Invited talk at 2014 Växjö quantum foundations conference

1. Lessons from experience:
engaging with quantum
crackpots
Richard Gill
Mathematical Institute, Science Faculty, Leiden University
http://www.math.leidenuniv.nl/~gill
In memoriam Rik Mayal 1958–2014
Växjö, 11 June 2014

2. In memoriam Rik Mayall 1958–2014
There were times when Rik and I were writing together when we almost died laughing. They were
some of the most carefree stupid days I ever had, and I feel privileged to have shared them with
him. And now he's died for real. Without me. Selfish bastard—Ade Edmondson

4. The Name of the Rose
• You are all individuals!
• You are all fascinated (obsessed)
by quantum … !
• You are all quantum crackpots!
Niels Bohr:
How wonderful that we have met with a paradox.
Now we have some hope of making progress.

5. 22 R.D. GILL
moment. The LHV theorist supplies a first run-set of values of (A, A0, B, B0). The
agency reveals the first setting pair, the LHV theorist generates a second run set
(A, A0, B, B0). This is repeated N = 800 times. The whole procedure can be re-
peated any number of times, the results are published on internet, everyone can
judge for themselves.
ACKNOWLEDGEMENTS
I’m grateful to the anonymous referees and to Gregor Weihs, Anton Zeilinger,
Stefano Pironio, Jean-Daniel Bancal, Nicolas Gisin, Samson Abramsky, and Sascha
Vongehr for ideas, criticism, references. . . . I especially thank Bryan Sanctuary,
Han Geurdes and Joy Christian for their tenacious and spirited arguments against
Bell’s theorem which motivated several of the results presented here.
Submitted to the Statistical Science
Statistics, Causality and Bell’s
Theorem
Richard D. Gill
Mathematical Institute, University of Leiden, Netherlands
Abstract. Bell’s (1964) theorem is popularly supposed to establish the non-
locality of quantum physics. Violation of Bell’s inequality in experiments
such as that of Aspect et al. (1982) provides empirical proof of non-locality
in the real world. This paper reviews recent work on Bell’s theorem, linking
it to issues in causality as understood by statisticians. The paper starts with
a proof of a strong, finite sample, version of Bell’s inequality and thereby
also of Bell’s theorem, which states that quantum theory is incompatible
with the conjunction of three formerly uncontroversial physical principles,
here referred to as locality, realism, and freedom.
Locality is the principle that the direction of causality matches the di-
rection of time, and that causal influences need time to propagate spa-
tially. Realism and freedom are directly connected to statistical thinking
on causality: they relate to counterfactual reasoning, and to randomisa-
tion, respectively. Experimental loopholes in state-of-the-art Bell type ex-
periments are related to statistical issues of post-selection in observational
studies, and the missing at random assumption. They can be avoided by
properly matching the statistical analysis to the actual experimental design,
instead of by making untestable assumptions of independence between ob-
served and unobserved variables. Methodological and statistical issues in
the design of quantum Randi challenges (QRC) are discussed.
The paper argues that Bell’s theorem (and its experimental confirma-
tion) should lead us to relinquish not locality, but realism.
AMS 2000 subject classifications: Primary 62P35, ; secondary 62K99.
Key words and phrases: counterfactuals, Bell inequality, CHSH inequality,
Tsirelson inequality, Bell’s theorem, Bell experiment, Bell test loophole,
non-locality, local hidden variables, quantum Randi challenge.
arXiv.org/quant-ph:1207.5103
“In print”: to appear in Statistical Science (2015) special issue on causality

6. Why? Well, it paid off!
• A paper resolving the memory loophole
• A paper on the coincidence loophole which is now even being
cited and used by experimentalists and simulators
• A paper with co-author Anton Zeilinger in PNAS
• The invention of Bell’s fifth position and a paper entitled
Schrödinger’s cat meets Occam’s razor
• A lot of fun and a lot of friends including three trips to Växjö
• A big (invited) survey paper in one of the most important
journals in my field

7. The downside
• “I am interested in proving that Gill is an
algebraically challenged third-rate statistician who
has no background in physics or understanding of
mathematics.”
• “Not even a mathematician, but merely a
statistician”
I wear these accusations as a badge of honour!

8. CRACKPOT
Ψ

9. Some “observations”
• On Bell’s theorem
• On anti-Bellists
• On the difference between mathematics & physics (*)
• On Bell’s theorem
(*) Vive la différence!
The more languages you know, the more human you are.

10. There is no Bell’s theorem
• Clauser, Horne, Shimony & Holt dreamed up a
slogan and called it Bell’s Theorem
• John Bell found an elementary calculus inequality
(i.e. a mathematical triviality; a tautology) and
called it “my theorem” or “the theorem”
Niels Bohr: The opposite of a correct statement is a false statement.
But the opposite of a profound truth may well be another profound truth.
Albert Einstein: As far as the laws of mathematics refer to reality, they are
not certain; as far as they are certain, they do not refer to reality.

11. Logic is difficult
• Bell proved a theorem that a certainly inequality
could not be violated
• Bell was delighted that experiment had violated
(or could be expected to violate) his inequality
XXX sees this as proof that Bell’s theorem is false

12. Almost no quantum crackpot
ever read “Bertlmann’s socks”
They read Bell (1964), and some anti-Bell literature

13. Bell’s experiment has nothing to
do with “quantum”, “particles”, …
You might suspect that there is something specially peculiar about spin-particles. In fact there are
many other ways of creating the troublesome correlations. So the following argument makes no
reference to spin-particles, or any other particular particles. Finally you might suspect that the very
notion of particle, and particle orbit, freely used above in introducing the problem, has somehow led
us astray. Indeed did not Einstein think that fields rather than particles are at the bottom of
everything? So the following argument will not mention particles, nor indeed fields, nor any
other particular picture of what goes on at the microscopic level. Nor will it involve any use of
the words ‘quantum mechanical system’, which can have an unfortunate effect on the
discussion. The difficulty is not created by any such picture or any such terminology. It is created
by the predictions about the correlations in the visible outputs of certain conceivable experimental
set-ups.

14. Many physicists have no
idea at all about statistics
• A decent local hidden variables model, tested by
simulation in a stringent (*) CHSH-type experiment,
can easily violate CHSH about 50% of the time
• Experiment cannot violate a mathematical inequality.
Experiment provides statistical evidence against the
hypothesis under which the inequality was derived
(*) = no “experimental” loopholes, only metaphysical
cf. Bertlmann’s socks: random delayed-choice settings;
event-ready-detectors; 100% efficiency

15. Top science journalists have
no idea of statistics
• The probability the Higgs doesn’t exist is less than
3 x 10 –7 (i.e. 5 sigma)
• This is called “the prosecutor’s fallacy” in law, and
it’s called the “fallacy of the transposed conditional”
in logic. In fact, it’s stupid. Yet almost all physicists
think this way.

16. Top QM experimenters have
no idea about logic
• A colleague published a paper in Phys. Rev. Lett. exhibiting
violation of Tsirelson’s inequality in a CHSH experiment
(ie disproof of quantum theory).
• Fortunately there were some loopholes in his experiment!
• A colleague told journalists that one run of his GHZ experiment
could exhibit an outcome impossible under local realism
• Unfortunately one run of his experiment could give an outcome
impossible under his quantum theory. (Fortunately he also knew
about error bars)
• In GHZ experiments, one tries to statistically significantly violate an
inequality

17. The words “the correlation” can mean
any of at least six different things
• Reality, versus model
• Finite N, or infinite N
• The algorithm or formula which defines it, or the
number which comes out
Name vs value.
Different worlds: the real world of physicists,
vs. the real world of mathematicians

18. A loophole-free experiment
is easy!
• The problem is to do the experiment “loop-hole
free” and simultaneously get the exciting results
which you hope for!
• A loop-hole afflicted experiment can often be made
loop-hole free merely by processing the data
differently!

19. Pearle (1970) and the
detection loophole
• X ~ uniform on S 2 … = unit vectors in R 3
• Y ~ uniform on (1, 4), independent of X
• C := (2 – √Y) / √Y
• a and b are Alice, Bob’s settings, in S 2
• A := sign(a . X) if |a . X | > C , otherwise “no detection”
• B := sign(– b . X) if |b . X | > C , otherwise “no detection”
(Open problems)

20. http://rpubs.com/gill1109/S2uniform

21. It’s not the cosine curve,
it’s a surface
• Both Alice and Bob’s settings need to be varied
• The shape of the curve (surface) is easy:
a 50-50 mixture of the singlet state and a completely
random state is a separable state – i.e., a mixture of
product states. So a LHV model giving you half the cosine
is … boring!
• Accardi multiplied outcomes by root 2 in order to violate
CHSH with a LHV
• Sanctuary multiplied N by 2 in order to show Weihs’
experiment does not violate CHSH

22. Conclusions (1)
• We have to be worried about what we are teaching young
physicists
• We have to be worried that (AFAIK) no science journalist ever
yet understood Bell’s theorem (cf. Werner’s ping-pong ball test)
• Communication between different fields of science is difficult
and we need to come more often to Växjö to learn how to do it
• How can we explain Bell’s theorem to smart teenagers?
• Why can’t we explain it to journalists?

23. Conclusions (2)
• There will always be quantum crackpots because
(a) Nature is run according to QM (if not worse),
(b) we can’t “understand” QM
• The QRC (*) (quantum Randi challenge) is a perfect vehicle
both for disengagement and for engagement
• Simulation experiments are perfect vehicle for explaining math/
physics bridge
• Subjective/objective (Bayes/frequentist) “conflict” is irrelevant
but confusing factor (alternative bridges)
• I think we need a paradigm shift (see next slide)
(*) QRC was invented by Sasha Vongehr

24. On understanding
• Our basic physical intuitions and our basic understanding of
elementary mathematics and logic are selected by evolution and hard-
wired in our brains (“Systems of core knowledge”, “embodied
cognition”)
• We also have Bayes’ theorem hard-wired in order, as babies, to learn
language etc, etc, etc; but most of our intuitive (instinctive) probabilistic
intuition for day-to-day decision making is effective but wrong (for good
reasons: efficient computation is not the same as correct computation).
• I believe that we cannot understand QM because we cannot
understand a non-classical physics because “understand” means (as
far as physics is concerned): local realism plus acts of God (magic, …)
• We need a paradigm shift (*)
(*) Sascha Vongehr again; Belavkin; Pearle

25. 22 R.D. GILL
moment. The LHV theorist supplies a first run-set of values of (A, A0, B, B0). The
agency reveals the first setting pair, the LHV theorist generates a second run set
(A, A0, B, B0). This is repeated N = 800 times. The whole procedure can be re-
peated any number of times, the results are published on internet, everyone can
judge for themselves.
ACKNOWLEDGEMENTS
I’m grateful to the anonymous referees and to Gregor Weihs, Anton Zeilinger,
Stefano Pironio, Jean-Daniel Bancal, Nicolas Gisin, Samson Abramsky, and Sascha
Vongehr for ideas, criticism, references. . . . I especially thank Bryan Sanctuary,
Han Geurdes and Joy Christian for their tenacious and spirited arguments against
Bell’s theorem which motivated several of the results presented here.
Submitted to the Statistical Science
Statistics, Causality and Bell’s
Theorem
Richard D. Gill
Mathematical Institute, University of Leiden, Netherlands
Abstract. Bell’s (1964) theorem is popularly supposed to establish the non-
locality of quantum physics. Violation of Bell’s inequality in experiments
such as that of Aspect et al. (1982) provides empirical proof of non-locality
in the real world. This paper reviews recent work on Bell’s theorem, linking
it to issues in causality as understood by statisticians. The paper starts with
a proof of a strong, finite sample, version of Bell’s inequality and thereby
also of Bell’s theorem, which states that quantum theory is incompatible
with the conjunction of three formerly uncontroversial physical principles,
here referred to as locality, realism, and freedom.
Locality is the principle that the direction of causality matches the di-
rection of time, and that causal influences need time to propagate spa-
tially. Realism and freedom are directly connected to statistical thinking
on causality: they relate to counterfactual reasoning, and to randomisa-
tion, respectively. Experimental loopholes in state-of-the-art Bell type ex-
periments are related to statistical issues of post-selection in observational
studies, and the missing at random assumption. They can be avoided by
properly matching the statistical analysis to the actual experimental design,
instead of by making untestable assumptions of independence between ob-
served and unobserved variables. Methodological and statistical issues in
the design of quantum Randi challenges (QRC) are discussed.
The paper argues that Bell’s theorem (and its experimental confirma-
tion) should lead us to relinquish not locality, but realism.
AMS 2000 subject classifications: Primary 62P35, ; secondary 62K99.
Key words and phrases: counterfactuals, Bell inequality, CHSH inequality,
Tsirelson inequality, Bell’s theorem, Bell experiment, Bell test loophole,
non-locality, local hidden variables, quantum Randi challenge.
arXiv.org/quant-ph:1207.5103
“In print” (to appear, 2015, in special issue on causality)