Monday, July 20, 2015

Topological order and quantum TGD

Topological order is a rather advanced concept of condensed matter physics. There are several motivations for the notion of topological order in TGD.

  1. TGD can be seen as almost topological QFT. 3-D surfaces are by holography equivalent with 4-D space-time surfaces and by strong form of holography equivalent with string world sheets and partonic 2-surfaces. What make this duality possible is super-symplectic symmetry realizing strong form of holography and quantum criticality realized in terms of hierarchy of Planck constants characterizing hierarchy of phases of ordinary matter identified as dark matter. This hierarchy is accompanied by a fractal hierarchy of sub-algebras of supersymplectic algebra isomorphic to the entire algebra: Wheeler would talk about symmetry breaking without symmetry breaking.

  2. heff=n× h hierarchy corresponds to n-fold singular covering of space-time surface for which the sheets of the covering co-incide at the boundaries of the causal diamond (CD), and the n sheets together with superconformal invariance give rise n additional discrete topological degreees of freedom - one has particles in space with n points. Kähler action for preferred extremals reduces to Abelian Chern-Simons terms characterizing topological QFT. Furthermore, the simplest example of topological order - point like particles, which can be connected by links - translates immediately to the collections of partonic 2-surfaces and strings connecting them.

  3. There is also braiding of fermion lines/magnetic flux tubes and Yangian product and co-product defining fundamental vertics, quantum groups associated with finite measurement resolution and described in terms of inclusions of hyper-finite factors.

In the article Topological order and Quantum TGD topological order and its category theoretical description are considered from TGD point of view - category theoretical notions are indeed very natural in TGD framework. The basic finding is that the concepts developed in condensed matter physics (topological order, rough description of states as tangles (graphs imbedded in 3-D space), ground state degeneracy, surface states protected by symmetry or topology) fit very nicely to TGD framework and has interpretation in terms of the new space-time concept. This promises applications also in the conventional areas of condensed matter physics such as more precise description of solid, liquid, and gas phases.

See the chapter Criticality and dark matter of "Hyper-finite Factors, p-Adic Length Scale Hypothesis, and Dark Matter Hierarchy"

For a summary of earlier postings see Links to the latest progress in TGD.


Anonymous said...


During my spare time, I do research on probability and statistics with basic knowledge of physics (up to QFT). I believe TGD is the next step once I master QFT, which still may take a while. Recently I have been trying to understand the functioning of the brain from statistical point of view and how it relates to quantum mechanics, which should enter the picture at some point as conciousness is hard to explain otherwise.

My question relates to the functioning of the Hippocampus. This far I found the most plausible idea is the Hopfield neural network, which is now rather well understood and shows how memories could be encoded in the synapses. I thought about this for a while and found out that it seems a rather robust mechanism.

On the other hand, you propose that quantum phenomena enter the picture already when considering human memory. May I ask, if there is specific evidence that a classical model such as the Hopfield network could not explain the formation of human memories?

Some years ago I posed a few questions on the open problems in the mathematics of TGD. Since then I moved to the private sector and my progress has slowed down, but I think I will eventually take on these issues as well. said...

Thank you for the question. I think that one must make distinction between memories as learned behaviours - I would not call them memories - and memories as episodal memories which are literally re-experiences, for instance, sensory ones.

I believe that Hopfield model and changes in synapses explain quite well memories as behaviors but fail in the case of episodal memories.

I read recently "Musicophilia" by Sacks: it is marvellous book and represents a lot of examples about sensory memories. People who are often idiot savants or suffered damage to left brain can listen music: on victim of this kind damage became composer. Phantom leg could be one example of sensory memories. Wittgenstein's brother who lost his hand in World War I played with his phantom hand and developed fingerings to piano pieces! Also the visual and auditory sensations just when one falls asleep or wakes up would be sensory memories.

Here the new view about time would make itself concrete in a rather surreal looking manner: Wittgenstein's right hand fingers would be literally in geometric the past located in the space-time before World War I! He played together with his past me!

Anonymous said...

Thanks for the reference. That book sounds interesting. Also, as for me personally, I realized I probably should not neglect the role of music. It is interesting that another aspect of the mind, imagination, relates to the episodic memories and savant skills. I have studied a lot the works of Dominic O'Brien and others in the memory sports and realized the human mind can memorize images quite efficiently.

Originally I wanted to disprove the validity of the Hopfield Network for bounded synaptic weights, but later on realized you could in principle allow this case as well without losing too much capacity.

It is true that it is not that easy to think about a process to store episodic memories in the Hopfield Network. You would probably need some sort of encoding mechanism and I am not sure if this makes sense. Do you think there are strong arguments for quantum phenomena related to episodic memory? As for the physiology, I am only at the beginning stages in learning neuroscience, as a hobby again :-)

By the way, did you work on the short-term (working memory) as well? I studied this at the level of Badley's model. It seems interesting that the visual and auditory working memory seems to be limited.

As a matter of fact, I am also from Finland but have emigrated to Belgium. I found the atmosphere in Finland getting too isolated and negative, but I am happy to see some people keep up the good work, like yourself! said...

In TGD framework the general mechanism does not distinguish between short term and long term memories.
Limitations for auditory and sensory working memory could derive simply from the finite information storage capacity of the brain areas in question. Also from finite metabolic resources: 7+/-2 rule.

You ask what problems Hopfield model has? The following is poorly articulated view.

*Time is crucial for memory and we do not understand time in standard physics framework. Hopfield
model accepts the identification of subjective time and geometric time. I have mentioned Libet's findings many times: they are taken as proof that free will is illusion.

*The identification of all memories as behavioral patterns is wrong- episodal memories are
the genuine memories and probably very little to do with the formation of association.

*Synaptic contacts develop all the time. How to avoid the change for longest term memories?
It is difficult to understand the fact that the episodal memories of youth seem to be the most stable one. My Grandma literally lived in her youth for several years!

*The neurons in hippocampus (at least) and therefore also their synaptic contents are regenerated. How the memories can survive in this process? I remember also a document program telling about a person had lost almost all his brain and was able to do mathematics!

To me memory recall looks different from memory storage: in Hopfield model this is not the case since essentially learned behaviours stimulated by inputs as association sequences are in question. said...

Something which I probably already more or less told. You can skip if you wish;-)!

In TGD framework where brain is essentially 4-D (I have talked a lot about ZEO, CDs and their hierarchy). Memory storage in the brain of geometric past when the event occurred is the most elegant option since it gives maximal storage capacity. Memory recalls also create automatically new copies of the memory.

Memory recall could be seen as communication with the brain of geometric past by negative energy signals reflected back- seeing in time direction. This is possible in ZEO based quantum theory only.

Episodal memories could be actually genuine experiences if one accepts the TGD view about self. Mental images are subselves and time reversed subselves give rise episodal memories with sensory input from geometric past, even childhood! I already told about Wittgenstein's brother. A person divided to two parts living in different geometric times is a good idea for a conscifi story!

One challenge is to gain a more concrete understanding of the role of hippocampus in generating signals to geometric past/building time reversed mental images. What this the relation to neuroscience. Ultra low frequency dark photons below EEG range, which yield bio-photons in their decays would be the communication tool. said...

I have lived my whole life in Finland. I like ordinary people although I cannot share the attitudes towards say Greeks which have become rather irrational thanks to the propaganda in finnish media. We are living a crisis of leadership: kind of ethical and moral decline.

Extreme negativity is the problem: the law of Jante expresses what this negativity is. I have worked almost 40 years with TGD without a single coin of funding and still labelled as a madman in academic circles. Often the attitudes of academic people are openly hostile. These people refuse from communications and even to admit my existence. "Ordinary" people behave differently in this respect.

Anonymous said...

Thank you for your answers! Libet's findings are interesting and I understood they seem to support backward causation. Though the community has also attacked the validity of these results.

I think it is indeed hard to store long-term memories in the Hopfield network. In the bounded synaptic weights case, memories tend to be forgotten. I will probably analyze this in detail later on.

I think the problems with the academic world relate to the social dynamics, indeed Jante's law. Success in the society, even in the supposedly enlightened academic world, does not seem to go hand in hand with actual competence as ability and will to control group dynamics is at least as important. Personally I was a researcher before, but dropped out at the post-doc phase and moved to companies. said...

I think that no-one denies that readiness potentials are real. One can of course imagine all kinds of explanations. For instance, one can argue that person is subconsciously thinking about initiation of the action before conscious decision.

Sticking to determinism has simple motivations: intentional free will does not allow a description in Newtonian world and also standard quantum theory allows only randomness at ensemble level. Phenomenon is accepted only after a language and concepts to describe it, exist.