Comments about the article in Nature: Bell's theorem still reverberates

Following is a discussion about this article in Nature News Vol 510 26 June 2014, by Howard Wisemann
To read the article select:
See also: Two Bell's Theorems of John Bell by Howard M.Wisemann
For a discussion about this subject in the discussion group sci.physics.research select this link:!topic/sci.physics.research/NXIuEEsAoUs In the last paragraph I explain my own opinion.


The article starts with the sentence:
In 1964 John Bell proved mathematically that certain quantum correlations unlike all other correlations in the Universe cannot arise from any local cause.
Meaning read faster than light signals in order to explain.
See also Reflection part 1 - "Bell inequality"
Generally speaking in science you perform experiments to uncover the laws of physics. The laws of physics are in many cases mathematical equations of a process subject to change. To develop these laws you perform different experiments under different conditions i.e. with different parameters.
What this means that you cannot uncover the laws of physics purely by means of mathematics without an actual experiment under consideration, in this case an experiment which shows quantum level behaviour like the decay of an radio-active element.
Next we read:
This theorem has become central to both metaphysics and quantum information science.
A clear explanation what metaphysics is, is required. The same what is meant with quantum information.
But 50 years on, the experimental verifications of these quanum correlations still have 'loopholes' and scientists and philosophers still dispute exactly what the theorem states.
This leaves the door open that the theorem is wrong.
By starting from experiments I think you make things easier.
It is the same with the question: Trough which hole does a single photon go. You should test this first one hole (different positions relative to the source) and secondly with many different distances between the two holes.
Quatum theory does not predict the outcomes of a single experiment but rather the statistics of possible outcomes.
The outcome of playing roulette is also based on statistics. The outcome of each individual experiment can not be predicted.
For experiments on pairs of 'entangled' quantum particles Bell realized that the predicted correlations between outcomes in two well seperated laboratories can be profoundly mysterious (See 'How entanglement makes the impossible possible')
Unfortunate the document does not explain what 'entangled' quantum particles are, nor how they are created nor how they are tested.
It is easy to write and discuss in theory a process which creates two particles, each having a spin in opposite direction (negative correlation) completely independent from the distance between the two particles. The problem comes to actual perform such an experiment and to uncover how accurate this description actual is.
Accordingly to Bell this leaves two options for the nature of reality:
The first is that reality is irreducibly random, meaning that there are no hidden variables that "determine the results of individual measurements"
The reality is what it is. To declare the reality as random reflects the fact we as human often can not perform two tests identical, meaning that the results are different every time. A typical cases are collisions between particles. A second problem is that the process of measuring has its own problems because by doing that you can influence the reality.
The second option is that the reality is 'non-local' meaning that "the setting of one measuring device can influence the reading of another instrument, however remote"
To call the reality local or non-local in relation to measuring, is also a human interpretation.
Entanglement can mean that two particles have a negative correlation in spin direction. To establish that you have to perform 1000's of almost identical experiments a certain distance away from each other. These 1000 experiments should be performed under different angles.
The central theme is that measuring one should not influence the other.

The defition of the two options is not clear specific because they both refer to measuring which is a human activity

Most physicist are localists: they recognize the two options but choose the first, because hidden variables are by definition empirically inaccessible.
When you want to make any progress in science you have to start from a real experiment.
Other physicists (the non-local camp) dispute that there are two options, and insists that Bell's theorem mandates non-locality.
Any (i.e. Bell's) theorem should reflect the reality. That means a description independent of any human involvement. The difficulties involved in the measurement process should be discussed separately.

Free Choice

Many localists cite Albert Einstein's 1905 principle of relativistic causality as a reason to reject non-locality. This principle states that causal influences cannot propagate faster than light.
In fact you need specific experiments to test that this principle is violated. You cannot use the "Bell inequality" theorem, which is strictly speaking a mathematical equation.
Faster-than-light communication has never been observed.
Which strictly speaking does not mean it is not possible.
Its impossibility follows from Einstein's principle of relativistic causality and the following axiom of causation: If an event is seen to depend statistically on a freely chosen action, then that action is a cause of that event.
The last part is correct but says nothing about the speed involved.

Another Theorem

Bell himself was a non-localist, an opinion he first published in 1976, after introducing a concept "local causality" that is subtly different from the locality of the 1964 theorem.
IMO the "Bell inequality" it self has nothing to do with locality. Locality becomes an issue when you want to understand "quantum entanglement" ie the correlation between the two photons or protons.
Colloquially this "principle of common cause" says that correlations have explanations.
That is true.
The issue is the thought experiment discussed in the november issue of Scientific American of 1979
Page 134 of that article shows a sketch of an thought experiment with protons.
           Detetector A+                     Detector B+     
                  _                               _
                 |\                               /|
                   \                             /
                    \                           /
                 Analyzer 1 <--- Source ---> Analyzer 2
                    /                           \
                   /                             \
                 |/_                             _\|
            Detetector A-                      Detector B-
				Picture 134
This experiment shows (negative) correlation when the angle between the analyzers is zero. That means the protons or photons are measured in the same plane.
The question is how do you explain this correlation (i.e. entanglement).
The answer is the common cause is the source, independent if the protons or photons are measured (or disturbed).
In 1976, Bell proved that his new concept of local causality (based implicity on the principle of common cause) was ruled out by Bell correlations.
IMO you can not explain the physical reality (how it behaves) by a mathematical statement (i.e. equation).
The only way is finally by performing experiments.
It is unfortunate that quantum scientists seldom distinquish the 1976 theorem from the 1964 theorem.
I think the main reason is because the difference are very subbtle.
What makes it much simpler if Bell clear made the statement that the 1964 theorem is wrong and explained why. In that case you do not have to reconcile the camps.

Reconciling the camps

The contradictory claims by the two camps thus arise because they mean different things by 'Bell's theorem' and diffrent things by 'local' (or 'non-local')
This keeps you thinking: What is science
Thus Bell's 1976 theorem can be restated as: either causal influences are not limited to the speed of light or events events can be correlated for no reason.
The question is for what type of experiments is this 1976 theorem important i.e. does it have to be taken into account in order to understand what is happening.
The article does not show this detail.

The path forward

Bell correlations can be seen as a problem or an opportunity
They are a mathematical statement. The author should clearly specify for what type of process or experiment they are relevant.
They present us which a dilemma; each of the principles at stake (relativistic causality and common cause) underpins a vast mesh of scientific inference and intuition and yet must be forgone. (give up)
Which one ?
As of now there are no loophole-free Bell experiments.
What is a loophole-free experiment ? Any experiment is an experiment. Immediate next we read:
Experiments in 1982 by a team led by Alain Aspect using well separated detectors with settings changed just before the photons were detected suffered from an 'efficiency loophole' in that most of the photons were not detected.
Of course to do any experiment when most protons or photons are not detected and when you are sure they should be detected does not make sense. That is not a loophole.
This allows the experimental correlations to be reproduced by (admittedly, very contrived) local hidden variable theories.
The results should be disposed.
The article ends with the sentence:
Such an Earth-Moon experiment is a worthy challenge for the next 50 years
First you should solve the most simple experiments here on earth and come to an agreement when correlations are detected that the cause is in the process happening inside the source and have nothing to do if anything is measured.

Bell Correlations

How Entangelment makes the imposssible possible

This box starts with the following text:
Quantum entanglement can link the quantum states of particles even when they are seperated by long distances
That may be true, but the article does not explain what it means nor how this is done.
Consider an impossible square -
For example if I ask for the second row and the third colomn and Rowan says 001 (odd answer) then Colin just has to select an (even) answer with 1 as the middle entry either 011 or 110
Suppose Colin selects 011
The following picture shows all the 16 "impossible squares" with the answers row two is 001 and column three is 011.
000  000  000  000  010  010  010  010  100  100  100  100  110  110  110  110
001  001  001  001  001  001  001  001  001  001  001  001  001  001  001  001
001  011  101  111  001  011  101  111  001  011  101  111  001  011  101  111

 0    1    2    3    4    5    6    7    8    9    10   11   12   13   14   15
 X                   X    x         X    X         X    X                   X             
                                  Picture 1
Investigating the 16 possiblities reveals that in the cases marked with an X one row or one column is wrong. In the cases 0, 5 10 and 15 one row is even. In the cases 4, 7, 8 and 11 one column is odd. In each of these cases when you randomly select a row and a column in 3 out of 9 you do it wrong.
In all the other 8 cases either 2 rows and 1 column (1,2,13 and 14) or 1 row and 2 colums ( 3,6,9,and 12) are wrong. In each of these cases when you randomly select a row and a column in 7 out of 9 you make a wrong selection.
This means when Rowan and Colin start with a bag which contains all "impossible squares" and randomly select one, in 80 out of 144 cases their answer is wrong and in 60 out of 144 cases their answer is correct.

The following picture shows based on the four possible correct answers for Rowan and as a function of which row and column I have selected, what the correct answers for Colin are

  Rowan          Colin
   001    000  011
   010    000  011  
   100              101  110
   111              101  110 
  row 1       column 1 
  Rowan          Colin
   001    000       101
   010    000       101  
   100         011      110
   111         011      110 
  row 2       Column 1 
  Rowan          Colin
   001              101  110
   010    000  011  
   100    000  011
   111              101  110 
  row 1       Column 3 
  Rowan          Colin
   001         011      110
   010    000       101  
   100    000       101
   111         011      110 
  row 2       Column 3 
Picture 2
What Picture 2 shows it that based which answer Rowan has selected, Colin has 50% chance of giving the correct answer.
So you agree to the trial as suggested; you ask questions to Rowan in one room and an assistant to Colin in the other room. To your consternation, Colin and Rowan give consistent answers every time. etc
They are using pairs of 'entangled' quantum particles - each pair was jointly prepared in the same way, and then one kept by Rowan an one by Colin. etc
By the 'magic' of quantum entanglement their results are correlated precisely so as to simulate an impossible square.
The biggest problem of the article is that no details are shown how the actual experiment is performed.

Reflection part 1 - "Bell inequality"

The "Bell inequality" is strictly speaking a mathematical equation.
The "Bell inequality" looks the same as when you throw dice.
n(1) < or = n(2) + n(3)
n(1) meaning the number of times you throw a "1" out of 1000 throws.
Generally speaking n(1) = n(2) = n(3) with the "=" sign meaning more or less. That explains the inequality.

The same subject is also discussed in Scientific American of November 1979 by Bernard d'Espagnat
The article explains that there are two theories: The topic of the article is that both can be used to describe the same experiment but that the predictions are different, implying that one is wrong.
The underlying reason is that both are completely different.
There are many problem with the article:

Reflection part 2 - "Impossible square"

The object of the experiment is to falsify the claim that Rowan and Colin have a large supply of these "impossible squares".
In the actual experiment both Rowan and Colin are locked up in a separate room. In each trial I will reveal one to Rowan and Rowan will answer me what the row contains (i.e. a binary number with an odd number of one's). My assistant will reveal one column to Colin and Colin will answe what that column contains (i.e a binary number with an even number of one's).
There are three ways to perform this experiment.
  1. With "Impossible squares". That means during each trial Rowan and Colin have to exchange the "Impossible square" and actual use the "Impossible square" to derive their answer.
    What Picture 1 shows that the best "Impossible squares" have still one row or one column wrong. That means in 3 out of every 9 trials one answer is wrong.
    If your "Impossible square" has at least one row and one column correct than this answer is 80 out of 144.
  2. Without "Impossible squares". That means Rowan selects randomly a row (odd number) and Colin selects randomly a column (even number). In both cases their individual answers are correct. However in 50% of the cases their answers do not match based on the row I have selected and the column my assistant has revealed.
  3. Without "Impossible squares" but with quantum entanglement as discussed in the box.
    To do this is IMO is impossible.
    The document does not explain how this is done using "quantum entanglement"
    The following table shows the problem involved assuming that Rowan always gives the same answer. (The simplest case)
     row  column  Rowan  Colin     row  column  Rowan  Colin    row  column   Rowan   Colin   
      1      1     001    000       2      1     001    000      3      1      001     000
      1      2     001    000       2      2     001    000      3      2      001     000  
      1      3     001    110       2      3     001    011      3      3      001     011
                                         Picture 3A
    What Picture 3A shows is that all the answers from Colin are correct but that they depent which row I have selected, which is unknown to Colin. This is also true the other way around.
    How is this done in practice?

    The following table shows the problem involved assuming that Rowan always gives the same answer for the same row I have selected.

     row  column  Rowan  Colin     row  column  Rowan  Colin    row  column   Rowan   Colin   
      1      1     001    000       2      1     010    000      3      1      100     011
      1      2     001    000       2      2     010    011      3      2      100     000  
      1      3     001    110       2      3     010    000      3      3      100     000
                                         Picture 3B
    What Picture 3B shows is that all the answers from Colin are correct but that they depent which row I have selected i.e. Rowan's answer, which is unknown to Colin. This is also true the other way around.
    How is that answer known in practice?
    IMO this is not possible using quantum entanglement.
    • If you supply a list of row numbers for 10 trials to Rowan and ask him to write down the answers on that same paper.
    • Your assistent supplies a separate list of column numbers for 10 trials to Colin and ask him to write down the answers on that same paper.
    IMO it does not matter how quick each does his 10 trials but as long as they do not communicate IMO when you check the results you will find some errors using quantum entanglement.
    As an extra test you repeat the same experiment with the only difference that you and Colin switch sides and the same with Rowan and your assistant to see if any cheating is involved.

There are two additional comments about this box:

Reflection part 3

The article by Bernard d'Espagnat is clear and easy understand. This article misses this clearity. Sorry.
The worst is the box with the impossible square.

For more about the same subject read the following articles in Nature:

  1. Guaranteed Randomness & Random numbers certified by Bell's theorem. In both articles of 15 April 2010 problems with true random numbers are discussed.
  2. Quantum Quest In this document of 12 September 2013 the solution over the paradoxes of Quantum Theory are discussed. Now a few of them are trying to reinvent it.
  3. Packet man Book review by Graham Farmelo (delights in study of Albert Einstein's contribytions to quantum theory) of the book "Einstein and the Quantum: The Quest of the Valiant Swabian". By A. Douglas Stone.
  4. QBism puts the scientist back into science In this document of 27 March 2014 the advantage of QBism to explain "Quantum Mechanics" (action at a distance) and "the Now" are explained
  5. The ultimate physical limits of privacy In this document of 27 March 2014 secure cryptographic key generating is discussed using entangled photons based on quantum mechanics



Created: 23 July 2014

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