Why are Bell's inequalities violated?

[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, Schrödinger 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.