Is it really a Higgs?

Peter Woit tells in This Week's rumour that CMS has found that the signal for what could be Higgs in gamma-gamma decay channel is two times higher than it should be. The optimistic interpretation is that both ATLAS and CMS have been a little bit lucky. But can we believe this? Statistics has been improving: how it is possible that also CMS is getting "lucky"!

If the good luck continues, one is forced to challenge the idea that the signal represents standard model Higgs. SUSY Higgs cannot help since standard SUSY itself is in deep difficulties experimentally. We cannot forget that there are also Higgs like signals at higher masses but these were "forgotten" in the midst of the Higgs hysteria - at least by bloggers who seem to suffer from rather short span of long term memory. Some of us even experienced a sudden conversion from a phanatic no-fairiest to an equally phanatic believer-in-Higgs;-).

In the zero energy ontology of TGD Higgs is not needed at all. A scaled up variant of ordinary hadron physics characterized by Mersenne prime M₈₉ is however "almost-predicted" (better to be cautious!) with mass scale 512 higher than that for ordinary hadron physics. This hadron physics can be said to replace Higgs.

The mesons of this hadron physics should be detected first at LHC. In particular, M₈₉ pion and spion (obtained by replacing quark and antiquark of pion with squark and antiquark) should be there if TGD SUSY is realized in the simplest possible manner meaning the same p-adic mass scale for both quarks and squarks. The few year old discovery of exotic satellite states of ordinary pion supports this radically new view about SUSY as also the mysterious X and Y mesons which in many respects look like charmonium states but are not charmonium states. I have told about all this in the earlier postings. Here is the most recent one.

The generalization of partially conserved axial current hypothesis (PCAC) allows to predict various decay rates and leads to very similar expressions for the decay rates of M₈₉ pseudoscalar mesons as standard model for those of Higgs. Higgs vacuum expectation is replaced with the decay constant f_π of pion-like (more generally meson-like) state which in sigma model corresponds to the vacuum expectation of sigma field. Sigma model is however not necessary except as a phenomenological description in which sigma field expectation would characterize the contribution of the classical color magnetic fields to the mass of M₈₉ baryons. Quark masses would follow from p-adic thermodynamics providing a microscopic description for particle massivation: also the need for this description has been forgotten by the main stream bloggers.

In particular, spion would have 1.5 times higher gamma-gamma decay rate if one extrapolates directly the PCAC for ordinary pion by the simplest possible scaling argument. Could it be that the Higgs candidate is actually spion and pion and other mesons are also there waiting to be discovered? This is the question.

My guess is that within year Higgs hypothesis is dead and one must begin serious work in trying to resolve the problems visible already now.

Tachyonic explanation of neutrino superluminality killed

New Scientist reported about the sad fate of the tachyonic explanation of neutrino superluminality. The argument is extremely simple.

1. You start by assuming that a tachyon having negative mass squared: m(ν)²<0 and assume that super-luminal velocity is in question. The point is that you know the value of the superluminal velocity v(1+ε)c, ε≈ 10^-5. You can calculate the energy of the neutrino as

   E= |m(ν)|[-1+ v²/(v²-1)]^1/2,

   |m(ν)|=(-m(ν)²)^1/2 is the absolute value of formally imaginary neutrino mass.

2. In good approximation you can write

   E= |m(ν)|[-1+ (2ε^-1/2]^1/2 ≈|m(ν)| (2ε)^-1/2.

   The order of magnitude of |m(ν)| is not far from one eV - this irrespective of whether neutrino is tachyonic or not. Therefore the energy of neutrino is very small: not larger than keV. This is in a grave contradiction whith what is known: the energy is measured using GeV as a natural unit so that there is discrepancy of 6 orders of magnitude at least. One can also apply energy conservation to the decay of pion to muon and neutrino and this implies that muon has gigantic energy: another contradiction.

What is amusing that this simple kinematic fact was not noticed from beginning. In any case, this finding kills all tachyonic models of neutrino super-luminality assuming energy conservation, and gives additional support for the TGD based explanation in terms of maximal signal velocity, which depends on pair of points of space-time sheet connected by signal and space-time sheet itself characterizing also particular kind of particle.

Even better, one can understand also the jitter in the spectrum of the arrival times which has width of about 50 ns in terms of an effect caused fluctuations in gravitational fields to the maximal signal velocity expressible in terms of the induced metric. The jitter could have interpretation in terms of gravitational waves inducing fluctuation of the maximal signal velocity c_#, which in static approximation equals to c_#=c(1+Φ_gr)^1/2, where Φ_gr is gravitational potential.

Suprisingly, effectively super-luminal neutrinos would make possible gravitational wave detector! The gravitational waves would be however gravitational waves in TGD sense having fractal structure since they would correspond to bursts of gravitons resulting from the decays of large hbar gravitons emitted primarily rather than to a continuous flow (see this). The ordinary detection criteria very probably exclude this kind of bursts as noise. The measurements of Witte attempting to detect absolute motion indeed observed this kind of motion identifiable as a motion of Earth with respect to the rest frame of galaxy but superposed with fractal fluctuations proposed to have interpretation in terms of gravitational turbulence - gravitational waves.

For details see the earlier posting, the little article Could the measurements trying to detect absolute motion of Earth allow to test sub-manifold gravity? or the chapter TGD and GRT of "Physics in Many-Sheeted Space-time".

The basic objection against TGD

The basic objection against TGD is that induced metrics for space-time surfaces in M⁴× CP₂ form an extremely limited set in the space of all space-time metrics appearing in the path integral formulation of General Relativity. Even special metrics like the metric of a rotating black hole fail to be imbeddable as an induced metric. For instance, one can argue that TGD cannot reproduce the post-Newtonian approximation to General Relativity since it involves linear superposition of gravitational fields of massive objects. As a matter fact, Holger B. Nielsen- one of the very few colleagues who has shown interest in my work - made this objection for at least two decades ago in some conference and I remember vividly the discussion in which I tried to defend TGD with my poor English.

The objection generalizes also to induced gauge fields expressible solely in terms of CP₂ coordinates and their gradients. This argument is not so strong as one might think first since in standard model only classical electromagnetic field plays an important role.

1. Any electromagnetic gauge potential has in principle a local imbedding in some region. Preferred extremal property poses strong additional constraints and the linear superposition of massless modes possible in Maxwell's electrodynamics is not possible.

2. There are also global constraints leading to topological quantization playing a central role in the interpretation of TGD and leads to the notions of field body and magnetic body having non-trivial application even in non-perturbative hadron physics. For a very large class of preferred extremals space-time sheets decompose into regions having interpretation as geometric counterparts for massless quanta characterized by local polarization and momentum directions. Therefore it seems that TGD space-time is very quantal. Is it possible to obtain from TGD what we have used to call classical physics at all?

The imbeddability constraint has actually highly desirable implications in cosmology. The enormously tight constraints from imbeddability imply that imbeddable Robertson-Walker cosmologies with infinite duration are sub-critical so that the most pressing problem of General Relativity disappears. Critical and over-critical cosmologies are unique apart from a parameter characterizing their duration and critical cosmology replaces both inflationary cosmology and cosmology characterized by accelerating expansion. In inflationary theories the situation is just the opposite of this: one ends up with fine tuning of inflaton potential in order to obtain recent day cosmology.

Despite these and many other nice implications of the induced field concept and of sub-manifold gravity the basic question remains. Is the imbeddability condition too strong physically? What about linear superposition of fields which is exact for Maxwell's electrodynamics in vacuum and a good approximation central also in gauge theories. Can one obtain linear superposition in some sense?

1. Linear superposition for small deformations of gauge fields makes sense also in TGD but for space-time sheets the field variables would be the deformations of CP₂ coordinates which are scalar fields. One could use preferred complex coordinates determined about SU(3) rotation to do perturbation theory but the idea about perturbations of metric and gauge fields would be lost. This does not look promising. Could linear superposition for fields be replaced with something more general but physically equivalent?

2. This is indeed possible. The basic observation is utterly simple: what we know is that the effects of gauge fields superpose. The assumption that fields superpose is un-necessary! This is a highly non-trivial lesson in what operationalism means for theoreticians tending to take these kind of considerations as mere "philosphy".

3. The hypothesis is that the superposition of effects of gauge fields occurs when the M⁴ projections of space-time sheets carrying gauge and gravitational fields intersect so that the sheets are extremely near to each other and can touch each other ( CP₂ size is the relevant scale).

A more detailed formulation goes as follows.

1. One can introduce common M⁴ coordinates for the space-time sheets. A test particle (or real particle) is identifiable as a wormhole contact and is therefore pointlike in excellent approximation. In the intersection region for M⁴ projections of space-time sheets the particle forms topological sum contacts with all the space-time sheets for which M⁴ projections intersect.

2. The test particle experiences the sum of various gauge potentials of space-time sheets involved. For Maxwellian gauge fields linear superposition is obtained. For non-Abelian gauge fields gauge fields contain interaction terms between gauge potentials associated with different space-time sheets. Also the quantum generalization is obvious. The sum of the fields induces quantum transitions for states of individual space time sheets in some sense stationary in their internal gauge potentials.

3. The linear superposition applies also in the case of gravitation. The induced metric for each space-time sheet can be expressed as a sum of Minkowski metric and CP₂ part having interpretation as gravitational field. The natural hypothesis that in the above kind of situation the effective metric is sum of Minkowski metric with the sum of the CP₂ contributions from various sheets. The effective metric for the system is well-defined and one can calculate a curvature tensor for it among other things and it contains naturally the interaction terms between different space-time sheets. At the Newtonian limit one obtains linear superposition of gravitational potentials. One can also postulate that test particles moving along geodesics in the effective metric. These geodesics are not geodesics in the metrics of the space-time sheets.

4. This picture makes it possible to interpret classical physics as the physics based on effective gauge and gravitational fields and applying in the regions where there are many space-time sheets which M⁴ intersections are non-empty. The loss of quantum coherence would be due to the effective superposition of very many modes having random phases.

The effective superposition of the CP₂ parts of the induced metrics gives rise to an effective metric which is not in general imbeddable to M⁴× CP₂. Therefore many-sheeted space-time makes possible a rather wide repertoire of 4-metrics realized as effective metrics as one might have expected and the basic objection can be circumvented In asymptotic regions where one can expect single sheetedness, only a rather narrow repertoire of "archetypal" field patterns of gauge fields and gravitational fields defined by topological field quanta is possible.

The skeptic can argue that this still need not make possible the imbedding of a rotating black hole metric as induced metric in any physically natural manner. This might be the case but need of course not be a catastrophe. We do not really know whether rotating blackhole metric is realized in Nature. I have indeed proposed that TGD predicts new physics new physics in rotating systems. Unfortunately, gravity probe B could not check whether this new physics is there since it was located at equator where the new effects vanish.

For background and more details see either the article Could the measurements trying to detect absolute motion of Earth allow to test sub-manifold gravity? or the chapter TGD and GRT of "Physics in Many-Sheeted Space-time".

Could the measurements trying to detect absolute motion of Earth allow to test sub-manifold gravity?

The history of the modern measurements of absolute motion has a long - more than century beginning from Michelson-Morley 1887. The reader can find in web a list of important publications giving an overall view about what has happened. The earliest measurements assumed aether hypothesis. Cahill identifies the velocity as a velocity with respect to some preferred rest frame and uses relativistic kinematics although he misleadingly uses the terms absolute velocity and aether. The preferred frame could galaxy, or the system defining rest system in cosmology. It would be easy to dismiss this kind of experiments as attempts to return to the days before Einstein but this is not the case. It might be possible to gain unexpected information by this kind of measurements. Already the analysis of CMB spectrum demonstrated that Earth is not at rest in the Robertson-Walker coordinate system used to analysis CMB data and similar motion with respect to galaxy is quite possible and might serve as a rich source of information also in GRT based theory.

In TGD framework the situation is especially interesting.

1. Sub-manifold gravity predicts that the effective light-velocity measured in terms of M⁴ time taken for a light signal to propagate from point A to B depends on space-time sheet, on points A and B, in particular the distance between A and B. The maximal signal velocity determined in terms of light-like geodesics has this dependence because light-like geodesics for the space-time surface are in general not light-like geodesics for M⁴ but light-like like curves. The maximal signal velocity is in general smaller than its absolute maximum obtained light-like geodesics of M⁴, depends on particle, and could be larger than for photon space-time sheets. This might explain neutrino super-luminality (see this).

2. Space-time sheets move with respect to larger space-time sheets and it makes sense to speak about the motion of solar system space-time sheet with respect to galactic space-time sheet and this velocity is in principle measurable. Maximal signal velocity can be defined operationally in terms of time needed to travel from point A to B using Minkowski coordinates of the imbedding space as preferred coordinates. It depends on pair of points involved: basically on the direction on and spatial distance along effectively light-like geodesic defined by the sum of the perturbations of the induced metric for the space-time sheets involved. The question is whether one could say something interesting about various experiments carried out to measure the absolute motion interpreted in terms of velocity of space-time sheet with respect to say galactic space-time-sheet.

Also in Special Relativity the motion relative to the rest system of a larger system is a natural notion. In General Relativistic framework situation should be the same but the mathematical description of the situation is somewhat problematic since Minkowski coordinates are not global due to the loss of Poincare invariance as a global symmetry. In practice one must however introduce linear Minkowski coordinates and this makes sense only if one interprets the general relativistic space-time as a perturbation of Minkowski space. This background dependence is in conflict with general coordinate invariance. For sub-manifold gravity the situation is different.

Could the measurements performed already by Michelson-Morley and followers could provide support for the sub-manifold gravity? This might indeed be the case as the purpose of the following arguments demonstrate. The basic results of this analysis are following.

1. The basic formulas for interferometer experiments using relativistic kinematics instead of Galilean one are same as the predictions of Cahill using different basic assumptions, and allow to conclude that already the data of Mickelson and Morley show the motion of Earth -not with respect to aether- but with galactic rest system.

2. The only difference is the appearance of the maximal signal velocity c_# for space-time sheet to which various gravitational fields contribute. In the static approximation sum of gravitational potentials contributes to c_#.

3. This allows to utilize the results of Cahill, who has carried out a re-analysis of experiments trying to detect what he calls absolute motion using these formulas. Cahill has also replicated the crucial experiments of Witte.

4. The value of the velocity as well as its direction can be determined and the results from various experiments are consistent with each other. The travel time data demonstrate a periodicity due to the rotation of Earth and motion with respect a preferred frame identifiable as a galactic rest frame. The tell-tale signature is the periodicity of sidereal day instead of exact 24 hour periodicity. The travel time for photons shows fluctuations which might be interpreted in terms of gravitational waves having fractal patterns. TGD view about gravitons would suggest that the emission takes place -not as a continuous stream- but in burst-wise manner producing fractal fluctuation spectrum. These fluctuations could show themselves as a jitter also in the neutrino travel times discovered by Opera collaboration.

One must answer several questions before one can make predictions.

1. The reduction of light velocity in the case that there are many space-time sheets whose M⁴ projections intersect, is described using common M⁴ coordinates for the space-time sheets. The induced metric for given space-time sheet is the sum of flat M⁴ metric and CP₂ contribution identified as classical gravitational field. The hypothesis is that in good approximation a linear superposition for the effects of the gravitational fields holds true in the sense that a test particle having wormhole throat contacts to these space-time sheets experiences the sum of the gravitational fields of various sheets. Similar description holds for induced gauge fields.

   From this one can identify the reduced light velocity in the static situation as c_#=(g_tt)^1/2. In a more realistic necessary non-local treatment one calculates the effective light-velocity by assuming that the orbit of massless state n geometric optics approximation is light-like geodesic for the sum of the metric perturbations: this line is not a light-like geodesic of any of the space-time sheets.

   In the general the effective metric defined in this manner is not imbeddable as induced metric. This description of linear super-position allows to circumvent the basic objection against TGD, which is that induced metric and gauge fields are extremely strongly correlated since they are expressible in terms of CP₂ coordinates and their gradients and that the variety of metrics representable as induced metrics is extremely restricted. Same of course applies to gauge fields. This resuls is extremely important and would deserve a separate blog posting.

2. How the reduced light-velocity c_# relates to the reduced light-velocity in medium which is usually described by introducing the notions of free and polarization charges and magnetization and magnetization currents. In the simple situation when polarization tensor is scalar, refractive index n characterizes the reduction of the light velocity: V=c_#/n. Since the reduction of maximal signal velocity due to sub-manifold is purely gravitational and its reduction in medium has an electromagnetic origin, one can argue that the two notions have nothing to do with each other. Hence c_# should be treated as a local concept possibly depending on direction of motion by taking the limit when light-like geodesic with respect to effective metric becomes infinitesimally short. This dependence can be deduced by comparing light-like geodesics emanating from a point and calculating the maximal signal velocity as a function of direction angles of the light-like geodesic and the spatial distance along it.

3. What happens to the boundary conditions between different media deduced from the structural equations of classical electrodynamics and Maxwell equations? For instance, does the refraction of light take place also when c_# changes? It might of course be that c_# changes only in astrophysical scales - maybe at the surfaces of astrophysical objects - and stays constant at the boundaries between two media in laboratory scale but nevertheless this issue should be understood. The safest guess is that at the level of kinematic local Lorentz invariance still holds true so that the tangential wave vectors identifiable in terms of massless momentum components are conserved at boundaries and one obtains law of refraction also now.

4. In TGD Universe space-time sheets can move with respect to each other and the larger space-time sheet defines the analog of absolute reference frame in this kind of situation. Also in cosmology one can assign to CMB radiation a specific frame and Earth indeed moves with respect to it rather than being at rest in the global Robertson-Walker coordinate system. For Earth solar system is one such frame. Galactic rest system is second such preferred reference frame. To both one can assign linear Minkowski coordinates, which play a special physical. The obvious question is whether this kind of motion could be detected and whether the measurements carried out to detect absolute motion could allow to deduce this kind of velocity with respect to galactic rest system.

5. The question is how photons in medium behave when this kind of motion is present. Assume that the medium is characterized by refractive index n so that one has V= c_#/n and that space-time sheet moves with respect to larger one by velocity v characterized by direction angles and magnitude. Here c_#<c₀ is the maximal signal velocity at the space-time sheet. For definiteness assume that the larger space-time sheet corresponds to galaxy.
   1. In the measurements of light velocity the light propagates in medium with velocity V<c_#<c₀, and the question is how to describe this mathematically. In his experiments Michelson assumed summation of velocities based on Galilean invariance. This is of course wrong and Special Relativity suggests summation of velocities according to the relativistic formula:

      V →V₁(v,u) == [V+ vu]/[1+ u(Vv/c_#²)] ,

      V= c_#/n , u=cos(θ) .

      Here θ is the direction of the light signal with respect to the velocity v. This formula might be justified in TGD framework: also photon has very small but non-vanishing mass and summation formula for velocities can be applied. This demands the assumption of local Lorentz invariance made routinely in General Relativity. Also it requires that the complex process of repeated absorption and emission of photons is described by a propagation of photon with the reduced velocity.

   2. This predicts two effects which might be seen in the experiments trying to measure absolute velocity and its direction. Both solar and galactic gravitational field and also its perturbations - even gravitational waves- can affect the signal velocity via fluctuations in c_# deduced from the superposition of the perturbative contributions of CP₂ to the effective induced metric. Second effect is due to the change of the propagation time. This change depends on the propagation direction. Note however that also c_# in general has the directional dependence and only in the situation when the components g_ti vanish, this dependence is trivial. In the Newtonian approximation the assumption g_ti≈ 0 is made and corresponds to the description of the situation in terms of gravitational potential.

For background and more details see either the article Could the measurements trying to detect absolute motion of Earth allow to test sub-manifold gravity? or the chapter TGD and GRT.

The TGD based interpretation of the God helmet experiments

In the previous posting I described the God helmet experiments of Persinger briefly and Persinger's own interpretation of the results. Anyone interested to understand what neurotheology is about should listen the inspiring talk God and the Brain - The Persinger 'God Helmet', The Brain, and visions of God by Todd Murphy.

In this posting I will discuss the TGD inspired interpretation of the results of Persinger's experiments. To put it in very concise manner: whereas Persinger interprets right brain as "visitor" explaining sense of presence experiences and even meeting of God, I identify the "visitor" of the visitor experiences as the personal magnetic body or in the case of enlightment experiences as the emergence of a new layer to its fractal structure. Magnetic body would be also responsible for the third person aspect of conscious experience, which means that we tend to see ourselves from bird's eye perspective. Magnetic bodies make as social animals, and are responsible for the cultural evolution and explain why we differ so much from our cousins although the genomes differ so little.

1. Frequency modulation as a "code of consciousness"

Maxwell's electrodynamics would suggest that a superposition of endogenous and external magnetic fields takes place in God helmet experimens and is partially responsible for the effects. This is clear from the fact that quite spesific magnetic stimulation is used (signals derived from EEG during the second stage). In TGD framework one should be able to interpret this.

1. In TGD Universe endogenous magnetic fields could form a fractal hierarchy: flux quanta inside flux quanta. Several critical values of magnetic field expected. Flux quanta could be flux tubes or sheets (DNA strands could be traversed by flux sheets and one could have hierarchy of genomes making possible collective gene expression at various levels).

2. There is a hierarchy of Planck constants so that one can assign to the cell membrane potential a Josephson frequency proportional to 1/hbar and to cyclotron frequencies photon energy proportional to hbar.

3. The code for the communications from biological body to various levels of the magnetic body relies on the modulation of the Josephson frequencies assignable to the cell membrane. Assuming that the value of Planck constant is integer multiple of its standard value these frequencies span an enormous range. In the case of EEG the Planck constant is of order 10¹³ in order to for photons with the energy of visible photon to have frequency about 10 Hz. Since Josephson frequency is proportional to the membrane potential, the modulations of the membrane potential induce modulations of Josephson frequency so that the signal sent to the magnetic body is modulated and this frequency modulation must define the "code of consciousness".

4. The frequencies involved with these communications are sums of harmonics of Josephson frequency and cyclotron frequency and also cyclotron frequencies can be modulated by modulating magnetic fields. The simplest possibility is that the external magnetic field induces modulation of the magnetic field. This modulation is small since the field strength is of order .01 Gauss and by a factor 1/20 smaller than the endogenous magnetic field B_end=.2 Gauss suggested by the effects of ELF em fields on vertebrate brain. Of course also other field values are expected to be present.

2. The basic philosophy behind the TGD based model

The basic philosophy behind the TGD based explanation of God helmet experiences differs in many respects from that behind the model of Persinger and Murphys. Therefore it is good to describe this philosophy first.

1. In the normal social consciousness based strongly on verbal communications the left brain self dominates and social interactions actually split the left brain self from right brain self so that right brain self remains a silent companion unable to express itself except throught intuitions. This raises some questions.

   Could just the need to communicate the experience verbally automatically project "me" to left brain me and cut if from "right brain self" so that only the memories of left brain self are communicated. What would happen if the subject person would communicate with external world by singing? Often persons who have lost their ability to speak and comprehend spoken language can communicate by singing. Would the the projection occur to left brain self and could the memories be different?

2. Persinger and Murphy seem to assume that right brain is God from the perspective of the left brain. Magnetic body is responsible for the third person aspect of consciousness and also for the ability to see the dying biological body from the bird's eye perspective during OBEs accompanying also NDEs, which accordingy to Murphy could be quite real. There is indeed evidence that a subject person unable to move from bed has been able to see objects which she should not have been able to see. If magnetic body is real it could also receive extra-sensory information.

   Could the magnetic body of right brain or of the entire brain be in some sense the God from the view point of the brain? The TGD based interpretation for the vision of Jaynes about bicameral consiousness as a predecessor of modern consciousness would conform with this. The God of old testament would be the personal magnetic body which would not have yet become a highly integrated part of self and could be experienced as an outsider. Jaynes also proposes that the consciousness of schizophrenic is much like bicameral consciousness.

3. It is not necessary to assume that the right amygdala is specialized to produce negatively colored motions and left amygdala positive emotions. Same applies also to the proposed roles of right and left hippocampi. In fact, according to Wikipedia article about lateralization of brain function depression is linked with hyperactive right hemisphere and selective involvement in "processing negative emotions, pessimistic thoughts and unconstructive thinking styles". A relatively hypoactive left hemisphere is said to be "specifically involved in processing pleasurable experiences" and "relatively more involved in decision-making processes". One can interpret this in many manners. The hyper-activity of right hemisphere could tend to cut its connection with its magnetic body and cause a depressive mood.

   Intense nerve pulse activity could cause this if nerve pulse generation breaks coherence of the EEG oscillation due to the oscillating membrane potentials inducing generation of signals to the magnetic body. The reduced neural activity of left hemisphere would mean a better connection to the magnetic flux tube and positive emotional coloring.

4. Note that this picture conforms with spiritual practices which teach that the manner to achieve piece of mind and bliss is to stop thinking, which indeed means reduce neural activity and more stable connection to the magnetic body. If one takes this conceptualization seriously, one could conclude that the modern hectic society tends to split the connections to the personal magnetic bodies. Since they represent higher levels in the hierarchy of conscious entities, this would lead to a loss of spirituality and also social regression if magnetic bodies are responsible for social structures and cultural evolution.

5. For about 26 years ago I had also a long-lasting "enlightment" experience - actually two of them. The general structure of these experiences fits with thde proposed general format. The first experience began with the experience of getting in contact with what I spontaneously called Great Mind. I started to make all kinds of questions which I imagined of writing to a monitor that I saw in front of me. Later I realized that the writing was not necessary. I also understood that our communication was severaly estricted by the fact that my language did not yet have words for to express the messages of this Great Mind so that the messages contained a lot of "blancos".

   I had an experience of profound understanding but did not know what I understood. I also felt that everything around me has extremely deep meaning. One of the first questions I did was "How long I will live?". From the humorous reply expressed as an endless rapid running of a counter containing a long sequence of digits I understood that there is no death. I also asked "Am I alone in this Universe?". The reply was enigmatic "You are a God!".

   Later it somehow became clear that this God like entity was actually in some sense me. A possible interpretation could be that a new higher layer to the hierarchy of layers of my personal magnetic body had emerged as this God like creature became a part of my personal magnetic body. Much later I realized that this paradoxical realization was the analog for Brahman=Atman identity of Eastern philosophies.

Consider now the more technical assumptions.

1. One can assume that right and left brain selves can entangle to form a single self and that magnetic flux tubes between brain hemispheres closely associated with the connecting nerve bundles serve as a correlate for this entanglement. In TGD framework the notion of negentropic entanglement makes sense and means entanglement entropy defined number theoretically is negative rather than being positive as usually. Negentropy Maximization Principle for quantum jumps guarantees the stability of negentropic entanglement. Entanglement probabilities must be rational or at most algebraic numbers or negentropic entanglement.

2. The basic mechanism would be reconnection of magnetic flux tubes. Typically two parallel connecting flux tubes would touch each other and reconnect to form U-shaped flux tubes representing flux tubes beginning and returning to left (right magnetic body). What is the role of the external magnetic field in this process? Could the closed flux tubes of the external magnetic fields reconnect with those connecting the right hemisphere to left hemisphere. Suppose that magnetic flux tubes indeed serve as geometric correlates for attention interpreted as negentropic entanglement.

   Could one say that the magnet creating chirp signal catches the attention of the right brain magnetic body directed to the right hemisphere? Could the splitting of the connection to the magnetic body create the negative emotions. It is enough that the magnet- magnetic body entanglement becomes entropic to destroy the entanglement in state function reduction if one believes in NMP and perhaps this occurs.

3. One an ask whether this kind of mechanism could explain also the effects of strong (or order 1 Tesla) fields on brain in transcranial magnetic stimulation or is the standard explanation in terms of eddy currents inducing nerve pulse patterns enough to explain the effects.

3. The model for God helmet experiences

Consider now a the general TGD inspired model explaining God helmet experiences.

1. The magnetic chirp during the first stage tends to decouple the right hemisphere from its magnetic body and possibly also from the magnetic body of left brain. This alone creates the negatively colored emotions- kind of feeling of being abandoned by God. This could be also general mechanism of depression and the manner to cure depression would be re-establishment of this connection.

   At quantum level the cutting of the magnetic connection would mean the desctruction of entanglement between parts of the two brain hemispheres or between part of right hemisphere and its magnetic body temporarily. This would lead to the splitting of self to right and left brain sub-selves or the loss of the right hemisphere magnetic body entanglement.

2. If one is ready to take seriously the notion of number theoretic entropy, the minimum condition would be that the magnetic chirp causes the entanglement probabilities become non-rational or even non-algebraic numbers so that the number theoretic entropy does not make sense. Ordinary entanglement entropy is always non-negative and state function reduction reduces the entanglement and self splits to two.

3. During the second stage the simultaneous activation of both hemispheres by artificial neuronal signals derived from the EEG of amygdala and hippocampus would fuse both hemispheres to single coherent unit so that the mental images of the right hemisphere would contribute to the conscious experience. The coherence could increase from what it is during ordinary wake-up consciousness dominated by verbal communications. "Being nearer to God" alone could give rise to highly positived colored emotions and to a direct experience of seeing the God/light being/magnetic body and explain the experience of meaningfulness and deep understanding without being able to express what one understands. This inability could be simply to the lack of appropriate language. There is no need to assign this experience to the right hippocampus.

For background and pdf version of the text see the new chapter TGD Based View about Classical Fields in Relation to Consciousness Theory and Quantum Biology of "TGD and EEG".

Persinger's work with God helmet

Anyone - atheist or believer - wanting to learn about Persinger's work and the basic insights of neuro-theology should listen the extremely inspiring talk God and the Brain - The Persinger 'God Helmet', The Brain, and visions of God by Todd Murphy. Persinger's work (for refereces to the articles by Persinger and collaborators see the Wikipedia article about God helmet) suggests that the temporal pattern of the modulation of magnetic field strength (FM would be in question for slow variations) is important. We do not however know the "code". Also the strength of the magnetic field can be important. Note that the effects of very weak ELF em fields on vertebrate brain take place in amplitude windows.

The modulation of magnetic field would probably induce FM of cyclotron frequencies. The model for hearing suggests this kind of modulation as a manner to represents the frequencies of the sound wave. Also phase information is very important: time reversed speech sounds very different as normal speech but has the same power spectrum. Modulations would be slow in the time scales defined by the audible frequency range. .1 seconds would represent lower limit for the variation rate of modulation. Audible frequencies above 20 Hz.

1. God helmet

God helmet or Koren helmet named after its inventor is the device used by Persinger and collaborators to study the effects of magnetic field on consciousness. Transcranial magnetic stimulation is not in question: TCMS uses fields of order Tesla whereas Persinger uses magnetic fields with strength of order .01 Gauss. This is 2 per cent of the nominal value of Earth's magnetic field. There is a coil above both temporal lobes and the active coil rotates counterclockwise.

1. At the first stage the coil above right temporal lobe rotates counterclockwise. A chirp sequence is used. Chirp means use of an oscillating magnetic field with maximum amplitude about 1 microTesla with oscillation frequency going gradually down. The interpretation is that right-brain self is activated and dominates conscious experiences. The experiences have negative emotional coloring and sometimes the subject person has even fearful experiences.

2. At second stage both coils rotate counterclockwise. The signal is derived from amygdala and hippocampal EEG. Faraday cage is used to eliminate external electromagnetic perturbations and also sensory deprivation is necessary (subject person is blind-folded and in an acoustic chamber). Earth's magnetic field is present, which might have relevance and is indeed used in experiments related to the hypothesis that the variations in Earth's magnetic field affect consciousness.

   A burst of left brain activity is reported to take place during second stage. Also visitor experience is reported to occur during this period. This can mean meeting of God/light being, of angels, of deceased or of group of "beings", or just sense the presence of some conscious entity. A strong sense of meaning can accompany the experience. 80 per cent of subjec persons experience at least the sense of presence.

2. Persinger's experiments and cyclotron frequencies

A more quantitative description of the God helmet experiment assuming that cyclotron frequencies are essential goes as follows.

1. The field strength used by Persinger is of the order .01 Gauss and very weak and different from B_end=.2 Gauss which is .4B_E with B_E=.5 Gauss the nominal value of the Earth's magnetic field. Cyclotron frequencies are by a factor of order 1/20 smaller than for B_end. This gives .75 Hz for Ca⁺⁺.

   From this it is clear that the changes of cyclotron frequencies would be small in static external field in Persinger's experiments and could be treated as a small perturbation. External magnetic field could superpose with B_end=.2 Gauss and affect cyclotron states and induce transitions between them. This would induce effects on EEG visible as frequency modulations. It seems that the period for the oscillation of B must be longer than cyclotron period for this picture to make sense.

2. One expects a fractal hierarchy of field strengths for endogenous magnetic fields and B≈ .01 Gauss could correspond to higher levels of consciousness so that cyclotron frequencies for these fields would be important. In this case the external magnetic field would not be a small perturbation. The cyclotron frequencies of DNA strand carrying charge density of 2 elementary charges per nucleotide from the phosphates depend only weakly on the length of DNA strand and are about 1 Hz in B_end. Could the cyclotron radiation from cyclotron states associated with the external magnetic field induce interaction with DNA cyclotron states in field B_end=.2 Gauss?

3. Consider next the time scales. The stimulation of right brain lasts during the first stage last about half an hour. There are however many lacking bits of data.
   1. In what range are the values of the rotation frequency for the magnetic field? ELf frequencies are used. If EEG frequencies are in question the rotation should be slower what the lowest EEG frequency involved and below 1 turn per second.

   2. The rotated magnetic field is time dependent. Chirp sequences are used to stimulate temporal lobe. What is the duration of single chirp and the frequency range covered during chirp? A good guess is that the frequency range is that of EEG. The natural expectation is that the duration of chirp is much longer than the periods in the frequency range considered. This would mean that one scan entire frequency range and that it makes sense to say that the changes of frequency during chirp is slow as compared to the instantaneous frequency.

   3. EEG signals from left amygdala or hippocampus are used to stimulate both temporal lobes during the second stage. This means that their natural frequency scale should be in the range 1-100 Hz. These time scales would be shorter than the time scale of order 1 second assignal to Ca⁺⁺. This suggests that small aplitude modulation of the cyclotron frequencies in EEG range is in question. The signals sent to the magnetic body would be determined by this modulation and at least in the second stage this modification would carry information.

3. Persinger's explanation

Persinger's own explanation for the findings relies on what might be called neurotheology.

1. The basic claim of Persinger is that the experiences in question are produced by brain so that meeting of God would not be real. Todd Murphy emphasizesthat it is actually impossible to conclude anything about the existence or non-existence of God on basis of these experiments. He however claims that evolution would have developed for brain the ability to produce visions of God which often accompany near death experiences and make it easier to accept the unavoidablity of the biological death. The reader can decide whether these two statements are consistent or not.

2. The general idea is that both right and left amygdala, which are the most sensitive parts of the brain because the membrane potential is nearest to the threshold for nerve pulse generation. The right hippocampus is assumed to be responsible for non-verbal, "silent" thinking and left brain hemisphere to verbal thinking. This general picture is used by Todd Murphy to understand the conscious experiences accompanying death process about which near death experiences give a information. The experiences generated by God helmet during the first stage would be akin to the fearful emotions associated with near death experiences (NDE). The experiences during the second stage bring in mind the spiritual experiences accompanying death process and having strong positive emotional coloring.

3. Persinger and Murphy propose that left amygdala is specialized to produce positive emotions (happiness, bliss, and even experience of encountering God or almost synonymously light being). Right amygdala would be specialized to produce negative emotions (such as fear and horror) and one can assign with it also depressive mood. This is not a generally accepted theory. If one accepts it, the natural question is whether right amygdala could serve as a kind of entropic dump pit and left amygdala as as a highly negentropic structure. The empirical data does not force the poor right amygdala to be a whole-daily sufferer.

Consider now the explanation of the experiences induced by God helmet. The lecture by Todd Murphy helps considerably in attempts to understand the gist of the explanation and also helsp to see its problematic aspects.

1. The selves of right and left brain fuse in some sense to form single self normally. The nerve bundles connecting the brain hemispheres allowing communications between them are essential for this integration. Right brain self is assumed to be sub-ordinate for left brain self. Magnetic pulses during the first period decompose self to two pieces: one could call them right and left self.

2. During the first stage the mental images from the right brain self become dominating and fearful experiences are due to the fact that right brain amygdala, which is specialized to produce negative emotions, is hyper-active. This phase is believed to break the connection between left and right brain hemispheres. The anecdotal evidence by Todd Murphy suggests a correlation between non-verbal mood of consciousness and negative emotions. One must be however very cautious because extreme fear and horror alone might make impossible not only verbal communication but any coherent action.

3. During the second stage both left and right brain are stimulated and expected contribute to the mental images of self when the connection between the hemispheres is intact. If I have understood correctly, the proposal is that the splitting of self to separate selves induced during the first phase is present almost permanently during the second phase and that left brain self dominates.

4. The temporary "intrusion" of the right hemisphere self to the consciousness of left brain self would give rise to visitor experience. Intrusions would mean occasional re-establishment of the connection between hemispheres. One can question the assumption that God experience and the sensed presence represent instances of the same basic experience due to the intrusion. One could also argue that sensed presence is a signal for the breakdown of the connection and is created by the realization that there is also another self using the same biological body.

5. The model of Todd Murphy for near death experiences would be that right amygdala can give rise to extremely frightening experiences but that the flow of the information to left amygdala transforms this experience to its emotional opposite. The right hippocampus suggested to be responsible for "silent" thinking would be responsible to the experiences of deep meaningfulness and of understanding. To my opinion this picture is too complex and involves too many ad hoc assumptions.

Somehow my personal feeling is that this model is not quite correct. For instance, I do not understand the meaning "intrusion"? This could be of course be just my misunderstanding. Also the hypothesis about the specialization of left and right amygdala looks strange. In the next posting I will describe the TGD inspired interpretation of Persinger's findings.

For background and pdf version of the text see the new chapter TGD Based View about Classical Fields in Relation to Consciousness Theory and Quantum Biology of "TGD and EEG".

TGD based view about classical fields, consciousness theory, and quantum biology

In TGD Universe gauge fields are replaced with topological field quanta. Examples are topological light rays, magnetic/electric flux tubes and sheets, and flux quanta carrying both magnetic and electric fields. Flux quanta form a fractal hierarchy in the sense that there are flux quanta inside flux quanta. It is natural to assume quantization of Kähler magnetic flux. Braiding and reconnection are the basic topological operations for flux quanta.

The basic question is how the basic notions assigned with the classical gauge and gravitational fields understood in standard sense generalize in TGD framework.

1. Superposition and interference of the classical fields is very natural in Maxwell electrodynamics and certainly experimentally verified phenomena. Also the notion of hologram relies crucially on the notion of interference. How can one describe the effects explained in terms of superposition of fields in a situation in which the theory is extremely non-linear and all classical gauge fields are expressible in terms of CP₂ coordinates and their gradients? It is also rather clear that the preferred extremals for Kähler action decompose to space-time regions representing space-time correlates for quanta. The superposition of classical fields in Maxwellian sense is impossible.

   How can one cope with this situation? The answer is based on simple observation: only the effects of the classical fields superpose. There is no need for the fields to superpose. Together with the notion of many-sheeted space-time this leads to elegant description of interference effects without any need to assume that linearization is a good approximation.

2. Topological quantization brings in also braiding and reconnection of magnetic flux tubes as basic operations for classical fields. These operations for flux tubes have also Maxwellian counterparts at the level of field lines. Braiding and reconnection are in a central role in TGD Universe and especially so in in TGD inspired theory of consciousness and quantum biology. The challenge is to build a coherent overall phenomenological view about the role of topologically quantized classical fields in biology and neuroscience. For instance, one can ask what is the precise formulation for the notion of conscious hologram and whether magnetic flux tubes could serve as correlates of entanglement (or at least negentropic entanglement suggested by the number theoretic vision and identified as a basic signature of living matter).

3. Topological quantization and the notion of magnetic body are especially important in TGD inspired model of EEG. The attempt to understand the findings of Persinger from the study of what is known as God helmet leads to a considerable progress in the understanding the possible role of topologically quantized classical fields in biology and neuro-science.

I do not bother to type more and instead give a link to the article TGD based view about classical fields, consciousness theory, and quantum biology.

About the notion of conscious hologram

In earlier posting Comparison of Maxwellian and TGD views about classical gauge fields I compared Maxwellian and TGD based notions of classical fields. The comparison was restricted to the linear superposition of fields which in TGD framework is restricted to linear superposition of effects of classical fields: the space-time sheets representing classical fields are indeed separate and it is enough that their M⁴ projections intersect. Summation of effects means at classical level summation of forces caused by them due to the fact that particles have topological sum contacts to both space-time sheets. The notion of hologram relies crucially on the superposition of fields and this this forces to reformulate the notion of hologram in TGD framework.

In TGD inspired theory of consciousness the idea about living system as a conscious hologram is central. It is of course far from clear what this notion means. Since the notions of interference and superposition of fields are crucial for the description of the ordinary hologram, the proposed general description for the TGD counterpart for the superposition of fields is a natural starting point for the more precise formulation of the notion of conscious hologram. In the following only the notion of conscious hologram is discussed. Also the formulation of the notion of ordinary hologram in TGD framework is an interesting challenge.

1. Consider ordinary hologram first. Reference wave and reflected wave interfere and produce an interference pattern to which the substrate of the hologram reacts so that its absorption coefficient is affected. When the substrate is illuminated with the conjugate of the reference wave, the original reflected wave is generated. The modification of the absorption coefficient is assumed to be proportional to the modulus squared fro the sum of the reflected and reference waves. This implies that the wave reflected from the hologram is in good approximation identical with the original reflected wave.

2. Conscious hologram would be dynamical rather than static. It would be also quantal: the quantum transitions of particles in the fields defined by the hologram would be responsible for the realization of the interference pattern as a conscious experience. The previous considerations actually leave only this option since the interference of classical fields does not happen. Reference wave and reflected wave correspond now to any field configurations. The charged particles having wormhole contacts to the space-time sheets representing the field configurations experience the sum of the fields involved, and this induces quantum jumps between the quantum states associated with the situation in which only the reference wave is present.

   This would induce a conscious experience representing an interference pattern. The reference wave can also correspond to a flux tube of magnetic body carrying a static magnetic field and defining cyclotron states as stationary state. External time dependent magnetic field can replace reflected wave and induces cyclotron transitions. Also radiation fields represented by MEs can represent the reference wave and reflected wave.

   If there is need for the "reading" of the hologram it would correspond to the addition of a space-time sheet carrying fields which in good approximation have opposite sign and same magnitude as those in the sheet representing reference wave so that the effect on the charged particles reduces to that of the "reflected wave". This step might be un-necessary since already the formation of hologram would give rise to a conscious experience. The conscious holograms created when the hologram is created and when the conjugate of the reference wave is added give rise to two different conscious representations. This might have something to do with holistic and reductionistic views about the same situation.

3. One can imagine several realizations for the conscious hologram. It seems that the realization at the macroscopic level is essentially four-dimensional. By quantum holography it would reduce at microscopic level to a hologram realized at the 3-D light-like surfaces defining the surfaces at which the signature of induce metric changes (generalized Feynman diagrams having also macroscopic size - anyons or space-like 3-surfaces at the ends of space-time sheets at the two light-like boundaries of CD. Strong form of holography implied by the strong form of general coordinate invariance requires that holograms correspond to collections of partonic 2-surfaces in given measurement resolution. This could be understood in the sense that the charged particles defining the substrate can be described mathematically in terms of the ends of the corresponding light-like 3-surfaces at the ends of CDs. The cyclotron transitions could be thought of as occurring for particles represent as partonic 2-surfaces topologically condensed at several space-time sheets.

One can imagine several applications in TGD inspired quantum biology.

1. One can develop a model for how certain aspects of sensory experience could be understood in terms of interference patterns for signals sent from the biological body to the magnetic body. The information about the relative position of the magnetic body and biological body would be coded by the interference patterns giving rise to conscious sensory percepts. This information would represent geometric qualia giving information about distances and angles basically. There would be a magnetic flux tube representing the analog of the reference wave and magnetic flux tube carrying the analog of reflected wavel which could represent the effect of neural activity. When the signal changes with time, cyclotron transitions are induced and conscious percept is generated. In principle it there is no need not compensate for the reference wave although also this is possible.

2. The natural first guess is that EEG rhythms (and those for its fractal generalization) represent reference waves and that the frequencies in question are either harmonics of cyclotron frequencies or linear combinations of these and Josephson frequency assignable to cell membrane (and possibly its harmonics). The modulation of membrane potential (membrane is regarded as a super-conductor) would induce modulations of Josephson frequency and if large enough would generate nerve pulses. These modulations would define the counterpart of the reflected wave. The flux tubes representing unperturbed magnetic field would represent reference waves.

3. For instance, the motion of the biological body changes the signal at the space-time sheets carrying the signal and this generates cyclotron transitions giving rise to a conscious experience. Perhaps the sensation of having a body is based in this mechanism. The signals could emerge from directly from cells: it could be that this sensation corresponds to lower level selves rather than us. Second option is that nerve pulses to brain induce the signals sent to the our magnetic body.

4. The motion of biological body relative to biological body generates virtual sensory experience which could be responsible for the illusions like train illusion and the unpleasant sensory experience about falling down from cliff by just imagining it. OBEs could be also due to the virtual sensory experiences of the magnetic body. One interesting illusion results when one swims long time in windy sea. When one returns to the shore one has rather long lasting experience of being in sea. Magnetic body gradually learns to compensate the motion of sea so that the perception of the wavy motion is reduced. At the shore this compensation mechanism however continues to work. This mechanism represents an example of adaptation and could be a very general mechanism. Since also magnetic body uses metabolic energy, this mechanism could have justification in terms of metabolic economy.

   Also thinking as internal, silent speech might be assigned with magnetic body and would represent those aspects of the sensory experience of ordinary speech which involve the quantum jumps at magnetic body- the associated geometric qualia- but not the primary sensory percept. This speech would be internal speech since there would be no real sound signal or virtual sound signal from brain to cochlea.

5. Conscious hologram would make possible to represent phase information. This information is especially important for hearing. The mere power spectrum is not enough since it is same for speech and its time reversal. Cochlea performs an analysis of sounds to frequencies. It it is not easy to imagine how this process could preserve the phase information associated with the Fourier components. It is believed that both right and left cochlea are needed to abstact the phase difference between the signals arriving to right and left ear allowing to deduce the direction of the source neural mechanisms for this has been proposed but these mechanism are not enough in case of speech. Could there exists a separate holistic representation in which sound wave as a whole generates a single signal interfering with the reference wave at the magnetic body and in this manner represents as a conscious experience the phase?

6. Also the control and reference signals from the magnetic body to biological body could create time dependent interference patterns giving rise to neural response initiating motor actions and other responses. Basically the quantum interference should reduce the magnitude of membrane resting potentials so that nerve pulses would be generated and give rise to motor action. Similar mechanism would be at work at the level of sensory receptors - at least retina. The generation of nerve pulses would mean kind of emergency situation at the neuronal level. Frequency modulation of Josephson radiation would be the normal situation.

For background see the chapter General View About Physics in Many-Sheeted Space-Time : Part I.

The latest Matrix model hype

Peter Woit told in his "This Week's Hype" series about a press release titled The mechanism that explains why our universe was born with 3 dimensions: a 40-year-old puzzle of superstring theory solved by supercomputer. Peter Woid gives a long citation of the hype and also discusses the background. I encountered a New Scientist article about this hype already few weeks ago and got so irritated that almost decided to write a blog posting but managed to calm down myself.

The challenge of a theoretician working with higher dimensions is to explain why our world seems to be 4-dimensional. No explanation for this fact has emerged in super string models: Kaluza-Klein approach led to Calabi-Yau's but led to the landscape catastrophe. Also 3-dimensional branes have been proposed to be in special role. The recent "solution" of the problem is actually rewarming of an old Kaluza-Klein spirited proposal. The idea is that somehow the symmetry-group of 10-dimensional space would reduce to SO(3) and this could be interpreted as isometries of 3-D Euclidian space. What the Japanese group has done are lattice calculations for what they call Matrix model, which is one of the extremely fuzzy variants of M-theory. It is suggested to provide nothing less than a non-perturbative formulation of M-theory.

In TGD framework the explanation for both the dimension 8 of imbedding space and the dimension D=4 of its Minkowski space factor and the dimension D=4 of space-time surface images from symmetry considerations. The world of classical worlds (space-time surfaces identified as preferred extremals of Kähler action) has Kähler geometry only if it has infinite-D isometry group. The conformal symmetries of the light-like 3-surfaces defining the surfaces at which the induce metric changes its signature and at the same time also generalized Feynman graphs extend the ordinary 2-D conformal symmetries and one obtains infinite-D isometr group. This is possible only for 4-D space-time surfaces. Also the light-cone boundary of light-cone of 4-D Minkowski space has extended conformal symmetries so that 4-D Minkowski space is unique.

There are also other reasons- in particular those related to the dimensions of classical number fields selecting these dimensions and M⁴× CP₂. It is of course useless to tell this to the colleagues: they refuse to listen to a pariah and prefer to contine beating their intelligent heads on the wall. The weird activities with Matrix represent only one example of this acticity.

The derivation of Matrix model

I decided to check what Matrix model means -if anything- and found an article by Tom Banks and some others about Matrix model. It is Christmas Eve so that I want to put it mildly: my feelings were mixed. There are long sequences of hand waving arguments before one ends up with what is christened as Matrix model.

1. One begins with M-theory and considers branes, which as such are very questionable objects physically. One suddenly decides that 0-branes representing point-like particles are fundamental rather than strings which would be analogous to 1-branes. All higher dimensional branes would be constructed from 0-branes. This would mean return to old days when particles where point-like. But do let this to disturb you. It is good to change the liturgy sometimes.

2. After this one puts an infinite number of 0-branes- point like particles- on top of each other at same point of 10-D space-time. Like putting infinite-number of point like particles on top of each other. Stay calm and trust the M-theoretician. He knows. Then M-theoretician tells that AdS-correspondence says that the 10 coordinates assignable to the the points form actually matrices in SU(N)×U(1) at the limit of infinite N so that the 10 coordinates have become 10 non-commutating matrix valued coordinates. If you have difficulties swallowing this remember that everyone learns that you are an imbecille with an intelligence quotient of amoeba if you say this aloud.

3. The AdS/CFT approach relies on the physical idea that the particles at different branes defined U(1) factors of gauge group. If the branes in the stack carry fermionic single particle states states one can indeed construct from them generators of SU(N)×U(1). This idea does not look non-sense to me: for finite number of N it might indeed give rise to a dynamical gauge group having interpretation as gauge symmetry allowing to describe finite measurement resolution in TGD framework. This however gives rise to gauge potentials with non-commutative gauge group, not non-commutative coordinates of 10-D space-time. This is a little problem- actually not so little - but let us trust M-theoreticians and identify vector potentials with 10-D space-time coordinates.

4. M-theoretician decides that the dynamics of everything is dictated by Yang-Mills Hamiltonian restricted to the world line of the stack of 0-branes. It should be possible to replace Yang-Mills Hamiltonian with corresponding Lagrangian and I shall indeed do this in the sequel to see what results.

This is the theory of everything in non-perturbative formulation! Certainly simple as will be found but to me- a crackpot with intelligence quotient of amoeba - this looks complete non-sense physically. The Japanese research group responsible for the hype has taken all this seriously and decided to do computer simulations. The value of N is replaced with a finite value for approximation purposes. One decides that Kaluza-Klein compactification to 4-D space-time takes places if symmetry breaking takes place reducing SO(9) as rotational symmetries to SO(3). The claim is that numerical calculations show that this happens.

Classical Lagrangian Matrix model

Just for fun I decided to check what YM Lagrangian in 1-D time-line would give.

1. The field equations express the vanishing of non-Abelian gauge currents. Gauge condition is naturally A₀=0 corresponding to vanishing of the time component of gauge potential. There would be no time in this Universe but let us not bet worried. One can write YM equations and they state the vanishing of YM currents: J^α=0.

2. J⁰=0 can be solved exactly and the solutions says that the other components of the potential are like the coordinates of a free particles A_i= x_i(0)+v_i(0) t. Particle interpretation happens to make sense except that time is constant.

3. Classically the conditions Jⁱ=[A_j,[A_i,A^j]]=0 give for matrix conditions on initial values of x_i(0) and v_i(0). Four conditions for each component corresponding to powers tⁿ, n=0,1,2,3. These equations are symmetric under the exchange of positions and momenta- kind of duality. Classically they represent infinite number of polynomial equations of third order in variables x_i(0) and p_i(0) restricting the motion to an algebraic surface in infinite-D space of 9-vectors with matrix valued components. The polynomials are homogenous so that scalings of initial values are symmetries.

4. An interesting ansatz consist of restricting the vector potentials to subgroup of U(∞). One obtains infinite hierarchy of solutions for which the motion of pseudo particle takes place in finite-dimensional subgroup U(n) or its subgroup. As a special case on also obtains solutions which correspond to Cartesian products ∏ U(n_i). The interpretation as N-particle solutions is attractive. For Cartesian powers of U(1):s the constraints are identically satisfied. For Cartesian powers of SU(2) one obtains what looks like particles in 3-space with coefficients of Lie-algebra generators of SO(3) interpreted as coordinates of 3-space.

Quantum variant of Lagrangian Matrix model

The classical solvability apart from constraints suggests that also the quantized variant of the theory is solvable.

1. Let us assume that wave functions are in the space defined by initial values x_i(0). The standard commutation relations for the matrix elements of A_i and p_i= dA_i/dt= p_i(0) reduce to those for x_i(0) and p_i(0). The matrix elements of these matrices are just like the position and momentum coordinates for free particle in Euclidian space. The conditions Jⁱ=0 reduces to four sets of equations corresponding to powers n=0,1,2,3 of t. n=0 gives infinite number of third order polynomial equations for initial values of x_i(0). n=1 gives second order partial differential equations linear in x_i(0). n=2 gives gives first order partial differential equations quadratic in x_i(0). n=3 gives infinite numer of third order partial differential equations in p_i(0).

2. Also in the quantum one has the hierarchy of solutions assignable to subgroups of U(∞) and their Cartesian products. If one wants something like emergent 3-space I would assign it to wave functions corresponding to the Cartesian powers of SU(2). I would try to show that the constraints favor this kind of solutions and that for higher dimensions of SU(N) or its subgroups the number of conditions is too large. I would also ask whether the fact that SU(2) Lie-algebra is in some sense the building brick of higher dimensional Lie algebras as the general form of the presentation of Lie algebras demonstrates could somehow mean that also more complex solutions are perturbations of those for Cartesian powers of SU(2). These questions are useful but it turns out that another 3-D Lie algebra- Heisenberg algebra- seems to be more interesting as effective gauge algebra.

The case of SU(2)

Are the resulting quantum equations sensible? For simplicity one can consider solutions restricted to SU(2) subgroup in the sense that the subgroup of U(∞) is N:th Cartesian power of SU(2) with interpretation in terms of N-particle state.

1. There are 3× 9=27 coordinates x_i(0). There are 3× 9 equations for n=0. The naive conclusion consistent with the scaling invariance and counting the number of conditions is that the only solution is x_i(0)=0.

2. This conclusion is too hasty. One can have solutions for which x_i is restricted to 1-D subspace of E⁹. In this case the conditions expressible in terms of 3-D cross product are identically satisfied since cross products vanish. In this case the situation is indeed 3-dimensional and one can say that solution describes a pointlike free particle moving in 3-D space defined by the SU(2) Lie algebra valued preferred coordinate of E⁹. I have failed to to find more general solutions to the conditions.

3. One can also consider wave functions restricted to 1-dimensional sub-manifolds of E⁹. Constraint conditions are identifically satisfied since the operators corresponding to n=1,2,3 vanish identically. The dimension of the higher dimensional space place no role since everything depends on the 3-D cross product characterizing quaternions and making SU(2) as a gauge group unique. The overall wave function would be restricted to a 2-D plane M² of M¹⁰. Amusingly, in TGD framework preferred planes M² of M⁴ play a key role.

The effectively one-dimensional solutions exist for any matrix algebra since gauge field vanishes identically and therefore also gauge current. Hence SU(2) is not in special position.

Effectively 3-dimensional solution ansatz based on Heisenberg algebra

One obtains effectively 3-dimensional solution ansatz by restricting the consideration to 3-D subspace of E⁹.

1. Using the notation [x_i(0) =A_i the solution ansatz reads is of form (A₁, A₂, t[A₁,A₂])

   Here t is arbitrary real parameter. n=0 contributions to the gauge currents vanish if one has

   [A₁,[A₁,A₂]]=0

   [A₂,[A₁,A₂]]=0.

   This implies that the algebra generated by A_i is a matrix representation of Heisenberg algebra and the Lie algebra of gauge group is replaced by non-compact Heisenberg group. Finite-dimensional representations of this algebra are non-unitary but infinite-dimensional representations can be unitary.

2. For n=3 the equations are also identically satisfied by the Heisenberg algebra property.

3. The equations for n=1 and n=2 one obtains conditions on the wave function. Heisenberg algebra characterizes harmonic oscillator and for the vacuum state the condition that annihilation operator creates vacuum can be regarded as the analog of this conditions. On physical grounds one expects something like harmonic oscillator wave functions. Could one apply the analog of standard quantization meaning that the wave functions depend only on single coordinate -say that associated with x₁(0).

   A possibility that comes into mind is that action of the differential operators representing momentum p₁(0) is given by

   p₁(0)Ψ= kx₁(0) Ψ

   so that the conditions on Ψ reduce to those for n=0 and are identically satisfied by Heisenberg algebra property.

   This kind of condition is also analogous to a covariant constancy condition and makes sense for single coordinate. The value of the parameter k characterizes the width harmonic oscillator Gaussian (scale of energy spectrum for harmonic oscillator).

   What is interesting is that one would have something analogous to what happens in TGD. The solution would be 3-dimensional and its time evolution would span a 4-D subspace. Uncertainy Principle for Heisenberg algebra would allow the wave function depend on single coordinate and one would effectively have 2-dimensional plane.

4. Whether it makes sense to generalize the solution ansatz so that the linear 3-D subspaces of E⁹ are replaced with more general 3-D sub-manifolds is not clear.

A more general solution ansatz is obtained by considering the Cartesian powers of 3-D Heisenberg algebra. One obtains also solutions for which Q_i= A_i, i=1,...,4 and P_i=A_i, i=5,...,8 commute the identity matrix in the generalization of Heisenberg algebra generated by the phase space coordinates Q_i and P_i. Again unitary representations are infinite-dimensional. In this case the harmonic oscillator wave function would be effectively 4-dimensional.

Could N=∞ limit for gauge theory interpreted in terms of generalized Heisenberg algebra

Could one think of D=4 gauge theory at the limit when the dimension N of gauge group approaches infinity. Just for Christmas fun let us assume that it is literally infinite and apply the idea that the gauge potentials form a 3-D Heisenberg algebra.

1. Assume A₀=0 as a gauge condition. Assume also Heisenberg algebra

   [A₁,A₂]= m A³

   with other commutators vanishing. This condition makes sense for Hermitian fields strength in an infinite-D representation of Heisenberg algebra using infinite-D unitary gauge group. The new element is the interpretation of gauge potentials as generators of local Lie-algebra representable as Hermitian objects in infinite-D unitary gauge algebra.

2. Consider first the vanishing of J⁰. The expression of the electric field strength reduce by gauge condition to F_0i = -∂_tA_i and is identical to that of Abelian gauge field theory.

3. What about the equations stating the vanishing of Jⁱ? In this case the Heisenberg algebra guarantees the vanishing of the trilinear terms in the currents. The gauge field strengths F₁₃ and F₂₃ reduce also to their Abelian expressions. F₁₂= ∂₂A₁ -∂₁A₂+mA₃. Field equations stating the vanishing of J³ are Maxwellian. In J¹=0 ( J²=0) the term m∂₂A³ (-m∂₁A³) appears as effective source term so that the field serves as a linear sources for itself.

4. Again one might apply the analogy with harmonic oscillator and argue that the wave functions in the space of field configurations can depend only on single component of gauge potential- say A₁. The interpretation would be in terms of polarization direction. The special role of A₃ corresponds to the direction of 3-momentum in gauge theory.

5. Also now Cartesian powers of Heisenberg algebra are possible and one obtains the analogs of many-particle states with varying directions of polarizations. One can assign to the solution also a preferred plane of M² defined by time axes and the preferred component of gauge potential. With a good will one might say that M² is analogous to string world sheet. One can ask whether symplectic transformations in E² could give rise to more general solutions with a local polarizaion direction.

What would be non-trivial is that the field equations would linearize completely by using Heisenberg algebra ansatz and the otherwise difficult-to-treat local non-linearity would reduce to well-understod local Lie algebra commutations.

Conclusions

What can one conclude from this exercise?

1. A rather general solution ansatz is expressible as a product solution corresponding to N:th Cartesian power of U(1). For U(1) factors the solutions can be said to be 9-dimensional since there are no constraints on the 9 coordinates x_i(0). Another solution -even more trivial - solution ansatz reduces to 1-dimensional sub-space of E⁹ and has vanishing gauge field strength for any gauge algebra. Constraint equations are trivially satisfied.

2. A genuinely 3-dimensional solution ansatz is obtained if one allows the gauge potentials to generate 3-D Heisenberg algebra. If the matrix algebra is infinite-dimensional, sub-algebra of U(&infty;), the matrices in question can be made unitary. Solution ansatz seems to work if one performs standard quantization in Heisenberg algebra so that wave functions depend on single coordinate x_i only. This solution ansatz generalizes by replacing the Heisenberg group with its Cartesian power.

3. The idea that 3-D space somehow emerges from Matrix theory is based on the reduction of isotropy group from SO(9) ⊂ SO(1,9) to SO(3). One might perhaps say that for the Heisenberg ansatz 3-dimensionality is obtained in this sense. Heisenberg group acts as gauge group. When the Cartesian power of Heisenberg group, the solution could be seen as describing free particles moving in 3-D space.

4. The Lagrangian variant of the Matrix model is a nice toy model but to my opinion has very little to do with physics.

Objection against TGD SUSY

TGD SUSY in its simplest form assumes that covariantly constant right-handed neutrino generates SUSY. The second purely TGD based element is that squarks would correspond to the same p-adic mass scale as partners.

This looks nice but there are objections.

1. The first objection relates to the tachyonicity needed to get rid of double degeneracy of light mesons consisting of u, d, and s quarks. Mesons and smesons consisting of squark pair mix and for large α_s the mixing is large and can indeed make second eigenvalue of the mass squared matrix negative. If so, these states disappears from spectrum. At least to me this looks however somewhat unaesthetic.

   Luckily, the transformation of second pion-like state to tachyon and disappearance from spectrum is not the only possibility. After a painful search I found experimental work claiming the existence of states analogous to ordinary pion with masses 60, 80, 100, 140,.... MeV. Also nucleons have this kind of satellite states. Could it be that one of these states is spion predicted by TGD SUSY for ordinary hadrons? But what about other states? They are not spartners: what are they?

2. The second objection relates to the missing energy. SUSY signatures involving missing energy have not been observed at LHC. This excludes standard SUSY candidates and could do the same in the case of TGD. In TGD framework the missing energy would be eventually right handed neutrinos resulting from the decays of sfermions to fermion and sneutrino in turn decaying to neutrino and right handed neutrino. The naive argument is that shadronization would be much faster process than the decay of squarks to quarks and spartners of electro-weak gauge bosons and missing energy so that these events would not be observed. Shadrons would in turn decay to hadrons by gluino exchanges. The problem with this argument is that the weak decays of squarks producing right handed neutrinos as missing energy are still there!

   This objection forces to consider the possibility that covariantly constant right handed neutrino which generates SUSY is replaced with a color octet. Color excitations of leptons of leptohadron hypothesis would be sleptons which are color octets so that SUSY for leptons would have been seen already at seventies in the case of electron. The whole picture would be nicely unified. Sleptons and squark states would contain color octet right handed neutrino the same wormhole throats as their em charge resides. In the case of squarks the tensor product 3⊗ 8=3+6bar+15 would give several colored exotics. Triplet squark would be like ordinary quark with respect to color.

   Covariantly constant right-handed neutrino as such would represent pure gauge symmetry, a super-generator annihilating the physical states. Something very similar can occur in the reduction of ordinary SUSY algebra to sub-algebra familiar in string model context. By color confinement missing energy realized as a color octet right handed neutrino could not be produced and one could overcome the basic objections against SUSY by LHC.

What about the claimed anomalous trilepton events at LHC interpreted in terms of SUSY, which however breaks either the conservation of lepton or baryon number. In have proposed TGD based interpretation is in terms of decays of W to sW and sZ which in turn decay and produce the three lepton signature. Suppose that sW and sZ are color octets and that sleptons replace the color octet excitations of leptons responsible for leptohadron physics. One possible decay chain would involve the decays sW⁺→ sL⁺+νbar and sZ→ L⁺+sL^-. Color octet sleptons pair combine to form leptopion which decays to lepton pair. This decay cascade would produce missing energy as neutrino and this seems to be the case for other options too.

This view about TGD SUSY clearly represents a hybrid of the two alternative views about X and Y bosons as composites of either color excitations of quarks or of squarks and is just one possibility. The situation is not completely settled and one must keep mind open.

The reader can find details in the article Do X and Y mesons provide evidence for color excited quarks or squarks? or in the chapter New Particle Physics Predicted by TGD: Part I.

Comparison of Maxwellian and TGD views about classical gauge fields

In TGD Universe gauge fields are replaced with topological field quanta. Examples are topological light rays, magnetic flux tubes and sheets, and electric flux quanta carrying both magnetic and electric fields. Flux quanta form a fractal hierarchy in the sense that there are flux quanta inside flux quanta. It is natural to assume quantization of Kähler magnetic flux. Braiding and reconnection are basic topological operations for flux quanta.

One important example is the description of non-perturbative aspects of strong interactions in terms of reconnection of color magnetic flux quanta carrying magnetic monopole fluxes. These objects are string like structures and one can indeed assign to them string world sheets. The transitions in which the thickness of flux tube increases so that flux conservation implies that part of magnetic energy is liberated unless the length of the flux quantum increases, are central in TGD inspired cosmology and astrophysics. The magnetic energy of flux quantum is interpreted as dark energy and magnetic tension as negative "pressure" causing accelerated expansion.

This picture is beautiful and extremely general but raises challenges. How to describe interference and linear superposition for classical gauge fields in terms of topologically quantized classical fields? How the interference and superposition of Maxwellian magnetic fields is realized in the situation when magnetic fields decompose to flux quanta? How to describe simple systems such as solenoidal current generating constant magnetic field using the language of flux quanta?

Superposition of fields in terms of flux quanta

The basic question concerns the elegant description of superposition of classical fields in terms of topological field quanta. What it means that magnetic fields superpose.

1. In Maxwell's linear theory the answer would be trivial but not now. Linear superposition holds true only inside topological light rays for signals propagating in fixed direction with light velocity and with same local polarization. The easy solution would be to say that one considers small perturbations of background space-time sheet and linearizes the theory. Linearization would apply also to induced gauge fields and metric and one would obtain linear superposition approximately. This does not look elegant. Rather, quantum classical correspondence requires the space-time counterpart for the expansion of quantum fields as sum of modes in terms of topological field quanta. Topological field quanta should not lose their identity in the superposition.

2. In the spirit of topological field quantization it would be nice to have topological representation for the superposition and interference without any linearization. To make progress one must return to the roots and ask how the fields are operationally defined. One has test particle and it experiences a gauge force in the field. From the acceleration of the test particle the value of field is deduced. What one observes is the superposition of gauge forces, not of gauge fields.
   1. Let us just assume that we have two space-time sheets representing field configurations to be effectively superposed. Suppose that they are "on top" of each other with respect to CP₂ degrees of freedom so that their M⁴ volumes overlap. The points of the sheets representing the field values that would sum in Maxwell's theory are typically at distance of CP₂ radius of about 10⁴ Planck lengths. Wormhole contacts representing he interaction between the field configurations are formed. Hence the analog of linear superposition does not hold true exactly. For instance, amplitude modulation becomes possible. This is however not essential for the argment.

   2. Test particle could be taken to be fermion which is simultaneously topologically condensed to both sheets. In other words, fermionic CP₂ type almost vacuum extremal touches both sheets and wormhole throats at which the signature of the induced metric changes is formed. Fermion experiences the sum of gauge forces from the two space-time sheets through its wormhole throats. From this one usually concludes that superposition holds true for the induced gauge fields. This assumption is however not true and is also un-necessary in the recent case. In case of topological light rays the representation of modes in given direction in terms of massless extremals makes possible to realize the analogy for the representation of quantum field as sum of modes. The representation does not depend on approximate linearity as in the case of quantum field theories and therefore removes a lot of fuzziness related to the quantum theory. In TGD framework the bosonic action is indeed extremely non-linear.

3. This view about linear superposition has interesting implications. In effective superposition the superposed field patterns do not lose their identity which means that the information about the sources is not lost - this is true at least mathematically. This is nothing but quantum classical correspondence: it is the decomposition of radiation into quanta which allows to conclude that the radiation arrives from a particular astrophysical object. It is also possible to have superposition of fields to zero field in Maxwellian sense but in the sense of TGD both fields patterns still exist. Linear superposition in TGD sense might allow testing using time dependent magnetic fields. In the critical situation in which the magnetic field created by AC current passes through zero, flux quanta have macroscopic size and the direction of the flux quantum changes to opposite.

Time varying magnetic fields described in terms of flux quanta

An interesting challenge to describe time dependent fields in terms of topological field quanta which are in many respects static structures (for instance, flux is constant). The magnetic fields created by time dependent currents serves as a good example from which one can generalize. In the simplest situation the magnetic field strength experiences time dependent scaling. How to describe this scaling?

Consider first the scaling of the magnetic field strength in flux tube quantization.

1. Intuitively it seems clear that the field decomposes into flux quanta, whose M⁴ projections can partially overlap. To get a connection to Maxwell's theory one can assume that the average field intensity is defined in terms of the flux of the magnetic field over a surface with area S. For simplicity consider constant magnetic field so tht one has B_aveS= Φ= nΦ₀, where Φ₀ is the quantized flux for a flux tube assumed to have minimum value Φ₀. Integer n is proportional to the average magnetic field B_ave. B_ave must be reasonably near to the typical local value of the magnetic field which manifest itself quantum mechanically as cyclotron frequency.

2. What happens in the scaling B→ B/x. If the transversal area of flux quantum is scaled up by x the flux quantum is conserved. To get the total flux correctly, the number of flux quanta must scale down: n → n/x. One indeed has (n/x)× xS= nS. This implies that the total area associated with flux quanta within total area S is preserved in the scaling.

3. The condition that the flux is exact integer multiple of Φ₀ would pose additional conditions leading to the quantization of magnetic flux if the total area can be regarded as fixed. This need not to be true.

Consider as the first example slowly varying magnetic field created by an alternating running in current in cylindrical solenoid. There are flux tubes inside the cylindrical solenoid and return flux tubes outside it flowing in opposite direction. Flux tubes get thicker as magnetic field weakens and shift from the interior of solenoid outside. For some value x of the time dependent scaling B→ B/x the elementary flux quantum Φ₀ reaches the radius of the solenoid. Quantum effects must become important and make possible the change of the sign of the elementary flux quantum. Perhaps quantum jump turning the flux quantum around takes place. After this the size of the flux quantum begins to decrease as the magnitude of the magnetic field increases. At the maximum value the size of the flux quantum is minimum.

This example generalizes to the magnetic field created by a linear alternating current. In this case flux quanta are cylinderical flux sheets for which magnetic field strength and thickness oscillators with time. Also in this case the maximum transversal area to the system defines a critical situation in which there is just single flux sheet in the system carrying elementary flux. This flux quantum changes its sign as the sign of the current changes.

For background see the chapter General View About Physics in Many-Sheeted Space-Time : Part I.