### Is non-associative physics and language possible only in many-sheeted space-time?

In Thinking Allowed Original there was very interesting link added by Ulla about the possibility of non- associative quantum mechanics.

Also I have been forced to consider this possibility.

- The 8-D imbedding space of TGD has octonionic tangent space structure and octonions are non-associative. Octonionic quantum theory however has serious mathematical difficulties since the operators of Hilbert space are by definition associative. The representation of say octonionic multiplication table by matrices is possible but is not faithful since it misses the associativity. More concretely, so called associators associated with triplets of representation matrices vanish. One should somehow transcend the standard quantum theory if one wants non-associative physics.

- Associativity therefore seems to be fundamental in quantum theory as we understand it recently. Associativity is indeed a fundamental and highly non-trivial constraint on the correlation functions of conformal field theories. In TGD framework classical physics is an exact part of quantum theory so that quantum classical correspondence suggests that associativity could play a highly non-trivial role in classical TGD.

The conjecture is that associativity requirement fixes the dynamics of space-time sheets - preferred extremals of Kähler action - more or less uniquely. One can endow the tangent space of 8-D imbedding H=M

^{4}× CP_{2}space at given point with octonionic structure: the 8 tangent vectors of the tangent space basis obey octonionic multiplication table.

Space-time realized as n-D surface in 8-D H must be either associative or co-associative: this depending on whether the tangent space basis or normal space basis is associative. The maximal dimension of space-time surface is predicted to be the observed dimension D=4 and tangent space or normal space allows a quaternionic basis.

- There are also other conjectures (see this) about what the preferred extremals of Kähler action defining space-time surfaces are.

- A very general conjecture states that strong form of holography allows to determine space-time surfaces from the knowledge of partonic 2-surfaces and 2-D string world sheets.

- Second conjecture involves quaternion analyticity and generalization of complex structure to quaternionic structure involving generalization of Cauchy-Riemann conditions.

- M
^{8}-M^{4}× CP_{2}duality stating that space-time surfaces can be regarded as surface in either M^{8}or M^{4}× CP_{2}is a further conjecture.

- Twistorial considerations select M
^{4}× CP_{2}as a completely unique choice since M^{4}and CP_{2}are the only spaces allowing twistor space with Kähler structure. The conjecture is that preferred extremals can be identified base spaces of 6-D sub-manifolds of the product CP_{3}× SU(3)/U(1)× U(1) of twistor spaces of M^{4}and CP_{2}having the property that it makes sense to speak about induced twistor structure.

- A very general conjecture states that strong form of holography allows to determine space-time surfaces from the knowledge of partonic 2-surfaces and 2-D string world sheets.

*single*space-time sheet. What about many-sheeted space-time? Could non-associative physics emerge in TGD via many-sheeted space-time? To answer this question one must first understand what non-associativity means.

- In non-associative situation brackets matter. A(BC) is different from (AB)C. From schooldays or at least from the first year calculus course one recalls the algorithm: when calculating the expression involving brackets one first finds the innermost brackets and calculates what is inside them, then proceed to the next innermost brackets, etc... In computer programs the realization of the command sequences involving brackets is called parsing and compilers perform it. Parsing involves decomposition of program to modules calling modules calling.... Quite generally, the analysis of linguistic expressions involves parsing. Bells start to ring as one realizes that parsings form a hierarchy as also do the space-time sheets!

- More concretely, there is hierarchy of brackets and there is also a hierarchy of space-time sheets, perhaps labelled by p-adic primes. B and C inside brackets form (BC), something analogous to a bound state or chemical compound. In TGD this something could correspond to a "glueing" space-time sheets B and C at the same larger space-time sheet. More concretely, (BC) could correspond to braided pair of flux tubes B and C inside larger flux tube, whose presence is expressed as brackets (..). As one forms A(BC) one puts flux tube A and flux tube (BC) containing braided flux tubes B and C inside larger flux tube. For (AB)C flux one puts tube (AB) containing braided flux tubes A and B and tube C inside larger flux tube. The outcomes are obviously different. A

- Non-associativity in this sense would be a key signature of many-sheeted space-time. It should show itself in say molecular chemistry, where putting on same sheet could mean formation of chemical compound AB from A and B. Another highly interesting possibility is hierarchy of braids formed from flux tubes: braids can form braids, which in turn can form braids,... Flux tubes inside flux tubes inside... Maybe this more refined breaking of associativity could underly the possible non-associativity of biochemistry: biomolecules looking exactly the same would differ in subtle manner.

- What about quantum theory level? Non-associativity at the level of quantum theory could correspond to the breaking of associativity for the correlation functions of n fields if the fields are not associated with the same space-time sheet but to space-time sheets labelled by different p-adic primes. At QFT limit of TGD giving standard model and GRT the sheets are lumped together to single piece of Minkowski space and all physical effects making possible non-associativity in the proposed sense are lost. Language would be thus possible only in TGD Universe! My nasty alter ego wants to say now something - my sincere apologies: in superstring Universe communication of at least TGD has indeed turned out to be impossible! If superstringy universe allows communications at all, they must be uni-directional!

- Could many-sheeted space-time of TGD provides the geometric realization of language like structures? Could sentences and more complex structures have many-sheeted space-time structures as geometrical correlates? p-Adic physics as physics of cognition would suggests that p-adic primes label the sheets in the parsing hierarchy. Could bio-chemistry with hierarchy of magnetic flux tubes added, realize the parsing hierarchies?

- DNA is a language and might provide a key example about parsing hierarchy. The mystery is that human DNA and DNAs of most simplest creatures do not differ much. Our cousins have almost identical DNA with us. Why do we differ so much? Could the number of parsing levels be the reason- p-adic primes labelling space-time sheets? Could our DNA language be much more structured than that of our cousins. At the level of concrete language the linguistic expressions of our cousin are indeed simple signals rather than extremely complex sentences of old-fashioned German professor forming a single lecture each. Could these parsing hierarchies realize themselves as braiding hierarchies of magnetic flux tubes physically and more abstractly as the parsing hierarchies of social structures. Indeed, I have proposed that the presence of collective levels of consciousness having hierarchy of magnetic bodies as a space-time correlates distinguishes us from our cousins so that this explanation is consistent with more quantitative one relying on language.

- I have also proposed that intronic portion of DNA is crucial for understanding why we differ so much from our cousins (see this and this). How does this view relate to the above proposal? In the simplest model for DNA as topological quantum computer introns would be connected by flux tubes to the lipids of nuclear and cell membranes. This would make possible topological quantum computations with the braiding of flux tubes defining the topological quantum computer program.

Ordinary computer programs rely on computer language. Same should be true about quantum computer programs realized as braidings. Now the hierarchical structure of parsings would correspond to that of braidings: one would have braids, braids of braids, etc... This kind of structure is also directly visible as the multiply coiled structure of DNA. The braids beginning from the intronic portion of DNA would form braided flux tubes inside larger braided flux tubes inside.... defining the parsing of the topological quantum computer program.

The higher the number of parsing levels, the higher the position in the evolutionary hierarchy. Each braiding would define one particular fundamental program module and taking this kind of braided flux tubes and braiding them would give a program calling these programs as sub-programs.

- The phonemes of language would have no meaning to us (at our level of self hierarchy) but the words formed by phonemes and involving at basic level the braiding of "phoneme flux tubes" would have. Sentences and their substructures would in turn involve braiding of "word flux tubes". Spoken language would correspond to a temporal sequence of braidings of flux tubes at various hierarchy levels.

- The difference between us and our cousins (or other organisms) would not be at the level of visible DNA but at the level of magnetic body. Magnetic bodies would serve as correlates also for social structures and associated collective levels of consciousness. The degree of braiding would define the level in the evolutionary hierarchy. This is of course the basic vision of TGD inspired quantum biology and quantum bio-chemistry in which the double formed by organism and environment is completed to a triple by adding the magnetic body.

_{eff}=n× h giving rise to a hierarchy of intelligences. What is the relationship between these hierarchies?

- I have proposed that speech and music are fundamental aspects of conscious intelligence and that DNA realizes what I call bio-harmonies in quite concrete sense (see this and this): DNA codons would correspond to 3-chords. DNA would both talk and sing. Both language and music are highly structured. Could the relation of h
_{eff}hierarchy to language be same as the relation of music to speech?

- Are both musical and linguistic parsing hierarchies present? Are they somehow dual? What does parsing mean for music? How musical sounds could combine to form the analog of two braided strand? Depending on situation we hear music both as separate notes and as chords as separate notes fuse in our mind to a larger unit like phonemes fuse to a word.

Could chords played by single instrument correspond to braidings of flux tubes at the same level? Could the duality between linguistic and musical intelligence (analogous to that between function and its Fourier transform) be very concrete and detailed and reflect itself also as the possibility to interpret DNA codons both as three letter words and as 3-chords (see this)?

See the article Is non-associative physics and language possible only in many-sheeted space-time? or the new chapter Is non-associative physics and language possible only in many-sheeted space-time? of "Towards M-matrix".

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

## 13 Comments:

https://en.wikipedia.org/wiki/K3_surface

Tori is the mystery word able to become intersecting branes and Calabi Yaw cogwheels :

https://www.flickr.com/photos/93308747@N05/albums/72157651413132259

Intersting Leo, are those images fron actual LHC UFO events?

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K3 surfaces are nice. It would be nice if one could realize them as preferred exremals. A small deformation of canonically imbedded CP_2 very probably cannot give rise to K3 or piece of it: since Ricci tensor of CP_2 should be cancelled.

K3 has 20-D homology H_{1,1}. CP2 1-D (Kahler form). Could on think of taking say 2-sheeted Euclidian region of M^4 (large deformation in CP_2 degrees of freedom to change the signature of the induced metric) with M^4 sheets connected by wormhole contacts (pieces of CP_2) to produce the 20 non-contractible 2-surfaces? Ricci tensor should vanish everywhere. Somehow I feel that this does not work.

6-D Calabi-Yaus are in twistorial approach to TGD replaced with 6-D twistor spaces, M^4xCP_2 is twistorially unique in the sense that corresponding twistor spaces are also Kahler manifolds (here I am a little bit sloppy, I should take signature of M^4 into account).

The idea is to generalise induction of twistor structure so that twistor spaces of space-time surface is 6-surface in the 12-D product of 6-D twistor space of M^4 and CP_2 with induced twistor structure. The complex surface property could allow to get mathematical insights comparable to those gained in string models.

Riemann surfaces.. I can almost see it, some of the superstringy/zeta stuff is pure madness. See the BPS paper by Michael Planet the 1/f, number theory time measurement guy. I do feel they are on the right track with the modular etc function stuff and the relation to the Monster group. I just wish they weren't so strange..

Nevermind that.. here

http://arxiv.org/abs/alg-geom/9510008g-geom/9510008

So complex. . I heard on the BBC a few weeks ago , lamenting that "physics has gotten so complicated" lol..

In the cold fusion community, it is generally accepted that the Surface Plasmon Polariton (SPP) plays a major part in cold fusion. That hybrid of photons and electrons form a soliton that directs all the spins of that waveform in a monopole magnetic field. Being a boson unlimited numbers of polaritons are packed into that soliton and at .25 nanometers the spin is multiplied many times by size compression (think a fast spin of an ice-skater in a tuck). Monopole magnetism is governed by non-associative quantum mechanics which is largely unknown but it is recognized the monopole will catalyze proton decay. When protons decay the nucleus is destabilized and nuclear reactions of all types occur. Certain nanoparticle topologies concentrate and focus these monopole beams. Rydberg matter (all types of alkali atoms) and water crystals are strings of graphite like planes that focus and amplify these monopole beams derived from SPPs. These nanoparticles also support a Bose Einstein Condensation of these SPPs which adds to the power of the monopole field. Cold Fusion will mark the beginning of the golden age of string theory.

There are three exceptional experiments that are unbelievable:

There three experiments point to physics beyond quantum mechanics.

Mark LeClair produces all the elements from water.

https://nanospireinc.com/Fusion.html

Leif Holmlid produces k-mesons from weak laser light and a catalyst.

http://tempid.altervista.org/SRI.pdf

And a 100 micron nickel particle is transmuted into pure Ni62 as a result of teleportation

of both energy and neutrons in a single cluster fusion event.

http://www.sifferkoll.se/sifferkoll/wp-content/uploads/2014/10/LuganoReportSubmit.pdf

Dear Axil,

I responded days ago but found that the comment had not gone through. This is happening quite often nowadays.

The links were extremely interesting and I wrote an article summarising the recent view about cold fusion according to TGD: fusion of two separate TGD inspired models emerges.

TGD can explain the known strange features of cold fusion experiments and I dare say that TGD provides the theory of cold fusion replacing also the standard theory of hot fusion using same mechanisms. Dark matter in TGD sense, p-adic length scale physics, etc. are basic elements of this approach.

I did not find anything abot the following highly interesting claim:

"And a 100 micron nickel particle is transmuted into pure Ni62 as a result of teleportation of both energy and neutrons in a single cluster fusion event."

Could you explain?

Matti

see mu long post in

http://www.e-catworld.com/2015/10/18/rossi-ash-sample-size-from-lugano-test-not-representative-of-whole-charge/

The post is too long to fit in your comment format

Please see me an e-mail address where I can send long info directly

My email address is matpitka6atgmaili.com .

Ni62 finding looks really strange. Ni62 is heaviest stable Ni isotope. Could this help to understand what happens?

Dear Axil,

I looked at the Ni62 mystery. One interesting finding is that the size 100 micrometers of the Ni62 block corresponds

to the secondary p-adic length scale for W bosons. Something deep?

One can imagine all kinds of exotic solutions but I guess that it is the reaction kinetics "dark fusion + subsequent ordinary fusion repeated again and again", which leads to a fixed point which is enrichment by Ni62 isotope. This guess seems to work!

a) The reaction kinematics in the simplest case involves two elements.

*The addition of protons to stable isotopes of Ni. One can add N=1,2,... protons to the stable isotope of Ni to get dark nuclear string NiX+N protons. As such these are not stable by Coulomb repulsion.

*The allowed additional stabilising reactions are dark W boson exchanges, which transfer charge between separate dark nuclear strings at flux tubes. Beta decays are very slow processes since outgoing W boson decaying to electron and neutrino is very massive. One can forget them. Therefore dark variants of nuclei decaying by beta decay are effectively stable.

*The generation of dark nuclei and their transformation to ordinary nuclei occurs repeatedly. Decay produces serve as starting point at the next round. One starts from stable isotopes of NiX, X=58,60,61,62 and adds protons some of which can by dark W exchange transform to neutrons. The process produce produces form isotope X heavier isotopes X1,X+2,.. plus isotopes of Zn with Z=30 which are beta stable in the time scale considered. Let us forget them.

b) The key observation is that this kinematics increases necessarily mass number!!

Starting from say X=58 one unavoidably ends up to the most massive stable isotope of Ni! The problem is however that Ni64 is the heaviest stable isotope of Ni rather than Ni62!!

The problem can be solved! The step Ni62+p leads to Cu63 which is the lightest stable isotope of Copper. No beta exchanges anymore and the sequence stops!

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