Bell's theorem and foundations of statistics

[hgeurdes]

Dear All,

Recently I have published a paper on Bell's theorem ASTP 4(20) 945-949 (2010). One can also find it on arXiv as http://arxiv.org/abs/1012.4990.

I am interested in a discussion about the results of the paper. The claim of the paper is that mathematically Bell's theorem is incomplete. In other words Bell's theorem does not at all exclude locality and causality to physics.

Now maybe you are sick and tired of hearing this kind of claim and I really can imagine that. I am really sick and tired of all the 'this cannot be true' remarks that are not suppoted by fact but just by reference to authority. I do not need to know your state of mind about this claim, I only would like to hear your opinion on the mathematics and the claims posed. There are certainly interesting philosophical consequences. However, philosophy should not be confused with finding clever remarks to avoid possible consequences of research.

Indeed I do not hold foundational research in high regards and I have my own silly reason for that. Nevertheless you represent an intelligent forum of people that know how to discuss important aspects of your field.

Yours
Han Geurdes

 

[sfs01]

The second paragraph of section 3.2 sounds like changing the setting of A affects the value of one of the hidden parameters (which are later measured by B) and vice versa. If that is what you meant, you are breaking the core assumption made in Bell's proof, which is that the settings of the 2 detectors are independent of the value/distribution of the hidden variable(s).

There are two ways of interpreting this:
- either you are breaking locality (A immediately affects a change of the distribution of the hidden variable during the experiment, which is measured by B)
or
- your second experiment after the change of parameters is an entirely different experiment because the distribution of the underlying object has changed, so comparing its correlation to the previous experiment is meaningless

It might help, of you could try explaining what the phrase 'locality obeying interval selection rules' means because I would think any change to the distribution of the hidden variables (as a result of the setting of one of the detectors) would break the independence of these variables and consequently locality.

 

[DrChinese]

Dear All,

Recently I have published a paper on Bell's theorem ASTP 4(20) 945-949 (2010). One can also find it on arXiv as http://arxiv.org/abs/1012.4990.

I am interested in a discussion about the results of the paper. The claim of the paper is that mathematically Bell's theorem is incomplete. In other words Bell's theorem does not at all exclude locality and causality to physics.

Now maybe you are sick and tired of hearing this kind of claim and I really can imagine that. I am really sick and tired of all the 'this cannot be true' remarks that are not suppoted by fact but just by reference to authority. I do not need to know your state of mind about this claim, I only would like to hear your opinion on the mathematics and the claims posed. There are certainly interesting philosophical consequences. However, philosophy should not be confused with finding clever remarks to avoid possible consequences of research.

Indeed I do not hold foundational research in high regards and I have my own silly reason for that. Nevertheless you represent an intelligent forum of people that know how to discuss important aspects of your field.

Yours
Han Geurdes

First, I would like to welcome you to PhysicsForums, Han!

I had "read" one of your earlier papers, "A remark on the use of Bell inequalities", when it came out. "Read" in the sense that I scan a lot of papers because there are far too many on Bell and related to analyze them fully. I bookmarked yours because I thought I might refer to it again. If you think about it logically, you will realize that there are many with highly complex issues with work that is clearly against the mainstream, so asking other scientists to "explain what is wrong" is really putting the shoe on the wrong foot.

Discussion of this paper probably doesn't belong here, but as long as we are on the subject I will ask you the same question I ask everyone: what is realism if it is not per the EPR/Bell definition? Which to me is usually the crux of various arguments.

Obviously, you cannot provide me a dataset of counterfactual simultaneously defined hidden variables or measurement results (angle settings 0/120/240 a la Mermin) that matches the predictions of QM. I know that from Bell, so that pretty much ends all arguments from my perspective. Until you can answer that, there is not much to talk about. Because Bell could be "wrong" and that is still true! So my point is: by the usual definition of realism, local realism is experimentally rejected. Now if you want to tell me your definition is viable, then I ask you to present a useful model that might be derived from it. (Otherwise, it is really an interpretation and we hardly need more of those!)

So let's talk about a useful model. It has been experimentally demonstrated that photons that have never existed in the same light cone can be entangled via swapping, and further that the decision to perform the swapping can be made after detection. This result clearly violates any classical notion of locality/causality. Can your "model" handle this?

The reason Bell is important is that it is useful.

 

[edguy99]

Thank you for posting your work. We had been discussing the paper http://arxiv.org/PS_cache/quant-ph/pdf/0205/0205171v1.pdf" that describes a hidden variable theory at (18)

Pvv(HTV)(γ, λ) = 1 if |γ-λ|≤π/4
Pvv(HTV)(γ, λ) = 1 if |γ-λ|>3π/4
Pvv(HTV)(γ, λ) = 0 if otherwise

Which I would simplify to:

If the spin axis points between 10:30 through 12 to 1:30, or the axis points between 4:30 through 6 to 7:30, it is vertical (1). Otherwise, it is horizontal (0). He, quite rightly, quickly finds and proves this model (or any of this group) does not work. The author does say "Our HVT is very simple, and yet it agrees pretty well with quantum mechanics. We might hope that some slight modification would bring it into perfect agreement." Videos of this type of spin on a bloch sphere can be seen http://www.animatedphysics.com/videos/spinningblochsphere.htm" (spin axis never moves). Notice how much the blue line jumps around as soon as the particle is tilted.

----------------------------------------

You are suggesting that we use two variables to describe this action. If we do, we may well be able to produce a model that is consistent with QM. I agree with you. It is very reassuring to see you go on and prove it. In addition, as far as I can figure out, you are specifically suggesting we try:

... a density for (λ1, λ2) ∈ [−1/√2, 1/√2] x [−1/√2, 1/√2] = Λ with n = 1, 2

ρλn = −1/√2 if -1/√2 ≤ λn ≤ 1/√2
ρλn = 0 otherwise

I have not yet been able to draw a picture in my mind of this particle, but will try. In the meantime, would you consider a model where not only is there a spin axis, but there is precession to the spin axis. This type of particle, when coming directly at you, will not present a consistent up or down, but rather a probability of being measured in a certain state. Larmor frequency is that type of spin precession and is widely used in modeling protons and neutrons, but not so much electrons or photons. No one seems to care about that second variable that you are suggesting would not have any Bell type problems. Videos of this type of spin on a bloch sphere can be seen http://www.animatedphysics.com/videos/larmorfrequency.htm" . Your average particle would present himself, somewhere along the line of the lower right-hand video.

 

[hgeurdes]

Dear all,

Thanks for welcoming me. It is good to consider philosophical foundational matters in this forum.

Indeed I know, already many remarks have been made about Bell's Theorem. My relatively modest position is mathematical statistics. I am aware of the absolute need to discuss the physics but let me start with the mathematics. Bell is incomplete is what I think I have demonstrated here in the ASTP.

First I would like to thank sfs01. But I fail to see why the use of the $$\Omega$$ sets imply a violation of locality. Settings of A restrict the interval of a single, uniform distributed, hidden variable (i.e. $$\lambda_1$$). Settings of B restrict the interval of the other (i.e. $$\lambda_2$$). That are local effects and can occur at lightyears distance. Then, the integrations

$$\int_{\Omega_{\pm}} d\lambda_1 d\lambda_2$$

bring them together, exactly as a consequence of what Bell prescribes.

Now, if I flip a coin and e.g. heads show, then the empty set is assigned to $$\Omega_{+}$$ i.e. $$\Omega_{+}=\emptyset$$ and $$\Omega_{-}$$ is the combined independent cartesian product of the two intervals, i.e.

$$\Omega_{-}=[\frac{-1}{\sqrt{2}},1-\frac{1}{\sqrt{2}}]\times[0,\frac{1}{\sqrt{2}}]$$.

For the other CHSH settings I do the same. Then there is a non vanishing probability, namely 1/16, that a local hidden variables model violates CHSH. Bell's theorem claims that this is impossible, i.e. has probability zero. If there is no reason to reject the probabilistic explanation, then, Bell is incomplete, no locality violations and a simple classical probability density that behaves nicely as required. Where is the need for non-locality in the previous explanation of the incompleteness of BT?

Then edguy99, I really need to study your suggestions and phrasings further. But please bear in mind, it is not the density but the random assignment to sets that produces a non-zero probability of LHV models explaining the correlation. Bell's theorem has this probability = 0.

The question of Dr Chinese about realism refers not to the mathematical part of my work. But it is a good question. Realism is perhaps too strong a word for what is philosophically the matter in the foundations of physics. I think, in all modesty that the word realism and the subsequent models that were invented to proposed are too strong and throw away a valuable part of a lesson of quantum physics, namely we measure and interpret the measurement. A measurement needs to help us further to get a view of what is going on 'out there'.

I do not know if you are aware of the Existentialistic / Phenomenological discussions started by Husserl and e.g continued by Heidegger or by Sartre about the difference between Idealism and Realism. Somewhere in the discussion Sartre comes with the remark that, although in a movie-theatre we do not observe the screen, we do observe its presence. This is what he calls being-in-itself (reference to Kant's Ding an sich seems inevitable). The being-for-itself is 'that what is projected on the screen'. Without the screen no projection, but without something to project the presence or absence of a screen cannot be concluded.

The peculiarities of a screen will interact with the peculiarities of the projection and none of us can tell which is which because they are "entangled" (to use this horrendous word). Let us please not fall into the trap by thinking that classical physics = realism. But let us also not fall into the trap thinking classical and quantum are worlds apart. Perhaps that the same philosophical analysis for the difference between screen and projection can also be applied to classical and quantum. I have a paper Phys Rev E 51 5151-5154 (1995) where I show that Maxwell's classical electromagnetic field equation can produce a quantum Dirac equation.

Yours,
Han

 

[hgeurdes]

First, I would like to welcome you to PhysicsForums, Han!

Thanks.

... If you think about it logically, you will realize that there are many with highly complex issues

with work that is clearly against the mainstream, so asking other scientists to "explain what is wrong" is really putting the shoe on the wrong foot.

Indeed but I had not much options left. I simply wanted to make public that there is
something wrong with BT. The trick 'what is wrong (with Bell's theorem) ' was applied to my argumentation many times. In this post I will enter your:

So let's talk about a useful model.

Ok, but please indulge an amount of speculation.

Perhaps you may know that in 1955 Lee and Yang predicted and in 1956 Wu et all discovered, parity non-invariance in weak-interaction. In addition, e.g. Robert Foot and Paolo Ciarcelutti studied a mirror matter explanation for dark matter gravity anomalies. Okun has written a readable history of the mirror matter hypothesis.

Foot and Ciarcelutti's idea (in turn derived from Lee and Yang's and Okun's work too) comes down to a 'mirror' matter universe that only has gravity interaction with ours. The mirror matter universe restores the Lorenzt invariance for the LT parity on a global scale where 'locally' parity LT is violated. Granted the existence of dark mirror matter has only been inferred (CoGENT experiments) and never truly confirmed. Of course a debate on the interpretation of gravity anomalies is still going on.

I use only a certain part of the hypothesis of dark mirror matter to explain the EPR paradox physically. This part follows from the Phys Rev E 51 5151-5154 (1995) paper. I have demonstrated in a similar way that Einstein's field equations for weak gravity can be
transformed into a Dirac form too. The crucial part is the d'Alembertian expression (equation (7) in the PRE). This implies, in a physical picture, that there is a gravity-to-quantum and a quantum-to-gravity transformation possible in weak gravity fields.

Now let us take a look at Hardy's paradox where 'measurement after mutual annihilation of positron and electron' is believed to be a proof that there are no premeasurement characteristics as proposed by Einstein. Hence, the Hardy argument argues like BT against local hidden causality. However, if in Hardy's experiment the hidden characteristics of electron and positron transform in the annihilation to a gravity anomaly, it escapes annihilation. If subsequently this gravity anomaly transforms back into a quantum form detectors can (perhaps) be triggered. This, I believe, is a model where locality and causality occur that connects to previous experiments (Wu) that is supported by mathematical theory (PRE paper and transformation) and has a counterpart in astrophysics and cosmology (dark matter).

 

[hgeurdes]

...
Discussion of this paper probably doesn't belong here, but as long as we are on the subject I will ask you the same question I ask everyone: what is realism if it is not per the EPR/Bell definition? Which to me is usually the crux of various arguments.
...

This question is important enough for a new posting.

The answer to the question is simple. The EPR hidden locality and causality restoring variables or extra parameters but predicted by relativistic quantum physics itself (i.e. the parity non-conservation). If I recall properly Okun has a paper in arXiv in which he suggests this possibility.

 

[DrChinese]

This question is important enough for a new posting.

The answer to the question is simple. The EPR hidden locality and causality restoring variables or extra parameters but predicted by relativistic quantum physics itself (i.e. the parity non-conservation). If I recall properly Okun has a paper in arXiv in which he suggests this possibility.

http://arxiv.org/abs/hep-ph/0606202

I saw the above, but again, I think this is too esoteric for discussion here. I don't think you really addressed my question about a definition of realism either. If realism (or whatever label you place on it) is not what Bell says it is (which I consider as simply following EPR), what is it?

 

[hgeurdes]

http://arxiv.org/abs/hep-ph/0606202
I saw the above, but again, I think this is too esoteric for discussion here.

Ok I can live with that.

I don't think you really addressed my question about a definition of realism either. If realism (or whatever label you place on it) is not what Bell says it is (which I consider as simply following EPR), what is it?

That is another matter and refers to an old philosophical debate. The definition of realism is really too esoteric indeed (but very much to the point at the same time). I think we would agree that 'realism-as-applied-to-the-problem' in a narrow and operational sense is the postulation of extra hidden variables.

Btw I am not at all saying that realism is not what Bell says it is. Realism is just a word and many philosophers have not a clue what is meant anyway. For instance in a Wittgensteinian way one could cross a border and stop make sense but still use words that suggest some sense (or semiotics) when talking about reality.

My argument turns against '...mathematical activities leading to an inequality'. One may postulate a correlation integral like Bell did. It is a general expression for statistical correlation (expectation covariance realy, the fact that E(A)=E(B)=0 and Var(A)=Var(B)=1 makes Bell's P(a,b)=E(AB) into a correlation). But may one generalize to a theorem using Bell's mathematics? That is the question.

And may one subsequently call experiments based upon that theorem 'conclusive evidence against LHV models' ? I think I showed that the answer is 'no'. To get at that point I did not need realism at all. I just used what Bell implemented. So why do you think it is essential to have a clear definitive conception of realism. It almost looks like an 'after the fact' requirement whereas science is possibly never finished and by definition possibly always 'before the fact'.

Either one accepts that in order to discuss about reality (realism) a whole lot more needs to be done before we even start making sense, or, one skips the whole debate about reality and notes that whatever it is, it is not in Bell's E(AB) inequalities like CHSH. Please explain why you think what Bell says is equal to what EPR meant to say about hidden locality and causality restoring variables and processes.

 

[Paolo 2008]

I am writing a theory (if it may be called theory) on the relationship between subatomic particles and causality. Now, I have a question that I hope someone may answer for me. Is the existence of Dark Matter and/or Dark Energy a problem to Bell's theorem? What I mean to say is, Do Dark Matter and Dark Energy follow locality and don't violate Bell's inequality?...or then again, can someone please explain Bell's inequality with a hypothetical detector for Dark Matter as one of the attributes to measure?

 

[hgeurdes]

I am writing a theory (if it may be called theory) on the relationship between subatomic particles and causality. Now, I have a question that I hope someone may answer for me. Is the existence of Dark Matter and/or Dark Energy a problem to Bell's theorem? What I mean to say is, Do Dark Matter and Dark Energy follow locality and don't violate Bell's inequality?...or then again, can someone please explain Bell's inequality with a hypothetical detector for Dark Matter as one of the attributes to measure?

Dear Paolo, Thanks for your question. Indeed I have reason to believe that there is a relation between dark matter and locality. I think dark matter, in the form of (a.o. Robert Foot and Paolo Ciarcelluti) mirror matter solves the problem of causality and locality in the sense that Einstein wanted it and derives from quantum theory itself.

In 1955 Lee and Yang solved a puzzle in nuclear weak interaction by postulating parity non-conservation. This was later experimentally confirmed by Wu et al in beta-decay of Co. In order to have an overall Lorentz invariance (parity is a Lorentz transformation) a sector of the cosmos was postulated that contained mirror matter, i.e. the parity inverted form of our O matter. There only exist a gravity interaction between O matter and M matter (plus weak photon mixing).

I met Paolo Ciarcelluti two times in Luik at the University and he told me that this idea is viable. Now I have in arXiv (http://arxiv.org/abs/1105.3348) a, mostly history of physics - like, paper in which I show that Einstein's gravity field and Dirac's relativistic quantum mechanical equation are equivalent for a weak gravity field. The matter is taken in a larger perspective in that paper but in essence this is that gravity transforms into a Dirac form and a Dirac form transforms into gravity (and possibly electromagnetism ).

Now if one takes a look at Hardy's experiment, a double Mach-Zehnder interferometer annihilation, which essence it is that particles are being measured after they have mutually annihilated each other, then there may arise the following physical picture.

In the Hardy annihilation of e.g. electron and positron, a hidden characteristic of the electron and of the positron escapes annihilation by transformation to a weak gravity(Minkowski metric) disturbance. That is where the mirror matter sector comes in because by transformation into gravity there is an exchange of matter between O and M sector (in the form of gravity disturbance). This escape via gravity transformation into mirror matter is not a stable situation and the matter that escaped annihilation returns via gravity-to-Dirac-form back to the O sector and subsequently trigger the detector. In this way the detector of the electron branch and of the positron branch in the double Mach-Zehnder interferometer is simultaneously triggered by remenants that escaped annihilation through the M sector by way of transformation to gravity disturbance.

Now this also 'goes' for EPRBA type of experimentation when one provides aims to provide a consistent LHV picture to the rejection of the validity of Bell's theorem in mathematical form (ASTP 4(20) 495-499 (2010) and e.g. http://arxiv.org/abs/0705.3378 together with the basis of a computer model that violates CHSH that I can send to you if you want).

It must come as no big surprise that mainstream orthodoxy in physics does not like, to say the least, what is being demonstrated here. Please do note however, that it was only *rejected* without much good reason anyway. It was *never* proved wrong. Even by the most severe attacks of e.g. Prof. Gill. Most of the time mainstream critics avoid argumentation altogether by claiming the proposal to be too difficult. That may be the case. I think by the same token my proposal, in line with Einsteins local hidden value idea, is the most physical of all explanations. Namely one can set up a EPRBA type of experiment (e.g. an Aspect like experiment with mass carrying particles e.g. protons like the EPRBA of Lamehi-Rachti and Mittig ) near a DAMA/LiBra measurement site and see if the fluctuations in the DAMA measurements correlate with possible fluctuations in the found quantum correlation. In addition, the explanation given above contains mostlly -be it speculative- elements from existing physical theories. Quantum mechanics provides parity in weak interaction, cosmology of dark matter provides observations in gravity (anomalies still) and last but not least Robert Foot and Paolo Ciarcelluti came with a consisten picture, in terms of galaxy formation, big bang nucleosynthesis etc, of a mirror sector ( a bi-sector cosmology).

Yours,
Han Geurdes

 

[DrChinese]

...It must come as no big surprise that mainstream orthodoxy in physics does not like, to say the least, what is being demonstrated here. Please do note however, that it was only *rejected* without much good reason anyway. It was *never* proved wrong. Even by the most severe attacks of e.g. Prof. Gill. Most of the time mainstream critics avoid argumentation altogether by claiming the proposal to be too difficult. ...

Nearly every writing physicist* has tales of woe regarding the publishing and acceptance of their work. Surely you must consider the practical nature of the situation (thousands of new papers a month) as being as big an obstacle as your perception of having a "David vs Goliath" battle with the scientific establishment. For example, I would say there are dozens of new "Bell is wrong" critiques per year. Only one of which, to date, has impressed me (that being the work of the De Raedt team, which is a computer simulation).

(*including this writer. )