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Physics in Many-Sheeted Space-Time
Note: Newest contributions are at the top!
The first interesting findings from LHC have been reported. The full article is here. In some proton-proton collisions more than hundred p"../articles/ are produced suggesting a single object from which they are produced. Since the density of matter approaches to that observed in heavy ion collisions for five years ago at RHIC, a formation of quark gluon plasma and its subsequent decay is what one would expect. The observations are not however quite what QCD plasma picture would allow to expect. What is so striking is the evolution of long range correlations between p"../articles/ in events containing more than 90 p"../articles/ as the transverse momentum of the p"../articles/ increases in the range 1-3 GeV (see the excellent description of the correlations by Lubos).
One studies correlation function for two p"../articles/ as a function of two variables. The first variable is the difference Δ φ for the emission angles and second is essentially the difference for the velocities described relativistically by the difference Δ η for hyperbolic angles. As the transverse momentum pT increases the correlation function develops structure. Around origin of Δ η axis a widening plateau develops near Δ Φ=0. Also a wide ridge with almost constant value as function of Δ η develops near Δ φ=π. What this means that p"../articles/ tend to move collinearly and or in opposite directions. In the latter case their velocity differences are large since they move in opposite directions so that a long ridge develops in Δ η direction.
Ideal QCD plasma would predict no correlations between p"../articles/ and therefore no structures like this. The radiation of p"../articles/ would be like blackbody radiation with no correlations between photons. The description in terms of string like object proposed also by Lubos on basis of analysis of the graph showing the distributions as an explanation of correlations looks attractive. The decay of a string like structure producing p"../articles/ at its both ends moving nearly parallel to the string to opposite directions could be in question.
Since the densities of p"../articles/ approach those at RHIC, I would bet that the explanation (whatever it is!) of the hydrodynamical behavior observed at RHIC for some years ago should apply also now. When RHIC was in blogs, I constructed a primitive poor man's model for RHIC events and found that I had mentioned stringy structures - among many other things that I would not perhaps mention anymore;-). The introduction of string like objects was natural since in TGD framework even ordinary nuclei are string like objects with nucleons connected by color flux tubes (see this): this predicts a lot of new nuclear physics for which there is some evidence. The basic idea was that in the high density hadronic color flux tubes associated with the colliding nucleon connect to form long highly entangled hadronic strings containing quark gluon plasma. The decay of these structure would explain the strange correlations.
Note: TGD is not string theory although I talk a lot about strings like objects: these objects are three-dimensional and they are an essential element of almost all physics predicted by TGD. Even elementary p"../articles/ should look string like objects in electro-weak length scales (Kähler magnetic flux tubes with magnetic charges at their ends).
Let us list the main assumptions of the model for the RHIC events and those observed now. Consider first the "macroscopic description".
For background see TGD and Cosmology.
Lubos Motl told about Discovery that quasars don't show time dilation mystifies astronomers by Hawkins. I also received a link from Kram about this: thank you. The finding is rather strange.
Consider first what one expects. Lorentz invariance implies red shift for frequencies and in time domain this means the stretching of time intervals so that the evolution of distant objects should look the slower the longer their distance from the observer is. In the case of supernovae this seems to be the case. What was studied now were quasars at distances of 6 and 10 billion years. The time span of the study was 28 years. Their light was red shifted by different amounts as one might expect but their evolution went on exactly the same rhythm! This looks really strange.
One must notice that the frequency assigned to electromagnetic signature is not ordinary light frequency. For instance, is it analogous to a frequency assignable to massive particle or massless particle? Consider ordinary Doppler effect as an analog. If the redsift is effectively that of a massive particle then the redshift is given by f→ (1-v2)1/2f =(1+z)f and for small relative velocities the redshift is about z=Δf/f =v2 smaller than for massless case f→ ((1-v)/(1+v))1/2× f=zf giving z=Δ f/f =v in the same approximation. In the recent case however redshifts are large. From z+1= Hr, with redshift z=7 associated with r=.75 billion years one deduces z=56 for 6 billion ly and z=93.3 for 10 billion ly. Therefore the redshifts for massive and massless case are related by a factor of 2 as one easily finds.
Consider now the situation in TGD framework.
For background see TGD and Cosmology.
The newest discovery relating to the galactic dark matter is described in the popular article Milky Way Has a "Squashed Beachball"-Shaped Dark Matter Halo. In more formal terms the title states that the orbit of the dwarf galaxy Sagittarius around Milky Way can be understood if the cold dark matter halo is not spherical but ellipsoid with different half axes in each three orthogonal directions. The dark matter distribution allowing the best fit is nearly orthogonal to the galactic plane and looks like a flattened sphere with height equal to one half of the diameter (see the illustration of the article).
The result is surprising since the most natural expectation is a complete spherical symmetry or ellipsoid with a rotational symmetry around the axes orthogonal to the galactic plane. The complete breaking of the rotational symmetry raises the question whether something might be wrong with the usual dark matter models. The following text is strongly updated version of the original one, which contained several errors and was badly organized.
Consider first in some detail what has been observed. Since the life span of the astronomers is not astronomical, they are not able to measure the orbit of the dwarf galaxy directly. The orbit of the dwarf galaxy can be however deduced from the stream of stars which Milky Way has ripped out from the dwarf galaxy.
Sagittarius is one of the 14 dwarf galaxies forming a gravitational bound state with Milky Way. It is an elliptic dwarf with a diameter of 104 light years (about size as the core of Milky Way). It has rotated about 1 My around Milky Way and already made about 10 full rotations. Now (in astronomical sense) Sagittarius is about to traverse the plane of Milky Way. During its motion Sagittarius experiences enormous tidal forces ripping out stars from it. The resulting stream of ripped out stars marks the orbit of Sagittarius. Obviously Sagittarius loses its mass to Milky Way and has already lost a considerable fraction. The ability of Sagittarius to maintain its coherence has been explained in terms of unusually high dark matter content.
The article states that the study of the paths for the parts of Sagittarius gives different parameters for the dark matter distribution. Maybe the "parts" refer to the four globular clusters of stars belonging to Sagittarius. In any case, a highly refined study of the structure of the star stream left behind by Sagittarius is carried out and one goal has been to find a gravitational potential allowing to fit the paths of the parts deduced from the star debris left behind by Sagittarius. The fact that Sagittarius has made several rotations around Milky Way explains why the "leading star debris" is present in the illustration. The Sagittarius flyaround movie gives an artistic simulation about the situation. It seems that an illustration of the actual track from different angles in the galactic plane must be in question.
The basic observation is that the track is in a good approximation in plane. What one can conclude from this depends on what happens in the ripping out process. The star becomes part of Milky Way in some sense. The ripped out star experiences a free fall in the gravitational field of the Milky way. The question concerns what happens to the velocity of the star as it is ripped out.
Two models of dark matter
TGD allows to consider two alternative models for the dark matter. Contrary to the first guess both models are consistent if the ripping out process is interpreted in the first manner and need not therefore be hydrodynamic. Both models are consistent with the assumption that dark matter corresponds to p"../articles/ at magnetic flux tubes, which are dark in the sense that they reside at different pages of the book like structure defined by the generalized imbedding space with pages labeled by differed values of Planck constant. Magnetic flux tubes can be regarded as outcomes of cosmic expansion thickening the extremely thing cosmic strings and weakening the extremely strong magnetic fields inside them.
Classically dark matter corresponds to the magnetic energy of cosmic string. This interpretation is not locally consistent with the General Relativistic form of the Equivalence Principle if one considers a model for the string like object itself. Einstein's equations however make sense when one considers only the long range gravitational fields created by cosmic strings.
The two models are following.
Consider next in detail the latter model. The very heavy cosmic string like object along the axis perpendicular to the galactic plane creates (in the Newtonian approximation) 2-D logarithmic potential forcing everything to rotate with a constant velocity around it. Besides this there is a weaker nearly vertical acceleration orthogonal to the plane created by the matter in the galactic plane. If the density of the matter in the galactic plane is approximated with a constant density, the motion of the individual star is a superposition of a free fall in the perpendicular direction and scattering in a logarithmic potential of form Klog(ρ/ρ0) in the approximation that the individual stars of the dwarf galaxy move completely independently. Second extreme would be a hydrodynamic flow.
Sagittarius rotates around the axis orthogonal to the plane of galaxy with the same velocity as the galactic matter identified as the velocity of the distant stars in the galactic plane (the constancy of this velocity led to the discovery of dark matter). Stating it differently, the motion of the stars of dwarf galaxy takes place in a a potential, which is sum of a potential V(ρ) depending on the radial coordinate of the plane and a potential V(z) depending on the vertical coordinate and created by the galactic matter.
The models differ from each other in several respects.
Some details related to the central string model
It is interesting to look in more detail the toy model based on cosmic string vertical to the galactic plane (also in this case matter in galactic plane could be decay remnants of a cosmic string). The energies for vertical and transverse motions are conserved separately as is also angular momentum component in vertical direction and one can solve the Newton's equations exactly. By Equivalence Principle one can speak about energy and angular momentum per unit mass: therefore notations ez, eT, l for energies and angular momentum are natural.
These conditions allow to solve the equations of motions for ez,eT, and l for each star involved and the mass of the star does not matter at all. In hydrodynamical model correlations between velocities of stars are forced by idealization as continuous matter. In this case the flow lines correspond to classical orbits with gradient of pressure added as an additional force to gravitational force. Energy and angular momentum are conserved along flow lines also now. Situation becomes more complex (and realistic) when one takes into account the gravitational forces between stars.
For background see the chapter Cosmic Strings.