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Hippolyte Dourdent

Dear George,

Thank you for your comment.

In fact, Hofstadter already pointed out that consciousness might also emerge from these "strange loops". You could look at the Cartesian definition of the cogito : "Cogito ergo sum". Every time I think, I am conscious about the fact that I am thinking, and so that I am a "thinking being". The definition of our own "being" seems to be intricated with self-consciousness, i.e. a form of self-referential thinking. However, since consciousness seems not to be very well defined in physics, I prefer to remain sceptical and be careful towards linking, maybe too hastily, consciousness, time or reality. Nevertheless, I would agree with you that, very interestingly, they seem to share some common logical structure.

All the best,

Hippolyte

Dear Irek,

Thank you very much for your nice comment.

All the best,

Hippolyte

Dear Jeffrey,

Indeed logic seems to be at the core of ability to communicate. However, what kind of logic ? To us, humans, it seems that our language and concepts, build on how we experience our interaction with the world, is based on some "classical logic". So should we revise our classical logic in order to adapt it to quantum phenomena ? In my opinion, it is not necessary.

Do we live inside the structure of time, or does time emerges because we are not "meta-universal object" but in fact we are part of the Universe, and try to describe it from inside ? Your reflexion on "undefined space-time and entropy" is quite interesting ! But if "time ends up being the non-local of space-time", isn't there a self-referential issue here ?

All the best,

Hippolyte

I forgot to log in, sorry for this !

Best,

Hippolyte Dourdent

Dear Michael,

Congratulations for your well written and interesting essay.

Your conclusion : " The processing logic of error-correction must come from an external processing unit also sourcing its power from the environment. By implication, the physical realisation of indefinite self-referential logical program such as the Halting problem relies on an external network of other external logical processors to prevent errors." is really appealing to me, as this is quite analog to my idea that self-referential issues inside quantum theory can be dissolved by invoking an "external object", an observer, and thus the measurement problem is just a logical tension between physics-from-inside and physics-from-outside.

However, I am not sure to follow you when you write that "the mathematical paradoxes uncovered by Turing and Gödel do not bear any consequence on the physical world because they can never be truly realised in physics." Or at least, they have a huge importance in meta-physics...

All the best,

Hippolyte

Hi Michael,

Thank you very much for your nice comment.

I will try to read your essay as soon as I can !

All the best,

Hippolyte

Dear Markus,

I really enjoyed reading your essay, and I sympathize with a lot of your ideas.

Especially, the fact that letting go of the concept of "things" and acknowledging that some questions have no answer, "dissolve" the paradoxes and avoid the invocation of weird ontological phenomena. Indeed, quantum theory invites to consider the notion of "entities" (as they were defined since Aristotle, individual objects with determinable intrinsic properties) as an "epistomological obstacle" as philosopher Gaston Bachelard might say. A metaphysical distancing from the notion of "things". While I was preparing my essay, I came across this quote from Rothstein, which I think might be in line with your "dissolution of questions" : an `` operational meaning can be assigned to question with respect to a system of interest which does not include the observer. Applied to the universe as a whole, these question lose their operational significance and become physically undecidable, they become metaphysical questions.''

I really enjoyed your defense of an "optimistic" view. It is true that interpretations acknowledging this analysis are very often mistaken with "incomplete" knowledge (epistemic restrictions) about ontic things ; or they are straightforwardly labelled as anti-realistic, without specifying "anti-realistic towards what". Not towards the existence of an external word, but towards the notion of "things".

I guess there might an ambiguity in your essay (or a misunderstanding from me), because I don't see QBism as "an epistemic restriction" which can be compared with Spekkens's view. I rather see it as something that might get along with your view, an optimistic position based on acknowledging that some "questions don't have answers" not because of a lack of human ability, but based on a fundamental, logical argument.

Instead of taking a metaphysical stance as you do, arguing for an ontological realism of structures ; I tend to be sceptical towards sentences such as "the world is" (which are often related to a naïve realism (based on "things")). So I am not sure that I completely rely on your view that "the world is about structure". The word "structure" seems quite vague and ambiguous... and I prefer (for now) to strive for an "epistemological modesty" rather than designating what is ontological or not. However, you solution is way more appealing than naïve realism, since it is proposed after a careful analysis about the (un)decidability of questions. So I rather prefer your conclusion : "We can know what there is to know." Which resonate with Bohr-like sentences : "There is no quantum world. Physics is about what we can say about nature".

If you ever find the time to read my essay, I would be glad to have your feedbacks on it. You go further than my analysis, proposing an ontological path to follow (structuralism) while I stopped at the dissolution step (for now). However, your notion of "Structural differentiation" seems rather close to my concept of "meta-contextuality", and I am very curious to have your thoughts on this.

I hope that your essay will do great in the contest.

Best,

Hippolyte

Dear Flavio,

Thank you for your very interesting essay. Your angle of attack is quite original, and I completely agree with your argument that indeterminism is a matter of interpretation, and can both be chosen for quantum or classical theory. Indeed Laplace's demon is often considered as being exorcised by quantum theory, but its existence is already facing difficulties by the only fact that if the demon is not external to the Universe, then it might predict its own behaviour, which might lead to logical inconsistencies.

Are you familiar with Breuer's theorem ? It reminds me of your principle of infinite precision. Breuer, analysing the measurement problem as emerging from self-reference, has shown that every observer cannot distinguish the states of a system in which it is contained, irrespective of the nature of the system (classical or quantum) and of the time evolution (deterministic are stochastic). In a paper entitled "Quantum meausurement and Gödel's proof", analyzing Maxwell's demon, Zwick also presents, as you do, a mesurement problem for classical mechanics : "To avoid infinite regress in the description of measurement, and paradoxes either of self-reference, one must assume that at some point, the perturbation by the measurement can be ignored, or introduce a statistical postulate as an arbitrary addition to the dynamics. If neither is allowed, on can simply accept the need for the two-levelled theory." Do you think that this might be in line with your essay ?

The "future undecidability" that is described in Gisin's final quote of your essay is an old problem of classical logic, that goes back to Aristotle and "Sea battle tomorrow", his introduction of the notion of contingency. This problem of future contingents was especially studied by the scholastics, who were trying to conciliate Aristotle's logic and the Biblical narratives. Ernst Specker, who was one of the father of the theorem showing "quantum contextuality", was motivated by these scholastic study of "Infuturabilien" when he found a result that will become later the Kochen-Specker theorem.

If you ever find some time to do it, I will be glad to have your feedback on my essay, that defends an indeterministic interpretation of quantum theory based on contextuality and an analysis of the measurement problem as self-reference (analysis that I believe could be extended to classical mechanics, an incompatibility between absolute universality, measurement as a meta-theoretical process and full measurability).

Best,

Hippolyte

Dear Jochen,

I finally had time to read your essay. I really appreciated the clarity of your arguments.

Your first example of the derivation of Heisenberg's principle from Finiteness and Extensibility is enlightening. Your introduction to superposition from diagonalisation is also very interesting. However, as you pointed out in your essay, "quantum mechanics, itself, does not fall prey to the same issues", notably because of the no-cloning theorem and the fact that the diagonal state yields a fixed point for the X gate. The fact that the superposition allows to avoid a logical contradiction reminds me of escaping the self-referential paradoxes by invoking a many-valued logic (e.g. trivalent), where '' (or "indeterminate") would be another kind of truth value, in addition to 0 and 1. But what about complex states ? I don't know if you are familiar with it, I heard about a book entitled 'Laws of Form' by Spencer-Brown which presents a calculus dealing with self-reference without running into paradoxes, by introducing an imaginary Boolean algebra. Take the equation x=-1/x , which entails in some way a self-reference, a mimic of the Liar. If x=1 then it is equal to -1 and vice-versa, leading to a contradiction. The solution is to introduce an imaginary number, i , defined by i=-1/i.

Your reading of Bell's theorem as revealing a counterfactual undecidability was enjoyable to read, as it is in line with my presentation of contextuality as a similar undecidability.

Another point : As you may have read as an epilogue in my essay, I am also interested in the Liar like structure that can emerge from "physical (hypothetical) loops" like CTCs. I am especially interested in quantum-based simulations of such CTCs, as Bennett and Loyd's P-CTCs. In the literature, e.g. https://arxiv.org/abs/1511.05444, people have studied the relation between logical consistency and the existence of unique fixed-point. I was wondering if you had also some kind of epistemic reading of such loops, if you think that this is also related to Lamvere's theorem.

Cheers,

Hippolyte

Dear Jochen,

No problem, I myself struggle to find the time to read and discuss other essays.

Concerning building a "Liar cycle" within your framework, I guess an idea would be to try to retrieve a proof of the Kochen-Specker theorem (e.g. Mermin-Peres square or the KCBS inequality) using Lawvere's theorem as you did with Bell inequality ? The major difference being that in general, these proofs (but not KCBS) are state-independent.

Concerning the Yablo paradox. I also happened to ask myself the same question. Indeed, the Yablo paradox is a kind of indirect Liar, and I also wondered if one could find some proof of quantum contextuality that would share a similar structure. Unfortunately, so far, I also have no idea how such referential structure could be formulated with observables.

I have finally found the time to read your essay, I'll leave a comment on your section !

Best,

Hippolyte

Dear Eckard,

I finally had the time to read your essay, that I found really "thought feeding".

I think that my Gödelian hunch and your encouragement for "being careful" to not idealize nor put on a pedestal mental mathematical constructions are quite compatible. This might be why you suggested (in your comment of my essay) that your analysis of Fourier was another "hint of contextuality". However, even if I understand that your argument relies on pointing at a hidden redundancy (and thus maybe a kind of self-referential structure ?), I still struggle to see the link with "contextuality" itself (as a logical obstruction of locally consistent data) ?

Another point : Are you familiar with the topic of "quantum causality" ? (cf. e.g. doi.org/10.1038/ncomms2076 ) . Your invitation to "calculate as if there was no causality" might be appropriate to analyze these "indefinite causal orders" ("correlations with no causal order").

Best regards,

Hippolyte

Dear Edwin,

Thank you for your comment.

"I believe that physicists project math structure onto the world, and then come to believe that the physical world actually has that structure. Your Penrose triangle is a perfect example. The 2D structure projected on paper is not a 3D reality."

Indeed, I believe this might be another way to go. I prefer another metaphysical approach, that would rather see this projection as epistemological (projection of the meta-theoretical on the theoretical).

I guess your conclusions on Bell are not so far from my Gödelian hunch, but instead of analyzing this in the relationship between meta-theoretical (observer, measurement) and theoretical (quantum systems), you prefer to have a more realistic / ontological approach, and thus be sceptical towards the projection (which is equivalent to dropping the universality assumption ?).

I will have you a look at your essay as soon as I can,

Best,

Hippolyte

Dear Eckard Blumschein,

I think you misunderstood my brief reply.

"To me, arguments are more important than votes." I completely agree !

I was (and still am) going to have look at your essay in order to give you a more constructive answer, whether it is on my forum or yours. I just did not find the time yet.

"Well, you have a hunch that what you learned is always true. Maybe, Alexei Grinbaum himself may challenge my unwelcome reasoning?"

I am sorry that you have this hunch, and I am afraid that this is pretty far from the truth. This is my essay and not Alexei's. Again, I will glad to give you an answer whenener I found the time to give a constructive comment.

Best,

Hippolyte

I agree that a simple "postulated" cut might left hungry for more. This analysis is a justification for a Gödelian hunch, and is more of a first step of a program rather than a definite claim.

Such mathematical study of cuts would nevertheless need to be done at a meta-theoretical level, otherwise it would lead to the return of logical inconsistencies.

Dear Jochen,

Thank you very much for your comment.

I came accross this idea that self-referential problems might be at the core of quantum weirdness while I was studying contextuality with Alexei Grinbaum in 2017. I was delighted to read your paper on ``Epistemic Horizons'' the next year, which was formulating so clearly my intuition and added a lot of fuel to it as well. I learned a lot from it, and as you may have guessed it was my principal source of inspiration for this essay.

Indeed a "Penrose pentagon" might have been enlightening to do the parrallel with the KCBS inequality !

I deliberately avoided to read your essay until now because I was afraid that I might get too influenced by it while I was writing my own essay. But now that it has been submitted, I am really going to enjoy the reading !

Best,

Hippolyte

Dear Eckard Blumschein,

Thank you for your interest. I will take a look at your essay too !

Best,

Hippolyte Dourdent

Dear Satyavarapu Naga Parameswara Gupta,

Thank you for your interest !

At first sight, I don't really know indeed how the Gödelian hunch might be found in Cosmology. If the Universe is treated as the largest system that an observer can studied (what the cosmologists do if I am not mistaken) , and not as "everything" included the observer itself, then no self-referential issue occurs. Maybe, on a very speculative note, the hunch would rather be found in the study of astrophysical objects at the frontier of relativity and quantum theory, e.g. black-holes or CTCs.

I will definitely have a look at your essay, thank you.

Best,

Hippolyte

Essay Abstract

What if the paradoxical nature of quantum theory could find its source in some undecidability analog to that of Gödel's incompleteness theorem ? This essay aims at arguing for such Gödelian hunch already suggested by Szangolies via two case studies. Firstly, using a narrative based on the Newcomb problem, the theological motivational origin of quantum contextuality is introduced in order to show how this result might be related to a Liar-like undecidability. A topological generalization of contextuality by Abramsky et al. in which the logical structure of quantum contextuality is compared with ``Liar cycles'' is also presented. Secondly, the measurement problem is analyzed as emerging from a logical error. A personal analysis of the related Wigner's friend thought experiment and and a recent paradox by Frauchiger and Renner is presented, by introducing the notion of ``meta-contextuality'' as a Liar-like feature underlying the neo-Copenhagen interpretations of quantum theory. Finally, this quantum Gödelian hunch opens a discussion of the paradoxical nature of quantum physics and the emergence of time itself from self-contradiction.

Author Bio

I am a 2nd year Phd student, studying quantum foundations. During my master studies, I worked on quantum contextuality, supervised by Alexei Grinbaum in CEA Paris-Saclay ; and I did my master thesis on the superpositions of quantum causal orders, supervised by Cyril Branciard in Institut Neel (Grenoble). My thesis, supervised by Cyril Branciard, aims at clarifying theoretically a conceptual connexion between quantum contextuality and quantum causality.

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