What do violations of Bell's inequalities tell us about nature?

ttn

Cool. But please describe this as "Rubi's formulation of locality", not Bell's, when you publish...

rubi

Why? You write in your own paper that for the locality criterion [itex]P(b_1|B_3 b_2) = P(b_1|B_3)[/itex],

So if i choose my beables to be the statistical properties (instead of the outcomes as you do for Copenhagen), then i can formally apply this criterion to the theory, where [itex]b_1 = <A>[/itex] and so on. I'm just using the general definiton and applying it to the special case of instrumentalist QM, where the beables are the statistical properties. This is precisely Bell's formulation of locality applied to the theory of QM with a particular choice of beables. It's not Rubi's formulation.


P.S.: I know that as a convinced Bohmian, you will say: "Nooo, the outcomes must be beables, because the world can't be without outcomes." But for someone who accepts that the world is "nothing but wave function", it is a perfectly valid viewpoint to claim that the beables are the statistical properties.

bohm2

But agreement with everything you wrote is not inconsistent with violation of Bell's implying non-locality. And I personally agree with pretty well everything you wrote.

Len M

I only made the post in terms of a very small part of ttn’s overall important contribution to this thread, namely when he said:


As I said in my post, I see nothing at all wrong in simply accepting that science (as an experimental discipline) belongs quite properly within phenomena. ttn seems to me to picking and choosing in an arbitrary manner between science as practiced within empirical reality (in terms of testability) and the extrapolation of those models to an independent reality that cannot (and does not) involve testability, without seemingly keeping track of what he is doing (at least not in a formal transparent manner that identifies the difference between the scientific status of a model in terms of empirical reality and the same model in terms of independent reality). It's easier for me to keep track of the mix between empirical reality and independent reality because I go the whole hog, I confine the scientific method to phenomena and I reserve the realm of independent reality as being unknowable in a scientific sense and having no correspondence to empirical models, but philosophically being free to conjecture about the nature (and importance) of its existence. For a less extreme stance though, it becomes more difficult to keep track, but I think you have to and be quite transparent about it in public because there is no question that a mix is being invoked between the scientific method involving testability and the extrapolation of that model to a realm of independent reality that cannot involve testability.

But ttn then says
implying that accepting the possibility that empirical reality (phenomena) is not close to independent (external) reality in some manner spells the end of science in that empirical science may all be “wrong”. I don’t see that at all, empirical science is always going to be “right” within empirical reality (in the sense of mathematical predictive models within their domain of applicability) and for me that fact is one of the most remarkable aspects of the scientific method – Newton’s predictive mathematical model, within its domain of applicability, is going to be valid ten thousand years from now, that for me has got enough solidity to more than compensate for being (as ttn says) “totally at sea” because we can't scientifically prove that empirical models have the same applicability within independent reality.

The extract from ttn seems to be something said from the "heart" with conviction and I wondered whether it had any specific relevance to his science as opposed to his philosophical stance. I guess I’m not going to know for sure now that ttn is back to teaching, but I certainly agree with you when you say
so perhaps that would also be the viewpoint of ttn?

Maui

Correct me if i am wrong, but the fundamental constituent of reality are not inadequate classical concepts like 'particle' and 'wave', but information. We are not seeing particles, but always seeing information about particles. The brain is not just a simple collection of particles(as newtonain perspective would dictate), but an(emergent) information processor. At the rock bottom of things, we are not seeing tables and chairs but information about tables and chairs and being such, information has no obligation to be material-like, corpusular-like ot classical-like. While there could be a stunning correspondence between tables and our sensation of tables, we should not overlook the simple fact that we only have access to the information about tables, not the tables themselves. Tthe ultimate nature of tables is not accessible, hence it is not a valid scientific question. I totally agree with Bohr, it's only what we can say about Nature, not what or how Nature is. It's surprizing that we have as good models of reality as we do, even if they fail to makes sense at certain scales.

Len M

Yes I think I would agree very much with what you say in that you seem to be placing phenomena as the only entity in which we have access to and it is within that framework that we use the scientific method with spectacular success - why should we ask any more of such a successful method in wanting it to be applicable in the same manner to a realm outside of phenomena where the very essence of the scientific method, namely testability cannot be carried out?

My only difference perhaps would be that I do see a need for "something" outside of phenomena from which empirical reality "emerges" (in an unknowable manner) otherwise we have to adopt solipism or radical idealism. I think the consistencies we all observe as phenomena (and agree on) depend on something other than ourselves, so in this sense I am a realist, it's just that I don't see that we can access my "something" that "exists" within independent reality (i.e outside of phenomena) in any scientific sense (at least not as I understand the scientific method in terms of the method requiring a notion of testability).

stevendaryl

I think there is a contrast between applied science, the basic research that underlies technology, and pure science, which I think has some kind of understanding as the goal. When you're trying to build a better bridge, or better electronics, or whatever, there really is a sense that you don't need to understand anything, you just need to know reliable rules of the form "In situation S, if you do X, you'll get result Y with probability Z". By this practical criterion for science, there is nothing wrong with describing the orbits of the planets or the energy levels of hydrogen, or the relationship between velocity and kinetic energy as an infinite series, all of whose coefficients are empirically determined. So the Ptolemy scheme for describing planetary motion, with its spheres within spheres within spheres, is really perfectly fine, and Balmer's formula for computing energy levels is perfectly fine. Explaining the null results of the Michelson-Morley experiment by an ad hoc velocity-dependent length contraction and time dilation is perfectly. There is no practical need for fundamental theories, at all.

But there is another kind of science that considers the job not to be done when you have a formula that empirically works pretty well. Some kinds of people are bugged by arbitrariness, by lots of parameters whose values seem meaningless. They prefer to try to understand how those successful formulas come about, why the parameters are what they are. They would like an understanding of the principles involved. Even though we may never experience gravity billions of times stronger than on the Earth, they want to be able to have an idea of what things would be like in those circumstances.

It's really hard to make a decisive partition of science into what's practical and what's pure, because a lot of science that was once considered a matter of intellectual curiosity ended up having practical applications. However, I think that the divorce between practical physics and pure physics has happened, and many of the new discoveries and ideas since maybe the 60s (quantum chromodynamics, supersymmetry, loop quantum gravity, string theory, Hawking radiation, the holographic principle, quark theory, etc.) will likely have no practical applications for decades, if ever.

So to me, it's pretty weird to talk about fundamental physics in purely instrumental terms: All we care about is a way of calculating probabilities for the outcomes of experiments. WHY? Why do you care about a way of calculating probabilities for the outcomes of experiments? If the experiment takes a multi-billion dollar collider to take place, then who cares? Knowing the answer has no practical purpose, it seems to me. If all you care about is the pragmatics of predicting what happens when we perform specific experiments, then fundamental physics is over, it seems to me.

harrylin

I agree; regretfully that was the paradigm for the last century, it seems.

DrChinese

Travis channels Bell. So he can present anything as being what Bell says, and you cannot.

bohm2

That's a good question and I'm not sure? But my gut hunch is that ttn would not agree with the Kantian and/or epistemic structural realist position that I think both you (if I'm understanding you) and myself seem to subscibe to but who knows?

bohm2

While many of these have been mentioned on various threads/posts I thought I'd post a list of the major papers I've come across arguing that violations of Bell's inequality implies non-locality, irrespective of any other issues (e.g. realism, determinism, hidden variables, pre-existent properties, etc.):

Bertlmann’s socks and the nature of reality
http://cds.cern.ch/record/142461/files/198009299.pdf

J.S. Bell’s Concept of Local Causality
http://chaos.swarthmore.edu/courses/...3_2012/002.pdf

Local Causality and Completeness: Bell vs. Jarrett
http://lanl.arxiv.org/PS_cache/arxiv...808.2178v1.pdf

Non-Local Realistic Theories and the Scope of the Bell Theorem
http://arxiv.org/ftp/arxiv/papers/0811/0811.2862.pdf

The uninvited guest: ‘local realism’ and the Bell theorem
http://philsci-archive.pitt.edu/5258...ll_theorem.pdf

A Criticism of the article "An experimental test of non-local realism"
http://arxiv.org/abs/0809.4000

John Bell and Bell's Theorem
http://www.mathematik.uni-muenchen.d...ech/rt/bbt.pdf

What Bell proved: A reply to Blaylock
http://www.stat.physik.uni-potsdam.d...Bell_EPR-2.pdf

Not throwing out the baby with the bathwater: Bell’s condition of local causality mathematically ‘sharp and clean’
http://mpseevinck.ruhosting.nl/seevi..._corrected.pdf

Can quantum theory and special relativity peacefully coexist?
http://mpseevinck.ruhosting.nl/seevi...k_Revised3.pdf

What is the meaning of the wave function?
http://www.fyma.ucl.ac.be/files/meaningWF.pdf

The Message of the Quantum?
http://www.maphy.uni-tuebingen.de/me...papers/zei.pdf

Was Einstein Wrong? A Quantum Threat to Special Relativity
http://www.stealthskater.com/Documents/Quantum_01.pdf

morrobay

For a counterweight to above :
http://www.iisc.ernet.in/currsci/jul...NIKRISHNAN.pdf

rubi

Unfortunately, all these papers include the hidden assumption that individual experimental outcomes correspond to some element of the theory of quantum mechanics. They either fail to understand the difference between values that come from the theory and values that are determined by experiment or they secretly use a non-standard theory of quantum mechanics (standard QM supplemented by a mechanism that can in principle predict individual outcomes; everyone knows that this is not the case in the standard theory) and claim it would be the standard theory.

Bell's criterion actually does capture our intuitive understanding of locality after all. You can for example apply it straightforwardly to any classical theory and it captures what we would consider locality of a classical theory. However, these papers apply it to a quantum theory without acknowledging that fact that the quantum theory isn't a classical theory anymore doesn't have something like trajectories of observables anymore (unlike for example Bohmian mechanics) and thus you can't check the criterion for them. You have to check it for the variables of of the quantum theory (or better: a subclass of them, called the "beables") instead. The word "beable" is assigned to those elements of the theory that correspond to what the theory claims to be physically real. In a classical theory or in Bohmian mechanics, the beables would be things like position. Standard quantum mechanics is basically a theory that describes the evolution of probability, so you would choose the beables to be the probability distributions. Notice that even if you wanted to, you couldn't choose position as a beable, because it isn't an element of the standard theory at all. Locality is a property of a theory, so you must apply the criterion to the theory alone without any supplements. So in the end, Bell's locality criterion is actually really good, but applied in a wrong way. It's just that all the generality and terminology involved makes it quite hard to understand what's wrong with the argument.

So what these papers actually prove is that if your theory assumes reality, which means that it does account for the individual outcomes of the experiment, then you can prove that it must be non-local. You can read the proof in ttn's post #204. However, you must note that this proof only holds if your theory really accounts for the outcomes. So the reality assumption ("the theory does account for individual outcomes") implies Bell-non-locality. If your theory is non-real ("it doesn't account for the individual outcomes of the experiment"), then it is still open, whether the it is local or non-local.

If you take standard QM serioursly (that means you accept that it doesn't account for individual outcomes), then Bell's locality criterion actually implies locality, whenever the no communication theorem holds.

bohm2

Probability of "what"?

rubi

The probability to measure a given value for an observable, just as every standard textbook says. But the value itself isn't included in QM, only it's probability distribution. There is no prediction about concrete values. QM just says that the statistics of the measurement is given by the probability distribution. There is no underlying "real" observable that has a particular value.

To say it as briefly as possible: These above papers prove that if a theory can account for the individual outcomes of the experiment, then it must be non-local. Standard QM doesn't do it, so it can be a local theory.

bohm2

Observable of what? If I'm understanding you (I may not be) this has been considered:
Can quantum theory and special relativity peacefully coexist?
http://mpseevinck.ruhosting.nl/seevi...k_Revised3.pdf

rubi

An observable like position or spin. That above paper also uses the individual outcomes as input for Bell's criterion and thus the same argument applies.

(By the way, he is even wrong with the statement that relativistic QFT presupposes locality. In fact, it is a framework that provides some general theorems under the assumption of locality. Whether a concrete theory satisfies it or not always has to be checked.)