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Richard Gill, Leiden University, Netherlands
31 May, 2024
Adventures in wonderland
Or: Richard down two rabbit holes
Open Peer Review on Qeios
Bell's theorem is an exercise in the statistical theory of
causality
Richard Gill1
1 Leiden University
Funding: No specific funding was received for this work.
Potential competing interests: No potential competing interests to declare.
Abstract
In this short note, I derive the Bell-CHSH inequalities as an elementary result in the present-day theory of statistical
causality based on graphical models or Bayes' nets, defined in terms of DAGs (Directed Acyclic Graphs) representing
direct statistical causal influences between a number of observed and unobserved random variables. I show how
spatio-temporal constraints in loophole-free Bell experiments, and natural classical statistical causality considerations,
lead to Bell's notion of local hidden variables, and thence to the CHSH inequalities. The word “local” applies to the way
that the chosen settings influence the observed outcomes. The case of contextual setting-dependent hidden variables
(thought of as being located in the measurement devices and dependent on the measurement settings) is automatically
covered, despite recent claims that Bell's conclusions can be circumvented in this way.
Richard D. Gill
Mathematical Institute, Leiden University
Qeios, CC-BY 4.0 · Article, March 21, 2023
https://www.qeios.com/read/K40UP4
https://arxiv.org/abs/2211.05569
https://www.mirror.co.uk/news/uk-news/lucy-letby-activist-who-argues-32151666
EXCLUSIVE: Lucy Letby activist who argues baby killer is
innocent gives talk at university.
Academic Richard Gill, who claims prosecution evidence against baby
killer Lucy Letby was bogus, was allowed to give a talk to maths
students at Liverpool University.
A professor who campaigns to free Lucy Letby was allowed to lecture
students near the hospital where she murdered babies.
Academic Richard Gill claims prosecution evidence was bogus and trolls
an NHS doctor who helped secure the serial killer’s conviction. But Gill’s
alarming web posts did not deter Liverpool University from inviting him to
lecture.
It is 17 miles from the Countess of Chester Hospital, where Letby was a
nurse. Gill, 72, a professor of statistics, travelled from his home in Holland for
the class at the department of mathematical scientists.
Although he did not mention the Letby case during his talk last Wednesday,
he later boasted online he had also visited Chester, and had given “an
informal talk on the Letby case”. Letby, 34, was jailed for life in August after a
10-month trial for murdering seven tots and attempting to kill six.
• Nodes stand for random variables
• Arrows stand for direct “causal” dependence: they specify the
causal structure of the following statistical simulation:
REPEAT: Till there are none left, pick a node whose parents
have all been instantiated, and simulate its value using a
conditional probability distribution for chosen node, given
values of all parent nodes
• Corollary: root nodes stand for some variables which
are all statistically independent of one another
Encapsulate assumptions about statistical dependencies and
independencies between a bunch of random variables (also conditional …)
Causal models based on DAGs
Really, the less said about it the better
Marian Kupczynski’s model
https://www.mdpi.com/2624-960X/5/2/32
• Let settings A, B be outcomes of measurements of spin in x
direction of two ancillary spin-half particles prepared in spin-up (z
direction) state
• So these models are allowed inside conventional quantum
information theory, do not require “free will” or “sentient agents
outside of quantum theory”
• As Sabine Hossenfelder (C) (TM) likes to say (and I agree), “super
determinism” is just a derogatory term for “determinism”
• Tim Palmer “thins” conventional QIT by deleting certain triples
(state, measurement)
“How can we be sure these models are
consistent with the laws of quantum physics?”
Tim Palmer’s model
• This is a conspiracy theory, dressed up in sophisticated maths
which no one can quickly understand (ie: obfuscation)
• Bell’s theorem does not depend on any conception that
measurement settings are set exactly
• Palmer asks us to believe that when we set a switch by hand to an
“up” or “down” position, them the trembling of our
fi
nger has an
immediate e
ff
ect at huge distances on the response of a
photodetector
• He does not give us any physical mechanism whereby this should
be expected
• Even if you believe in determinism, you do not believe this
“How can we be sure these models are
consistent with the laws of quantum physics?”
Tim Palmer’s model
• My
fi
nal questions to Tim Palmer on queios.com:
• Dear Tim, Thanks for your comments. As you know, I fundamentally disagree with you. I
planned for a long time to write up a careful analysis and refutation of your arguments, but
right now I’m rather tied up with
fi
ghting the biggest miscarriage of justice in UK history ever:
the Lucy Letby case. In particular, we are developing causal models for the events at
Countess of Chester Hospital to show that beyond reasonable doubt, Lucy is innocent. You
might
fi
nd your claim that these models are inconsistent with the laws of physics soon being
adopted by the hysterical mobs incited by the UK tabloids, so: maybe we will be reading
about it in the Daily Mail or The Telegraph, any day soon! I hope soon to be visiting Oxford so
we can discuss your theory of quantum physics (not my theory of Lucy Letby) at the
blackboard. Would you even like to invite me to give a seminar? That is a causal intervention
which you could make, if (FAPP) you have free will, that will force me to write up my ideas
properly. Yours, Richard.
• Actually, Tim’s model can also be represented in a causal model, according to his claim that
his model reproduces quantum mechanics in a mechanistic way. It is obtained by adding just
one node to my graph, and two arrows from that node to my graph’s two root nodes. The
new root node could be called “the deep past, including the laws of quantum mechanics”. It
is a very powerful model.
How many angels can dance on the tip of a pin?
End of quantum talk
• Gerard ’t Hooft anecdote concerning the case of Lucia de Berk
• Without intervention of Gerhard ’t Hooft, Lucia de Berk might still
be in jail
• Watch “Lola runs”. You can make a di
ff
erence
• Your UK colleagues can more easily make a di
ff
erence, than you
can, and you can in
fl
uence them
• Oh yes, you can! Butter
fl
y e
ff
ect
• Or do you really believe in superdeterminism? In predestination?
Does that absolve you from making moral choices?
Yes, everything is connected
So, did those rabbit holes meet?
• Summary: Theorem, the model is equivalent to a deterministic
model where each node equals a deterministic function of parent
nodes and an independent random “innovation”
• So we can de
fi
ne the counterfactual outcomes “what each node
would have been had the parent nodes been di
ff
erent”
• Now just follow Bell’s - CHSH proof … but please rewrite it in the
modern notation of probability theory
• Basic fact: for X1, X2, Y1, Y2 = +/-1
X1 Y1 - X1 Y2 - X2 Y2 - X2 Y1 = -2 or +2
Please read the paper
Appendix: the proof

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Richard's entangled aventures in wonderland

  • 1. Richard Gill, Leiden University, Netherlands 31 May, 2024 Adventures in wonderland Or: Richard down two rabbit holes
  • 2. Open Peer Review on Qeios Bell's theorem is an exercise in the statistical theory of causality Richard Gill1 1 Leiden University Funding: No specific funding was received for this work. Potential competing interests: No potential competing interests to declare. Abstract In this short note, I derive the Bell-CHSH inequalities as an elementary result in the present-day theory of statistical causality based on graphical models or Bayes' nets, defined in terms of DAGs (Directed Acyclic Graphs) representing direct statistical causal influences between a number of observed and unobserved random variables. I show how spatio-temporal constraints in loophole-free Bell experiments, and natural classical statistical causality considerations, lead to Bell's notion of local hidden variables, and thence to the CHSH inequalities. The word “local” applies to the way that the chosen settings influence the observed outcomes. The case of contextual setting-dependent hidden variables (thought of as being located in the measurement devices and dependent on the measurement settings) is automatically covered, despite recent claims that Bell's conclusions can be circumvented in this way. Richard D. Gill Mathematical Institute, Leiden University Qeios, CC-BY 4.0 · Article, March 21, 2023 https://www.qeios.com/read/K40UP4 https://arxiv.org/abs/2211.05569
  • 3.
  • 5. EXCLUSIVE: Lucy Letby activist who argues baby killer is innocent gives talk at university. Academic Richard Gill, who claims prosecution evidence against baby killer Lucy Letby was bogus, was allowed to give a talk to maths students at Liverpool University. A professor who campaigns to free Lucy Letby was allowed to lecture students near the hospital where she murdered babies. Academic Richard Gill claims prosecution evidence was bogus and trolls an NHS doctor who helped secure the serial killer’s conviction. But Gill’s alarming web posts did not deter Liverpool University from inviting him to lecture. It is 17 miles from the Countess of Chester Hospital, where Letby was a nurse. Gill, 72, a professor of statistics, travelled from his home in Holland for the class at the department of mathematical scientists. Although he did not mention the Letby case during his talk last Wednesday, he later boasted online he had also visited Chester, and had given “an informal talk on the Letby case”. Letby, 34, was jailed for life in August after a 10-month trial for murdering seven tots and attempting to kill six.
  • 6.
  • 7. • Nodes stand for random variables • Arrows stand for direct “causal” dependence: they specify the causal structure of the following statistical simulation: REPEAT: Till there are none left, pick a node whose parents have all been instantiated, and simulate its value using a conditional probability distribution for chosen node, given values of all parent nodes • Corollary: root nodes stand for some variables which are all statistically independent of one another Encapsulate assumptions about statistical dependencies and independencies between a bunch of random variables (also conditional …) Causal models based on DAGs
  • 8. Really, the less said about it the better Marian Kupczynski’s model https://www.mdpi.com/2624-960X/5/2/32
  • 9. • Let settings A, B be outcomes of measurements of spin in x direction of two ancillary spin-half particles prepared in spin-up (z direction) state • So these models are allowed inside conventional quantum information theory, do not require “free will” or “sentient agents outside of quantum theory” • As Sabine Hossenfelder (C) (TM) likes to say (and I agree), “super determinism” is just a derogatory term for “determinism” • Tim Palmer “thins” conventional QIT by deleting certain triples (state, measurement) “How can we be sure these models are consistent with the laws of quantum physics?” Tim Palmer’s model
  • 10. • This is a conspiracy theory, dressed up in sophisticated maths which no one can quickly understand (ie: obfuscation) • Bell’s theorem does not depend on any conception that measurement settings are set exactly • Palmer asks us to believe that when we set a switch by hand to an “up” or “down” position, them the trembling of our fi nger has an immediate e ff ect at huge distances on the response of a photodetector • He does not give us any physical mechanism whereby this should be expected • Even if you believe in determinism, you do not believe this “How can we be sure these models are consistent with the laws of quantum physics?” Tim Palmer’s model
  • 11. • My fi nal questions to Tim Palmer on queios.com: • Dear Tim, Thanks for your comments. As you know, I fundamentally disagree with you. I planned for a long time to write up a careful analysis and refutation of your arguments, but right now I’m rather tied up with fi ghting the biggest miscarriage of justice in UK history ever: the Lucy Letby case. In particular, we are developing causal models for the events at Countess of Chester Hospital to show that beyond reasonable doubt, Lucy is innocent. You might fi nd your claim that these models are inconsistent with the laws of physics soon being adopted by the hysterical mobs incited by the UK tabloids, so: maybe we will be reading about it in the Daily Mail or The Telegraph, any day soon! I hope soon to be visiting Oxford so we can discuss your theory of quantum physics (not my theory of Lucy Letby) at the blackboard. Would you even like to invite me to give a seminar? That is a causal intervention which you could make, if (FAPP) you have free will, that will force me to write up my ideas properly. Yours, Richard. • Actually, Tim’s model can also be represented in a causal model, according to his claim that his model reproduces quantum mechanics in a mechanistic way. It is obtained by adding just one node to my graph, and two arrows from that node to my graph’s two root nodes. The new root node could be called “the deep past, including the laws of quantum mechanics”. It is a very powerful model. How many angels can dance on the tip of a pin? End of quantum talk
  • 12. • Gerard ’t Hooft anecdote concerning the case of Lucia de Berk • Without intervention of Gerhard ’t Hooft, Lucia de Berk might still be in jail • Watch “Lola runs”. You can make a di ff erence • Your UK colleagues can more easily make a di ff erence, than you can, and you can in fl uence them • Oh yes, you can! Butter fl y e ff ect • Or do you really believe in superdeterminism? In predestination? Does that absolve you from making moral choices? Yes, everything is connected So, did those rabbit holes meet?
  • 13. • Summary: Theorem, the model is equivalent to a deterministic model where each node equals a deterministic function of parent nodes and an independent random “innovation” • So we can de fi ne the counterfactual outcomes “what each node would have been had the parent nodes been di ff erent” • Now just follow Bell’s - CHSH proof … but please rewrite it in the modern notation of probability theory • Basic fact: for X1, X2, Y1, Y2 = +/-1 X1 Y1 - X1 Y2 - X2 Y2 - X2 Y1 = -2 or +2 Please read the paper Appendix: the proof