# Why are Bell's inequalities violated?

morrobay
Gold Member
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' 6s 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

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.

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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 [Broken]
Thank you bohm2.

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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
Gold Member
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' 6s 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.

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).

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DrChinese
Gold Member
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.

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.

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DrChinese
Gold Member
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.

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

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morrobay
Gold Member
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 alot 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.

[..] It seems there is alot 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).

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.

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
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.

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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

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
Gold Member
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.

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
Gold Member
... 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.

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

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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.

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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).

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
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
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.

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