A Gödelian Hunch from Quantum Theory by Hippolyte Dourdent

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

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

The question is whether different cuts can be studied systematically (mathematically). Which one are possible, which aren't?

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

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

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

Dear Hippolyte,

Hopefully you understood my reply. I would just like to add that I don't argue against idealization but against taking ideals for reality.

And I am sure any reply by a Greenbaum was not more convincing to me than your one.

Best,

Eckard

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

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

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

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

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.