Evidence for Many-Sheeted Space-Time in RHIC?!

While performing the usual morning walk in the web I encountered an astonishing news fragment from the latest New Scientist. Since it was not April First I decided to glue the fragment here, and felt extremely frustrated of not being able to continue reading without subscribing to New Scientist. The article was by Eugenie Samuel Reich in New Scientist 19 March 2005, issue 2491. It turned out that this piece of data led to a beatiful unification of several loosely related pieces of TGD.

A fireball created in a particle accelerator bears a striking resemblance to a black hole - but thankfully not the sort that could consume the Earth. A FIREBALL created in a particle accelerator bears a striking similarity to a black hole. But don't panic: even if the controversial claim is true, it is not the sort of black hole that would cause Earth to disappear in a puff of radiation. At the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory in Upton, New York, beams of gold nuclei travelling at close to the speed of light are smashed into each other. The intense heat of the collision breaks down the nuclei into quarks and gluons, the most basic building blocks of all normal matter. These particles form a ball of plasma about 300 million times hotter than the surface of the sun (New Scientist, 16 October 2004, p 35). The fireball, which lasts a mere 10-23 seconds, can be detected because it absorbs jets of particles produced by the collision. But 10 times as many ...

Here it ended! Just when the fireball had started to absorb jets of particles! What a pity! Next day I went to RHIC homepage and found that Physics Today article What Have We Learned From the Relativistic Heavy Ion Collider? gives a nice account about experimental findings. Extremely high collision energies are in question: Gold nuclei contain energy of about 100 GeV per nucleon: 100 times proton mass. The expectation was that a large volume of thermalized Quark-Gluon Plasma (QCP) is formed in which partons lose rapidly their transverse momentum. The great surprise was the suppression of high transverse momentum collisions suggesting that in this phase strong collective interactions are present. This has inspired the proposal that quark gluon plasma is preceded by liquid like phase which has been christened as Color Glass Condensate (CGC) thought to contain Bose-Einstein condensate of gluons. I also learned that there is M-theory inspired article "The RHIC fireball as a dual black hole" by Hortiu Nastase (hep-th/0501068). I read the article but it could not inspire me too much. In the following I try to articulate TGD inspired impressions.

Minibang model for the events

I have written already earlier about the unexpected properties of the quark-gluon plasma (see Simulating Big Bang in laboratory. At that time the puzzle was the observed breaking of longitudinal Lorentz boost invariance for rapidity distributions reported already 2002. This has been later interpreted in terms of strong collective interactions due to liquid like character of the phase in question. The proposed model was based on direct scaling of TGD inspired very early cosmology to hadronic context. TGD inspired cosmology involves cosmic string dominated phase during which ordinary notion of 3-space does not make sense. The cosmic strings decay to ordinary matter and space-time in the usual sense emerges during quantum critical period with flat 3-space: this cosmology is fixed completely apart the parameter fixing its duration. Then follows the ordinary cosmology with sub-critical density. A direct translation of this picture to hadronic context would suggest following.

• The color-glass condensate (CQC) believed to correspond to a Bose-Einstein condensate gluons, which has been introduced later, could correspond to the period dominated by color magnetic flux tubes containing the gluon condensates. These strings could be also seen as TGD counterparts black holes in the sense that the mass is determined by the length of the string just as the mass of black hole is determined by its radius. This picture conforms with the description as an incompressible liquid flow. In TGD based view about hydrodynamics the flow lines of liquid flow correspond to magnetic (em, Z^0, or color: as you like) flux tubes and the local incompressibility of the flow corresponds to the vanishing divergence of the magnetic field telling that there are no magnetic charges.
• The critical period with flat 3-space to the phase transition to radiation dominated cosmology identifiable as QGP.
• Hadronization would correspond to the transition to matter dominated cosmology.

An important difference as compared to the standard cosmology is that the gravitational mass density approaches zero at the moment of big bang so that the cosmology is not actually singular: this is what makes it possible to model the growth of phase transition from small seed using the critical cosmology. Single parameter, the duration, characterizes the critical cosmology and determines the critical temperature for the transition to QGP and all other parameters. While reading what I had written for years ago I was a little bit surprised since I had ended up with the view that the space-time sheet containing quark gluon pasma is created from vacuum and matter flows to it. This state could correspond to the formation of the hadronic analog of black hole which then explodes in hadronic minibang. Of course, big bang is more or less time reversal of the black hole collapse. At that that time I did not realize that the different phases of minibang could correspond to new phases of hadronic matter but talked only about QGP.

Conformal confinement as TGD counterpart of CGC?

The next twist in the story was the shocking finding, compared to Columbus's discovery of America, was that, rather than behaving as a dilute gas, the plasma behaved like a liquid with strong correlations between partons, and having density 30-50 times higher than predicted by QCD calculations. Liquid character means strong correlations. When I learned about these findings, I proposed how TGD might explain them in terms of what I called (see conformal confinement). Since I was doing busily some other things, I did not have time to find how earlier picture could relate to this new idea. In TGD super canonical conformal weights of particles are predicted to be complex and closely related to complex zeros of Riemann Zeta. For physical states the net conformal weight must be always real and this forces what I call conformal confinement and strong correlations between composite particles and could give the system liquid like characteristics. In the ordinary phase conformal confinement would occur already at single parton level meaning that quarks and gluons would be always conformal "singlets". One can of course wonder whether the difference between valence and sea quarks might relate to conformal confinement. Whether conformal confinement is needed at all or whether it really occurs for Bose-Einstein condensed gluons at color magnetic flux tubes and makes them to behave like a single particle, is a fascinating question. An equally interesting question is whether ordinary liquid flow could involve Bose-Einstein condensates of particles which are not "conformal singlets".

Classical gravitation and color confinement

Just some time ago it became clear that strong classical gravitation might play a key role in the understanding of color confinement (see TGD and QCD. Whether situation looks confinement or asymptotic freedom would be in the eyes of beholder: one example of dualities filling TGD Universe. If you look the situation at the hadronic space-time sheet you have asymptotic freedom, particles move essentially like free massless particles. But, and this is absolutely essential, in the induced metric of hadronic space-time sheet. This metric represents classical gravitational field becoming extremely strong near hadronic boundary. From the point of view of outsider, the motion of quarks slows down to rest when they approach hadronic boundary: confinement. The distance to hadron surface is infinite or at least very large since the induced metric becomes singular at the light-like boundary! Also hadronic time ceases to run near the boundary and finite hadronic time corresponds to infinite time of observer. When you look from outside you find that this light-like 3-surface is just static surface like a black hole horizon which is also a light-like 3-surface. Hence confinement.

Dark matter in TGD

The evidence for hadronic blackhole like structures is especially fascinating. In TGD Universe dark matter can be (not always) ordinary matter at larger space-time sheets in particular magnetic flux tubes. The mere fact that the particles are at larger space-time sheets might make them more or less invisible. Matter can be however dark in much stronger sense, should I use the word "black"! The findings suggesting that planetary orbits obey Bohr rules with gigantic Planck constant (see Gravitational Schrödinger equation as a quantum model for the formation of astrophysical structures and dark matter?) would suggest quantum coherence of dark matter even in astrophysical length scales and this raises the fascinating possibility that Planck constant is dynamical so that fine structure constant for these charged coherent states would be proportional to 1/hbar_gr and extremely small: hence darkness. This quantization saves from blackhole collapse just as the quantization of hydrogen atom saves from infrared catastrophe. The obvious questions are whether

• black hole like objects/magnetic flux tubes/cosmic strings could consist of quantum coherent dark matter, and whether
• this quantum coherence is due to the conformal confinement. This would be of enormous importance even for the understanding of living matter since dark matter at magnetic flux tubes could be responsible for the quantum control of the ordinary matter in TGD inspired biology.

From outside non-stringy TGD counterparts of black holes would look just like ordinary black holes but the interior metric would be of course different from the usual one since matter would not be collapsed to a point. Dark matter option cannot be realized in a purely hadronic system at RHIC energies since the product GM_1M_2 characterizing the interaction strength of two masses must be larger than unity (hbar=c=1) for the phase transition increasing Planck constant to occur (the hypothesis is that the system does its best to stay perturbative). Hence the collision energy should be above Planck mass for the phase transition to occur if gravitational interactions are responsible for the transition. The hypothesis is however much more general and states that the system does its best to stay perturbative by increasing its Planck constant in discrete steps and applies thus also in the case of color interaction and governs phase transition to the TGD counterpart of non-perturbative QCD. Criterion would be roughly alpha_sQ^2_s>1 for two color charges of opposite sign. Hadronic string picture would suggests that the criterion is equivalent to the generalization of the gravitational criterion to its strong gravity analog nL_p^2M^2>1, where L_p is p-adic length scale characterizing color magnetic energy density (hadronic string tension) and M is the mass of the color magnetic flux tube and n is a numerical constant. Lepto-hadron physics, one of the predictions of TGD, is one instance of a similar situation. In this case electromagnetic interaction strength defined in an analogous manner becomes larger than unity in heavy ion collisions just above the Coulomb wall and leads to the appearance of mysterious states having a natural interpretation in terms of lepto-pion condensate. Lepto-pions are pairs of color octet excitations of electron and positron.

Description of RHIC events in terms of hadronic blackhole

The following view about RHIC events represents my immediate reaction to the latest RHIC news in terms of black-hole physics instead of notions related to big bang. Since black hole collapse is roughly time reversal of big bang, the description is complementary to the earliest one. In TGD context one can ask whether the fireballs possibly detected in RHIC are produced when a portion of quark-gluon plasma in the collision region formed by to Gold nuclei separates to form a larger space-time sheet separated from the remaining collision region by a lightlike 3-D surface (I have used to speak about light-like causal determinants) mathematically completely analogous to a black hole horizon. A formation of an analog of blackhole would indeed be in question. Of course, the relationship between mass and radius would be completely different with gravitational constant presumably replacement by the the square of appropriate p-adic length scale presumably of order pion Compton length. I have long time ago in the context of p-adic mass calculations formulated quantitatively the notion of elementary particle blackhole analogy making the notion of elementary particle horizon and generalization of Hawking-Bekenstein law. Could one then regard this space-time sheet as a larger space-time sheet to which matter from the exterior flows in? This would seem reasonable since p-adic length scale would be larger than p-adic length scale characterizing nucleons. It must be however emphasized that the hadrons have complex many-sheeted structure since quarks feed their em, color, and Z^0 gauge fluxes to different space-time sheets. The size L of the "hadronic blackhole" would be relatively large using protonic Compton radius as a unit of length. Pion Compton radius is a rather reasonable first order of magnitude guess for L. The density of partons would be very high and large fraction of them would have been materialized from the brehmstrahlung produced by the de-accelerating nuclei. Partons would be gravitationally confined inside this region. The interactions of partons or conformal confinement would lead to a generation of a liquid like dense phase and a rapid thermalization would occur. The collisions of partons producing high transverse momentum partons occurring inside this region would yield no detectable high p_T jets since the matter coming out from this region would be somewhat like a thermal radiation from an evaporating black hole. This space-time sheet would expand and cool down to QQP and crystallize into hadrons. For a more detailed discussion of the still continuing intense interaction between theoretical ideas and RHIC findings see the chapter TGD and Cosmology of TGD. Matti Pitkanen