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RECENT POSTS IN THIS TOPIC

Jeffrey Schmitz: on 5/19/20 at 16:18pm UTC, wrote Hippolyte, There is no major self-referential issue because time is a...

Peter Jackson: on 5/19/20 at 1:12am UTC, wrote Hippolyte, One of the best wrestling matches against quantum theory I've...

Hippolyte Dourdent: on 5/18/20 at 14:17pm UTC, wrote Dear George, Thank you for your comment. In fact, Hofstadter already...

Hippolyte Dourdent: on 5/18/20 at 14:06pm UTC, wrote Dear Irek, Thank you very much for your nice comment. All the best, ...

Hippolyte Dourdent: on 5/18/20 at 14:06pm UTC, wrote Dear Jeffrey, Indeed logic seems to be at the core of ability to...

George Gantz: on 5/16/20 at 18:03pm UTC, wrote Hippolyte - A brilliant essay - and I'd like to thank Irek for pointing...

Irek Defee: on 5/16/20 at 11:16am UTC, wrote Dear Hippolyte, This is by far the best essay I read until now. It is...

Jeffrey Schmitz: on 5/16/20 at 5:29am UTC, wrote Dear Hippolyte, 1) Pigs can fly. 2) This statement is false. Both of the...


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FQXi FORUM
August 12, 2020

CATEGORY: Undecidability, Uncomputability, and Unpredictability Essay Contest (2019-2020) [back]
TOPIC: A Gödelian Hunch from Quantum Theory by Hippolyte Dourdent [refresh]
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Author Hippolyte Dourdent wrote on Apr. 24, 2020 @ 00:31 GMT
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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Satyavarapu Naga Parameswara Gupta wrote on Apr. 24, 2020 @ 03:17 GMT
Dear Hippolyte Dourdent,

Very nice essay on discussing Godels Hunch, you wonderfully discussed good history to disprove Godel. After seeing all these i got a small question, whether this hunch is applicable to Cosmology also?

I never encountered any such a problem in Dynamic Universe Model in the Last 40 years, all the the other conditions mentioned in Godels statement are applicable ok

I hope you will have CRITICAL examination of my essay... "A properly deciding, Computing and Predicting new theory’s Philosophy".....

Best Regards

=snp

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Author Hippolyte Dourdent replied on Apr. 24, 2020 @ 12:22 GMT
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

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Jochen Szangolies wrote on Apr. 24, 2020 @ 05:32 GMT
Dear Hippolyte,

you've produced a fantastic and highly readable essay. The linkage of contextuality graphs to inconsistent cycles of propositions seems, in hindsight, almost obvious---but requires a great creative leap to realize. (Perhaps, to make this more vivid, you could've chosen a 'Penrose pentagon', the structure of which should essentially yield the KCBS-incompatibility graph. But I think the point is clear either way.)

Likewise, your introduction of levels of meta-description, paralleling the introduction of meta-languages in mathematical logic, is highly illuminating---ultimately, as 'paradox' in mathematical logic enters through the ability to formulate meta-language predicates within the object-language (for sufficiently expressive systems), it enters into physics with the application of the same theory to object and observer ('meta-object'). And ultimately, neither is, of course, paradoxical in the true sense: the Gödel sentence, unlike the liar, does not talk of truth, but of provability within some formal system---it is only through the misguided attempt of identifying this notion with truth that something genuinely paradoxical emerges. Likewise, quantum mechanics only appears to be paradoxical upon the---similarly misguided---attempt to assign truth values to all propositions, regardless of context.

My original idea for this contest was to try and apply my own ideas to the Frauchiger-Renner paradox, but I felt this would get to unwieldy. Hence, I'm more than happy to see it given such a capable discussion from your perspective. I hope this essay will do well in the contest!

Cheers

Jochen

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Author Hippolyte Dourdent replied on Apr. 24, 2020 @ 12:41 GMT
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

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Jochen Szangolies replied on May. 1, 2020 @ 09:54 GMT
Dear Hippolyte,

sorry for taking so long to respond. I'm afraid I've somewhat overstretched my time budget in starting so many threads of correspondence in this essay contest.

One thing I've been thinking about, which I think needs some more thinking about (?), is how one could formulate these self-referential 'chains' of observables within my framework. Basically, I construct an 'inconsistent' observable by means of Lawvere's theorem---something not too dissimilar from Russell's set that contains itself iff it does not contain itself. It would be interesting to see whether one could extend this to yield something like the 'liar-cycles' which have no consistent assignment of truth values. Perhaps one could 'daisy-chain' the Lawvere argument.

Another question, it seems, might be whether there's an analogue to something like Yablo's infinite set of paradoxical sentences, too. This concerns sentences of the form:

(S_n): For each i > n, S_i is not true

Assuming S_n to be true, we get some later S_k, k > n, such that it is both true and not true; but then, assuming that each S_i is not true, yields the conclusion that S_n must be true, because that S_i for i > n is not true is exactly what it asserts. Hence, we obtain a contradiction.

This is an 'indirect' sort of self-reference, in that each sentence does not refer to itself, either directly or via a circle of intervening propositions, but rather, to the whole set of sentences, with a contradiction arising from that. I'm not sure, however, how one would go about finding an analogue of this in terms of observables.

Anyway, that's still sorta open-ended speculation on my part. I'd be very interested to hear your thoughts on my essay!

Cheers

Jochen

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Author Hippolyte Dourdent replied on May. 3, 2020 @ 12:45 GMT
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

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Eckard Blumschein wrote on Apr. 24, 2020 @ 07:01 GMT
Dear Hippolyte Dourdent,

I realized that Landsman seems to be interested in his Landsmann Brouwer.

Just another hint concerning contextuality:

My essay tries to show that Fourier was wrong when he claimed that complex FT is exactly as comprehensive as nature. I rather see it introducing an unnecessary redundancy that seems to play a key role in QM too.

Eckard Blumschein

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Author Hippolyte Dourdent replied on Apr. 24, 2020 @ 12:24 GMT
Dear Eckard Blumschein,

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

Best,

Hippolyte Dourdent

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Eckard Blumschein replied on Apr. 30, 2020 @ 02:55 GMT
Dear Hippolyte Dourdent,

To me, arguments are more important than votes. Don't hunch. Well, you have a hunch that what you learned is always true. Maybe, Alexei Grinbaum himself may challenge my unwelcome reasoning?

Best hope,

Eckard Blumschein

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Author Hippolyte Dourdent replied on Apr. 30, 2020 @ 12:04 GMT
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

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Member Alexei Grinbaum wrote on Apr. 26, 2020 @ 14:01 GMT
The question is whether different cuts can be studied systematically (mathematically). Which one are possible, which aren't?

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Author Hippolyte Dourdent replied on Apr. 27, 2020 @ 13:24 GMT
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.

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Edwin Eugene Klingman wrote on Apr. 27, 2020 @ 18:51 GMT
Dear Hippolyte,

You exhibit mastery of the topic and argue it well. You conclude:

Quantum theory does not only defy common sense, but it also defies classical logic, i.e. our common language and semantic. (...) But is nature itself paradoxical?

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.

Similarly, qubits are reasonable structure for spins in magnetic domains, but do not match the Stern-Gerlach measurement data shown on the famous postcard, of single spins in an inhomogeneous field. Under the influence of “quantum universality” (that is, absolute commitment to the projected structure) Bell forced qubit structure (A, B = +1,-1) onto SG, and derived his theorem. In actuality, 3D spins produce exactly the data shown on the postcard and the deflection measurements yield exactly the correlation that Bell claims is impossible.

This is ontological error based on absolute belief in projection, which works well statistically in some cases and leads to entanglement in others.

I put this heresy out for you to consider, some day, years from now, when things still don’t make sense.

I invite you to read my essay which focuses on ontology.

My best regards,

Edwin Eugene Klingman

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Author Hippolyte Dourdent replied on Apr. 30, 2020 @ 12:29 GMT
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

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Flavio Del Santo wrote on May. 3, 2020 @ 22:56 GMT
Dear Hippolyte,

thank you for a well-written essay, that I enjoyed very much reading.

It was a pleasant surprize to find that your main arguments come from the (semantic approach to) the quantum measurement problem analyzed through "Wigner's Friend Paradox". In fact, this is my main research topic, despite my essay focuses on something else. I think that your analysis based on objectes, meta-objects and meta-meta-objects is promising. If anything, although I intuitively understand how these problem realte, I would have liked a more explicit comparison between the quantum paradoxes you reassess and the logical paradox of the liar.

Anyways, congratulation on a great essay and I wish you good luck for the contest!

Flavio

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Michael James Kewming wrote on May. 6, 2020 @ 20:14 GMT
Hi Hippolyte,

Thank you for the very beautifully written essay. The introduction section discussing the topology of contextuality, the tension relating between local and global observations combined with Penrose Triangle was really very intuitive! Also the similarities between Hardy's paradox and the Liar's paradox were very clearly articulated.

The Wigner's friend paradox and freindification has always sat a little uneasily with me, although that is the experimental physicist in me coming out. Your conclusion ``Quantum paradoxes are not physical, but emerge from a lack of metaphysical distancing'' is certainly on the right track to explain these theoretical paradoxes.

Again, thanks for the great essay. It was really well written and I really enjoyed it! I hope you have enough time to take a look at my essay too.

Thanks,

Michael

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Author Hippolyte Dourdent replied on May. 6, 2020 @ 22:46 GMT
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

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Member Christopher A. Fuchs wrote on May. 10, 2020 @ 15:25 GMT
Dear Hippolyte,

I enjoyed a number of things in your essay. Indeed, collaborators and I are presently (finally) constructing a response to the Frauchiger-Renner issue, and there is a small section of our paper that concerns a question of self-reference, which we dismiss summarily. Perhaps though there is a more solid argument for what we want to assert, and perhaps your paper, even if not directly addressing our concern, will inspire an idea in us. I encourage you to continue these lines of thought. “Although it can describe anything, a quantum description cannot include everything.” – Asher Peres. Hear hear!

You correctly characterize QBism as having a “movable cut [which] is functional and not ontological.” Jacques Pienaar has recently made a very nice contribution toward mathematizing the movability of the cut from a QBist perspective. In case it is of interest to you, it can be found here:

https://arxiv.org/pdf/2004.14847.pdf

I don’t know if any of that will be expressible in your framework, but it might be worth thinking on.

All the best,

Chris Fuchs

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Jeffrey Michael Schmitz wrote on May. 16, 2020 @ 05:29 GMT
Dear Hippolyte,

1) Pigs can fly.

2) This statement is false.

Both of the above statements have something wrong with them. For statement 1, one would need knowledge of pigs to know that the statement is false. For statement 2, there is no need for external information; the knowledge of logic is all that is needed. If one did not know “logic” then how could the flaw with statement 2 and logic itself be explained? One would need to step outside of logic to explain the nature of logic. Languages as we know them (yes, even the communicates of animals) have logic, so we might not know a way to communicate with a being that did not possess logic. “Logic” seems to be hard-wired by evolution into our language center well before we became human because in evolution nothing so useful and complete language just appears.

Time is the problem with Quantum Theory. We live in the structure of time, so thinking outside of that structure is difficult. What if time was a function of entropy? The problem with entropy is that it is a collective state. A lone electron does not have a temperature or entropy state. We need an ensemble of atoms to define a state of entropy, which would define the “state” of time. Time ends up being the non-local of space-time. Going forward and back in time is possible and common at the quantum scale (I like to say “undefined” in space-time), but going “back” in macroscopic entropy is not possible. A positron could be considered an electron going backwards in time. A human-size time machine has entropy and must interact with the rest of the Universe to lower its entropy. Thermal dynamics is not reversible, while Quantum mechanics is fully reversible. An electron could kill its grandfather in childhood, but your grandfather is safe from that fate.

Sincerely,

Jeff Schmitz

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Author Hippolyte Dourdent replied on May. 18, 2020 @ 14:06 GMT
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

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Jeffrey Michael Schmitz replied on May. 19, 2020 @ 16:18 GMT
Hippolyte,

There is no major self-referential issue because time is a function of (in reference to) entropy. The observer effecting the observed state of a particle is a self-reference issue which is dealt with in Quantum Mechanics. Having time as a function of entropy ends up looking just like Quantum Mechanics (although harder to work with) with a non-local time instead of non-local space.

The self-consistent system of communication needs something outside of that system to define that system. "Logic" is one of the building blocks. We think of logic as being created by humans in the past few centuries, but training an animal requires the "if then" of a reward. Sometimes you can watch an animal solve a problem. This is primordial logic.

All the best,

Jeff

P.S. I know the contest is over, but, if possible, I would still like your opinion on my essay. Thank you.

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Irek Defee wrote on May. 16, 2020 @ 11:16 GMT
Dear Hippolyte,

This is by far the best essay I read until now. It is highly illuminating, it is possible to understand it without a deep dig into literature first and one learns why becoming meta-observer is not a good thing:). 10/10.

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Author Hippolyte Dourdent replied on May. 18, 2020 @ 14:06 GMT
Dear Irek,

Thank you very much for your nice comment.

All the best,

Hippolyte

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George Gantz wrote on May. 16, 2020 @ 18:03 GMT
Hippolyte -

A brilliant essay - and I'd like to thank Irek for pointing it out.

You've done a masterful job at building the theoretical case for what is intuitively obvious (at least since Godel) - that the world is fundamentally "liar-like" and therefore fraught with undecidables.

Although my essay lacks the rigor of yours, we are saying the same thing. Undecidability is a feature, not a bug, of physical and mathematical reality. I argue we can also extend this to the mind, and from an examination of the features of autonoetic consciousness (the mind looking at itself looking at itself) build a robust approach to understanding reality.

So far your's is the best essay I have read.

-George Gantz: The Door That Has No Key: https://fqxi.org/community/forum/topic/3494

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Author Hippolyte Dourdent replied on May. 18, 2020 @ 14:17 GMT
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

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Peter Jackson wrote on May. 19, 2020 @ 01:12 GMT
Hippolyte,

One of the best wrestling matches against quantum theory I've seen! Excellent stuff. And of course I agree the conclusive question; "..quantum theory is more paradoxical than other physical theories. But is Nature itself paradoxical?"

However might there be a different possible starting assumption and mechanistic physical measurement sequence producing the data? Shockingly I suggest there might. Neils Bohr carefully made NO assumptions about pair morphology, but if we assume simple Poincare sphere vector distributions, and the same for polariser electrons, we have TWO distribution; polar curl and equatorial linear, going inversely to 0 over 90 degrees. Whats more, the change rates are Cos Theta Latitude (of the absorption interaction tangent point).

We now only need 'entanglement' as matching axis orientation angle, and vector addition in 3D, we can produce Malus' Law at the 2nd (photomultiplier) interaction, and NOT require non-locality! (think of it as changed ellipticity of re-emission, only the major axis triggering ONE channel, or 50:50 if circular polarity. I identify John Bell anticipated such a solution (touched on in this years essay but given in more detail last year). It was independently verified to violate bells inequalities by Trails computer code and plot.

Few seem able to follow this (DFM) process. I hope you can. Do question it.

But well done for your essay and good understanding of QM.

Very Best

Peter

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