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Physics in Many-Sheeted Space-Time

Note: Newest contributions are at the top!

Year 2010

Quark gluon plasma which does not behave as it should

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".

  1. A critical system associated with confinement-deconfinement transition of the quark-gluon plasma formed in the collision and inhibiting long range correlations would be in question.

  2. The proposed hydrodynamic space-time description was in terms of a scaled variant of what I call critical cosmology defining a universal space-time correlate for criticality: the specific property of this cosmology is that the mass contained by comoving volume approaches to zero at the the initial moment so that Big Bang begins as a silent whisper and is not so scaring;-). Criticality means flat 3-space instead of Lobatchevski space and means breaking of Lorentz invariance to SO(4). Breaking of Lorentz invariance was indeed observed for particle distributions but now I am not so sure whether it has much to do with this.

The microscopic level the description would be like follows.
  1. A highly entangled long hadronic string like object (color-magnetic flux tube) would be formed at high density of nucleons via the fusion of ordinary hadronic color-magnetic flux tubes to much longer one and containing quark gluon plasma. In QCD world plasma would not be at flux tube.

  2. This entangled string like object would straighten and split to hadrons in the subsequent "cosmological evolution" and yield large numbers of almost collinear p"../articles/. The initial situation should be apart from scaling similar as in cosmology where a highly entangled soup of cosmic strings (magnetic flux tubes) precedes the space-time as we understand it. Maybe ordinary cosmology could provide analogy as galaxies arranged to form linear structures?

  3. This structure would have also black hole like aspects but in totally different sense as the 10-D hadronic black-hole proposed by Nastase to describe the findings. Note that M-theorists identify black holes as highly entangled strings: in TGD 1-D strings are replaced by 3-D string like objects.

For background see TGD and Cosmology.

Anomalous time dilations for quasars

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.

  1. Causal diamond defined as the intersection of future and past directed light-cones is the fundamental geometric object in zero energy ontology. In cosmological scales a possible interpretation of CD is as sub-cosmology. In particular, our comology would correspond to this kind of CD having sub-CDs having .... CDs possess moduli space. CD has M4 position identified as say that of the lower tip. One can perform Lorentz boosts for CD leaving the lower tip invariant. The proper time distance between tips of CD is Lorentz invariant and defines an internal time standard of CD. For instance, for electron, d, and u quarks this time is .1 seconds, 1/1.28 milliseconds, and 6.5 milliseconds defining fundamental biorhytms.

  2. p-Adic length scale hypothesis follows if the light-cone propert time distance between the tips of the CD is quantized in powers of two. This means that future light-cone is replaced with a union of light-cone proper time constant hyperboloids with size scales coming as powers of two. Cosmic time identified as the distance between the tips would be quantized and cosmic time would increase in jumps. As a matter fact, the relative coordinate between the tips should be quantized quite generally so that the light-cone proper time constant hyperbloids would be replaced with discrete lattice like structures. This would predict quantization of cosmic redshifts and explain the claimed strange phenomena like God's fingers containing galaxies along the line of sight with a quantized redshift.

  3. Could the quantization of cosmic time relate to the strange observation? What does the dynamics of objects with a frozen value of cosmic time look like when viewed from Earth? What is clear that the distant object does not recede away during the studied evolution period. The overall redshift for the studied events during its evolution is same. No dilation of the time interval between periodic events would takes place. But isn't this the case in good approximation also in the measurements? And obviously this argument does not say anything about the time dilations associated with the samples at different distances.

  4. Let us make a second trial. The above idea that the observed system behaves like a particle would make sense at the level of sub-CD assignable to it. One can perform Lorentz boosts to the CD and from the point of view of observer this induces a dilation of the time scales of internal dynamics expressible as fractions of the proper time distance between its tips. Should one speak about two kinds of redshifts: the cosmic redhift associated with all radiation coming from the CD and the internal redshift associated the dynamics of CD. The observations about supernovae would suggests that cosmic expansion implies CDs of distant objects have systematically suffered a radial Lorentz boost in radial direction in the manner dictated by Hubble's law.

    This means that the time-like direction defined by the vector connecting tips of CD in M4 is same as the direction of the time-like vector pointing from the tip of the very big CD defining what we call our Big Bang cosmology a to the M4 point at which the CD containing astrophysical object is located. This position characterizes all points of given CD so that the time dilation is constant the for internal dynamics of systems inside the CD.

  5. Why the Lorentz boosts of quasar CDs in the two samples should be identical? Could the explanation relate to the fact that quasars are extremely distant objects meaning that the corresponding CDs are very large? Could the quasars in the two samples belong to the same CD?! If so then the internal dynamics would obey same rhytm but there would be a purely cosmological redshift! This effect would be basic prediction of zero energy ontology in cosmological scales and would become visible in very long length scales.

For background see TGD and Cosmology.

New information about the distribution of galactic dark matter

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.

  1. The most natural guess is that the initial velocity is in a good approximation parallel to the velocity at the moment of ripping out.
  2. A much stronger assumption is that the star eventually rotates with the same velocity as the distant stars of Milky Way around its center after the ripping out. If the dark matter is also rotating as it should be and forms a halo the gravitational interactions with it could force the hydrodynamic behavior. If one believe that dark matter in astrophysical length scales can have gigantic value of Planck constant, then hydrodynamics behavior looks natural.

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.

  1. The first model is very similar to the standard models of dark matter. If the galactic dark matter consists of decay products of a closed non-circular cosmic string approximately vertical to the galactic plane, a non-spherically symmetric distribution of dark matter is expected and there is qualitative consistency with the observed squeezed sphere character. If the ripping out leads rapidly to a hydrodynamic behavior the stream of the p"../articles/ should rotate around Milky Way destroy the planarity of the debris stream. This would be like rocket in straight path through a rotating liquid: the used fuel would start to rotate with fluid.

  2. In the second model galactic dark matter as matter resides at long cosmic string perpendicular to galactic plane. The matter in galactic plane could be also partially dark and visible matter could have resulted as decay products of the cosmic string transformed to magnetic flux tube. Galactic strings would have been linked around the long strings like pearls in necklace and this would explain the observed long strings of galaxies.

    Addition: The article Missing matter mystery of small galaxies in the latest New Scientist tells about mysterious missing dark matter. Roughly half of the dark matter predicted by theories is missing. The dark matter at the long cosmic strings would be the natural candidate for this missing dark matter if visible and dark matter in the plane of galaxy identifiable as decay products of galactic cosmic strings is responsible for the visible matter and already identified dark matter.

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.

  1. In the first model the simplest gravitational potential would be some function V(r) of the 3-D radial coordinate and in the first approximation logarithmic. The rotation around the axes of Milky way takes place with a smaller velocity as in case of Milky Way and dark matter. The ripping out process is not consistent with the hydrodynamic behavior. The necessity to modify the spherically symmetric distribution of matter might reflect the fact the behavior is actually hydrodynamic.

  2. In the second model galactic matter and Sagittarius itself would rotate with approximately the same velocity around the cosmic string and the ripping out process could be rather smooth since the velocity component in the galactic plane would not be affected in the ideal case. This model is consistent with the hydrodynamic behavior. In the optimal situation only the vertical gravitational forces due to the matter in the galactic plane would tend to rip out stars. This might relate to the fact that Sagittarius has been able to maintain its coherence so long.

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.

  1. Energy conservation in the vertical direction gives

    vz2+ 2gG×z = 2ez

    where gG is the analog of gravitational acceleration at the Earth's surface and created by a constant density of the galactic matter in the galactic plane.

  2. Angular momentum conservation gives


  3. The conservation of energy in plane orthogonal to z-axis gives the third conservation law

    (dρ/dt)2 +l22 +2Klog(ρ/ρ0)= 2eT.

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.

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