It from qubit: how to draw quantum contextuality by Michel Dr Planat

Dear Dr. Michel Planat

Thanks and congratulations for your poetic qubits.

I am mere a learner of physics here who have huge interests to know the fundamentals in nature. I think that to resolve the issues like "quantum non-locality and contextuality' in your essay, why not we ask the nature in different ways? I invite you to read my submitted essay for a quite new approach of asking the nature.

With my regards

Dipak

Dear Michel,

Thank you for reading my essay and commenting on it. I have had a chance to review the two papers you referenced there. The Riemann paper discusses the details of a specific partition function, which I find interesting as I base the applicability of the Born probability to my wave function model on the partition function. The other paper, on time perception is also interesting. I had not seen the Poincare discussion of the Continuum, and found that fascinating, as well as your connection. I am somewhat confused as to whether you are proposing the phase locking as the 'mechanism' of time perception or of the 'scaling' of time perception? I can understand how this could relate to scaling, but not perception as I understand it.

Thanks again for reading my essay. I hope it stimulates some ideas for you.

Best,

Edwin Eugene Klingman

Dear Michel,

thank you for stopping by to comment on my essay. I was very much intrigued by your work and remember it from last year. It appears your presentation is more technical this year. I wish your interesting work reserves recognition is deserves among the specialists.

Best of luck :)

Dear Dr. Michel,

I have rated your innovative essay with maximum honors and wish you best of luck in the essay contest.

Best regards,

Sreenath

Dear Dr. Planat,

Your highly technical treatise was most absorbing, though in many parts I had difficulty following it. I will therefore state my comments along the broadest lines.

My view is that even if the emergence of random outcomes can be explained and contextualized in a variety of ways, the nature of information remains unchanged: It still defines the Observer's 'patch of reality' at any given moment, and continues to do so throughout evolution.

Even if we could describe the quantum world in perfect mathematical language, we would still have only described some small part of our Cosmos perfectly; and we would still be involved in our distinctive human Cosmos ... one that displays a continuous correlation between Bit and It over the course of evolution.

The observer does not interact with the whole field of reality regardless of how probabilities emerge, or how context affects them. Mathematics is the projection of the human mind on to the Cosmos - it will always be this, and it will always be entirely composed of Bits, thus keeping the Bit-It conundrum relevant to any definition of the Cosmos.

Though it is doubtless critical to investigate quantum reality as thoroughly as you do, I think we must also ask: 'Why do Bits 'match' Its so consistently at every instant of evolution - whatever their mathematics?' It would be interesting if the mathematics could be applied to the larger context of the perpetual Correlation of Bit to It.

As you can probably tell, this is one of the strands of my essay - which I think you would find interesting for the reasons I've stated.

Once again, yours is a very serious work, one with consequences; I am eager to hear your feedback, and wish you all the best.

John

Dear Michel,

I think it is always good when someone examines the connection between ostensibly unrelated fields, finds certain parallels and then explores these to guide further research.

I am impressed by the fact that your approach permitted automating the search for proofs of Bell's theorem and related mathematical objects. I wonder if the different versions are sufficiently different from each other that this may also translate into differences in the difficulty of experimental set up. It seems that it might be useful to have a catalog/library of the objects found by your approach publicly available (perhaps even sortable by certain parameters), if only because it seems natural to assume that some versions may suggest certain deeper insights more readily than others.

At the conclusion it was not clear to me if you think that the dessin d'enfant for the Mermin Pentagram definitely does not exist or if this is still subject to further research. If it does not exist, how would you characterize the qualitative difference in contextuality between the two-qubit and three qubit case in terms of standard quantum mechanics?

All the best,

Armin

Hi Michel,

I had the same question as Armin regarding the Mermin pentagram so I will have to read your forthcoming works on this topic. If a dessin d'enfents does *not* exist for the Mermin pentagram, what, in your opinion, does this mean for contextuality and, more generally, the Kochen-Specker theorem?

Ian Durham

Hi Michel,

Interesting. I'll have to think about that a bit.

Ian

Dear Michel Planat,

I have been reading a paper by Maldacena and Susskind. This is a fairly bold paper that advances a pretty speculative idea. In keeping with my paper, which advances an associativity issue with quantum fields near the horizon , this seems to have a higher associator structure that is five fold. The most elementary is a three way associator (ab)c - a(bc) = [a,b,c], that defines a fundamental form for a quantum homotopy but a five fold system is a second homotopy group, The fluctuations across the inner and outer horizons of a black hole results in a 5-fold associative system. This is also a pentagonal system for the Kochen-Specker theorem.

The Susskind-Maldacena paper requires there to exist two black holes with the same BPS charge and angular momentum. Even if such black hole pairs exist it is not clear how they become EPR pairs. In most standard QM systems it requires some sort of mutual interaction to establish an EPR pair. To argue that a black hole is an EPR pair with another it means there exist in the multiverse some other black hole with an identical quantum configuration. This demands a multiverse landscape, for it is probably not likely this exists within the observable universe.

The idea is interesting though. The odd thing about this idea, which has been making the rounds these days, is it makes some physical sense of the interior of a black hole. Maldacena and Susskind work with a Schwarschild black hole. There idea is there are entanglements between black holes through wormhole. This sort of multiply connected topology does exist with black holes. A BPS or rotating black hole has two event horizons at r_{+/-} = m +/- sqrt{m^2 - Q^2}, where Q can be either a gauge charge or angular momentum parameter. There are then two event horizons and three regions; region I being where r > r_+, region II where r_+ > r > r_-, and region III where r < r_-. These regions are timelike, spacelike and timelike respectively. The region III has been regarded as suspect, since the r_- event horizon has a pile up of UV divergent radiation or quantum fields that implies the horizon is physically singular. This region has been regarded as a sort of mathematical fiction. However, maybe this region does play some sort of physical role.

The Kerr black hole appears in the first diagram is attach. The second attachment is a Penrose diagram of the Kerr black hole. It is evident that upon leaving region I (the normal timelike universe) the observer enters region II which is shared by another black hole. The horizon is split so the observer may enter two III type regions. The ring singularity in region III is where x^2 + y^2 = Q^2. In this III region the geodesics around the ring are similar to the flow of a hurricane around the eye. Also the singularity is repulsive; you can't reach it. In complex coordinates this singularity has a branch cut. If you make a complete orbit around the ring there is a branch cut which pops you into an identical copy of the III region as branch cuts link Riemann sheets of the complex plane. The interior region of a BH is naturally in a sense a sort of wormhole, and this approach might segue into this equivalency between wormhole multiple connectivity and entanglements. This interior region may physically play the role as an "entangler."

The argument for a firewall associated with a black hole concerns entanglement swaps between states in region I and II. These states are H_h ∊ I for Hawking radiation, H_s ∊ I for states on or near the stretched horizon associated with r_+ and interior states H_n ∊ II for states near the horizon and H_s ∊ II on the singularity. In the Kerr-Newman metric this singularity is identified with r_-. Physically r_- is a region with UV divergent quantum fields. However, we may remove this as a singularity if this divergence is regulated in some manner. That of course is an open question. The singularity states H_s are split into H_r- for states in the region II near r_- and those in the core region H_{III}. We now have a 5-fold system of states.

I have argued that three quantum states along a null ray are an associated quantum system. If the middle state is very near the horizon and the horizon has a quantum uncertainty the entanglement between the three states is an associator system [a,b,c] = (ab)c - a(bc). In quantum homotopy this is a fundamental group π^1. A 5 fold system is a set of states in a permuting structure that gives π^2, and there is a higher system that defines the Stasheff polytope π^3, and it goes on from there. The five fold system is equivalent to the pentagonal arrangement of states in the Kochen-Specker theorem in four dimensions. The associator system is then a form of the KS theorem. The KS theorem in 4 dimensions is a result of a three color graph with pentagonal symmetry.

If there is then this sort of black hole entanglement that is equivalent to a worm hole it may then be of this nature. Again the interior region, if it is physically real, is such that an orbit around the singularity pops the geodesic into an equivalent spacetime. It is a form of the multiple sheets of the complex plane connected by a branch cut. The argument for spacetime would be rather difficult, for this is not an elementary conformal argument in two dimension, but four dimensions.

Lawrence B. CrowellAttachment #1: kerr_bh.jpgAttachment #2: Penrose_diagram_for_Kerr.png

Dear Michel,

Nice to see such an original idea around geometry - I've learned a lot from your essay. I appreciated how you utilised Mermin's pentagram and as above mentioned by Ian, think that it is interesting that it is unique with regard to Dessin d'enfents. I like anything relating to geometry an certainly anything we discover to be unique ought to be crying out for further study.

My essay is based around n-dimensional simplexes, entropy and the Fibonacci sequence around Black Holes. I hope you find the time to read it.

Best wishes & great work!

Antony

The program of finding physics with [0, 1, ∞] can be found with the SL(2,C) group and the linear fractional transformation (LFT)

f(z) = (az b)/(cz d),

which has a correspondence with matrices of SL(2,C). The Mobius transformation or LFT is an automorphism group on the Argand plane, and this is equivalent to PSL(2,C). This projective linear group is then the automorphism group of C. If we let the constants a, b, c, d be points in C then the LFT

f(z) = [(z - z_1)/(z - z_2)][z_3 - z_2)/(z_3 - z_1)]

is for the identity f(z) = z a case where z_1 = 0, z_3 = 1, and z_2 = ∞. A matrix representation may be found by dividing through by z_i and taking the limit z_i --- > ∞.

From this comparatively simple example we may move up to SL(2,H) and SL(2,O). In the case of SL(2,O) ~ SO(9,1), there is an embedding of SO(9) ~ B_4. This in turn is defined with the short exact sequence

F_4: 1 --- > B_4 ---> F_{52/36} ---> OP^2 --- > 1

where the strange symbol in the middle means that the 52 dimensions of F_4 - the 36 dimensions of B_4 ~ SO(9) defines the OP^2 projective Fano plane or OP^2 ~ F_4/B_4.

The B_4 group is the SUSY group that Susskind employs with the holographic principle.

The group F_4 is a centralizer in the E_8, which means it commutes with the automorphism of E_8, which is G_2. We then have a somewhat Rococo form of the same construction. A projective form of SL(2,O), PSL(2,O), defines matrices ~ aut(O) ~ G_2 which map three points to [0, 1, ∞] with the action of the 7 elements in the Moufang plane. I think I can find this matrix in the near future.

Unfortunately I am moving shortly, so that is complicating plans to do much analysis. If I do this in the immediate future it will have to be in the next week.

Cheers LC

Dear Michel, and apologies if this does not apply to you. I have read and rated your essay and about 50 others. If you have not read, or did not rate my essay The Cloud of Unknowing please consider doing so. With best wishes.

Vladimir

Dear Michel,

I have rated your essay on 10th of July with maximum rating and I would like to know whether you have rated mine. Please inform me in my thread.

Best,

Sreenath