A Gödelian Hunch from Quantum Theory by Hippolyte Dourdent

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

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

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

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.