistic.

 

[bohm2]

I think of retro-causal as being non-realistic. That is because realistic implies PRE-existing hidden variables. If the hidden variables are in the future, then it is not realistic.

I've seen retro-causal interpretations also described as being non-local. In fact, that's how it's typically described but I've also read what I wrote above (e.g. backward causation does not imply non-locality) so I'm a bit confused.

 

[DrChinese]

I've seen retro-causal interpretations also described as being non-local. In fact, that's how it's typically described but I've also read what I wrote above (e.g. backward causation does not imply non-locality) so I'm a bit confused.

I think it comes down to your (or perhaps my) definition. The time symmetric (TS) and retrocausal interpretations do not have any effects propagating directly faster than c. But obviously you do have correlations and indirect effects that exceed c. I call that non-realistic, you might call it non-local.

I call anything non-realistic if the interpretation has as adjunct that there are no values for counterfactual measurements - i.e. there is a dependency on the observer. I call anything local if there exists a light cone bounded by c which limits propagation of effects. So by that, TS is local non-realistic. MWI is the same. And to me, Bohmian class theories are non-local AND non-realistic (because there is always a measurement context to consider).

By contrast: I have seen Relational Blockworld (a TS class theory) described by one of its authors as both local and realistic. MWI is often called local realistic. And Bohmian is often described as non-local realistic. Yet by the definitions of EPR, I think my viewpoint is just fine. I don't think it matters all that much, the essential points seem to come out the same in the end.

 

[bohm2]

I think it comes down to your (or perhaps my) definition. The time symmetric (TS) and retrocausal interpretations do not have any effects propagating directly faster than c. But obviously you do have correlations and indirect effects that exceed c. I call that non-realistic, you might call it non-local.

Yes, I think the paper by Wood and Spekkens summarizes a lot of the problems with these definitions. On pages 16-18:

Superluminal causation: One option for explaining Bell correlations causally is to assume that there are some superluminal causes, for instance, a causal influence from the outcome on one wing to the outcome on the other, or from the setting on one wing to the outcome on the other, or both. In the most general case one allows hidden variables that can causally influence the measurement outcomes.

Retrocausation: "Retrocausation" refers to the possibility of causal influences that act in a direction contrary to the standard arrow of time. It has been proposed as a means of resolving the mystery of Bell-inequality violations by purportedly saving the relativistic structure of the theory: rather than having causal influences propagating outside the light cone, they propagate within the light cone although possibly within the backward light cone.

The authors also discuss some of the difficulties in distinguishing retrocausality from superluminal causation:

Even if one takes spatio-temporal notions to be primary, the fact that the location of μ seems to be mere window-dressing in the context of a causal explanation of Bell-inequality violations undermines the distinction between retrocausation and superluminal causation. Fine-tuning is just as necessary within the retrocausal explanations as it was in the ones that posited superluminal influences or superdeterminism.

The lesson of causal discovery algorithms for quantum correlations: Causal explanations of Bell-inequality violations require fine-tuning
http://arxiv.org/pdf/1208.4119v1.pdf

To be honest, I've always found Gisin's description as quantum correlations lying *beyond* spacetime as the most interesting suggestion. At first it didn't make sense to me but then, when one thinks about the early "creation" of matter and space, it seems that it appeared out of something pre-spatial/temporal. So, why can't a remnant of that "pre-spatial stuff" still be with us at some level and play some role in physical laws. I understand this is mere speculation. But others have suggested this:

While the wave-function realist will deny that 3-dimensional objects and spatial structures find a place in the fundamental ontology, this is not to say that the 3-dimensional objects surrounding us, with which we constantly interact, and which we perceive, think and talk about, do not exist, that there are not truths about them. It is just to maintain that they are emergent objects, rather than fundamental ones. But an emergent object is no less real for being emergent...It is also worth keeping in mind that many workers in quantum gravity have long taken seriously the possibility that our 4-dimensional spacetime will turn out to be emergent from some underlying reality that is either higher-dimensional (as in the case of string theory) or not spatio-temporal at all (as in the case of loop quantum gravity). In neither case is it suggested that ordinary spacetime is non-existent, just that it is emergent.

Against 3-N Dimensional space
http://spot.colorado.edu/~monton/BradleyMonton/Articles.html

 

[morrobay]

Its a fact that the Bells inequalities are violated for expected spin measurements when detector settings are not parallel. And its natural to consider: loopholes . Clifford algebra, disproofs.superluminal signals. time reversal, many worlds, no conspiracy, and other theories to explain the experimental results that do not agree with local realism.A local realism that assigns ± spin values based on perfect correlations when detector settings are parallel. It seems there is a lot of talent here and out there devoting time to the above theories to the exclusion of exactly what the mechanism is that is causing the violations. When the research focus should be on why and how spins of entangled particles change.

 

[harrylin]

[..] It seems there is a lot of talent here and out there devoting time to the above theories to the exclusion of exactly what the mechanism is that is causing the violations. When the research focus should be on why and how spins of entangled particles change.

I agree; some research is going on to investigate explanations, but not enough (some of this came up in https://www.physicsforums.com/showthread.php?t=597171).

 

[my_wan]

I call anything non-realistic if the interpretation has as adjunct that there are no values for counterfactual measurements - i.e. there is a dependency on the observer. I call anything local if there exists a light cone bounded by c which limits propagation of effects. So by that, TS is local non-realistic. MWI is the same. And to me, Bohmian class theories are non-local AND non-realistic (because there is always a measurement context to consider).

What is highlighted in blue actually makes a good answer to the OP question.

This very succinctly defines something I suspected about your perspective from previous debates, and indicates a lot of disagreement is mere semantics. I even considered a thread asking for how people defined non-realism in this context.

Has it occurred to you that Relativity is a non-realistic theory under this definition? In fact you can use an ad hoc characterization of the addition of velocities equation to violate Bell's inequality, even slightly more so than EPR correlations do.

To illustrate consider the composition law for velocities. If we try to call a velocity 'real' in the EPR sense it is easy to demonstrate that the counterfactual velocities do not add up. For instance consider 2 spaceships A and B leaving a point of origin at 50% c. This entails that A and B have a velocity of 80% c relative to each other. If you boost the point of origin toward A then A will lose relative velocity faster than B gains relative velocity. In effect there is no counterfactual total value for composite velocities. All thermodynamic state variables as well as velocity, momentum, energy, entropy, etc., associated with a classical object can be demonstrated to have the same lack of counterfactual properties.

From this you can create an ad hoc analogy with EPR correlations, which can be made to violate Bell's inequality even more than EPR correlations. Just assign a probability for a gun at the point of origin to destroy the spaceships in proportion to the relative velocity, or total momentum. You can also treat the ships as doppelgangers such that if a given speed destroys A that same speed destroys B, or other variations. The key feature is that velocities lack a counterfactual total value. A destroyed ship is then analogous to an EPR path A, and survival is path B. The survival correlations between spaceship A and B will then not counterfactually add up under different boost of the gun.

If this is the nature of the variables you define as non-realistic then I would go so far as to bet that all variable we have direct empirical access to are non-realistic, that the world we perceive as physical is actually a purely relational construct. Once you recognize the classical absurdity of parts with a background of absolute space and time, where space and time are pre-existing independent variables as if by magic, this notion of realism is prima facie absurd. Once you accept these variables we call space and time, as we measure them, as state variables then the loss of counterfactual variables, even for a basic variable like velocity or photon paths in EPR, is assured.

Classically we had masses or particles to underpin the relational variables lacking counterfactuals, which we replaced with 'proper' values requiring an observer frame. It is the nature of these particles we are now dealing with. The real difference in the perspective of a realist, at least a serious one, is not the loss of counterfactuals, but a lack of underpinning real variables to generate them. Yet the problem is we know that we can't use a backdrop of space and time to put them in, since these variables are required to be the generators of space and time itself.

Bottom line is that given you definition of non-realism a serious realist can't honestly object. What realist seek is a substructure model that provides what particles provided for classical physic. We can't return to Newtonian style realism but we already know how wrong this is even without resorting to QM. I don't think you have addressed the issues of interest to realist.

 

[danR]

To be honest, I've always found Gisin's description as quantum correlations lying *beyond* spacetime as the most interesting suggestion. At first it didn't make sense to me but then, when one thinks about the early "creation" of matter and space, it seems that it appeared out of something pre-spatial/temporal. So, why can't a remnant of that "pre-spatial stuff" still be with us at some level and play some role in physical laws. I understand this is mere speculation. But others have suggested this:

Against 3-N Dimensional space
http://spot.colorado.edu/~monton/BradleyMonton/Articles.html

I mentioned this notion speculatively last week and assumed it was nothing but another of my usual own layperson's metaphysical babblings.

Inasmuch as most inflationary cosmogenies seem to entail some sort of 'quantum fluctuation' originating at a nanoscopic scale, why should we assume that its quantum attributes were necessarily entrained in the expansion of 4-space, or dependent on the evolution of the forces? Since the evidence shows non-locality only too clearly and no force-mediation involvement whatever, isn't it simpler, more elegant, and more Einsteinian-ly beautiful to assert locality (I find realism 'meh, take it or leave it'—I have no preference) to be an extraordinary claim requiring extraordinary evidence?

Edit: or to use a biological analogy: all living systems, however much evolved, retain something of the original RNA-world.

 

[bohm2]

I mentioned this notion speculatively last week and assumed it was nothing but another of my usual own layperson's metaphysical babblings...or to use a biological analogy: all living systems, however much evolved, retain something of the original RNA-world.

As an aside and to pursue somewhat analogous speculations, I've come across arguments that the breakdown of spatio-temporality can be seen as a minimum requirement to make sense of consciousness or the so-called "hard" problem of consciousness. For example consider Mcginn's "spatial problem for mind" argument:

How do conscious events cause physical changes in the body? Not by proximate contact, apparently, on pain of over-spatialising consciousness, and presumably not by action-at-a-distance either. Recent philosophy has become accustomed to the idea of mental causation, but this is actually much more mysterious than is generally appreciated, once the non-spatial character of consciousness is acknowledged. To put it differently, we understand mental causation only if we deny the intuition of non-spatiality. The standard analogy with physical unobservables simply dodges these hard questions, lulling us into a false sense of intelligibility...

Conscious phenomena are not located and extended in the usual way; but then again they are surely not somehow 'outside' of space, adjacent perhaps to the abstract realm. Rather, they bear an opaque and anomalous relation to space, as space is currently conceived. They seem neither quite 'in' it nor quite 'out' of it. Presumably, however, this is merely an epistemological fact, not an ontological one. It is just that we lack the theory with which to make sense of the relation in question. In themselves consciousness and space must be related in some intelligible naturalistic fashion, though they may have to be conceived very differently from the way they now are for this to become apparent. My conjecture is that it is in this nexus that the solution to the space problem lies. Consciousness is the next big anomaly to call for a revision in how we conceive space-just as other revisions were called for by earlier anomalies. And the revision is likely to be large-scale, despite the confinement of consciousness to certain small pockets of the natural world. This is because space is such a fundamental feature of things that anything that produces disturbances in our conception of it must cut pretty deeply into our world-view...That is the region in which our ignorance is focused: not in the details of neurophysiological activity but, more fundamentally, in how space is structured or constituted. That which we refer to when we use the word 'space' has a nature that is quite different from how we standardly conceive it to be; so different, indeed, that it is capable of 'containing' the non-spatial (as we now conceive it) phenomenon of consciousness.

Consciousness and Space
http://www.nyu.edu/gsas/dept/philo/courses/consciousness97/papers/ConsciousnessSpace.html

 

[my_wan]

DrChinese, given your definition of non-real, and that position and momentum fall under this particular definition, how could it ever be expected that an ensemble derived from these position/momentum operators would correspond to a real value under that definition?

This is in essence how RQM (relational quantum mechanics) purports to resolve the issue, simply by accepting such properties are in fact relational.

 

[DrChinese]

This very succinctly defines something I suspected about your perspective from previous debates, and indicates a lot of disagreement is mere semantics. I even considered a thread asking for how people defined non-realism in this context.

Has it occurred to you that Relativity is a non-realistic theory under this definition? In fact you can use an ad hoc characterization of the addition of velocities equation to violate Bell's inequality, even slightly more so than EPR correlations do.

...

I couldn't agree with this at all. GR can present answers for counterfactual measurements.

 

[my_wan]

I couldn't agree with this at all. GR can present answers for counterfactual measurements.

I was referring only to SR, and the addition of velocities equation in particular. I was also only referring to the capacity of arbitrary values, like velocity compositions, to violate Bell's inequality. Given that EPR counterfactual properties is something you derive solely from a violation of Bell's inequality, how well defined you presume the counterfactuals are in another system with values that violate Bell's inequality is immaterial.

One other difference in this particular analogy is that you can't preclude the knowledge of the relative velocities involved on the basis that this knowledge is non-local information about a distant object. You can also boost spaceship velocities after the gun has fired and before the other spaceship can have knowledge of this boost before it is destroyed or not. This lack of knowledge has no effect on coincidence rates defined by that boost.

A disagreement thus requires a denial that velocity compositions under SR can add up in ways that can be characterized as a violation of Bell's inequality, not on how well defined the counterfactuals are presumed to be. Do you deny velocity compositions can be characterized as a violation of Bell's inequality?

 

[DrChinese]

... A disagreement thus requires a denial that velocity compositions under SR can add up in ways that can be characterized as a violation of Bell's inequality, not on how well defined the counterfactuals are presumed to be. Do you deny velocity compositions can be characterized as a violation of Bell's inequality?

Yes, I deny that. SR is realistic by my definition and that of most others. I have never heard it characterized otherwise.

 

[danR]

As an aside and to pursue somewhat analogous speculations, I've come across arguments that the breakdown of spatio-temporality can be seen as a minimum requirement to make sense of consciousness or the so-called "hard" problem of consciousness. For example consider Mcginn's "spatial problem for mind" argument:

Consciousness and Space
http://www.nyu.edu/gsas/dept/philo/courses/consciousness97/papers/ConsciousnessSpace.html

But I don't want to take the matter to far down the speculative road of consciousness and philosophy. In my own liberal arts hand-wavey fashion, I'm even considering if the notion of some a-temporospatial realm, where quantum stuff entirely does its business, is falsifiable. In the hard sense. Are there any experiments done or doable that require some kind of space or time involvement (as opposed to common-sense 'violation') for quantum phenomenon X to appear? Obviously apart from the time and space and measurement-locale arrangement of the apparatus required, eg. for the Bohm-Aharonov solenoid.

"It requires only one experiment to prove relativity wrong." --Einstein

 

[bohm2]

But I don't want to take the matter to far down the speculative road of consciousness and philosophy. In my own liberal arts hand-wavey fashion, I'm even considering if the notion of some a-temporospatial realm, where quantum stuff entirely does its business, is falsifiable. In the hard sense. Are there any experiments done or doable that require some kind of space or time involvement (as opposed to common-sense 'violation') for quantum phenomenon X to appear? Obviously apart from the time and space and measurement-locale arrangement of the apparatus required, eg. for the Bohm-Aharonov solenoid.

What do you mean by speculative? I'm more sure about my consciousness than I am about any laws of physics or science. Although I have no clue how the brain does it. With respect to your latter question, I'm convinced that violation of Bell's theorem implies some type of non-locality. One can consider such instantaneous "private communication lines" to be "outside" space-time as argued by Gisin:

To put the tension in other words: no story in space-time can tell us how nonlocal correlations happen, hence nonlocal quantum correlations seem to emerge, somehow, from outside space-time.

Quantum nonlocality: How does Nature perform the trick?
http://lanl.arxiv.org/pdf/0912.1475.pdf

If so, whatever causes entanglement does not travel from one place to the other; the category of “place” simply isn't meaningful to it. It might be said to lie *beyond* spacetime. Two particles that are half a world apart are, in some deeper sense, right on top of each other. If some level of reality underlies quantum mechanics, that level must be non-spatial.

How Quantum Entanglement Transcends Space and Time
http://www.fqxi.org/community/forum/topic/994?search=1

Of course, non-locality or non-spatiotemporality isn't close to enough to shed light on the so-called "hard" problem but it is a minimum requirement, in my opinion as per McGinn's argument.

 

[Len M]

If so, whatever causes entanglement does not travel from one place to the other; the category of “place” simply isn't meaningful to it. It might be said to lie *beyond* spacetime. Two particles that are half a world apart are, in some deeper sense, right on top of each other. If some level of reality underlies quantum mechanics, that level must be non-spatial.

I agree with that extract you gave entirely, but of much more standing it is the considered viewpoint of Bernard d’Espagnat (see his book “Veiled Reality” amongst others). The emphasis with d’Espagnat however concerns independent reality (reality outside of the phenomena of empirical reality), QM is a part of empirical reality (phenomena) just as much as the trajectory of a cricket ball is, the breakdown of space can be conceived (which is the line d'Espagnat takes) as existing on the borderline between empirical reality and independent reality, he feels it to be quite a unique condition because we can observe the breakdown of space but cannot make any practical use of that knowledge within empirical reality. It’s as if we have a “glimpse” of independent reality but that’s as far as it goes, that “glimpse” can’t be exploited within our realm of phenomena (empirical reality).

 

[bohm2]

It’s as if we have a “glimpse” of independent reality but that’s as far as it goes, that “glimpse” can’t be exploited within our realm of phenomena (empirical reality).

This isn't particularly surprising given that like all other animals our cognitive structures will necessarily have limits. What is interesting is that we can know so much (or so it seems) in comparison to other animals, particularly in physics/sciences and it does appear that something "out" there (independent reality) seems to be pushing us in one direction versus another. D'Espagnat's book was one of the first books on philosophy of QM that I read. What has always struck me as kind of strange (is it just a coincidence?) is the similarity between some of the conceptual/interpretational difficulties in QM and the analogously similar conceptual difficulties in philosophy of mind/cognitive sciences. Some philosophers of mind have argued that non-locality or at least, non-spatiality would be the minimum requirement to even begin to understand how something that appears to be localized in 3-dimensional space like our nervous system/brain/body can spit out something like qualia/mind/experientiality. It seems to be located "there" and yet to defy spatiality. It is interesting to look at the anologies between this so called "hard" (mind-body) problem and the interpretation difficulties in QM of trying to understand/explain the relationship between our everyday 3-dimensional space vs. wave function in 3N-dimensional configuration space. Consider these quotes by Einstein and some other physicists:

In order to describe multiparticle systems, Schrodinger had replaced de Broglie’s waves in 3-space with waves in configuration space, and had abandoned the notion of particle trajectories. But Einstein was dubious of this move: “The field in a many-dimensional coordinate space does not smell like something real”, and “If only the undulatory fields introduced there could be transplanted from the n-dimensional coordinate space to the 3 or 4 dimensional!”

Einstein, incompleteness, and the epistemic view of quantum states
http://arxiv.org/PS_cache/arxiv/pdf/0706/0706.2661v1.pdf

But the problem is that this cannot be done because there are predictions of QM that depend on the 3N-dimensional space that get lost in the 3-dimensional representation (e.g. information about correlations among different parts of the system, that are experimentally observed are left out). Similar quotes can be seen elsewhere:

We have two disconnected spaces, with presumably no causal connection between the particles in the one space and the field in the other space, and yet the stuff in the two spaces is evolving in tandem. Presumably there is a nomic connection between the stuff in the two spaces, which supports counterfactuals of the following form: if the stuff in one space had evolved differently, the stuff in the other space would have evolved differently. But having that nomic connection without a causal connection makes it all the more mysterious how these spaces are associated with each other.

Quantum Mechanics and 3N Dimensional Space
http://spot.colorado.edu/~monton/BradleyMonton/Articles_files/qm%203n%20d%20space%20final.pdf

There are two related problems that immediately arise here. First, if both multi-dimensional configuration space and ordinary 3-dimensional space are to be equally physically real, then unless one spells out the physical relation between them, one will have divided the quantum world into two disparate realms. Second, if the quantum field (in whatever sense it is to be understood) exists in configuration space and particles move in ordinary 3-dimensional space, how is the quantum field to act causally upon the particles in order to guide their trajectories? Solving the second problem depends, of course, upon solving the first. One might reply to the first problem that ordinary 3-dimensional space can be regarded simply as a sub-space projection of the multi-dimensional configuration space.

But, for an N-particle system described by a 3N-dimensional configuration space, there are mutually orthogonal sub-space projections. Do we then have multiple disjoint ordinary spaces for each many-particle system, one for each particle? The significance of this situation can be brought out by considering the case of an N-particle system in a factorizable quantum state– ψ(q1,..., qN) = ψ1(q1)...ψN(qN). In contrast to the general case of a non-factorizable quantum state, in this case one can represent the system in terms of N ‘waves’, where ψi(qi) depends upon only the coordinates of the ith particle so that each ‘wave’ can be associated with a separate particle. But, the sub-spaces of the 3N-dimensional configuration space to which the respective ψi(qi)’s belong are all mutually orthogonal so that the N ‘waves’ and particles do not all exist in one and the same 3-dimensional space (unless one were to equivocate on the meaning of the qi ).

Thus, even in this case, one cannot simply regard the total quantum system as existing in ordinary 3-dimensional space, but rather must still regard it as existing irreducibly in configuration space, with each part existing in a ‘separate’ sub-space. And that would undercut any sense of a single system existing in one and the same physical space, which is surely requisite for a coherent physical theory.

Formalism, Ontology and Methodology in Bohmian Mechanics
http://link.springer.com/article/10.1023/A:1023925900377?no-access=true

Bohm draws attention to what he calls 'a serious problem' that confronts us when the theory is extended to deal with more than one particle. The problem with N particles is that the wave function is not in ordinary 3-dimensional space, but instead, in an abstract 3N-dimensional configuration space. While of course this space is logically consistent, the concept of a wave in a 3N-dimensional space is far from physically obvious. At this stage Bohm simply regarded his proposals as an artifice that could be used provisionally until a better theory emerges "in which everything is expressed once more in ordinary 3-dimensional space". This problem of configuration space was eventually resolved by introducing the notion of 'active information' . However there remains a deeper problem as Bohm points out:

Finally, our model in which wave and particle are regarded as basically different entities, which interact in a way that is not essential to their modes of being, does not seem very plausible. The fact that wave and particle are never found separately suggests instead that they are both different aspects of some fundamentally new kind of entity which is likely to be quite different from a simple wave or a simple particle, but which leads to these two limiting manifestations as approximations that are valid under appropriate conditions

.
Some Remarks on the Evolution of Bohm's Proposals for an Alternative to Standard Quantum Mechanics.
http://www.bbk.ac.uk/tpru/BasilHiley/History_of_Bohm_s_QT.pdf

You can basically take these quotes and just slightly change a few words and you can transpose them to the so-called "hard" problem.