Now Jester tells that there are rumours that BICEP2 group might have underestimated the effect of galactic foreground. There is also a little article in Science Now.

BICEP signal is taken only at single frequency: 150 GHz. Planck has published a polarization at 353 GHz demonstrating that there may be a significant foreground emission from the galactic dust in the parts of sky studied by BICEP. The Planck collaboration has masked the results in BICEP patch: this does not certainly help BICEP team in their work. It is a pity that competition between research groups leads to this kind of secrecy.

Whether or not the BICEP finding is correct does not affect much neither inflationary models or TGD model. In inflationary approach there are so many variants to consider that one can always find candidate models. The reduction of B-mode contribution would be actually well-come since it would allow to get rid of the internal consistency problem. In TGD framework there is also rapid accelerating expansion analogous to that of inflationary expansion but the no inflatons are needed. Quantum criticality implies vanishing 3-curvature and this fixes the cosmology apart from the duration of the critical phase. The model is not quantum field theoretic anymore: gas of cosmic strings inside Minkowski space light-cone prevails before the inflationary period which is critical period for the phase transition to a radiation dominated cosmology. The problem is that one (more precisely, I) cannot really calculate precise prediction for the size of the effect.

The B-mode contribution should be disentangled from two foreground contributions from synchrotron radiation and galactic dust. The problems with BICEP are possibly related to the latter one. I cannot of course say anything interesting about the experimental side of the problem.

One can however ask TGD might predict new kind of synchrotron contribution. In TGD Universe magnetic flux tubes in various scales are basic objects and essential also in the model for temperature fluctuations and polarization of CMB resulting from slightly different temperatures for the two polarization of CMB. The magnetic flux tubes carry monopole fluxes making their existence possible without currents generating then. Their magnetic energy can be identified as dark energy. They carry also dark variants of ordinary particles identified as phases with Planck constant coming as integer multiple of the ordinary one. Could the charged particles - in particular electrons - rotating at cyclotron orbits at these flux tubes produce cyclotron radiation at CMB frequencies and thus giving rise to its apparent polarization?

Concerning cyclotron radiation one can consider relativistic/non-relativistic and classical/quantal situations.

- In Wikipedia there is article about classical model for cyclotron radiation. One expects that the qualitative aspects remain the same in quantal treatment. For planar motion around magnetic field the radiation has dipole pattern around the axis of motion in non-relativistic situation. In relativistic situation it is strongly peaked around the direction of motion at frequency of order γ
^{3}/ρ where ρ is the radius of the orbit which gradually decreases. Most of the radiation is in the plane orthogonal to the orbit and the polarization in the plane of the orbit is parallel to the plane and orthogonal to the line of sight.

- Quantum model might be relevant if the charged particles are in large h
_{eff}phase at magnetic flux tubes and emit dark photons with scaled up energies. Dark photons would later transform to bunches of ordinary photons and if their energies are in the region corresponding to CMB they might produces additional contribution.

In quantum case the charged particles behaves like a 2-D harmonic oscillator in degrees of freedom orthogonal to the magnetic field and energy is quantized as multiples of the cyclotron energy E= n× h

_{eff}ω, ω = ZeB/m. Note the upwards scaling of energy by h_{eff}. The frequencies of the emitted radiation come a multiples of the cyclotron frequency and can be rather high. The Bohr radii of the orbits are quantized and the spiral orbit with decreasing radius is replaced with a sequence of circular orbits with instantaneous jumps to orbit with smaller radius. One expects that the general polarization characteristics are same as in the classical case and that classical description is a good approximation also now.

Could this kind of radiation give an apparent contribution to CMB? The following very naive scaling estimate is an attempt to answer the question.

- The local direction of the vector field defined by the local polarization of CMB photons should be equal to the local direction of magnetic flux tubes in question so that the polarization map would give a map of flux tubes carrying dark matter. This would be of course extremely nice.

- The condition that the radiation is in CMB range implies that the frequency is of order 100 GHz. Electron or electron Cooper is the best candidate for the dark charged particle in question. The cyclotron frequency of electron is $f= 6×10
^{5}Hz in the magnetic field of .2 Gauss (familiar to me from TGD inspired quantum biology!). From this one deduces that a magnetic fields in question should be in Tesla range if they are to affect the CMB background.

- If one requires quantization of the flux then minimal flux quantum for ordinary value of Planck constant would have a minimal thickness of order R=10 nm. By naive scaling the flux quantum is proportional to h
_{eff}so that by a naive scaling the minimal radius of flux tube would scale like h_{eff}^{1/2}and be thus larger than 10 nm lower bound.

Macroscopic situation would correspond to very large thickness scaling as n

^{1/2}, where integer n characterizes the quantized flux. Macroscopic effective thickness is of course required by data. Very large values of h_{eff}or n would be required to give realistic values for the flux tube radius. In the fractal Universe of TGD a fractal hierarchy of flux tubes within flux tubes picture is expected and one could have bunches of flux tubes with thickness h_{eff}^{1/2}× R.

For details of TGD model see the chapter TGD and Cosmology or the article BICEP2 might have detected gravitational waves.

## 8 comments:

http://www.physicsforums.com/showthread.php?t=693845

Thank you.

Interesting. I have not previously though this. Light-like vectors contracted to gamma matrices naturally define representation for Grassmann algebra since square gives something proportional to momentum squared. Multiplicative character of norm guarantees that products of light-like vectors contracted with gammas are still light-like. Light-like vectors with multiplicative structure might be interesting also in M^4 regarded as subspace of complexified quaternions. By restriction to light-cone boundary one would seem to obtain product structure! Could this be so simple? Conformal invariance would have number

theoretic meaning?? Probably there is mistake somewhere;-) .

The products of massless Clifford algebra elements in general belong to the complexified light cone. In twistor Grassmann approach these appear at twistor lines so that this might have some relevance there. In TGD complexified M^8 appears in the M^8-CP_2 correspondence: 4-surfaces in M^8_c wold be mapped to M^4xCP_2.

Dear Matti,

Ordinary QM gives us a general picture about an atom. a dense central nucleus surrounded by wave functions of electrons.

I want to understand how much the classical picture of atom changes if we regard the developments of QFT(or TGD) after QM. For example we know that between electrons in the atom there is the weak force like Z field. Hence in the classical picture in addition to electrical potential between electrons, one must regard Z field(potential) between them.

Now one can ask the question: is there W+ or W- fields around the nucleus and interacts with electrons? If they are there, this leads to the result that there must be neutrino fields too and electrons are transformed to neutrinos or vice versa. Hence in addition to wave functions of electrons, there are wave functions of neutrinos.

if this is correct, is there for every electron a corresponding neutrino in the orbitals?

another question;

Suppose there are two electrons localized to two positions. We know from classical electrodynamics the force between them are repulsive. Now suppose we want to describe weak force in the classical picture. I guess if we have two electrons (or two neutrino) , the z force between them are repulsive. If we have one electron and one neutrino, they interacts by superposition of w+ and w- fields, But the superposition is repulsive or absorbing?

Dear Hamed,

thank you for a good question. The question about

classical W and Z^0 fields is central and one of the most troublesome ones during these 37 years. These fields should give rise to long range weak forces and strong parity breaking which are not observed. Also particles would not be in eigenstates of em charge if classical W force is present.

It is an amusing co-incidence that I returned again to this question while updating CMAP files about TGD giving overall view. Just yesterday.

a) As I have explained earlier, to get rid of classical W forces on spinors, one must assume that classical W fields are vanishing in region in which spinor modes other than right-handed neutrino are non-vanishing. This gives a condition stating that CP_2 projection in this region is 2-D. There are many solutions to this condition: one parameter depending on position characterises the solutions.

b) If one also assumes that Z^0 field vanishes, the parameter is fixed completely. The generic solution are string world sheets where only em field is present classically. Fermions are localised at strings. Also partonic 2-surface can be considered. Just like physical intuition requires in long length scales at least. One can have also surfaces for which entire space-time sheet has 2-D CP_2 projection. They would have slicings by

string world sheets or partonic 2-surfaces.

Guess: these space-time surfaces are possible and CP_2 projection is geodesic manifold or even complex manifold of CP_2 and that cosmic strings are this kind of externals. Cosmic strings would be a phase consisting of 4-D string like objects. Later the fermion number would go to 2-D string world sheets in transition to radiation dominated cosmology during the analog of inflation period.

The challenge is to check that these conjectures are wrong or right. Young brains would be needed;-).

This picture is needed to make sense only above weak scale. Weak scale for dark matter is however scaled up and this allows to consider W and Z^0 fields above this scale. I leave it open whether vanishing of classical em fields on regions containing spinors isa law of nature or an approximation holding above weak scale. Large

parity breaking in living matter suggest that large h_eff phases with long weak scale are there and

at least classical Z^0 fields at least are.

The reactions involving exchange of W boson or Z boson would in this case always be described by vertices defined as partonic 2-surfaces at which orbits of partonic surfaces would meet along their ends. Generalization of Feynman diagram.

I cannot say yes or not to your second question.

In any case charge entanglement would result if one wants to keep up from charge conservation.

Dear Matti,

Thanks,

For a space like 3-surface, can one define spin? or it is only defined over the wave function over 3-surfaces?

if one can define spin of a 3-surface, is the spin of it, just rotation of it over some axis? classically(spin up or spin down and not in superposition)?

To Hamed,

somehow your comment disappeared as I started to answer it. I glued it here again.

Hamed: For a space like 3-surface, can one define spin? or it is only defined over the wave function over 3-surfaces? if one can define spin of a 3-surface, is the spin of it, just rotation of it over some axis? classically(spin up or spin down and not in superposition)?

Spin corresponds at quantum level WCW spinors. The analogs for spin states of spinor are many fermion states obtained using fermionic oscillator operators. The linear combinations of oscillator operators define anticommuting gamma matrices for WCW so that Fermi statistics is not mystery anymore: it is natural part of WCW Kahler geometry.

One can or course ask for the possible existence of a space-time correlate of spin 1/2. There is an old suggestion that dyons having odd magnetic and electric charges behave like spin 1/2 objects.

See http://quantumfrontiers.com/tag/magnetic-monopole/ .

Elementary particles correspond to effectively to pairs of self-dual magnetic monopoles (Q_em=Q_m) consisting magnetic flux tubes at parallel world sheets and wormhole contacts connecting them. Simplest possible dyons are in question. Monopole flux with closed flux lines (necessarily so).

For fermion the second throat at the other end contains fermion but not second one. Could one think that dyonic character is somehow space-time correlate for fermion and spin 1/2 property

Hi,

your comment had appeared. This blog program behaves strangely.

Hi,

second candidate for space-time correlate of spin 1/2. Space-time sheet is a little bit misleading expression. It cannot have boundaries. Boundary conditions are the problem. One must have pairs of sheets glued together along their boundaries. This is what leads to the notion of elementary particle consisting wormhole contacts connecting space-time sheets.

Fermions are basic objects in TGD by emergence of bosons as essentially fermion pairs. Could it be that this double sheetedness could serve as a correlate for spin 1/2 property?

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