Friday, October 09, 2009

How TGD emerges from number theory?

An interesting possibility is that quantum TGD could emerge from a condition that a local version of hyper-finite factor of type II1 represented as a local version of infinite-dimensional Clifford algebra exists. The conditions are that "center or mass" degrees of freedom characterizing the position of causal diamond (CD) defined as an intersection of future and past directed light-cones separate uniquely from the "vibrational" degrees of freedom being represented in terms of octonions and that for physical states associativity holds true. The resulting local Clifford algebra would be identifiable as the local Clifford algebra of the world of classical worlds (being an analog of local gauge groups and conformal fields).

The uniqueness of M8 and M4×CP2 as well as the role of hyper-quaternionic space-time surfaces as fundamental dynamical objects indeed follow from rather weak conditions if one restricts the consideration to gamma matrices and spinors instead of assuming that M8 coordinates are hyper-octonionic as was done in the first attempts.

  1. The unique feature of M8 and any 8-dimensional space with Minkowski signature of metric is that it is possible to have an octonionic representation of the complexified gamma matrices and of spinors. This does not require octonionic coordinates for M8. The restriction to a quaternionic plane for both gamma matrices and spinors guarantees the associativity.

  2. One can also consider a local variant of the octonionic Clifford algebra in M8. This algebra contains associative subalgebras for which one can assign to each point of M8 a hyper-quaternionic plane. It is natural to assume that this plane is either a tangent plane of 4-D manifold defined naturally by the induced gamma matrices defining a basis of tangent space or more generally, by modified gamma matrices defined by a variational principle (these gamma matrices do not define tangent space in general). Kähler action defines a unique candidate for the variational principle in question. Associativity condition would automatically select sub-algebras associated with 4-D hyper-quaternionic space-time surfaces.

  3. This vision bears a very concrete connection to quantum TGD. In the octonionic formulation of the modified Dirac equation is studied and shown to lead to a highly unique general solution ansatz for the equation working also for the matrix representation of the Clifford algebra. An open question is whether the resulting solution as such defined also solutions of the modified Dirac equation for the matrix representation of gammas. Also a possible identification for 8-dimensional counterparts of twistors as octo-twistors follows: associativity implies that these twistors are very closely related to the ordinary twistors. In TGD framework octo-twistors provide an attractive manner to get rid of the difficulties posed by massive particles for the ordinary twistor formalism.

  4. Associativity implies hyperquaternionic space-time surfaces (in a more general sense as usual) and this leads naturally to the notion of WCW and local Clifford algebra in this space. Number theoretic arguments imply M8-H duality. The resulting infinite-dimensional Clifford algebra would differ from von Neumann algebras in that the Clifford algebra and spinors assignable to the center of mass degrees of freedom of causal diamond CD would be expressed in terms of octonionic units although they are associative at space-time surfaces. One can therefore say that quantum TGD follows by assuming that the tangent space of the imbedding space corresponds to a classical number field with maximal dimension.

The importance of this result is that the Universe of Quantum TGD is mathematically completely unique: both classical and quantum dynamics follow from associativity alone.

For details and background see the chapter TGD as a Generalized Number Theory II: Quaternions, Octonions, and their Hyper Counterparts of the book "TGD as a Generalized Number Theory".

9 Comments:

At 12:20 AM, Blogger Matti Pitkanen said...

Dear Donkerheid,

experimental neuroscience of course makes a lot of sense.

The philosophical basis is however wrong so that the existing enormous data has not provided much understanding about consciousness. Consider only useless attempts to identify "consciousness module" in brain (aarghhhh!!), the attempts to understand qualia in terms of nerve pulse patterns, the modeling brain as electric circuitry, spin net or classical computer.


There is empirical data representing the most important bits and wise theoretician should use these bits instead of drowning herself into data. Libet's findings, effects of ELF em fields on vertebrate brain, the finding that cells in general do not dissipate much energy to ionic currents but in brain a lot of metabolic energy however goes somewhere, the strange anomalies related to cell membrane and nerve pulse,..: all these findings show that something in the basic assumptions is badly wrong.

This badly wrong has several aspects. The naive length scale reductionism. The treatment of living brain as dead deterministic machine so that consciousness becomes an uninteresting epiphenomenon. The wrong views about quantum, time, and energy.


Worst of all, in physics frontier prevails still the idiotic belief that neuroscience and biology cannot give anything to fundamental physics, that all this stuff is just complexity. Even most quantum consciousness theorists take physics as given and try to understand consciousness from wave mechanics.

 
At 9:47 AM, Blogger Ulla said...

"Drowning herself into data"? Suppose you think of me? There are a lot of data indeed, too much:) But to get an holistic picture you need that flood. When I talked to the professor he said: "There is the whole biology involved", meaning I should chose some bit of it. But holism is just the whole of it. You surely know that:-)

I know there are a lot of ad hoc and certainly anomalias too in biology. But a phycist is also doing it wrong. Often he (not you!) has a small little problem, but he blow it up and do all his calculations about that little bit. So it seems so important. And the worst is that he also think himself that it is important:-)Brain can be a trickster:) That's the way we have for instance the nuclear industry (totally idiotic!), taken together with the money aspect, that also distort things very much.

I know a biologist can do the same, for instance a bacteria-scientist, but usually she is very much aware of the fact it is only a small bit, genetics not included. It is distorted by money. It is made much more important than it is in reality.

Biophysics gives very much to our understanding of the function of biology. Also the system effects. It is an expanding field, and in future many phycists will do science in biology:) Complexity can also tell something.

You often talk of the lag phase in physic. That no real contribution to the physics have been done for a long time. That we need new physic.

Now I say something 'heretic'???? Can it be so that Einstein has something to do with this? Why is his both theories not on the same line? Can he have done some calculation wrong, as Haramein says? You have looked very much at this.

In psychology there is something similar. Freud was a very clever man, but he has done much harm to psychology as a science.

 
At 7:37 AM, Blogger donkerheid said...

Dear Matti,

The anomalies you mention are remarkably unknown to most biologists. I wouldn't say that these facts are ignored, it's more than that, there is a good chance that even professors will never come across them. Just because they aren't published in respectable journals, and biologists (I've come across) do not believe anything that's not referenced.
Scientists can be surprisingly confident :). Once I was told that the brain's design is flawed, because it could work just as well with much fewer circuits, so the brain's structure is an evidence for suboptimal design! He is a geneticist, not a neuroscientist, but still.
I wanted to ask a professor's opinion about the solitonic model, and guess what her first objection was: the site of publication wasn't written horizontally under the title, but being an article from arXiv, vertically on the left side. She doesn't know arXiv, so the paper automatically must be rubbish, whatever I said she refused to listen.
And my favourite excuse is: "that's not a biological problem" :). This is really an evergreen.

Regarding arrogance, physicists are surely at the pinnacle. Once I read on the net, that physicists working at particle accelerators loathe even their collegues who work with lower energies. Smolin says also interesting things in his book: what stringists do is a well-known phenomenon, an elite isolates itself and do not trust anyone else.

.............................................................................................

It's amazing if the ignored anomalies find an explanation in TGD, that's the only way to progress, a coherent theory :).
You didn't mention the holographic brain, does it also find a place in TGD somehow?

And what for you think the brain uses so much energy?

There's also an interesting link from Ulla's blog, rewiring neuroscience:
http://nine-radical.blogspot.com/

Your views are so unique. The brain being 4-dimensional, with a magnetic body, superconduction and many more things. What you think our brains do? How can we send signals to geometric past, I mean how to create and direct signals?

best regards,
Gábor

 
At 8:21 PM, Blogger Matti Pitkanen said...

To Gabor:

Concerning your questions about hologrammic brain. First some general ideas which I have certainly expressed already many times. Apologies for repeating myself.

a) In TGD Universe light-like 3-surfaces represent generalized Feynman diagrams-the quantum level proper and the interiors of 4-D space-time surfaces represent the classical physics correlates of basically 3-D quantum physics. In hologram picture it is light-like 3-surfaces which would represent 4-D physics. It might not be a mere matter of taste which interpretation one chooses since classical representation is not complete;-).

b) I have written a book about living systems a conscious 4-D (dynamical) hologram. For instance, see the chapter this about living system as a conscious hologram.


c) One concrete mechanism related to hologrammic brain is building temporally scaled down or scaled up versions about event sequences of the external world. For instance, "stories" in long period of experience is compressed to a simulation lasting one minute. There is neuroscientific support by Japanese researchers that this kind of "stories" are formed in hippocampus. I have discussed this somewhere in some chapter of TGD and EEG.

d) Dark matter hierarchy would be ideal in this respect since the scaling of hbar would make zooming and anti-zooming in both temporal and spatial aspects possible.

 
At 8:22 PM, Blogger Matti Pitkanen said...

To Gabor:

Concerning the questions relating to brain metabolism and what brain does.

a) The energy used by brain would go to the generation of positive energy signals sent to communicate sensory information (in very general sense including also information about immediate biochemical environment of neurons and also other cells) to magnetic body. The magnetic body in turn would use metabolic energy by sending negative energy signals to induce motor actions.

b) I see brains as a factory of standardized symbolic mental images by using heavily virtual world feedback to sensory organs to transform sensory input to a caricature about external world. Division of perceptive field to objects, naming what is there. Sensory organs would be responsible for sensory qualia (I will not go to the standard objections here).


You ask about how can we send negative energy signals to geometric past.

a) Sending of negative energy signals should occur by the time reversed variants of the mechanisms generating positive energy signals. Second law of thermodynamics brings in asymmetry but only in time scales which are long as compared to the time scale of dissipation. For large values of hbar this time scale is long and second law does not apply and symmetry between positive and negative energies emerges: macroscopic quantum coherence at work! Dark photons with large hbar provide therefore the mechanism. Intentional action would be the basic example about sending of negative energy signals (remember Libet's findings!). Also memory recall.

b) As I have actually told boringly many times, negative energy signals of light could correspond phase conjugate laser beams routinely created in laboratory. They have just the correct properties. For instance, second law applies in reversed direction of geometric time, which is used in error correction. In accordance with the teachings of Wittgenstein, positive energy ontologists refuse to talk about time reversed signals with negative energy. Zero energy ontologists can speak freely;-).


c) Dropping of a particle to a large space-time sheet generates positive energy signal. For the time reversal of this mechanism, the particle would just (intentionally!!) jump to a smaller space-time sheet sending negative energy to get the needed positive energy as a recoil effect. When time reversal invariance is not broken badly this process is as every-daily process than its reverse! This assumption leads to a correct prediction for basic metabolic currency of about .5 eV and predicts a fractal hierarchy of currencies coming as half octaves of it (also negative).

d) One can imagine kind of flip-flop mechanism: jumping of particle to smaller space-time sheet receives energy from the dropping of particle elsewhere to a larger space-time sheet. Continual feed of metabolic energy would be needed to take care of dissipative energy losses.

e) Population reverted laser could receive the negative energy. Its analog would be pair of space-time sheets with smaller space-time sheet containing large number of particles which drop to larger space-time sheet as they receive the negative energy photon.

f) The negative energy signal could also serve as a kick generating a domino like process sending much more positive energy to the receiver than the dropping of single particle.

 
At 8:24 PM, Blogger Matti Pitkanen said...

To Ulla:

You are right that one must receive information flood. The art is how to pick the essentials and avoid drowning. Not going to the river at all- known as specialization- is the easy manner to avoid drowning and build a respectable career but leads to the respected-journal idiocy that Gabor mentioned. A fully educated academic person can completely seriously argue that the truth value of the statement depends on what kind of paper it is typed and what kind of font is used. Sad that this kind of idiocy is so common.

 
At 1:55 AM, Blogger donkerheid said...

Sorry for making you repeat yourself. I'm too thick for these things.

 
At 3:39 AM, Blogger Ulla said...

Glad to make you repeat yourself:) Every time it comes out a bit different. Perhaps at last the picture comes into sight.

You know, as a biologist it is extremely difficult to get this new way of thinking, as you have seen:-) A biologist learn very little physic and algebra.

Take the brain. All is in the wires, have we learned. You say it is not. And new science say it is not. But to change ones mind...

Also that with positive and negative energy signals is difficult. From Zero energy position it is possible, but still very difficult. What induce that electron jump to a higher shell, for instance? It demands energy.

Now I will try to do a summary from what you said: From dark photons with large hbar, that is the magnetic body? Or metabolism directly from ordinary light/water burning? In that jump to a higher shell lies the energetic communication to the magnetic body, and the magnetic body asks for action by negative signals in the dropping of the electrone. That is by phase transitions. That happens in the receptor for instance. The energy can the body use, it is only its radiation as a magnetic wave that the magnetic body register? Tiller used the magnetopole as a similar explanation. Creating a wormhole?

But how can the dark photone interact with the electrone? Or is the interaction with the atomic nucleus, and the energetic change in the nucleus induce the electronic change by some kind of vibration? Where is the intention? And so I read that also without conscious intention this may happen synergetically. You need not even have to think. It will still happen- as though some new kind of force or law. The law of Karma? :-) There are some research pointing to that. Something with the second law of order? The order is not endless, it has a strict range?

I chase that interaction between dark and luminous energy/materia.

BTW very interesting postings lately. Can you tell something about the Gaussian curve too?

 
At 12:11 AM, Blogger Matti Pitkanen said...

Dear Gabor,

I fully understand that these ideas are not easy to comprehend. I am just worried about mechanically repeating myself.

To Ulla:

I assume that brain is association machine besides a builder of standard symbolic mental images and also sensory ones by sending virtual sensory input to sensory organs.

I give up only those assumptions that do not make sense: say the assignment of sensory qualia to brain circuits and the view about what memories are.

Metabolism certainly involves standard chemical energy sources plus possibly the energy stored as dark photons leaking out as biophotons which are ordinary photons.

The essentially new element is how energy is transferred- instead of user sending a request to get energy as positive energy signal possibly answered by sending positive energy- a negative energy signal is sent and the whole thing takes place instantaneously.


The interactions between particles at different pages of book like structure take place by exchange of particles, say photons, which leak between the two pages -suffer a phase transition changing Planck constant.

 

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