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From time to time, I will post important historical articles on foundational issues, which I believe have not received the attention that they deserve. I invite everyone to do the same.

The first entry in the series will be

George Boole's "Conditions of Possible Experience" and the Quantum Puzzle
ITAMAR PITOWSKY, Brit. J. Phil. Sci. 45 (1994). 95-125
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.829.1315&rep=rep1&type=pdf

Abstract:
In the mid-nineteenth century George Boole formulated his 'conditions of possible
experience'. These are equations and inequalities that the relative frequencies of
(logically connected) events must satisfy. Some of Boole's conditions have been
rediscovered in more recent years by physicists, including Bell inequalities, Clauser
Horne inequalities, and many others. In this paper, the nature of Boole's conditions
and their relation to propositional logic is explained, and the puzzle associated with
their violation by quantum frequencies is investigated in relation to a variety of
approaches to the interpretation of quantum mechanics.
...
3 CAN BOOLE'S CONDITIONS BE VIOLATED?
One thing should be clear at the outset: none of Boole's conditions of possible
experience can ever be violated when all the relative frequencies involved have been
measured in a single sample. The reason is that such a violation entails a logical
contradiction. For example, suppose that we sample at random a hundred balls
from an urn. Suppose, moreover that 60 of the balls sampled are red, 75 are
wooden and 32 are both red and wooden. We have p1=0-6, p2 = 0.75,
p12 = 0.32. But then p1 + p2 - p12 > 1. This clearly represents a logical impossibility,
for there must be a ball in the sample (in fact three balls) which is 'red', is
'wooden', but not 'red and wooden'; absurd.
Similar logical absurdities can be derived if we assume a violation of any of
the relevant conditions, no matter how complex they appear to be. This is the
reason for the title 'conditions of possible experience'. In case we deal with
relative frequencies in a single sample, a violation of any of the relevant Boole's
conditions is a logical impossibility.

***

This is an excellent paper. It has faired far better than some other papers that may appear later in your anthology. Itamar Pitowsky was an excellent scholar. He was a student of Jeff Bub, who, in turn, was a student of David Bohm. Pitowsky visited our group of philosophers of physics in Oxford a few times, so I had opportunities to meet him. He also visited the Perimeter Institute in Canada and attended my seminars there on Time and Quantum Gravity. I refer to him in the past tense because he passed away prematurely some years ago (a victim of cancer).

***

minkwe wrote:From time to time, I will post important historical articles on foundational issues, which I believe have not received the attention that they deserve. I invite everyone to do the same.

The first entry in the series will be

George Boole's "Conditions of Possible Experience" and the Quantum Puzzle
ITAMAR PITOWSKY, Brit. J. Phil. Sci. 45 (1994). 95-125
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.829.1315&rep=rep1&type=pdf
[...]

This is indeed a very good paper, a so-called classic. I urge everyone to read from section 4 and out, where all the common arguments against Bell's theorem is thoroughly rebutted.

The law of large numbers asserts that, with high probability, the relative frequency of a property in a (finite) random sample approximates the proportion of that property in the population. For that reason we expect Boole's conditions to obtain even when the relative frequencies involved have been measured on distinct samples.

Heinera wrote:This is indeed a very good paper, a so-called classic. I urge everyone to read from section 4 and out, where all the common arguments against Bell's theorem is thoroughly rebutted.

The law of large numbers asserts that, with high probability, the relative frequency of a property in a (finite) random sample approximates the proportion of that property in the population. For that reason we expect Boole's conditions to obtain even when the relative frequencies involved have been measured on distinct samples.

As soon as one resorts to probability and statistics in support of Bell, one obfuscates the extremely silly physical mistake Bell has made in his argument: https://arxiv.org/abs/1704.02876

***

Joy Christian wrote:

Heinera wrote:This is indeed a very good paper, a so-called classic. I urge everyone to read from section 4 and out, where all the common arguments against Bell's theorem is thoroughly rebutted.

The law of large numbers asserts that, with high probability, the relative frequency of a property in a (finite) random sample approximates the proportion of that property in the population. For that reason we expect Boole's conditions to obtain even when the relative frequencies involved have been measured on distinct samples.

As soon as one resorts to probability and statistics in support of Bell, one obfuscates the extremely silly physical mistake Bell has made in his argument: https://arxiv.org/abs/1704.02876

***

s***. I thought this was a good paper. So now it's a bad paper?

Heinera wrote:

Joy Christian wrote:

Heinera wrote:This is indeed a very good paper, a so-called classic. I urge everyone to read from section 4 and out, where all the common arguments against Bell's theorem is thoroughly rebutted.

The law of large numbers asserts that, with high probability, the relative frequency of a property in a (finite) random sample approximates the proportion of that property in the population. For that reason we expect Boole's conditions to obtain even when the relative frequencies involved have been measured on distinct samples.

As soon as one resorts to probability and statistics in support of Bell, one obfuscates the extremely silly physical mistake Bell has made in his argument: https://arxiv.org/abs/1704.02876

***

s***. I thought this was a good paper. So now it's a bad paper?

Bell's paper is indeed a bad paper and it should be retracted.

***

The second article in the series is not very old (only 10 years) continues the theme from Pitowsky.

Possible experience: From Boole to Bell
K. Hess1, K. Michielsen2 and H. De Raedt3
Published 9 October 2009 • Europhysics Letters Association
https://iopscience.iop.org/article/10.1 ... 60007/meta


Abstract
Mainstream interpretations of quantum theory maintain that violations of the Bell inequalities deny at least either realism or Einstein locality. Here we investigate the premises of the Bell-type inequalities by returning to earlier inequalities presented by Boole and the findings of Vorob'ev as related to these inequalities. These findings together with a space-time generalization of Boole's elements of logic lead us to a completely transparent Einstein local counterexample from everyday life that violates certain variations of the Bell inequalities. We show that the counterexample suggests an interpretation of the Born rule as a pre-measure of probability that can be transformed into a Kolmogorov probability measure by certain Einstein local space-time characterizations of the involved random variables.

The one to one correspondence of mathematical abstractions to actual experiments and a measure on the set of these abstractions are both necessary to give meaning to the word probability in a set-theoretic sense. The less familiar reader is encouraged to look at these definitions in the original work of Boole [4] or, for the Kolmogorov framework, in textbooks such as [15]. For such a model to make general sense in all experimental situations, we must assume that (1) a given and well-defined logical element representing an experimental outcome or, in the language of Kolmogorov, an elementary event will occur with the same probability measure throughout all experiments and that (2) the physical characterization of the logical elements of Boole (elementary events of Kolmogorov) is consistent and complete throughout the experimental sequence.

Many mathematical papers on probability theory simply start with the phrase “given a Kolmogorov probability space...”. It is, however, well known and has been particularly well pointed out by Vorob'ev [16] that there are cases in which a Kolmogorov probability space does not exist. In particular, there exist numerous classical experiments that subject to certain characterizations by simple settings, cannot be described on one probability space in a logically consistent way.

Boole included into eq. (2) a cyclicity: the outcomes of the first two products determine the outcomes in the third product. Because all outcomes can only be ±1 the cyclicity gives rise to eq. (3). Vorob'ev showed precisely 100 years after Boole's original work in a very general way that it is always a combinatorial-topological cyclicity that gives rise to non-trivial inequalities for the mathematical abstractions of experimental outcomes. Boole pointed to the fact that eq. (3) cannot be violated. However, in order to come to that conclusion, the Aol(n) need, in the first place, to be in a one to one correspondence to Boole's elements of logic that follow the law “aut A = +1 aut A = −1 tertium non datur”. As discussed in the introduction, eternally valid statements about physical experience such as “aut A = +1 aut A = −1 tertium non datur” can usually not be made when describing the physical world without the use of some coordinates. In the example above these coordinates where the places of birth, the places of examination and the numbering of the exams that were randomly taken. All these coordinates when added need to still allow for a cyclicity in order to make Boole's inequality non-trivial. Therefore, if we have a violation of a non-trivial Boole inequality, then we must conclude that we have not achieved a one to one correspondence of our variables to the elementary eternally true logical variables of Boole and that we need further “coordinates” that will then remove the cyclicity.

***

Let me contribute to this list the following, not only underrated but largely unknown paper: https://www.worldscientific.com/doi/abs ... 7506003240

Title:

CLASSICAL TELEPORTATION OF CLASSICAL STATES

Abstract:

The standard quantum teleportation scheme is deconstructed, and those aspects of it that appear remarkable and "non-classical" are identified. An alternative teleportation scheme, involving only classical states and classical information, is then formulated, and it is shown that the classical scheme reproduces all of these remarkable aspects, despite the fact that they had seemed non-classical. This leads to a re-examination of quantum teleportation, which suggests that its significance depends on the interpretation of quantum states.

***

I agree 100% with what’s written in that abstract. And this fact was very well known to insiders from the very, very start. I have certainly known it since the first time I was taught quantum teleportation, both what it is and what it is not, by Klaus Mølmer, then in Aarhus, who was very excited because he had only just heard the trick, and he believed he might be the first to *do* it. Which would bring in even more money for his science. Which he did and does passionately believe in.

Mathematically, it is all absolutely trivial linear algebra in C^8. You can also make it in some sense yet more trivial and intuitive with Geometric Algebra, avoiding complex numbers altogether, but at the cost of using less familiar geometry (and a steep learning curve) in R^16. You can teach it to bright teenagers. I know because I’ve often done it. And you can explain that what it “means” depends on what you think QM “means”, which is a matter of debate.

It has been deliberately hidden from the knowledge of non-experts for (US) “political” reasons. i.e. for science funding. That’s in fact the reason for the “sexy name” quantum teleportation in the first place. Star Trek, Star Wars, Extract Science Funding from the US Defence Budget i.e. from the military/industrial complex. You could say - to divert taxpayer’s money, which they are going to pay anyway, to *good* use. Swords to plough-shares. Of course it also feeds scientific egos, which are just as big as politicians’ or opera divas’.

Quantum mechanics is simply about real probability factors for real physical events. Nothing more; nothing less. Only an idiot would try to make more out of it.

FrediFizzx wrote:Quantum mechanics is simply about real probability factors for real physical events. Nothing more; nothing less.

I agree entirely, Fred! Trouble is people have been trying to make more out of it for more than 100 years, now.

I think moreover, that when you think about it in those terms - real probability factors for real physical event - i.e. the events are real and the probabilities are real, the rest is a construction of our own minds which may or may not be useful - when you think about it in those terms you can immediately jettison a huge amount of crap in the quantum debate. The whole many worlds theory and "there is just one universal wave function" are just ... many words, and absolutely useless words at that. Many is one? Pseudo Buddhist hippy crap.

I think moreover, that when you do follow Fred's philosophy and look carefully at the experimental data, it becomes useful to say that certain of those real events confirm "spooky passion at a distance".

Now, that's another five words and maybe some could be improved or the number reduced. I'm particularly unhappy with "spooky" because it has too many negative connotations. It says that this is something which we don't understand hence it is scary. Now things we can't understand are an important part of life - love, God, death ... - we can't understand them and don't, but by God, they do exist and life wouldn't be life without them. Hence: something we don't or even can't understand is not necessarily *scary*.

Maybe we should say *perfect passion at a distance*? As Joy says, the quantum correlations are exquisitely restrained. That's the *wonder* of them. Nature is *wonderful*. That's why we are scientists.

gill1109 wrote:

FrediFizzx wrote:Quantum mechanics is simply about real probability factors for real physical events. Nothing more; nothing less.

I agree entirely, Fred! Trouble is people have been trying to make more out of it for more than 100 years, now. ...snip...

I think moreover, that when you do follow Fred's philosophy and look carefully at the experimental data, it becomes useful to say that certain of those real events confirm "spooky passion at a distance".
...snip...

Sorry, but we already have a classical local-realistic model that explains the correlations 100 percent so there is absolutely no spookiness whatsoever. There is also some recent classical-like experiments that confirm it. You are being tricked into trying to make more out of QM than what I said.

FrediFizzx wrote:

gill1109 wrote:

FrediFizzx wrote:Quantum mechanics is simply about real probability factors for real physical events. Nothing more; nothing less.

I agree entirely, Fred! Trouble is people have been trying to make more out of it for more than 100 years, now. ...snip...

I think moreover, that when you do follow Fred's philosophy and look carefully at the experimental data, it becomes useful to say that certain of those real events confirm "spooky passion at a distance".
...snip...

Sorry, but we already have a classical local-realistic model that explains the correlations 100 percent so there is absolutely no spookiness whatsoever. There is also some recent classical-like experiments that confirm it. You are being tricked into trying to make more out of QM than what I said.

I don't know whether this paper is underrated or not, but so far it is probably not very well known. In fact, the introductory chapter of a whole book. You can download the complete pdf, free. Vaidman himself finds the most exciting recent results that of Brassard and Raymond-Robichaud ... which nobody so far seems to have talked about here, either (except that I mentioned it a few times).

https://www.mdpi.com/1099-4300/21/5/447/htm

Entropy 2019, 21(5), 447; https://doi.org/10.3390/e21050447

Editorial
Quantum Nonlocality
Lev Vaidman
Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University
Received: 23 April 2019 / Accepted: 24 April 2019 / Published: 29 April 2019

Keywords: nonlocality; entanglement; quantum

The role of physics is to explain observed phenomena. Explanation in physics began as a causal chain of local actions. The first nonlocal action was Newton’s law of gravity, but Newton himself considered the nonlocal action to be something completely absurd which could not be true—and indeed, gravity today is explained through local action of the gravitational field. It is the quantum theory which made physicists believe that there was nonlocality in Nature. It also led to the acceptance of randomness in Nature, the existence of which is considered as another weakness of science today. In fact, I hope that it is possible to remove randomness and nonlocality from our description of Nature [1]. Accepting the existence of parallel worlds [2] eliminates randomness and avoids action at a distance, but it still does not remove nonlocality. This special issue of Entropy is an attempt to more deeply understand the nonlocality of the quantum theory. I am interested to explore the chances of removing nonlocality from the quantum theory, and such an attempt is the most desirable contribution to this special issue; however, other works presented here which characterize the quantum nonlocality and investigate the role of nonlocality as an explanation of observed phenomena also shed light on this question.
It is important to understand what the meaning of nonlocality is in quantum theory. Quantum theory does not have the strongest and simplest concept of nonlocality, which is the possibility of making an instantaneous observable local change at a distance. However, all single-world interpretations do have actions at a distance. The quantum nonlocality also has an operational meaning for us, local observers, who can live only in a single world. Given entangled particles placed at a distance, a measurement on one of the particles instantaneously changes the quantum state of the other, from a density matrix to a pure state. It is only in the framework of the many-worlds interpretation, considering all worlds together, where the measurement causes no change in the remote particle, and it remains to be described by a density matrix. Another apparent nonlocality aspect is the existence of global topological features, such as the Aharonov-Bohm effect [3]. I believe I succeeded in removing this kind of nonlocality from quantum mechanics [4], but the issue is still controversial [5,6,7,8]. Unfortunately, no contributions clarifying this problem appear in this issue.

It is of interest to analyze nonlocal properties of composite quantum systems, the properties of systems in separate locations [9]. These properties are nonlocal by definition, and the nonlocality of their description does not necessarily tell us that the Nature is nonlocal. It is not surprising that nonlocal properties obey nonlocal dynamical equations. Although unrelated to the question of nonlocality in Nature, it is a useful tool for quantum information which, due to quantum technology revolution, becomes not just the future, but the present of practical applications. See the discussion of this aspect of quantum nonlolcality in this issue and note the recent first experimental realization of measurements of nonlocal variables [10].

For the problem of nonlocality of Nature, the important question is: which of the nonlocal features of composite systems cannot be specified by local measurements of its parts? More precisely, this is the question of nonlocality of a single world, would it be one of the worlds of the many-worlds theory or the only world of one of the single-world interpretations. Even if it does not answer the question of nonlocality of the physical universe incorporating all the worlds, this is the question relevant for harnessing the quantum advantage for tasks which cannot be accomplished classically.

What seems to be an unavoidable aspect of nonlocality of the quantum theory—which is present even in the framework of all worlds together—is entanglement. Measurement on one system does not change the state of the other system in the physical universe, but in each world created by the measurement, the state of the remote system is different. The entanglement, that is, the nonlocal connection between the outcomes of measurements shown to be unremovable using local hidden variables, is the ultimate nonlocality of quantum systems.

Very subjectively—I find the most interesting contribution to be the work by Brassard and Raymond-Robichaud [11], “Parallel Lives: A Local-Realistic Interpretation of ‘Nonlocal’ Boxes”. The work challenges the ultimate question of nonlocality of entanglement. It is part of the ongoing program which was introduced by Deutsch and Hayden [12] to completely eliminate nonlocality from quantum mechanics. The present authors promise to complete it in a future publication. The current paper, instead, provides a wider picture, considering, in a local way, different theories that are currently viewed as nonlocal. The analysis of Popescu Rohrlich (PR) boxes [13], the Einstein–Podolsky–Rosen argument, and Bell’s theorem puts the picture in proper and clear perspective. I am optimistic that Brassard and Raymond-Robichaud will succeed in building their fully local picture as they promise. However, I am also pretty sure that they will have to pay a very high price for removing all aspects of nonlocality by carrying a huge amount of local information in order to reconstruct the consequences of entanglement. Currently, I feel that I will not adopt the “parallel lives” picture, and will stay with the many-worlds interpretation [2], an elegant economical interpretation that has no randomness and action at a distance, but still has nonlocality in the concept of a world. However, I am very curious to see the quantum theory of the parallel lives. The possibility of the construction of a fully local theory, even if it is not economical, is of great importance.

...

gill1109 wrote:I don't know whether this paper is underrated or not, but so far it is probably not very well known. In fact, the introductory chapter of a whole book. You can download the complete pdf, free. Vaidman himself finds the most exciting recent results that of Brassard and Raymond-Robichaud ... which nobody so far seems to have talked about here, either (except that I mentioned it a few times).

This paper does not qualify for this thread. In fact, some of the claims or cavalier statements are very problematic and reflective of the state of decay in theoretical physics and quantum mechanics in particular.

Take a few examples:

The role of physics is to explain observed phenomena. Explanation in physics began as a causal chain of local actions. The first nonlocal action was Newton’s law of gravity

Newton never thought of gravity as a nonlocal action. Of course there were mysterians back then but to state so confidently that the first nonlocal action was Newton's law of gravity, it just plain false.

 Isaac Newton wrote:It is inconceivable that inanimate Matter should, without the Mediation of something else, which is not material, operate upon, and affect other matter without mutual Contact…That Gravity should be innate, inherent and essential to Matter, so that one body may act upon another at a distance thro' a Vacuum, without the Mediation of any thing else, by and through which their Action and Force may be conveyed from one to another, is to me so great an Absurdity that I believe no Man who has in philosophical Matters a competent Faculty of thinking can ever fall into it. Gravity must be caused by an Agent acting constantly according to certain laws; but whether this Agent be material or immaterial, I have left to the Consideration of my readers.[5]

— Isaac Newton, Letters to Bentley, 1692/3

It is the quantum theory which made physicists believe that there was nonlocality in Nature. It also led to the acceptance of randomness in Nature, the existence of which is considered as another weakness of science today.

Wait! what? Physicists believe there is non-locality in Nature? That is a highly dubious statement. Certainly some physicists do, but a very small minority. Does the author know what randomness is? What does it even mean to talk of "randomness in Nature". That is a very imprecise statement.This author really believes the existence of randomness is a weakness of science? How can the existence of something in Nature become a weakness of science? Come on man! Again more imprecision of expressing what they are actually trying to say. This level of imprecision is not limited to this author.

The quantum nonlocality also has an operational meaning for us, local observers, who can live only in a single world. Given entangled particles placed at a distance, a measurement on one of the particles instantaneously changes the quantum state of the other, from a density matrix to a pure state.

Quesiton: So what is this "mythical" quantum state of an entangled particle. Where does it exist, in the mind of the physicist doing the calculation/prediction, or in nature somewhere. If the latter, please describe some of the physical properties of this quantum state. Oh, don't forget to provide space-time coordinates for the location of the quantum state of entangled particle, without which it is nonsensical to suggest instantaneous change at a distance.

It is only in the framework of the many-worlds interpretation, considering all worlds together, where the measurement causes no change in the remote particle

Hold on, no magician's tricks allowed. I thought we were talking about instantaneous changes to the "quantum state". Now we are doing a bait and switch to "remote particle", without any successful demonstration that the "quantum state" is the same as the "remote particle". Please demonstrate that the two are the same thing.

etc, etc.

This author, like many in the community (1) portray history falsely to fit the narrative they want to promote, (2) communicate very imprecisely, (3) fail to distinguish clearly separate concepts such as "our description of nature" and "nature itself", (4) perform bait-and-switch between concepts that have not been demonstrated to be equivalent.

This is the problem in theoretical physics today.

OK, back to applied category theory.

See this posting by John Carlos Baez:
https://johncarlosbaez.wordpress.com/2018/02/11/linguistics-using-category-theory/
John refers to a paper which "sets up a weird analogy between linguistics and quantum mechanics".
It's also mentioned in the discussion of Scott Aaronson's "three updates" https://www.scottaaronson.com/blog/?p=3638, namely in comment #92 on category theory,
https://www.scottaaronson.com/blog/?p=3638#comment-1753713

Back to the classical efficient simulation of quantum mechanics.

In the same Aaronson blog discussion, there's an interesting discussion of Johansson and Larsson's (in my humble opinion) interesting and underrated https://link.springer.com/article/10.1007%2Fs11128-017-1679-7.
It starts with comment #3 on the same Aaronson blog "three updates",
https://www.scottaaronson.com/blog/?p=3638#comment-1752678
It led to a back and forth discussion between Larsson and Aaronson. Aaronson does not understand Larsson. It ends with Jan-Åke's *unanswered* and therefore final comment
https://www.scottaaronson.com/blog/?p=3638#comment-1753725

I think not many people understand Johansson and Larsson's work. But I think it is very important and very significant. I think it needs to be explained better.

We investigate in detail the role that oracles play for the advantage of quantum algorithms. We do so by using a simulation framework, Quantum Simulation Logic (QSL), to construct oracles and algorithms that solve some problems with the same success probability and number of queries as the quantum algorithms. The framework can be simulated using only classical resources at a constant overhead as compared to the quantum resources used in quantum computation. [...]. Using the same assumptions on oracles within the simulation framework we show that for some specific algorithms, such as the Deutsch-Jozsa and Simon’s algorithms, there simply is no advantage in terms of query complexity.

Oops.
https://www.mdpi.com/1099-4300/21/8/800
Quantum Simulation Logic, Oracles, and the Quantum Advantage
Niklas Johansson and Jan-Åke Larsson
Institutionen för Systemteknik, Linköpings Universitet, 581 83 Linköping, Sweden
Entropy 2019, 21(8), 800; https://doi.org/10.3390/e21080800

gill1109 wrote:

We investigate in detail the role that oracles play for the advantage of quantum algorithms. We do so by using a simulation framework, Quantum Simulation Logic (QSL), to construct oracles and algorithms that solve some problems with the same success probability and number of queries as the quantum algorithms. The framework can be simulated using only classical resources at a constant overhead as compared to the quantum resources used in quantum computation. [...]. Using the same assumptions on oracles within the simulation framework we show that for some specific algorithms, such as the Deutsch-Jozsa and Simon’s algorithms, there simply is no advantage in terms of query complexity.

Oops.
https://www.mdpi.com/1099-4300/21/8/800
Quantum Simulation Logic, Oracles, and the Quantum Advantage
Niklas Johansson and Jan-Åke Larsson
Institutionen för Systemteknik, Linköpings Universitet, 581 83 Linköping, Sweden
Entropy 2019, 21(8), 800; https://doi.org/10.3390/e21080800

That's an interesting article. Although it is too recent to be underrated but we will see. I suspect it will not be liked very much for the same reasons why anti-bell papers are always ignored, because it challenges the status-quo of "Quantum Supremacy". Obviously, very few people if any, understand Quantum Computing. This article definitely has some clues about why Quantum Computing appears to work. I hope the authors will retreat from the edge but jump into the abyss of enlightenment about not just Quantum Computing but entanglement, and Bell's theorem.

You will soon realize that the proponents of Quantum Computing will simply dismiss it, attack straw-men and then find excuses to ignore it. Now where have we seen this before?