### Support for the notion of magnetic flux tube

The notion of magnetic flux tube as space-time sheet is one of the key concepts of TGD and represents a special case of topological field quantization forced by the notion of induced gauge field. This notion is especially relevant for the applications of TGD to quantum biology but is central also for TGD inspired cosmology. Therefore it is encouraging that the empirical support for the notion is accumulating.

The latest news tells about strange cosmic ray hot spots observed in southern sky by Icecube neutrino detector at South Pole. Cosmic muons with median energy of 20 TeV seem to come from certain preferred hotspots, and one can assign to a particular hotspot to the direction of the Vela supernova remnant with a distance of about 1000 light years. The problem is that Vela is so distant that the muons should be deflected in galactic magnetic fields so that all information about the direction should be lost. The hot spot property would require a distance smaller than .03 light years and it is very difficult to imagine anything like this since even the nearest star is at distance of 4 light years.

One of the proposed explanations (by Felix Aharonian) is that the cosmic ray flux indeed arrives along magnetic flux tube channelling the cosmic ray flux. This notion has however now justification in standard physics context. Many-sheeted space-time of TGD is needed.

Second explanation proposed for the muonic hot spots is that there is particle accelerator in the solar scale. Also this explanation has a TGD variant. There is experimental evidence for anomalously high accelerations from lightnings. The energies gained by electrons are above MeV. This is completely out of question in standard physics since the friction of the atmosphere implies that electrons dissipate their energy. Again mainstream manages in an admirable manner to forget facts which could mean revolution in theoretical physics. TGD explanation is in terms of large values of Planck constant reducing friction dramatically. Also now magnetic flux tubes would be the places where dark electrons accelerate in the electric field between the cloud and Earth. If this acceleration mechanism is at work for muons it might explain the hot spots. Energies would be enormous- by a factor of 10^{6} higher than the energies gained by electrons from thunderclouds.

Topological field quantization involves also the notion is topological light ray representing the analog of laser beam at the level of space-time topology, and I have proposed for more than decade ago an explanation of extremely high energy gamma rays arriving from quite too large distances in terms of topological light rays. In this case the scattering from microwave background should have caused the loss of the information about direction and confinement inside topological light ray prevents this.

The difficult political problem is that TGD is officially decided to be a crackpot theory so that no one in his right mind dares to mention the existence of TGD in public space. The consequences of this long term policy are becoming manifest in experimental particle physics with the rate of one hype per week. In the lack of a theory able to really predict something, the experimentalists use their time and resources to either kill the ad hoc models cooked up by phenomenologists or by imagining that they have verified one of the very few almost-predictions that hegemony is able to make. ATLAS rumor was a good example of this. Situation is absurd but nothing can be done since the old men at the top of the power ladder will not give up.

## 11 Comments:

Hi!

I like to read your blog, even though I did not yet have time to look deeply into TGD. Anyway its great you have patience to focus on this particular framework.

Myself, I'm interested in decoherence and quantum mechanics of the brain from mathematics viewpoint. Rigorously I only know quantum mechanics, and it seems there's inherent randomness in that theory, which is hard to explain with anything. For a scientific theory that's not satisfying, because randomness should have some sort of cause.

There are some authors such as W. Pauli and K. V. Laurikainen who in their later work write about this matter.

How does TGD view the randomness in quantum mechanics (and relatedly, Heisenberg uncertainty)? In addition, I have to admit I'm not sure what's the view of string theory?

My another question is, what kind of mathematical open questions there would be in TGD? It's always interesting for mathematicians find open problems from physics.

Dear Anonymous,

you asked about mathematical open questions inspired by TGD. All new theories are forced to

develop using shaky mathematical background based on mathematical conjectures inspired by physical intuition and internal coherence and it takes decades before mathematical rigor is possible.

I shall concentrate in this response to the classical sector of the theory.

One important class of new mathematics is related to the understanding of preferred extremals of Kähler action defining the basic variational principle of classical TGD (recall that classical physics is exact part of quantum theory in TGD framework which has interpretation in terms of holography).

Kahler action for the preferred extremal associsted with given 3-surface defines Kahler function for the Kahler geometry of the space of 3-surfaces: "the world of classical worlds". The variational principle is extremely non-linear- essentially Maxwell action but for Kahler form of CP_2 projected to space-time surface so that numerical approach does not help much.

The preferred extremals have the property that Kahler action reduces to a boundary term which is Chern-Simons term: this has enormous implications concerning calculability and also because TGD reduces to almost topological QFT. The natural conjecture is that an integrable system is in question.

Rather detailed conjectures about properties of preferred extremals exist but rigorous mathematical proofs would require huge amount of work and mathematical insights and background. There are many conjectures. One especially interesting conjecture motivated by physics as a generalized number theory vision states that the extremals of Kahler action decompose to regions which are either quaternionic (and thus associative) or co-quaternionic) in certain well-defined sense. The dynamics would be thus purely number theoretical and dictated by associativity/co-associativity. This would generalize the corresponding postulate of conformal field theories to classical realm.

It might of course be that a lot of physical understanding is still required before precisely enough formulated mathematical problems emerge.

I will tell about the challenges of quantum TGD in separate response.

There seem to be two solar polar hotspots producing these cosmic rays.

My proposal is that two Stellar POLAR Anchor Black Holes (SABHs) are the origin . see:

Quantum FFF theory

http://bigbang-entanglement.blogspot.com/2007/02/higgs-vacuum-energy-lensing-effect-and.html

perhaps see also:

Stellar Anchor Black Holes the remnants of former Herbig Haro Hotspopts on Vixra:

http://vixra.org/abs/1104.0002

Dear Anonymous,

you asked about mathematical open questions inspired by TGD. All new theories are forced to

develop using shaky mathematical background based on mathematical conjectures inspired by physical intuition and internal coherence and it takes decades before mathematical rigor is possible.

I shall concentrate in this response to the classical sector of the theory.

One important class of new mathematics is related to the understanding of preferred extremals of K�hler action defining the basic variational principle of classical TGD (recall that classical physics is exact part of quantum theory in TGD framework which has interpretation in terms of holography).

Kahler action for the preferred extremal associsted with given 3-surface defines Kahler function for the Kahler geometry of the space of 3-surfaces: "the world of classical worlds". The variational principle is extremely non-linear- essentially Maxwell action but for Kahler form of CP_2 projected to space-time surface so that numerical approach does not help much.

The preferred extremals have the property that Kahler action reduces to a boundary term which is Chern-Simons term: this has enormous implications concerning calculability and also because TGD reduces to almost topological QFT. The natural conjecture is that an integrable system is in question.

Rather detailed conjectures about properties of preferred extremals exist but rigorous mathematical proofs would require huge amount of work and mathematical insights and background. There are many conjectures. One especially interesting conjecture motivated by physics as a generalized number theory vision states that the extremals of Kahler action decompose to regions which are either quaternionic (and thus associative) or co-quaternionic) in certain well-defined sense. The dynamics would be thus purely number theoretical and dictated by associativity/co-associativity. This would generalize the corresponding postulate of conformal field theories to classical realm.

It might of course be that a lot of physical understanding is still required before precisely enough formulated mathematical problems emerge.

I will tell about the challenges of quantum TGD in separate response.

Dear Anonymous,

I continue about mathematical challenges related to TGD. Quantum TGD involves many mathematical challenges. I list what comes first in mind without any attempt to be systematic.

a) Physics as infinite-dimensional spinor geometry of world of classical worlds tentatively identified as a union of infinite-D symmetric Kahler spaces with infinite-D isometry group so that all points of these spaces are metrically equivalent: this is the basic vision which should be developed in detail and would require a work of mathematicians.

The spinors of this space correspond to second quantized fermions at space-time surface defining what is known as hyper-finite factor of type II1 closely related to quantum groups. This notion should be also developed.

b) Conformal invariance of string models generalizes in TGD context and implies mathematical challenges. For instance, delta M^4_+xCP_2, product of light-cone boundary and CP_2 allows

generalization of Kac-Moody algebra with finite Lie algebra replaced with infinite-D symplectic algebra of delta M^4_+xCP_2. One should do for this algebra all what has been done for ordinary Kac-Moody algebras. Basic pieces of WCW can be seen as coset spaces of this symplectic group so that they should be rather well-defined mathematically.

c) The Yangian algebra of YM theories discovered in twistor approach to SYMs generalizes: the finite-D Lie algebra of gauge group is replaced with infinite-D conformal algebra since points are replaced with partonic 2-surfaces at boundaries of causal diamond. This is an enormous generalization and everything should be worked out.

d) The fusion of real physics and various p-adic physics involves several challenges. The failure of definite integral for p-adic number fields is the main technical problem and the possibility to algebraize integrals in terms of harmonic analysis in symmetric spaces suggests an elegant solution of the problem. Quite generally: everything related to p-adics is algebraic whereas real physics is about magnitudes.

e) There also challenges related to the number theoretical vision. One should improve the understanding about the relationship of TGD to classical number fields. The hierarchy of infinite primes leading to a new -number theoretic- notion of infinity not equivalent with that provided by the surreal numbers having very concrete physical interpretation in terms of hierarchy of second quantization would provide a lot of work for a mathematician.

Infinite integers and primes would have direct physical interpretation and one also ends up to a generalization of the notion of point of real axis and imbedding space since the rations of infinite integers reducing to real unit define an infinite-dimensional space and the conjecture is that this space allows to represent WCW and quantum states defined as spinor fields of WCW. One would have algebraic holography: the whole structure would reduce to 8-D imbedding space (note connection with octonions) with real points given this hidden number theoretical anatomy.

To Leon Vyuk:

Second explanation proposed for the muonic hot spots is that there is particle accelerator in solar scale. Also this explanation has a TGD variant.

There is experimental evidence for anomalously high accelerations from lightnings. The energies gained by electrons are above MeV. This is completely out of question in standard physics by the friction of the atmosphere. Again mainstream manages in an admirable manner to forget facts which could mean revolution in theoretical physics.

TGD explanation is in terms of large values of Planck constant reducing friction dramatically. Again magnetic flux tubes would be the places where dark electrons accelerate in the electric potential between the cloud and Earth.

If this acceleration mechanism is at work for muons it might explain the hot spots. Energies would be enormous as compared to the energies gained by electrons from thunderclouds. By a factor of 10^6 higher.

Dear Matti,

Could you also imagine that micro black holes does the job to create x-ray effects inside Thunderclouds and Sprites, just as Dr. Dwyer has found out?

perhaps see :

Fireballs and micro Comets inside Sprites and Ball lightning.

http://bigbang-entanglement.blogspot.com/2011/04/splitting-micro-black-holes-x-ray.html

One can of consider also this kind of explanation. Hierarchy of Planck constants is certainly more science fictive than micro blackhole from the main stream point of view;-).

In the case of thunder storms the bursts of charged particles should be short lasting and the electric field of Earth should play a key role. The presence of strong electric fields during thunder storms should correlate with the bursts of charged particles from micro blackholes. Can you explain this?

I can explain this not by math, but by observation of the first slow motion video of a stepped leader in progress, at my blog:

http://bigbang-entanglement.blogspot.com/

You will observe the splitting of many fireballs in the form of a forked tree.

Prof Dwyer described that just at the splitting moment of this stepped leader in progress, he measured x-ray bursts.

So if we assume that these splitting fireballs are a new kind of micro black holes, as I described also at my blog, then we may come to an explanation.

Leo,

a very creative blog and ideas. The fireballs have been a mystery for ages, and early view and thinking about lightning inspired some of my own thoughts. I liked the chart on the new sort of micro black hole scenario. Certainly such things have internal structure (not sure they are technically black holes) Such things for now seem only to exist in the shadow of something that does.

But all these issues are in the same new physics ball park. Those fireballs are very powerful, one blew out 25 water heaters in my apt. complex after a storm and bolt from the blue as I was watching to see how far away my apt was and thinking lightning could happen because I had talked about it to my wife "what do you think, God is going to send a lightning bolt or something?"

Now here is a consideration, philosophy I guess, some reports say inside one there is sometimes seen a figure of a human form.

Of course I do not think there is some sort of creature inside- but I do think the bilateral symmetry is a universal and higher structure when we resolve the higher dimensions, as is the universe. In this sense the decay modes of things can make sense whatever we call these topological entities.

The PeSla

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