I have been been waiting with fear in my heart the moment when some-one boldly and independently represents the idea about dark matter as phases with large Planck constant at magnetic flux tubes as a basic structure of Universe - or something picking up suitable pieces of this vision. Tom Banks, the teacher of Lubos has independently represented two key ideas of TGD as his own (hypefinite factors and causal diamonds): it is amazing how miserable web skills a prominent theoretician can have;-). Susskind as veteran has understandably rather poor web skills and has proposed p-adic physics as his own discovery to the problems of multiverse.

In TGD framework dark energy corresponds to Kähler magnetic energy and primordial cosmology corresponds to magnetic flux tubes, which are exactly string like objects having 1-D M

^{4}projection. Later the flux tube projection of thickens and magnetic fields get weaker although the fluxes are conserved. The model leads to a fractal model of Universe explaining the formation of galaxies and even the formation stars and planetary systems and of course - the generation of cosmic magnetic fields, which is a mystery in the standard approach. It also replaces inflationary scenario with a new one in which no exponential inflation takes place: negative pressure corresponds to magnetic tension and thus has completely natural physical interpretation. Inflaton field is replaced with magnetic field and the transformation of magnetic energy identified as dark energy to particles generates ordinary matter and dark matter. The path of inflationary theories has been full of tortures but now inflation is in especially grave difficulties because the experimental evidence for the absence of a spherical distribution of galactic dark matter is accumulating. This I told in previous posting.

In recent New Scientist the notion of dark magnetism appeared and the obvious question was whether the notion was finally "independently discovered". Unfortunately, I do not have access to New Scientist article . Maybe some-one has and could kindly send it to me. I found however an article of Jimenez and Maroto about the topic from web and a paper by Martinez et al summarizing the development of the concept. Bacry has proposed the notion around 1993. At that time I had understood the role of cosmic strings but had not discovered the hierarchy of Planck constant and the vision about dark matter. In Bacry's model the apparent number of particles in the magnetic field would be larger than the actual one so that in this sense one can speak about apparently existing dark matter. This is hopelessly tricky and has nothing do with the TGD based notion of dark magnetism.

Mark Williams kindly told how to get the dark magnetism article from New Scientist web page. I read the article discussing the work of Beltran and Maroto.

- The authors propose a modification of Maxwellian electrodynamics by giving up gauge invariance realized in terms of Lorentz gauge condition, and interpreting the scalar component of the gauge potential as a dynamical degree of freedom and giving rise to an effective cosmological constant in energy momentum tensor. Inflation is assumed be responsible for the generation of the scalar modes. Giving up gauge invariance at the level of Maxwell equation - even in long length scales- looks very ad hoc and very bad to me.

- The modified scalar modes are claimed to generate also magnetic fields and it is a well-known fact that cosmos is full of magnetic fields with un-known origin. This looks good.

- I could have made a bet that the accelerating expansion would have been explained in terms magnetic tension giving rise to "negative pressure" and vacuum energy identified as magnetic energy but if I understood correctly this was not done. Of course, this is only one description among many provided by TGD. In shorter length scales one has critical cosmologies predicting negative pressure automatically from imbeddability. The counterparts of black-holes in GRT limit correspond to regions of space-time with Euclidian signature and correspond to non-vanishing cosmological constant which can give via averaging rise to the observed small value of cosmological constant.

- In TGD gauge invariance is trivially true and also gauge fixing is trivial for classical gauge fields. One can assign to K\"ahler gauge potential U(1) gauge transformations but this degree of freedom is trivially eliminated because of the geometrization of the gauge fields.

- The symplectic transformations of CP
_{2}induce to Kähler gauge potential effective U(1) gauge transformations. These transformations are not gauge symmetries nor even symmetries of the Kähler action (they are however isometries of "world of classical worlds") since also the induced metric describing classical gravitation changes and extremal property is not preserved.

- There is is a huge number of vacuum extrema: any space-time surface with CP
_{2}a Lagrangian manifold - is vacuum extremal and symplectic transformations give new vacuum extremals. Small deformations of these represent non-vacuum states classically. Symplectic transformation means a concrete deformation of the space-time surface so that a gauge symmetry is not in question. The transformation is approximate symmetry of action associated with 4-D spin glass degeneracy broken only by classical gravity.

- The simplest scenario in zero energy ontology is that all particles, including photon, have at least a small mass and the size scale of causal diamond containing the photon defines the mass scale of photon. In TGD framework this need not mean loss of gauge invariance since basic quanta, which are fermions at the throats of wormhole contacts, are exactly massless. Mass is associated with many-fermion states purely kinematically because the massless building bricks do not have parallel four-momenta.

- Authors talk about scalar potential (voltage) and currents in cosmological scales. This is actually natural in the fractal Universe of TGD too. Magnetic flux tubes can carry longitudinal electric fields and one has kind of electric circuitry in all scales. The applications of this picture to biology are of special interest and I have discussed them

in recent postings.

- The physicality of third polarization means usually massivation. The simplest TGD based scenario predicts that also photons have very small mass.

- At classical level both electroweak and color gauge fields are geometrized in terms of CP
_{2}spinor connection and Killing vector fields. The basic objection is that the implied huge reduction in degrees of freedom is unphysical. This objection is circumvented in many-sheeted space-time: superposition for classical fields is replaced with the superposition for their effects. Particles can condense on several space-time sheets simultaneously and the fields of separate space-time sheets effectively sum up.

- Field quanta, or rather Feynman diagrams, are replaced with generalized Feynman diagrams consisting of regions of space-time with Euclidian signature of the induced metric. In ZEO also virtual lines consist of on mass shell massless wormhole throats giving extremely powerful kinematical constraints on loops and guarateeing finiteness.

To sum up, there is still long way to the discovery of the geometrization of classical fields in terms of sub-manifold gravity and from this to the discovery that quantum theory can be reduced to the (spinor) geometry of world of classical worlds! The basic question is how to communicate this idea to colleagues who read only respected journals? I try to stay patient!;-).

## 18 comments:

Matti,

even if someone claims your vision belately or even independently I must add they have no philosophic skills either because (in my last post) I have the counter to that part of a more general theory as part of a bigger picture.

Does this imply Lubos would now call his teacher a crackpot for the "discovery" of some of your ideas? :-)

Magnetism dark or otherwise in the spirit of it I am sure has firm foundation where it applies (and in the standard eyes is the only game left, or something like it, to explain transfer of momenta from black holes. I am sure our problem where we do not understand each other is one of language and not the content of ideas.

Now, with such computer skills it is all to easy to put some idea out for general discussion- such as I suspect Gardner of alerting Conway to my idea on the matrix and he brought it up on the bulletin boards so published not as mature article in scientific american in my opinion. But I have only begun to catch up with him in the use of the computers over methods by hand in writing and solving puzzles (not that I dont consider him our greatest current mathematician of our day)

I will try to find that article for you in new scientist.

ThePeSla

Oh, my problem seems to be having to wait for decades for something to come along as it will eventually and that could make a difference or might have with people I know for biological reasons. Still, life is short, too short to worry about credit for wealth or fame.

Note to Ulla: I just realized the significance of the fact (I read some months ago) there two forms of diamond (carbon).

The Pe Sla

And look here. Is this a creation of a wormhole?

Imagine cushions that lift up instead of sinking when you sit on them. Impossible? Not according to a blueprint for new materials with 'negative compressibility': the materials compress when they are pulled and expand when they are pushed. Metamaterials that do this have been built before. For example, vibrating aluminium bars with tiny cavities inside them create waves that oppose the push or pull applied. But the designs must be vibrated at just the right frequency to see the effect. Zachary Nicolaou and Adilson Motter of Northwestern University in Evanston, Illinois, have now designed a metamaterial that stretches when compressed, and vice versa, under any circumstances. 'What is interesting is that they study systems that are not responding to a vibration but to a steady applied force,' says John Pendry [Physics] of Imperial College London.

http://www.newscientist.com/article/dn21839-impossible-material-would-stretch-when-compressed.html?DCMP=OTC-rss&nsref=online-news

http://www3.imperial.ac.uk/people/m.mccall/publications look at this man. What are these? A wormhole??? (a compressed-extended state?)

McCall MW, What is negative refraction?, JOURNAL OF MODERN OPTICS, 2009, Vol:56, Pages:1727-1740, ISSN:0950-0340(publication doi) http://dx.doi.org/10.1080/09500340903324818

Kinsler P, Favaro A, McCall MW, Four Poynting theorems, EUROPEAN JOURNAL OF PHYSICS, 2009, Vol:30, Pages:983-993, ISSN:0143-0807(publication doi) http://dx.doi.org/10.1088/0143-0807/30/5/007

see also http://dx.doi.org/10.1088/2040-8978/13/2/024003

in 2007 devised wormholes in which waves disappear in one place and pop up somewhere else. http://www.washington.edu/news/archive/id/50286

science Daily 2009

The team helped develop the original mathematics to formulate cloaks, which must be realized using a class of engineered materials, dubbed metamaterials, that bend waves so that it appears as if there was no object in their path.

http://www.washington.edu/news/archive/id/29883

And Finns, really kaimas Matti, are there too :D

Invisibility cloaking and electromagnetic wormholes, http://www.rni.helsinki.fi/~mjl/invisibility_publications.html

This question is linked to the magnetic monopoles.

I become speechless :D

PeSla,

links, links,...

An artificial wormhole would work only for electromagnetic waves with a specified frequency. The wormhole device is just an optical device similar to a lens; It would not be similar to space-time wormholes studied in general relativity, they point out.

But maybe the math can be used?

Wow Ulla,

you certainly have intense interest and amazement- commendable!

I am not sure what links you desire as I did not see if something was on line... scientific american 1979 or so for Conway and discover magazine had a good article on the negative index of refraction four or five years back. I just Googled my brain or memory is all (but I will think about linking more - the early days of the computer had no such links or only those a few could access such as grade school teachers and by the time I put some original work of authors like Cloak (pre meme theory) or Glossa the technology did these rapidly.

Maybe you can see something that we cannot, that is the hope.

I may put up the hexagonal forms but it is clear the symmetry groups in the nucleus are greater than those of electron crystallography.

While I have encountered those who would hold Planck's constant variable or there are things smaller than that to which the standard theoreticians treat harshly or can be the violation of physical law that make a plot of sci fi possible- and they have their point (after all N14 is fusible, 7 and all that- but how? Do we not have a hierarchy of at least the model of abstract Planck considerations as in Matti's original insight?

I have had second thoughts this morning about the motivation of fame, passionate or indifferent as for science. If I listened to Plato somewhere as part of his explanation for why humans do what they do. Fame is a sort of immortality that lives after us. I find it hard to believe that not long ago until the discovery involving nitrogen there was not enough food to feed the population, who did that? the man that also put gas in the trenches. Is there any point in recalling his name?

Oh, way back before I met you guys on line... there is a flat form of such a lens- that is the math I use of quasics. Before microwaves my Dad used to cook hotdogs with the radar in the 50's. But engineers prod on and do not really understand us- and few have the intuitions for breakthroughs.

Again, Ulla, of what do you drink Of the water or the wave?

Sorry, no links supplied here as I am still organizing and adjusting to the computer world since 95.

ThePeSla

http://www.st-andrews.ac.uk/~ulf/invisibility.html

Remarcable!

See also his artificial black holes!

http://www.st-andrews.ac.uk/~ulf/

PeSla, links to the two types of carbon diamonds. After all this Journey started after a DREAM of giant diamonds :-)

Dear Matti,

Don’t worry! As ThePeSla said TGD have firm philosophical bases. Also TGD is not only some ideas that glue together. Unifying these ideas in a very rich structure without very deep understanding is not possible. It is not possible in this framework of common physics any big work. It is needed at least 34 years hardworking of a different physicist:) . I am very optimistic for TGD. Hardships will be over as soon as you may think.

Thanks for the answer about warped imbedding. I struggled with it and now it is simple:). Although the M4+ projection of the surface is random light like curve but in contrary to common physics, we don’t live in M4 but we live in higher space-time sheet. Then it should be very difference in interpretation of this in comparison to that?

kahler form in CP2 is J=-i*g_mnbar*dxi^m*dxibar^n (Excuse me if it is not correct, I am freshman in Latex notation ;) )

What is physical interpretation of the kahler form? and Why does the kahler form in CP2 satisfies free Maxwell equations?

Dear Hamed,

we live in - or perhaps I should say- we are part of 4-dimensional space-time surface (to be precise one should of their quantum superposition;-)). This space-time surface has not only Minkowskian regions - familiar to us - that I call space-time sheets but also Euclidian regions -deformations of CP_2 type vacuum extremals. The latter is the news:-! These Euclidian regions define generalized Feynman diagrams: lines are deformations of CP_2 type vacuum extremals defining light-like random curves in M^4 as their projections. The notion of Feynman diagram is therefore geometrized and topologized.

For CP_2 type vacuum extremals and their deformations the roles of M^4 and CP_2 degrees of freedom are changed. For space-time sheets (4-D M^4 projection) it is natural to speak about CP_2 sigma model like theory in M^4. For CP_2 type vacuum extremals one has field theory in CP_2 and dynamical variables are M^4 coordinates. There are also string like objects X^2xY^2 subset M^4xCP_2 and their deformations: this corresponds to string model like sector of TGD. I call these objects cosmic strings and they are crucial in TGD cosmology. Their M^4 projection thickness during cosmic evolution and their energy is responsible for the dark energy and the magnetic pressure for accelerated expansion of cosmos.

Consider first Kahler form in CP_2. The situation changes for the induced Kahler form somewhat. CP_2 Kahler form J_kl is derivable from Kahler gauge potentials A_k via the usual formula: therefore one has the analog of U(1) gauge invariance. This means that the analogs of Nabla.B=0 and Faraday law are satisfied. The Kahler current D_lJ^kl vanishes also identically because Kahler form is covariantly constant. Therefore vacuum Maxwell equations are satisfied. J_kl is self dual meaning that one has a situation analogous to that of having constant electric and magnetic fields with same magnitude. Maxwell energy momentum tensor vanishes identically: also for CP_2 vacuum extremals which are inherently just CP_2s.

For induced Kahler form the representation in terms of Kahler gauge potential still holds true so that in this sense one has U(1) gauge invariance. This implies nabla.B=0 and Faraday's law. The remaining equations j^alpha=0 (vacuum Maxwell equations) need not be satisfied.

Dear Hamed,

you asked about interpretation of CP_2 Kahler form and I already told something. Her comes something more.

For so called massless extremals Kahler current j^alpha is indeed light-like rather than vanishing so that a deviation from Maxwell's theory emerges. If one takes effective 3-dimensionality seriously as a property of action then for preferred extremals j^alpha must be either light-like or proportional to instanton current so that action reduces to "boundary" terms since j^alpha A_alpha=0 holds true and to Chern-Simons terms if weak form of em duality holds true.

You asked about the physical interpretation of Kahler gauge potential. It corresponds to U(1) piece of electroweak gauge group. Classical photon field is sum of Kahler gauge potential with certain coefficient and of a neutral component of spinor connection (SU(2)_weak). The different couplings of Kahler gauge potential to quarks and leptons (n=1 and n=3) explain different charges of quarks and leptons.

Kahler gauge potential and Kahler action has also different thermodynamic interpretation that would realize quantum classical correspondence by representation of thermodynamics as space-time geometry (TGD is square root of thermodynamics in ZEO!). This would also generalize black hole thermodynamics. I realize this from topological thermodynamics of Kiehn. See previous posting http://matpitka.blogspot.fi/2012/05/does-thermodynamics-have-representation.html .The posting contains also link to Kiehn's homepage: Kiehn's articles might provide a good way to learn about differential forms.

Symplectic transformations of CP_2 are not symmetries of Kahler action except for vacuum extremals since classical gravitational field defined by induced metric is not invariant under them (the interpretation of vacuum degeneracy is in terms of spin glass degeneracy). Symplectic group acts as isometries of WCW however. This symmetry is very profound and I wish I would understand it better.

Here you have it again:

the implied huge reduction in degrees of freedom is unphysical. This objection is circumvented in many-sheeted space-time: superposition for classical fields is replaced with the superposition for their effects. Particles can condense on several space-time sheets simultaneously and the fields of separate space-time sheets effectively sum up.

Can you explain a bit, please. Are there many fields too, many waves or sheets? As time can have many sheets with different waves? But they are connected with ? 'strings' or flux-tubes of many different lengths (p-adics?)? Where is the center? The 'I'?

Position is only an an effect of momentum? Waves need no particle? As also particles can break loss and surf the waves? Is the wave-particle duality somehow wrong? And Uncertainty/randomness?

I have struggled with this quite a time now.

You said your model was impossible to copy, but it can be broken in pieces and distorted, which would be worse.

The braneworld theory.

http://arxiv.org/abs/1112.3035

open string theory on backreacting D3-branes using a spacetime approach. .. in detail the half-BPS

supergravity solutions describing open strings ending on D3-branes, in the near horizon of the D3-branes. .. quantitatively several non-trivial features of open string physics including the appearance of D3-brane spikes, the polarization of fundamental strings into D5-branes, and the Hanany-Witten effect.... detail the computation of the gravitational potential between two open strings, and contrast it with the holographic computation of Wilson lines. .. the D-brane backreaction has a large influence on the low-energy gravity, which may lead to experimental tests for string theory brane-world scenarios.Ulla,

Not sure where I got this blog to follow but here is the link:

http://erkdemon.blogspot.com/2012/02/hexagonal-diamond-other-form-of-diamond.html

Thanks,

I have tried to summarize about invisibility and bent spacetime. The Riemannian surfaces/sheets in Leonhardts text I cannot manage, but interesting.

http://zone-reflex.blogspot.fi/2012/06/invisible-hats-and-bent-spacetime.html

To Ulla:

One TGD inspired variant of invisibility cloak would be based on phase transition transforming photons to dark photons at the surface of the invisible objects so that they would not be reflected nor absorbed. In this case one would however have a shadow. This would imply strange mirage like effects. An object in certain place would be seen it completely different position: image would travel along flux tubes.

If photons flow like hydrodynamical flow along the surface, even the shadow is absent. In TGD framework Maxwell's equations are replaced with conservation laws- essentially hydrodynamical equations- I have proposed that one obtains what could be called perfect hydrodynamical flow. This might give rise to perfect invisibility cloak.

U. Leonhardt and T. Tyc, Broadband Invisibility by Non-Euclidean Cloaking, Science Express, November 20 (2008).

A free copy here, http://www.sciencemag.org/cgi/rapidpdf/1166332?ijkey=AmRp24B6rB6O.&keytype=ref&siteid=sci

or see the last part of his intro text http://www.st-andrews.ac.uk/~ulf/invisibility.html

And my earlier question? Please!

Dark solitons!

Experimental Observation of Oscillating and Interacting Matter Wave Dark Solitons (Phys. Rev. Lett. 101, 130401 (2008))

http://www.kip.uni-heidelberg.de/matterwaveoptics/research/bosons/

We create dark solitons by means of matter wave interference. Our method starts with a BEC confined in a double well potential. By switching off the barrier between the two wells we merge the two condensates in the remaining harmonic trap, which creates dark solitons as fringes in a nonlinear interference pattern.

In former experiments, which were performed in a genuine 3D regime, the solitons decayed, due to the so called snaking instability, too fast for the observation of their oscillation and collisions in the trap. In our case the dark solitons are more stable due to their creation in a crossover regime between 1D and 3D.

Our observations are in full agreement with numerical simulations of the Gross Pitaevski Equation. Using an analytic approximation for the inter-soliton interaction [Opt. Commun. 114, 353; PRA 47(4), 3213] we can explain the essentials of the oscillation dynamics by an ordinary differential equation. In this model the solitons are regarded as particles in an effective potential arising from their mutual interaction and the trapping confinement.

A trap, versus cloak? Light has de facto also been slowed down and been totally trapped.

The difference between dark (no shadow, only gravital), virtual shadow and 'ghoast' like seems luddy.

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