### Some fresh ideas about twistorialization of TGD

I found from web an article by Tim Adamo titled "Twistor actions for gauge theory and gravity". The work considers the formulation of N=4 SUSY gauge theory directly in twistor space instead of Minkowski space. The author is able to deduce MHV formalism, tree level amplitudes, and planar loop amplitudes from action in twistor space. Also local operators and null polygonal Wilson loops can be expressed twistorially. This approach is applied also to general relativity: one of the challenges is to deduce MHV amplitudes for Einstein gravity. The reading of the article inspired a fresh look on twistors and a possible answer to several questions (I have written two chapters about twistors and TGD giving a view about development of ideas).

Both M^{4} and CP_{2} are highly unique in that they allow twistor structure and in TGD one can overcome the fundamental "googly" problem of the standard twistor program preventing twistorialization in general space-time metric by lifting twistorialization to the level of the imbedding space containg M^{4} as a Cartesian factor. Also CP_{2} allows twistor space identifiable as flag manifold SU(3)/U(1)× U(1) as the self-duality of Weyl tensor indeed suggests. This provides an additional "must" in favor of sub-manifold gravity in M^{4}× CP_{2}. Both octonionic interpretation of M^{8} and triality possible in dimension 8 play a crucial role in the proposed twistorialization of H=M^{4}× CP_{2}. It also turns out that M^{4}× CP_{2} allows a natural twistorialization respecting Cartesian product: this is far from obvious since it means that one considers space-like geodesics of H with light-like M^{4} projection as basic objects. p-Adic mass calculations however require tachyonic ground states and in generalized Feynman diagrams fermions propagate as massless particles in M^{4} sense. Furthermore, light-like H-geodesics lead to non-compact candidates for the twistor space of H. Hence the twistor space would be 12-dimensional manifold CP_{3}× SU(3)/U(1)× U(1).

Generalisation of 2-D conformal invariance extending to infinite-D variant of Yangian symmetry; light-like 3-surfaces as basic objects of TGD Universe and as generalised light-like geodesics; light-likeness condition for momentum generalized to the infinite-dimensional context via super-conformal algebras. These are the facts inspiring the question whether also the "world of classical worlds" (WCW) could allow twistorialization. It turns out that center of mass degrees of freedom (imbedding space) allow natural twistorialization: twistor space for M^{4}× CP_{2} serves as moduli space for choice of quantization axes in Super Virasoro conditions. Contrary to the original optimistic expectations it turns out that although the analog of incidence relations holds true for Kac-Moody algebra, twistorialization in vibrational degrees of freedom does not look like a good idea since incidence relations force an effective reduction of vibrational degrees of freedom to four. The Grassmannian formalism for scattering amplitudes generalizes practically as such for generalized Feynman diagrams.

For background and details see the new chapter Some fresh ideas about twistorialization of TGD or the article with the same title.

## 34 Comments:

interesting, Matti, can you kindly point me towards the basic definition of M4?

M^4 denotes just Minkowski space. Flat geometry with distance defined by ds^2 =c^2dt^2-dx^2-dy^2-dz^2. Lorentz transformations and translations as symmetries. Probably any text book in special relativity gives the basic definitions and describes basic implications.

Ahh, so M4xCP^2 is the product of Minkowski space and the complex projective plane ... in retrospect things seem much more clear

What do you make of all this?

http://lightsinthetexassky.blogspot.com/2013/08/recent-texas-ufo-sightings-possible.html

To Stephen:

Both M^4 and CP_2 allow twistorialization. Since the existence of twistor structure is very rare occurrence and does not occur for general four-manifold, this is is a strong additional support for sub-manifold gravity.

This was meant to be the original message of the article as I started to write it. It however turned out that one ends up to a proposal for twistorialization of the "world of the classical worlds" providing completely new insights about meaning of the basic incidence relation. Again zero energy ontology is in crucial role.

Grassmannian representation of scattering amplitudes whose core-elments would be formally practically identical with the twistorial representation in N=4 SUSY. This could make TGD a calculable theory at fundamental level.

The gigantic form preserving generalization is the replacement of pairs of spinors defining twistors with fermionic parts of zero energy states. There are three interpretations.

a) Incidence relation would state quantum classical correspondence: fermionic parts of zero energy states corresponds to light-like 3-surfaces.

b) At the level of consciousness theory incidence relation has also interpretation: Boolean cognition described by fermions corresponds to geometry characterized by light-like 3-surfaces (sensory perception roughly).

c) A third interpretation of incidence relation is in terms of WCW supersymmetry. Bosonic sector that is WCW geometry corresponds in 1-1 manner to fermionic sector: WCW spinor fields which correspond to fermionic parts of zero energy states.

If this picture is true, Grassmannian formalism would be much much more that an elegant calculational tool.

To Bob:

TGD does not help much in the problem. I am nothing against UFOs and I have even written a chapter about Fermi paradox: http://tgdtheory.com/public_html/freenergy/freenergy.html#mantleufo .

It would be surprising if we were the only civilization in cosmos. These kind of reports do no however help much: very often the photons are also manufactured by photoshop and more advanced programs.

Dear Matti,

I want to hear your critique against the following sentence about SUSY in TGD viewpoint:

a strong support for Standard SUSY is unification of coupling constants at high energies in well accuracy.

Dear Hamed,

excellent question.

The unification of couplings constants is assumed in GUTs - I think around 10^-4 Planck masses or so, correct me if I remember wrong.

It is of course interesting SUSY is consistent with this unification of coupling constants and even predicts this. I do not know how genera gauge groups this holds true: you might actually tell something about this;-).

GUT approach has however severe problems (about problems of SUSY approaches we who live post-LHC era of course now): for instance, the choice of GUT gauge group is very ad hoc and does not explain why standard model gauge group is what it is. Just the question "Is the standard model gauge group mathematically very special" might lead to breakthrough.

Proton decay is predicted but has not been observed and this leads to fine-tuning. The value of Higgs mass leads also to fine tuning and the recent situation is seen by specialist as rather desperate - see the posting in Resonaances. Also the huge desert between TeV and Planck scales looks to me extremely implausible to me.

In light of these arguments I see the unification of coupling constants as an unlucky accident which has delayed the development of theoretical particle physics for decades (actually a rather short time as compared to 4 centuries from Newton to Einstein and Bohr;-)).

If I should defend supersymmetry (certainly I want to do it since it is mathematically quite too beautiful to be not realized in some form) I would speak about super-conformal symmetry and give up the N=1 assumption since it forces Majorana fermions and non-conservation of B and L. To my uneducated opinion the basic problem of SUSY approach is the same as that of super string models: quite too strong and also quite un-necessary assumptions quite too early - and made only to make calculations possible. Lazy philosophers is what theoretical physics desperately needs;-).

Dear Matti,

Thanks,

"The choice of GUT gauge group is very ad hoc and does not explain why standard model gauge group is what it is"

But if we see the whole picture, do you think it is ad hoc yet?

I note the following from Baez:

GUT can explain "Why do both leptons and quarks come in left- and righthanded varieties, which transform so diﬀerently? Why do quarks come in charges

which are in units 1/3

times an electron’s charge? Why are there the same number

of quarks and leptons?

Also, the seemingly ad hoc hypercharges in the Standard Model must be exactly what they are for this description to work."

I hope you don't say all of these are unlucky accident too;-).

Of course GUTs can reproduce these empirical facts but they do not predict them. I am convinced that there are endless number of other spectra which GUTs can reproduce in internally consistent manner. There is not a slightest idea for why just standard model group is realized. If this were the case, the theoreticians would not be telling that physics has achieved a state in which only anthropic arguments are possible.

The same number of quarks and leptons is also an empirical fact, not a prediction of GUT but only a reproduction of empirical fact. GUT however also predict: proton should decay: no decays have been detected.

The problem of GUT is that they are not ambitious enough. To get out of the recent dead alley theoreticians should finally start to pose more ambitious questions (they could have done it for three decades ago;-)) .

Why standard model gauge group? Is quark color really what we believe it to be? What is behind family replication?: for the mass differences between various families GUT description in terms of symmetry breaking is extremely ugly. Is it enough to have just two scales: elementary particle mass scale and Planck scale? Huge desert between weak scale and Planck scale is simply physical non-sense.

I do not have anything against these people: I am only sad that their are beating their brilliant heads against the wall.

Thanks, you are right, GUT reproduce the empirical facts not predict them. this can be interest thinking.

Dear Matti,

I realized something better and it leads to some better view about TGD. I write them bellow. If anything is misunderstood please tell me.

One can construct a configuration space from the Space of all 3-surfaces at boundary of CD or G/H, so that the points of the configuration space are 3-sufaces. WCW spinor fields are physical states. Their arguments are the 3-surfaces.

One can go to the next level. At the level, I guessed all possible physical states of before are the points of the new configuration space. I tried to form abstraction hierarchy. But after, I understood it isn't correct in TGD. The correct is that for this level there is another G/H corresponds to space of 3-surfaces at boundary of CD at this scale and WCW spinor fields are new physical states at this scale.

Continue this process and make hierarchical structure of quantum TGD:-)

In other hand, in my mind there is a hierarchy of jones inclusions. The space M/N would correspond to the operators creating physical states modulo measurement resolution. It seems for me that these physical states are different from the before that were spinor fields of WCW? Because in before, there was not any cutoff process for making spinor fields of WCW at each scale. But in the latter it is needed. if it is different, what is the physical states creating by M/N?

You are beginning to understand my vision! I am happy to learn that I am not just a madman who believes in some weird nonsense ideas!

Hierarchies of CDs characterized by their scales and hierarchies of space-time sheets topologically condensed on each other correspond to inclusion hierarchies in WCW. Spinor field for the inclusion hierarchies correspond to hierarchies at the level of quantum states in ZEO if the size of the topologically condensed sheets or CDs defines the scale resolution (also in time direction).

States created by smaller scale WCW spinor fields- that is physical states consisting of various particles are interpreted in ZEO quantum fluctuations whose contribution correspond to radiative corrections/loop corrections.

Here is something which I do not understand well. Electron is stable particle characterised by Mersenne prime M_127.

a) Common sense says that in the case of topological condensation hierarchy labeled by p-adic primes one should treat it as a pointlike particle in the p-adic length scales longer than M_127 scale.

b) What about electron in the scales of CD (of observer) longer than .1 seconds for M_127? Electron has always delocalised wave function in the space of CDs involving CDs of all sizes: delocalisation of upper or lower boundary of CD depending on previous quantum jump. If this wave function has cutoff in CD size then quantum fluctuation would be in question. If not then it is real electron lasting for ever: experimenter characterised by CD defining her spotlight of consciousness cannot distinguish between these wo alternatives. M_127 would characterize the minimal CD for electron. This interpretation seems ok for me but is it ok?

About the inclusion hierarchy at the level of WCW.

Symplectic group for delta M^4xCP_2 corresponds to non-zero modes of WCW. The factor spaces of it by its normal subgroups are also groups and one obtains a hierarchy of normal subgroups in division by normal subgroups. These normal subgroup hierarchies are good candidates for the hierarchies defined by Jones inclusions. These hierarchies would appear as arguments of WCW spinor fields and would define measurement resolution hierarchies.

Thanks,

;-)

The minimal CD for electron means the least time interval for creation and annihilation of electron positron pair as virtual particles?

"Symplectic group for delta M^4xCP_2 corresponds to non-zero modes of WCW. The factor spaces of it by its normal subgroups are also groups and one obtains a hierarchy of normal subgroups in division by normal subgroups."

This means at G/H, H is a normal subgroup and one can divide H by it's normal subgroup too. if i call it H2, H has the role of G in H/H2. is it correct?

supposed that G/H corresponds to an object at the level of WCW. H/H2 corresponds to it's molecules?

Your point about minimal interval is good. Annihilation can of course occur much faster than than .1 seconds if electron and positron are near enough each other. Could one say that .1 seconds is the minimal size of CD for observer able to perceive electron. This time scale would tell more about observers able to detect electrons!

Your interpretation of normal subgroup seems to be correct. One could say that H_n defines measurement resolution for H_{n-1}. Going down the latter would improve measurement resolution. The number of degrees of freedom in ideal resolution would be reduced at each step as it should and the subgroup defining measurement resolution would become smaller.

Is also G/H_n group that is is H_n normal subgroup of also G if it is normal subgroup of H_{n-1}? This does not seem to be the case since G is larger than H_{n-1} and its action can lead out of H_n. Exercise for you;-).

Still to Stephen:

My original vision about the twistorialization of vibrational degrees of freedom of WCW assumed too much.

It seem that the twistorialization has analogy in terms of Kac-Moody algebras. Incidence relations correspond to the condition that sum of bosonic Kac-Moody generators and fermionic generators bilinear in fermion and antifermion annihilate physical states. This is analogy for the expression of momentum as something quadratic form of the spinors defining twistor.

The crucial condition expressing momentum conservation as expression quadratic in twistors does not however generalized. The reason is simply that one cannot assign to vibrational degrees of freedom infinite-D analog of momentum since Kac-Moody type algebras develop central extension and only cm degrees of freedom define conserved quantum numbers.

In any case twistorialization generalizes to M^4 and CP_2 since both have self-dual Weyl tensor. Hawking and others indeed discovered CP_2 as gravitational self-dual instanton but did not realize the connection of its symmetries with standard model.

One can also select between various options for the details of generalized Feynman diagrammatics. The most conservative option is realised. Maybe the ultraconservative Lubos is right here;-).

To Stephen:

Still a little comment concerning the differences between TGD and N=4 super Yang Mils.

In SYM the 3-vertex is fundamental in twistorial formulation. For real momenta the light-like momenta are parallel and this induces infrared divergences, which are the basic problem of gauge theories. The momenta on internal lines are massless but complex.

In TGD framework 4-fermion vertex is fundamental and the emission of gauge boson corresponds to emission of fermion and antifermion at opposite throats of wormhole contact. The real momenta need not be parallel anymore and there is no IR divergence. Also the internal light-like momenta can be real as has been assumed. This implies huge reduction in the number of contributing twistor and fermion diagrams.

Also N=4 SUSY could have TGD analogy. Covariantly constant right-handed neutrinos with two spin directions plus their antiparticles could generate the analog of this symmetry but without Majorana fermions. The breaking of SUSY could be due to different p-adic primes characterizing different members of super-multiplets. The mass formulas would be identical. No super counterpart of Higgs mechanism would be needed.

Thanks dear Matti,

Suppose there is a CD that is at the scale of an ordinary object. at the level of quantum TGD the molecules of the object, corresponds to 3-surfaces at G/H.

“3-surfaces are actually not connected 3-surfaces. They are collections of components at both ends of CD and connected to single connected structure by 4-surface. This is like incoming and outcoming particles in connected Feynman diagrams”

It is because the molecules colliding with other molecules at classical view?

In this picture, those paths of molecules that have velocity of faster than light aren't possible classically but they considered at the level of quantum TGD. Therefore if we want to calculate entropy of the system, the number of degrees of freedom at classical is smaller than it at quantum. So entropy at classical is smaller than it at quantum level?

If the object is solid, there should be very constraints on the motion of the molecules. How these constraints can be considered at quantum TGD?

I try to answer from ipad. Iwould assign to cd secondaryn p-adic length scale much longer than the primary one: size of order eart (.1 lihtsecods) viz electron compton length in case of electron.

Generalization of poitlike particle with three-surface: this is the basic idea.

The notion of vitual particle is different from the usual allowing tachyonic vitual momenta. Also vitual fermions have lihgt like momenta which can however have negative energy. Therefore virtual bosons defined by wormhole contacts wit fermion and antifermion at opposite throats can have spacelike momenta. Virtual fermions have non-physical helicity: this is what guarantees that they give nonvanishing contribution to diagram. Quantum TGD is very classical!

The number of contributing twistor diagrams is very small from kinematic constraints.

Thanks,

If you are in travel and it is difficult to answer by ipad, I will wait.

Different pieces are glued together gradually. This is very beautiful:)

Macroscopic particles are fermions! Yes, we know they can't be at the same position, like the notion of familiar fermion. Now I can understand why fermionic oscillators operator associated with it‘s CD must create them, not any other! But

1-what does it means spin of a macroscopic fermion? Rotating around it’s axis? Therefore it isn’t intrinsic with the size of half integer also from spin statistic theorem?

2-But about bosons, macroscopic bosons seem very different form familiar notion. Why? Please tell some similarities.

3-For an observer at the scale of CD of earth, we are in superposition of generalized Feynman diagrams . Oh my god;-). All possible configurations exist. But where are them? And why we don’t see them? as you know, this is basic critique against many world theories.

Some mistake in my comment:

the fermionic oscillator operators create fermionic fock states and not 3-surfaces. My argument doesn't work now!

Dear Hamed,

There is probably some misunderstanding. I am not talking about macroscopic fermions.

With fermions I mean even something more elementary than the observed fermions.

Observed fermions - like gauge bosons - correspond in TGD framework to two wormole contacts connected by magnetic flux tubes. A closed flux tube going along "upper" space-time sheet turning back at second wormhole contact and reducing along the lower space-time sheet and through first wormhole contact to the upper, is formed. The Kahler magnetic charge of wormhole throats forces this picture.

The "ur-fermions" associated with induced spinor field are located at the wormhole throats whereas observed fermions like electron is expected to contain neutrino and antineutrino at the wormhole throats its second wormhole to neutralize weak isospin. This is just the simplest picture I am able to imagine.

There are only fermionic oscillator operators associated with second quantized spinor fields and the bosonic generators of symplectic algebra and Kac-Moody algebra of light-like 3-surfaces available to create states: the latter are analogs of bosonic creation operators and excite states in WCW degrees of freedom: this is something new as compared to QFT picture.

Concerning scales there is some confusion.

a) CP_2 scale (10^4 Planck lengths) is the scale of wormhole throat. For dark large hbar particles it is scaled up accordingly.

b) Compton length is the *primary* p-adic length scale proportional to sqrt(p) characterizing the space-time sheet containing elementary particle.

c) The scale of particle's CD - *secondary* p-adic length scale proportional to p- is the scale characterizing perhaps the field body of particle. This is new.

One can argue that the secondary p-adic time scales for particles are actually seen. .1 second time scale for electron defines a fundamental biological rhythm and also the alpha rhythm of brains: Cooper pairs of electrons might be behind this and are key players in TGD inspired model of cell membrane as high Tc superconductor.

That we are in superposition involving field bodies in Earth scale and even longer scales can be also argued to be directly visible. We have EEG at frequencies correspond to wavelength of order Earth's size. EEG correlates strongly with contents of consciousness so that it should communicate something to some-one. This "some-one" could be our magnetic body. We know from experiments of Libet that our sensory data is fraction of second old: as if it would come from biological body to som-one- why not the magnetic body.

Dear Matti,

thanks,

About the last paragraph: if we are in superposition, why i am not conscious of my body in other points of the configuration space? i am just conscious of one body. for example in another state of the superposition , maybe my body is in Finland! but why i am not conscious of it?

this question can be asked in another form for electrons. does electrons themselves are conscious of other states in the superposition?

Good point. The other end of CD is localized after each state function reduction but the same state function reduction delocalizes the other end, which is now in superposition. This follows also from basic properties of non-trivial quantum dynamics: Think of action of S-matrix in reduced state.

This is kind of flip-flow. When the other end is localized - we know what it is- the other one gets delocalized and now we do know what it is! Quantum reality is very slippery!

This relates also to Uncertainty Principle. When another end of CD becomes analogous to eigenstate of position, second one becomes analogous to eigenstate of momentum.

The reduction creates conscious experience and localizes, makes classical. In the next quantum jump the second boundary of CD is localized and reduced and this determines the next experience.

The interpretation is as a generalization of sensory perception (SP) and motor action (MA) as its time reversal: the sequence would be SP-MA-SP-MA-....: analog of breathing or of sleep awake cycle.

Libet found also evidence that motor action is initiated by neural activity a fraction of second before the conscious decision. This seems to conform with the idea that it happens in time reversed direction and is initiate from magnetic body.

Question that one cannot avoid: Do these two ends of CD correspond to two distinct conscious entities? Do we have "shadow me". Ancient egyptians believed in shadow me and called it "ka".

To Hamed:

A short answer to your question. The very act of consciousness localizes and selects one state from superposition. It is therefore impossible to experience of being delocalized somewhere between Finland and Iran. Localization requires that density matrix which is measured is such that its eigenstates are localized - in the limits of measurement resolution of course.

Thanks, now it is more clear. I need to think more.

Matti! I am not sure whether it is a good or bad thing that I understood the last few comments here :) It makes "sense" but the idea seems a bit crazy really even though it really works quite well... can you elaborate a bit upon the transition between Euclidean and Minkowskian signatures?

Peace,

Stephen

Understanding just happens now and then for some mystic reason. Rather rarely in any case;-).

I understand that your question about relates to the spinor pairs defining twistors. For the real Minkowski signature time these spinors are not independent of each other: essentially plus minus times complex conjugates of each other. For Euclidian signature they are independent complex spinors so that the number of twistorial degrees of freedom is larger.

But what I wnat to express in boldface is that M^4 and CP_2 have self-dual Weyl tensors (for M^4 it is course trivial). This gives one additional very very strong reason for sub-manifold gravity in M^4xCP_2. I had not realized before that twistors do not exist for generic space-time.

In secondary p-adic time scale, k = 5 would correspond to time scale of short term memories measured in minutes.

At this scale some kind of flip-flop, would occur for our consciousness too. from lower boundary of corresponding CD to upper and Vice versa.

this means for example at first some minutes, my attention is on lower boundary of the CD. after this at the second some minutes, my attention is on upper boundary.

It is not clear for me this view, because we don’t feel this flip flop in the minutes. But at least at the case of sleep awake cycle, or entire life we feel or experience something another at each boundary. But in other hand, in the case of sleep awake cycle, or entire life, we experience very differently!, So this is unclear for me too!, because observing the every boundary of CD, seems to be like the another boundary not very different!

Dear Hamed,

I did not quite understand your k=5 argument. For k=5 the time scale would be extremely short, 32 time CP_2 time scale T=R/c, about 32*10^4*Planck time.

Electron with k=127 (M_127= 2^127 -1) corresponds to .1 seconds. For k= 127+5 (Delta k=5) one would have 2^5=32 times longer time scale, 3.2 seconds. Not far from minutes.

Some misunderstanding seems to be involved. In any case the rule is simple. For given k the *secondary* p-adic time scale defining temporal distance between tips of minimal CD is

T_{2,p}= 2^(k-127)*.1 seconds.

I will comment your further questions separately.

Dear Hamed,

I share your confusion concerning the questions about how flip flop is experienced.

Fractal structure means hierarchy of flip-flop scales. My sensory mental images have duration of order .1 seconds and correspond one scale in hierarchy. Me as a conscious entity going to bed before 8 a'clock and waking up next morning would correspond to a higher level in the hierarchy

Flip-flop could replace "me" with "us": me and my ka;-). Is my ka my guardian angle staying conscious when I sleep?;-)

Do I experience both aspects of the flip flop in the case of sensory mental images? Does the reduction to the second boundary of CD appear subjectively as a sleep period for the conscious entity defining my sensory mental image and as a motor action for outsider (identifying motor action as time reversed sensory percept?

Objection: If one forgets snoring and frequent visits to toilet, my own sleep period does not look very much like motor action to outsider - at least in time scales shorter than 12 hours;-).

Question: How Libet's finding that conscious decision to raise a finger is preceded by neutral activity in time scale of fraction of second fits with this picture.

*Negative energy signal from upper boundary of CD would precede to lower (past) boundary and would generated by state function reduction (conscious decision).

*The me at the lower boundary would receive the signal and generate the needed neural activities and at next state function reduction at upper boundary motor action would become manifest?

*What if this me refuses from co-operation and makes undesired motor action. Does statistical determinism save the situation: certainly there must be an ensemble of .1 second me:s to guarantee predictivity?

?Could one generalize and say, that also our sleeping period is analogous to the time period of neural actitivies preceding the value of geometric time at which conscious decision about motor action is made.

To add confusion: It is known that sensory consciousness is not temporal continuum but discrete: there are gaps in it due to the saccadic motion of eye necessary to stay in visually conscious state. We are not conscious of gaps. If saccadic motion is prevented, one first sees just darkness and then visual consciousness disappears.

Dear Matti,

Thanks, I understand what my mistake was.

and also in the case of “k = 5 would correspond to time scale of short term memories measured in minutes.”, I just see this sentence at the chapter of introduction that is the same in all of your books. Maybe I don’t care about it)

If we assign to a nonliving matter a conscious observer corresponding to the highest level of dark matter of it. This observer as a self, experience average on mental images of it’s subselvies at highest level in form of a moment of consciousness. this is like living matter. only difference is that in living matter there is more layer of dark matter so the highest level is larger.

What is the time interval of this largest CD about nonliving matter? In other words, for living matters, this is entire life time of them, but what is the time interval for nonliving matters?

The cascade of self-measurements starts from the largest CD. The observer is conscious of the object by attention to the CD. At this level it is just a unit moment of consciousness for the observer to experience the CD. But one can go further in down warding of the cascade. I want to know then what does it occurs for statistical mechanics at the level of configurations of the particles in the object? Does the cascade leads to choosing just one state of the configuration space?

in other hand, there is entanglement between macroscopic and microscopic degrees of freedom. or Between spinor fields associated with the particles of the object and the spinor fields associated with the object. at the cascade, this entanglement will be lost?

Dear Hamed:

k=5 must be a typo, which I do not understand. I must check it.

What the time scale of highest hbar for a general system is, cannot be answered without knowledge about time scale of long term memories and of planned action. The systems with degenerate states resulting in n-furcations for Kahler action might be quite rare. It is quite possible that so called dead matter corresponds to ordinar non-negentropic entanglement.

In standard quantum theory negentropic number entanglement would not possible and the cascade would stop when bound state is encountered. Otherwise it would proceed down to elementary particle level. Note however that Bose-Einstein and Fermi statistics forces entanglement in this scale.

Note also that although systems in longer scale are unentangled, their subsystems in smaller scale (such as elementary bosons or fermions) can entangle: the space-time correlate is flux tube connecting space-time sheets condensed on larger disjoint space-time sheets. Statistics does not allow the decomposition of say many fermion state to tensor product of single particle state and the rest.

The possibility of negentropic entanglement means that the cascade can stop much earlier: negentropy gain in quantum jump would be negative if negentropic entanglement were destroyed. This is of importance for quantum computation.

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