lessons from experience: engaging with quantum crackpots
DESCRIPTION
Invited talk at 2014 Växjö quantum foundations conferenceTRANSCRIPT
Lessons from experience: engaging with quantum
crackpotsRichard Gill
Mathematical Institute, Science Faculty, Leiden University http://www.math.leidenuniv.nl/~gill
Växjö, 11 June 2014
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.
22 R.D. GILL
moment. The LHV theorist supplies a first run-set of values of (A,A0, B,B0). Theagency 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 canjudge 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 SaschaVongehr for ideas, criticism, references. . . . I especially thank Bryan Sanctuary,Han Geurdes and Joy Christian for their tenacious and spirited arguments againstBell’s theorem which motivated several of the results presented here.
APPENDIX: PROOF OF THEOREM 1
The proof of (3) will use the following two Hoe↵ding inequalities:
Fact 3 (Binomial) Suppose X ⇠ Bin(n, p) and t > 0. Then
Pr(X/n � p+ t) exp(�2nt2).
Fact 4 (Hypergeometric) Suppose X is the number of red balls found in asample without replacement of size n from a vase containing pM red balls and(1� p)M blue balls and t > 0. Then
Pr(X/n � p+ t) exp(�2nt2).
Proof of Theorem 1 In each row of our N⇥4 table of numbers ±1, the productAB equals ±1. For each row, with probability 1/4, the product is either observedor not observed. Let NobsAB denote the number of rows in which both A and B areobserved. Then NobsAB ⇠ Bin(N, 1/4), and hence by Fact 3, for any � > 0,
Pr⇣N
obs
AB
N
1
4
� �⌘ exp(�2N�2).
Let N+AB denote the total number of rows (i.e., out of N) for which AB = +1,
define N�AB similarly. Let Nobs,+AB denote the number of rows such that AB = +1
among those selected for observation of A and B. Conditional on NobsAB = n,
N
obs,+AB is distributed as the number of red balls in a sample without replacementof size n from a vase containing N balls of which N+AB are red and N
�AB are blue.
Therefore by Fact 4, conditional on NobsAB = n, for any ✏ > 0,
Pr⇣N
obs,+AB
N
obs
AB
�N
+
AB
N
+ ✏⌘ exp(�2n✏2).
Recall that hABi stands for the average of the product AB over the wholetable; this can be rewritten as
hABi =N
+
AB �N�AB
N
= 2N
+
AB
N
� 1.
imsart-sts ver. 2012/04/10 file: gill-causality-final.tex date: May 5, 2014
Submitted to the Statistical Science
Statistics, Causality and Bell’sTheoremRichard 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 experimentssuch as that of Aspect et al. (1982) provides empirical proof of non-localityin the real world. This paper reviews recent work on Bell’s theorem, linkingit to issues in causality as understood by statisticians. The paper starts witha proof of a strong, finite sample, version of Bell’s inequality and therebyalso of Bell’s theorem, which states that quantum theory is incompatiblewith 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 thinkingon 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 observationalstudies, and the missing at random assumption. They can be avoided byproperly 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 inthe 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.
1. INTRODUCTION
Bell’s (1964) theorem states that certain predictions of quantum mechanics areincompatible with the conjunction of three fundamental principles of classicalphysics which are sometimes given the short names “realism”, “locality” and“freedom”. Corresponding real world experiments, Bell experiments, are supposedto demonstrate that this incompatibility is a property not just of the theory ofquantum mechanics, but also of Nature itself. The consequence is that we areforced to reject at least one of these three principles.
http: // www. math. leidenuniv. nl/ ~ gill (e-mail: [email protected])
1imsart-sts ver. 2012/04/10 file: gill-causality-final.tex date: May 5, 2014
arXiv.org/quant-ph:1207.5103“In print”: to appear in Statistical Science (2015) special issue on causality
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
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!
CRACKPOT
Ψ
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.
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.
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
Almost no quantum crackpot ever read “Bertlmann’s socks”
They read Bell (1964), and some anti-Bell literature
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.
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
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.
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
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
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!
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 0
• B := sign(– b . X) if |b . X | > C , otherwise 0
(Open problems)
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
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?
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
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
22 R.D. GILL
moment. The LHV theorist supplies a first run-set of values of (A,A0, B,B0). Theagency 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 canjudge 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 SaschaVongehr for ideas, criticism, references. . . . I especially thank Bryan Sanctuary,Han Geurdes and Joy Christian for their tenacious and spirited arguments againstBell’s theorem which motivated several of the results presented here.
APPENDIX: PROOF OF THEOREM 1
The proof of (3) will use the following two Hoe↵ding inequalities:
Fact 3 (Binomial) Suppose X ⇠ Bin(n, p) and t > 0. Then
Pr(X/n � p+ t) exp(�2nt2).
Fact 4 (Hypergeometric) Suppose X is the number of red balls found in asample without replacement of size n from a vase containing pM red balls and(1� p)M blue balls and t > 0. Then
Pr(X/n � p+ t) exp(�2nt2).
Proof of Theorem 1 In each row of our N⇥4 table of numbers ±1, the productAB equals ±1. For each row, with probability 1/4, the product is either observedor not observed. Let NobsAB denote the number of rows in which both A and B areobserved. Then NobsAB ⇠ Bin(N, 1/4), and hence by Fact 3, for any � > 0,
Pr⇣N
obs
AB
N
1
4
� �⌘ exp(�2N�2).
Let N+AB denote the total number of rows (i.e., out of N) for which AB = +1,
define N�AB similarly. Let Nobs,+AB denote the number of rows such that AB = +1
among those selected for observation of A and B. Conditional on NobsAB = n,
N
obs,+AB is distributed as the number of red balls in a sample without replacementof size n from a vase containing N balls of which N+AB are red and N
�AB are blue.
Therefore by Fact 4, conditional on NobsAB = n, for any ✏ > 0,
Pr⇣N
obs,+AB
N
obs
AB
�N
+
AB
N
+ ✏⌘ exp(�2n✏2).
Recall that hABi stands for the average of the product AB over the wholetable; this can be rewritten as
hABi =N
+
AB �N�AB
N
= 2N
+
AB
N
� 1.
imsart-sts ver. 2012/04/10 file: gill-causality-final.tex date: May 5, 2014
Submitted to the Statistical Science
Statistics, Causality and Bell’sTheoremRichard 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 experimentssuch as that of Aspect et al. (1982) provides empirical proof of non-localityin the real world. This paper reviews recent work on Bell’s theorem, linkingit to issues in causality as understood by statisticians. The paper starts witha proof of a strong, finite sample, version of Bell’s inequality and therebyalso of Bell’s theorem, which states that quantum theory is incompatiblewith 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 thinkingon 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 observationalstudies, and the missing at random assumption. They can be avoided byproperly 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 inthe 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.
1. INTRODUCTION
Bell’s (1964) theorem states that certain predictions of quantum mechanics areincompatible with the conjunction of three fundamental principles of classicalphysics which are sometimes given the short names “realism”, “locality” and“freedom”. Corresponding real world experiments, Bell experiments, are supposedto demonstrate that this incompatibility is a property not just of the theory ofquantum mechanics, but also of Nature itself. The consequence is that we areforced to reject at least one of these three principles.
http: // www. math. leidenuniv. nl/ ~ gill (e-mail: [email protected])
1imsart-sts ver. 2012/04/10 file: gill-causality-final.tex date: May 5, 2014
arXiv.org/quant-ph:1207.5103“In print” (to appear, 2015, in special issue on causality)