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FQXi FORUM
September 28, 2021

CATEGORY: Undecidability, Uncomputability, and Unpredictability Essay Contest (2019-2020) [back]
TOPIC: Undecidability of States and Epistemic Horizons as Quantum Gravity by Lawrence B. Crowell [refresh]
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Author Lawrence B. Crowell wrote on Feb. 11, 2020 @ 01:09 GMT
Essay Abstract

Quantum mechanics places limits on what can be observed. Further, while it is a deterministic wave theory, outcomes of specific measurements are purely stochastic. The geometry of quantum entanglements, or quantum phases in general, describes a topological obstruction to unitary transformations between GHZ and W states or bipartite and tripartite entanglements. The momentum map defined on Kirwan polytopes is in the framework of a fractal sets in state space has p-adic measure. Axiomatic incompleteness of any p-adic algorithm illustrates how these obstructions define these obstructions. This is similar to how the Euclid 5th axiom is undecidable, and geometry has different model systems. This is then argued to connect with quantum gravitation in how spacetime is an epiphenomenology from entanglement. .

Author Bio

Doctoral work at Purdue. Worked on orbital navigation and currently work on IT and programming. I think it is likely there is some subtle, and in some ways simple, physical principle that is not understood, or some current principle that is an obstruction. It is likely our inability to work quantum physics and gravity into a coherent whole is likely to be solved through new postulates or physical axioms, or the removal of current ones.

Download Essay PDF File
Note: This Essay PDF was replaced on 2020-04-04 22:00:34 UTC.

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Jonathan J. Dickau wrote on Feb. 13, 2020 @ 22:04 GMT
A fun paper to read Lawrence...

It also gives me a deeper appreciation of Tim Palmer's work, and of his ability to make those ideas comprehensible to a lay audience. You bring a delightful and different perspective to these contests; that is to say you think in a way that is more mathematical.

The Vector Calculus Bridge program developed by Dray and Manogue highlights the differences in how Maths are taught in Math and Physics classes, where in one case the focus is on solving a small set of problem cases quickly and well, while in the other there is a focus on the general case, and explicating specific cases. So it makes a difference if you learned things better in Physics or Math classes.

You bring the latter approach to Physics problems, by trying to show that the ordinary or simple case IS an example of a more general rule that applies. And by looking at the generalities in detail; you give more meaning or significance to the specific circumstances physicists deal with. Kudos for that, and high marks overall for a paper I'll want to read over before rating.

I find it interesting that you focus in large part on the work of two other contest participants. I will have more to say about what happens at the horizon, after reading for detail. But you know I've gotta love a paper that talks about both octonions and fractals - as do I. Best of luck.

Regards,

Jonathan

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Author Lawrence B. Crowell replied on Feb. 14, 2020 @ 00:48 GMT
Thanks for the interest. Due to time pressures I have only read 4 papers here. I will try to get to more in due time. I unfortunately have not read your yet.

This does carry from Palmer's ideas, though my concept of incompleteness is different. since this incompleteness exists it is my conclusion that quantum outcomes obtained occur for no computable reason. They simply are. Now one can appeal to a quantum interpretation, but none of them appears more demonstrable, let alone more provable, than any other.

Cheers LC

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Jonathan J. Dickau replied on Feb. 14, 2020 @ 00:55 GMT
That's a cool way to describe it Lawrence...

You might enjoy my essay this time out, because it is more mathematical and focuses on the idea of convergence. I do keep the derivations in the endnotes however. Good to see you in the contest regardless.

All the Best,

Jonathan

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Jonathan J. Dickau wrote on Feb. 14, 2020 @ 02:25 GMT
I wanted to comment further...

You have achieved a greater level of clarity with this paper than in some of your previous work Lawrence. A lot of prior knowledge was assumed. I know I've picked up a few things, but it seems there is more ease of comprehension and also a greater congruency insofar as a nice conversation between the descriptions and the Math and good agreement between them or applicability throughout. This adds to the paper's impact and clarity.

Of course; there are a few flubs. Right in the abstract; it's a tautology to say obstructions cause obstructions. You might have meant considerations, conditions, limitations, restrictions - or something like that - causes obstructions. And I have no knowledge of Hamitlonians. But overall; it is well-written, where you get your point across, and you have a good point to get across. I was able to understand most of it, and since I didn't come into the process with an understanding of your topic; I have to credit good writing.

Best,

Jonathan

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Author Lawrence B. Crowell replied on Feb. 14, 2020 @ 11:46 GMT
It is a case of editing that resulted in:

Axiomatic incompleteness of any p-adic algorithm illustrates how these obstructions define these obstructions.

Where the first instance of the word obstructions should be incompleteness. Dang! it is something that happens when you write and do all your own proof reading.

LC

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Jonathan J. Dickau replied on Feb. 14, 2020 @ 16:18 GMT
It keeps getting better...

And that's good. Even the finest textbooks have lists of errata published later. So there is no shame nor a reason for it.

Best,

Jonathan

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Jochen Szangolies wrote on Feb. 16, 2020 @ 10:58 GMT
Dear Lawrence,

I'm glad you found the time to place an entry in this year's contest. There is, as usual, much to unpack in your contribution, and I'm sure it will amply repay repeated reading.

For now, one thing I'd like to understand better is the relation to set-theoretic forcing you see. Of course, part of this is simply that I don't have a good understanding of forcing...

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Author Lawrence B. Crowell replied on Feb. 16, 2020 @ 12:50 GMT
Jochen,

The crux centers around the p-adic solutions of Diophantine equations. My paper references Palmer’s work, in fact a paper by Hossenfelder and Palmer [ S. Hossenfelder, T. N. Palmer, "Rethinking Superdeterminism," https://arxiv.org/abs/1912.06462v1 ] with the fractal sets in state space. It is a nifty idea in one sense, though I doubt the superdeterminism concept it is meant to...

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Peter Jackson wrote on Feb. 27, 2020 @ 16:43 GMT
Hi Lawrence,

Thanks for your post on mine; "There are identical particles in QM"

I respond;

"Yes, only 2 types so 50% must be. But 'conjugate pairs' are opposite! Bohr assumed if one is 'spin up' the other MUST be 'spin down'. THAT was the shockingly simple error leading to all the 'weirdness' nonsense.

In the CORRECT version (DFM); Bob and Alice can reverse their OWN finding, so we don't need 'action at a distance' to violate Bells inequalities and reproduce the data set & Dirac equation.

But doctrine now seems embedded in such a deep hole I doubt we'll find anyone with both the intellect and influence to advance understanding. Do you?"

I hope to read yours soon.

Best

Peter

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Author Lawrence B. Crowell replied on Feb. 28, 2020 @ 17:08 GMT
With spins you can have entanglements that are singlet or triplet for spins anti-aligned or aligned. In fact you can have a superposition of all fur Bell states. With bosons the exchange is positive or with Z cyclicity for n particles. With fermions you have Z_2 for two fermions, indicating a different topology from bosons, and for N fermions this is generalized with Slater determinants.

The connection with gravitation implies there is some generalization of what is meant by entanglement.The equivalency of quantum entanglement with measure of spacetime is some generalization of how entangled and separable states are correlated with each other. This might also be seen in how quantum gravitation as an UV physics is dual to gauge fields at lower energy (smaller mass) or IR scale:

Quantum gravitation at UV = quantum fields at IR,

which is one way of writing the Einstein field equations.

LC

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Peter Jackson wrote on Feb. 28, 2020 @ 21:58 GMT
Indeed. But your explanation of 'entanglement' shows you haven't read or understood how the need for that assumption is removed when derived classically. This is big stuff Lawrence! You're locked into Bohr's assumptions leading to tangled solutions & weirdness and ignoring the direct route Bell insisted must exist.

Bob's ability to reverse HIS OWN finding in each case by turning his dial (for ANY particle set) negates the need for ANY 'entanglement' beyond parallel spin axes with opposite orientation. That then reproduces the data and the solution Bell couldn't find.

But you do need to ontologically UNDERSTAND QM's experimental set ups, data set, and the mechanistic sequence which reproduces it. I'm sure you understand the key is in producing Cos^2Theta, the spin stats theorem, and so Dirac equation. Do you have that understanding of 'QM'.

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Author Lawrence B. Crowell replied on Mar. 3, 2020 @ 10:55 GMT
If one works with classical physics of course there is no entanglement. Entanglement is a representation of topological difference between quantum and classical mechanics. The N-tangle that separates entropy configurations with N states in different entanglements is a topological obstruction that does not occur in classical physics.

LC

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Peter Jackson replied on Mar. 4, 2020 @ 21:18 GMT
Lawrence,

Interesting way to describe entanglement, statistical not physical as assumed. Yet if QMs experimental data set can be shown to reproduced, as Bell suggested it should be, with a classical deterministic model, is that not likely a conclusive proof that Bells view was correct? (As Tim Palmers view).

Peter

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Author Lawrence B. Crowell replied on Mar. 13, 2020 @ 11:23 GMT
Updated comment: The idea of superdeterminism is really a statement of nonlocality. The idea that no two points or events in the universe are completely independent is a nonlocality expected of quantum gravity. Anything approaching a black hole is never seen to cross the event horizon, but at the same time Hawking radiation occurs. This means that quantum states do not have a unique location in space, but rather have a nonlocality that is probably a salient feature of quantum gravitation.

Palmer and Hossenfelder place this in the context of hidden variables, where an average over these gives standard QM result. This has a Gaussian or standard statistical distribution that on average removes this dependency between regions of spacetime. This means the statistical independence of establishing initial states and the subsequent measurements are not entirely secure. Palmer places this in the setting of undecidability, but on a version of undecidability that is somewhat controversial. This is the Blum, Shub, and Smale (BSS) concept of undecidability of fractals. I work within a more standard idea, where the complement of fractal sets are undecidable. This leads into the undecidable nature of Diophantine sets and p-adic numbers.

Cheers LC

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Author Lawrence B. Crowell wrote on Mar. 5, 2020 @ 00:51 GMT
If you read my paper, you can see I discuss a fair amount of material on the geometric aspects of quantum mechanics and entanglement. The references I include are from authors who have contributed to these developments. The most elementary form of this is the Fubini-Study metric.

Quantum mechanics is curious in that it is completely deterministic as a wave dynamics, but the amplitudes of...

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Peter Jackson replied on Mar. 26, 2020 @ 20:31 GMT
Thanks Lawrence,

I think 'stance' is about 'beliefs', which I eschew. Let me ask you this;

Let's say Bohr came up with TWO options for interpreting QM's data set;

FIRSTLY a classical mechanistic sequence of orthogonal 'curl' AND linear OAM momenta with rotational vector additions, orthogonal, and uncertain at the changeovers.

SECONDLY what we have now; one as a weird 'quantum spin' state, so a string of other irrational or non causal effects EPR rejected.

Which would any intelligent physicist have been likely to go for? Bear in mind John Wheeler anticipated exactly the first option & John Bell firmly agreed.

I simply identify the sequence achieving that. It seems to me only embedded flawed beliefs, following the flock or poor understanding cause most to chose the 2nd.

Do you REALLY believe that's not possibly the case?

Peter

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Author Lawrence B. Crowell replied on Mar. 27, 2020 @ 20:28 GMT
Quantum mechanics is a wave mechanics that is as I say perfectly deterministic. It is once there is a so-called collapse, or a transfer of quantum phase out of the system on a time scale t

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Author Lawrence B. Crowell replied on Mar. 27, 2020 @ 20:41 GMT
Carrot sign cut off post

Quantum mechanics is a wave mechanics that is as I say perfectly deterministic. It is once there is a so-called collapse, or a transfer of quantum phase out of the system on a time scale t ltlt 1/ν, for ν the fundamental frequency of the quantum system, that things get a bit odd. There have been various attempts to rescue this situation, where hidden variables are...

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Christian Corda wrote on Mar. 12, 2020 @ 15:00 GMT
Hi LC,

As usual, you made an excellent work. I see that your Essay has connections with the Essay of Szangolies, that I have found interesting too. In a certain sense, you extends Szangolies’ approach to the search of quantum gravity. I like a lot your sentence that "Spacetime built from entanglements or QM equivalent to GR means conservation of quantum information and the equivalence principle are either equivalent themselves or are in some duality with each other". I really hope that you are correct on this. But, till now, it seems that Nature needs to generate a breakdown of one of them if it wants to save the other. This is the big problem in order to realize a theory of quantum gravity.

I wish you good luck in the contest.

Cheers, Ch.

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Author Lawrence B. Crowell replied on Mar. 12, 2020 @ 16:27 GMT
This implies some relationship between CHSH polytopes and Kirwan polytopes. I am not exactly sure how that will work. To be honest I seems to at least tangentially have something to do with the Born rule. The CHSH polytope pertains to conditional probabilities with entanglements and the Kirwan polytope with eigenvalues of entanglements.

Cheers LC

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Steve Dufourny wrote on Mar. 12, 2020 @ 16:31 GMT
Hi Lawrence, a very good essay I must say. I am curious so I am going to ask you several simple questionS. What are for you the causes of our geometries, topologies, matters and properties ? and philosophically speaking also , what is the cause of all this ? Regards

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Author Lawrence B. Crowell replied on Mar. 13, 2020 @ 10:59 GMT
The word cause is probably not quite appropriate. The word source might be better. I would say a source for the topological obstruction may be this epistemic horizon or a fundamental undecidability of states. The entanglement symmetries of GHZ and W states are separated by this 3-tangle for 3 states. This is a topological obstruction that has a measure based on the degree of uncomputability of states of one entanglement by another. As a result the basis for these topological obstructions should be a measure of unobservability or of deciding one set of measured states based on another set of measured states.

Cheers LC

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Steve Dufourny replied on Mar. 13, 2020 @ 14:47 GMT
Hi , it is well generalised. What is this source, it is what I try to encircle. What is the cause of our reality and its geometries, topologies, matters and properties? and why all this is undecidable and uncomputable, is it due to philosphical limitations or errors or is it because we know so few about our main physics? If I can Lawrence, I d klike to have your general philosophy about these mathematical and physical objects and the philosophy correlated , why we have these geonetriesm topologies, matters and properties? and how this universe transforms and codes this energy to create this physicality for you, That will permit us to go deeper about the generality . I liked your essay, it is one of my favorites, friendly, regards.

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Steve Dufourny replied on Mar. 13, 2020 @ 14:59 GMT
I beleive that in fact Lawrence the generality of this philosophy about this source is important and the link with the foundamental objects. The fact to consider that all is Waves , strings and fields instead of particles or the opposite becone a main general key to really understand why we have this physicality. If we consider that this universe is just an energy oscillating tranformaing the enery in matters and if we consider that we have just photons like main essence, it is a kind of prison of beleifs for me. I see that these strings or geometrodynamics are a real fashion inside the theoretical sciences Community, maybe the main cause is due to Witten and Einstein, many maybe have counfound the field medal of Witten for a relevant work in maths about the fields and his theoriy of strings. It is two things totally different in fact, we cannot affirm that these strings are foundamental objects at this planck scale and the same for the Cosmic fields linked with thes quantum strings. We cannot affirm simply, I consider personally in my model coded 3D particles and they can explain also all our geometries, topologies, matters and properties. That is why I d like to know your general philosophy about the source like you told me.

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Author Lawrence B. Crowell wrote on Mar. 21, 2020 @ 14:12 GMT
Todd Brun found [ https://arxiv.org/pdf/gr-qc/0209061v1.pdf ] that P = NP is true for closed timelike curves. This is a short, readable and decent paper. The extension to all PSPACE and undecidable propositions is of course difficult to prove explicitly. However, a spacetime that permits CTCs will present Cauchy horizons, and in principle an observer can in a finite time verify whether a Turing...

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Jonathan J. Dickau wrote on Mar. 21, 2020 @ 20:22 GMT
Thanks for your kind comments Lawrence...

I have not made the rounds of doing ratings yet, and yours is one essay I especially liked, so stay the course and keep the faith; you have fought a good fight. I think your paper is far more on-topic than some others, and I find your answers satisfying for the most part.

I'll comment further, once I do make the rounds for the first batch I read. I will re-read your paper for detail, and I'll keep in mind what you said about its content, back on my page. I may ask for clarification on one or two points.

All the Best,

Jonathan

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Author Lawrence B. Crowell replied on Mar. 21, 2020 @ 22:40 GMT
Hi Jonathan,

Actually that was a general note, However thanks for the kind words.

I too have only read a handful of papers here. I have been pretty hard at work on this. I have not had much time to read papers or communicate with authors. I am now off work, as we are now into "social distancing." So we have to endure this exercise in Camus' existential angst in his novel The Plague with the expectation this will lessen the impact.

Stay safe and away from crowds. This virus seems to take older people down a lot. I am not worried about myself much, but I have some concerns with others. My mother is over 90 and I concerns there.

Cheers LC

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Author Lawrence B. Crowell wrote on Apr. 4, 2020 @ 22:00 GMT
Lawrence Crowell re-uploaded the file Crowell_fqxi_2020.pdf for the essay entitled "Undecidability of States and Epistemic Horizons as Quantum Gravity" on 2020-04-04 22:00:34 UTC.

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Author Lawrence B. Crowell replied on Apr. 24, 2020 @ 14:52 GMT
I am not sure whether it is worth trying here, but I cured a word tangle in the abstract, I also include below some additional study and work that goes along with this.

I recently re-read the paper The Page curve of Hawking radiation from semiclassical geometry by Almheiri, Mahajan1, Maldacena, and Zhao arXiv:1908.10996v1. There is no paper of late that I have read so many times as this....

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Andrew Beckwith wrote on Apr. 12, 2020 @ 14:31 GMT
quote

Wheeler with his question, “Why the quantum,” pondered whether quantum mechanics was built from

more elementary nuts and bolts. In the old Oxford symposium book on quantum gravitation Wheeler

speculated quanta were built from some undecidability of an elementary system [18]. Wheeler was

thrown out of G¨odel’s office for asking this question, and for anyone who has pondered this and deigned

to mention this, it is often greeted with disapproval. Szangolies presents arguments for undecidability by

considering an elementary model and a Cantor diagonalization [6]. This leads to a form of information

barrier or epistemic horizon. In this paper it is argued that different entanglements are obstructed away

from each other. This obstruction is fundamentally the same as the epistemic horizon is what keeps two

entanglement types topologically separate. In what is presented here the door is further opened

end of quote

This is in my reasons why I gave you a solid 10 - I concur with your viewpoint

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Author Lawrence B. Crowell wrote on Apr. 12, 2020 @ 23:56 GMT
Thanks, and my essay does take off in a different direction from Szanglolies, but is framed around his idea.

I have yet to read many essays. I have been saddled with this Covid-19 for over 2 weeks. There is a lot of fatigue with this. It has pneumonia-like symptoms, though comparatively mild. The biggest issue now is just the fatigued feeling and having to sleep 12 hours a day.

Anyway I will make a real effort to start reading essays and yours first.

Cheers LC

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Stefan Weckbach replied on Apr. 14, 2020 @ 12:24 GMT
Dear Lawrence,

i had a similar illness two years ago during the last essay contest. It was the influenza-virus and even after being cured i needed much more sleep. Without that additional sleep i think my that fatigue would have turned into cronical fatique. So please regenerate yourself properly.

I read your essay several times and i like that you try to get the bigger picture on QM. I also liked what you have to say about p-adic numbers, locality and decidability.

Take care and best wishes

Stefan

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James Lee Hoover wrote on Apr. 17, 2020 @ 18:20 GMT
Lawrence,

Welcome back.

Quite a scholarly piece that penetrates the underlying quantum world and entanglement quite well to prove prediction limits in our classical world. I wonder if you have seen the studies that seem to bridge the two worlds: https://phys.org/news/2018-11-quantum-criticality-supercondu
ctivity.html. I cite them in my essay re bridging efforts in overcoming limits. Your topological obstruction theory is quite interesting, at least what I can understand of it.

Jim Hoover

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James Lee Hoover replied on Apr. 17, 2020 @ 18:39 GMT
Lawrence,

Mine is your 6th rating. I say this because there is someone who gives 1s to a number of us w/o comments.

Jim Hoover

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Christian Corda wrote on Apr. 20, 2020 @ 10:38 GMT
DEARS READERS,

LAWRENCE CROWELL CANNOT CURRENTLY POST IN FQXI WEBSITE. THUS, HE ASKED ME TO POST THE FOLLOWING MESSAGE FOR ALL OF YOU:

"TO ALL WHO POST ON MY SITE. FOR SOME REASON I CAN'T ACCESS THE BLOG WRITING. AS A RESULT DON'T BE PUT OFF IF I CAN'T RESPOND. SUPPOSEDLY THE FQXI TECH FOLKS ARE GOING TO FIX THIS.

THANKS LC"

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Author Lawrence B. Crowell wrote on Apr. 23, 2020 @ 20:52 GMT
I am back in action now. I can now write and vote.

LC

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Author Lawrence B. Crowell wrote on Apr. 24, 2020 @ 14:51 GMT
I tried to post this last week and it would not let me. I try again.

I recently re-read the paper The Page curve of Hawking radiation from semiclassical geometry by Almheiri, Mahajan1, Maldacena, and Zhao arXiv:1908.10996v1. There is no paper of late that I have read so many times as this. This paper relies heavily upon the idea of quantum extremal surfaces and this paper Quantum Extremal...

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James Lee Hoover replied on Apr. 27, 2020 @ 02:37 GMT
Lawrence,

The problem could be your browser. I use google and have only had trouble posting ratings since yesterday.

Jim Hoover

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Author Lawrence B. Crowell wrote on Apr. 24, 2020 @ 14:51 GMT
This is a follow on with this. I am not sure if it is worth pressing on with this, but these are additional studies and developments.

I recently re-read the paper The Page curve of Hawking radiation from semiclassical geometry by Almheiri, Mahajan1, Maldacena, and Zhao arXiv:1908.10996v1. There is no paper of late that I have read so many times as this. This paper relies heavily upon the...

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Michael muteru wrote on Apr. 30, 2020 @ 10:08 GMT
Hi Dr Cromwell. I am particularly excited by the 3-tangle turple in Quantum mechanics.maybe it means from the default two observers in the Michelson morley double experiment,what we interpret as qm may be the virtual "third picture/observation" borne from the Human brain supposition of dual state of matter in the quantum world. I have a simple piece on bias out of the paradox in my essay https://fqxi.org/community/forum/topic/3525.you may kindly review/rate on the simple diagrams,any input will be appreciated. thanks .All the best in the essay.

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Author Lawrence B. Crowell replied on Apr. 30, 2020 @ 11:51 GMT
The 3-tangle is a case with GHZ and W entanglements. These are separated by a topological obstruction. This just means there is no unitary basis by which one can evolve into the other. This is at least as a closed system. These entanglements can lose quantum phase to a reservoir of quantum states, or quantum noise, which mean that ignoring those states, say tracing them out, gives the appearance of the same state. This is then a coarse grained perspective of decoherence.

I will take a look at your page ASAP. I have been dealing with this Covid19 and it has made me quite fatigued and I have difficulty doing as many things as I used to just 6 weeks ago. I have made a self-promise to really read as many papers here as possible, but by evening time I find myself too tired out.

Cheers LC

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Jonathan J. Dickau wrote on May. 7, 2020 @ 21:27 GMT
I enjoyed your earlier version Lawrence...

I am returning to offer my rating, but I must peruse the revised copy first. It appears that you added some interesting new content, as well as cleaning things up. I commend you for persevering despite being ill. Hopefully you will return to full strength. I know that the recovery can take a while for some, even after the virus is eliminated.

Best,

Jonathan

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Author Lawrence B. Crowell replied on May. 7, 2020 @ 22:40 GMT
All I did was to change about 4 words in the abstract. There was a bad misstatement in there. In fact I think you pointed it out.

I am largely done with the flu-like symptoms, and have been for several weeks. The one problem is the fatigue is still a bit persistent. I am sleeping more, but not up to the 12hour/day a month ago.

Cheers LC

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Jonathan J. Dickau replied on May. 7, 2020 @ 23:14 GMT
Glad to hear you are out of the woods,

We will all need our strength to get things going and back to normal.

Best,

JJD

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Jonathan J. Dickau wrote on May. 7, 2020 @ 23:28 GMT
This paper is a significant work Lawrence...

From my view; your work is coming to resemble more and more that of Ed Witten. I mean that both as a compliment and a criticism. On the one hand; you are a truly deep thinker with a good grounding in the Maths that let you express your thoughts. On the other hand; your paper is dense with Math and the reader gets immersed pretty quickly, which can overwhelm some who are less Math-agile, and overload some who are - before they get your point. I get the same effect from reading Connes. I know there is something amazing there, and it's exciting to try to follow it, but it's easy to get lost if you don't know some of the technical terms and techniques well.

So I give you high marks but not full credit. This work is patently amazing, and it is obvious that it addresses the organizers' questions in a detailed way, but you make me go back to the books a bit too often - in order to fully grasp your point. I am not 100% sure I understand you completely yet, and I feel that this contest is a forum for people like yourself to prove their ability to reach a broader audience. All in all; I think you did quite well. It almost comes across as a advertisement for Szangolies and Palmer in places, though, and they may not need the boost. But I will help you a bit.

This is a paper I'll probably read multiple times, for what it is worth. There is a lot of meaning to mine from this exploration.

All the Best,

Jonathan

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Branko L Zivlak wrote on May. 10, 2020 @ 16:37 GMT
Dear Lawrence Crowell

The only thing I'm sure of in quantum mechanics is your next sentence:

"Quantum mechanics requires an extension of real variables of classical mechanics into complex variables."

After all, I came to that conclusion with my theory, but I can't go further.

Please answer me if you agree with my general position (assumption):

Quantum mechanics occurs, in frame exp (i * pi).

Since I am not educated for the field you are writing about, I do not understand your formulas. So, if you don't understand the formulas in my essay then we are 1: 1.

The text I wrote is nothing special anyway. In any case, your work deserves high marks. By my criteria, and because it contains formulas.

Regards,

Branko

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Author Lawrence B. Crowell replied on May. 10, 2020 @ 17:51 GMT
The equation e^{iπ} = -1 is called the Euler equation. It also leads to complex number. Consider the natural logarithm of a negative number ln(-x). In the field of real numbers we are stuck but we can use the rule of logarithms ln(ab) = ln(a) + ln(b). So, ln(-x) = ln(x) + ln(-1) and we can at least peel off the part we don’t understand. As a result, with Euler equation write

ln(-x) = ln(x) + ln(e^{iπ}) = ln(x) + iπ

due to the inverse function of the exponent e^{iπ}. We can also use e^{iπ/2} = I to evaluate the logarithm of an imaginary number ln(ix) = ln(x) + iπ/2.

Quantum mechanics can be thought of as a map of classical mechanics to the quantum according to the Poisson bracket formalism. This bracket {q, p} = (∂q/∂q)(∂p/∂p) – (∂q/∂p)(∂p/∂q) = 1 is replaced with the commutator {q, p} → i/ħ[q, p], where these are now operators. The commutator is then equal to i = √(-1). So, in that sense quantum mechanics does have this funny relationship with imaginary numbers.

The wave function in QM is complex valued. A complex number is z = x + iy. The magnitude of this number is computed with its conjugate z* = x - iy and so zz* = x^2 + y^2. Then with a little trigonometry we have z = zz*(cosθ + isinθ) = zz*e^{iθ}. A polar form of a wave function is of this form.

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Branko L Zivlak replied on May. 11, 2020 @ 06:29 GMT
Dear Lawrence Crowell

Thanks for your comprehensive comment, even though you didn’t answer my question. Ultimately, it is evident that you are one of the few who speaks about the universe and understands logarithms. My question was related to the boundary case when theta = pi.

Why is it important. Because in all my works and earlier FQX essays you can see the importance of another borderline case (frame), ie. Exp (2 * pi). You can see the results of such an approach to classical physics through the predictive formulas at the end of my essay this year.

Regards,

Branko

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Author Lawrence B. Crowell replied on May. 12, 2020 @ 00:42 GMT
I will try to read your essay in the near future. This issue with the Euler formula hinges around the unit circle in the complex plane with

e^{iθ} = cosθ + isinθ,

where this is a way of thinking about trigonometry. the multiplicity of these functions for angles θ → θ + 2π is a part of the reason ln(-x) = ln(x) + iπ, but also the entire set {…, -3iπ, -iπ, iπ, 3iπ, …}. This leads to the concept of Riemann sheets, where the complex plane has multiple copies.

Cheers LC

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James Lee Hoover wrote on May. 12, 2020 @ 06:10 GMT
Lawrence,

Hope you have time to check mine out before the deadline: https://fqxi.org/community/forum/topic/3396

Jim Hoover.

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Cristinel Stoica wrote on May. 15, 2020 @ 07:38 GMT
Dear Lawrence,

Very good and informative essay, with interesting insights and connections, thank you! I liked how you connected different structures and techniques in quantum mechanics to build an argument about the relation with undecidability. Particularly, I am interested in the topological obstructions, but for independent reasons. Thanks again, and I wish you success with the essay!

Cheers,

Cristi

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Author Lawrence B. Crowell replied on May. 15, 2020 @ 12:24 GMT
Thanks for the boost. Try to read Szangolies’ essay on a related development, and Palmer's on the fractal geometry.

Your paper works with the connection between Gödel theorem or self-reference and consciousness. I have thought that consciousness is a sort of epiphenomenology that is an illusion having an illusion of itself. I have not read it in its entirty, and I do see you connect with what look like fractals.

I have been slow. I have had Covid-19. It hit me at the 3rd week of March and lasted about 10 days. It relapsed in April and the fatigue part of this was serious. I still sleep more than I used to, but the most pernicious aspect of this has been dogging me. It is as if my brain has been rewired, or maybe hormone setpoint levels changed. I am not quite the same person I was; I feel as if I am an abruptly changed person. The worst part of this change is that I am more depressed and irritable than I was. It has been hard for me to participate much in this contest.

Cheers :LC

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Cristinel Stoica replied on May. 15, 2020 @ 18:30 GMT
Dear Lawrence,

Here's what I replied to your comment on my page:

Thanks for the visit. I am very sad that you got Covid-19, I hope it is the easiest form and you'll be well as soon as possible. Don't worry about my essay until you get well, but please get well, because I would love to hear some feedback from you, if possible about the longer version, even if it will be long after the contest ends.

> Your paper works with the connection between Gödel theorem or self-reference and consciousness. I have thought that consciousness is a sort of epiphenomenology that is an illusion having an illusion of itself. I have not read it in its entirty, and I do see you connect with what look like fractals.

I didn't appeal to self-reference or fractals, although I'd agree with you that they play a role. But it has strong relation with no-go theorems. As for consciousness, I am interested in the hypothesis that there is something irreducible about it (this irreducible I called "sentience"), and I try to see if this makes testable predictions. My claim is that it does. Indeed, for many who think consciousness is irreducible, the epiphenomenal position seems a good refuge, since it makes the hypothesis unfalsifiable. But I think we should be brave and don't avoid the fact that it does make predictions. So we can test it. We risk, those who deny it risk to see the predictions confirmed, but they can still continue to deny it, since the test of a prediction is not necessarily a proof of what led to the prediction. A rejection of the prediction is a rejection of what led to the prediction, so it is more risky for those who endorse the position that consciousness is not fully reducible. If we want to bring the hard problem into science, we have to take this risk.

I wish you to get back in shape soon!

Cristi

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Vladimir Nikolaevich Fedorov wrote on May. 18, 2020 @ 05:56 GMT
Dear Lawrence,

Glad to read your work again.

I greatly appreciated your work and discussion. I am very glad that you are not thinking in abstract patterns.

While the discussion lasted, I wrote an article: “Practical guidance on calculating resonant frequencies at four levels of diagnosis and inactivation of COVID-19 coronavirus”, due to the high relevance of this topic. The work is based on the practical solution of problems in quantum mechanics, presented in the essay FQXi 2019-2020 “Universal quantum laws of the universe to solve the problems of unsolvability, computability and unpredictability”.

I hope that my modest results of work will provide you with information for thought.

Warm Regards, `

Vladimir

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Author Lawrence B. Crowell replied on May. 18, 2020 @ 22:40 GMT
I brought your essay up and I find that today is the deadline. I thought it was a bit later. I have a several of these to read.

LC

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Torsten Asselmeyer-Maluga wrote on May. 18, 2020 @ 22:05 GMT
Dear Lawrence,

I beg for the best and a full recovering from COVID19. Here in Germany, everybody try to enforce the goverment to open the restaurants, we have demonstrations agains the lock-down. I hate it. your case show it that it is wrong and we have to be careful to not getting the virus.

But now back to your very thoughtful essay. I'm a fan of the magic Tits square and now I use very much discrete groups, fractals (or the higher-dimensional generalizations like wild embeddings),...

I gave your essay the highest vote,

Good luck for you

Cheers

Torsten

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Author Lawrence B. Crowell replied on May. 18, 2020 @ 22:38 GMT
Hi Torsten,

I somehow missed that you had an essay in lot here. I will queue that up to read. I just looked and today is the deadline! Somehow I thought it was in June. I will surely pull you essay up and make a quick judgment about it. I remember your previous work was interesting.

The Covid=19 was not that bad at first. Last years beginning 2019 I had influenza that made me a whole lot more sick, threateningly so. I had a mild fever, a dry and not compulsive cough, lost my sense of smell, etc, but the next to worst part is that I have been very fatigued, and that has persisted.. However, the most disturbing part is that I feel as if this has rewired my brain. Seriously, I feel slightly different or that I am a different person now.

I think Europe is better set than the US, where the hybrid between Godzilla and an orange baboon, Don-the-Con t'Rump, who runs this country is leading us into complete ruin. It can be worse, a friend of mine in Brazil has given me the fill on Bolsanoro, who is a complete moron.

Gotta get to some essays.

Cheers LC

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