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Topological Geometrodynamics: an Overview
Note: Newest contributions are at the top!
LIGO has reported that it has found no evidence for so called cosmic strings, which are a basic prediction of GUTs. It is becoming painfully clear that GUTs have led the entire theoretical physics to a wrong track. Regrettably, we have spent for more than four decades at this wrong track now. Also superstring models and M-theory assume GUT as their limit at long length scales so that this finding should finally wake up even the most sleepy colleagues.
As Peter W*it tells in N*t Even Wr*ng (for some reason Lubos wants to write "o":s as "*":s in this context), cosmic strings have been one of so called qualitative predictions of many variants of superstring theory. This is true but since Lubos is one of the few remaining superstring fans, Woit's blog post made him very irritated.
What about TGD? Do I have reasons to get irrirated? Cosmic strings appear also in TGD but are very different objects than those of GUTs. They differ also from those of superstrings theories, where they can appear at the GUT limit or as very long fundamental strings.
Cosmic strings in GUTs and superstring theories
What mainstream cosmic strings are?
The dynamics of string like objects is almost universal.
To discuss the question whether cosmic strings radiate in TGD one must say something general about the dynamics of space-time surfaces in TGD.
There are two kinds of space-time surfaces in TGD Universe. These two kinds fo space-time surfaces appear at the boths sides of M8-H duality: here one has H=M4× CP2. In the following I stay at the H-side of the duality.
There is a rather precise analogy with the vision about what happens in particle reactions. External particles decouple from interactions and interactions take place in interaction regions, where interactions are in some sense coupled on. This is realized for the preferred extremals of the action determining space-time surfaces in rather precise sense. The twistor lift of TGD predicts that the action is sum of Kähler action and volume term analogous to cosmological term.
Cosmic strings in TGD sense
Also TGD predicts what I call cosmic strings.
The question of the title reduces to the question whether the cosmic strings in TGD sense emit gravitational radiation.
The standard view about dark matter is as a halos associated with galaxies and also other astrophysical objects. Nature however seems to be reluctant to behave according to the dictates of halo theorists. The reproduction of the simple flat velocity spectrum for distant stars in galactic plane requires tuning of the parameters characterizing the dark mass distribution in the halo. There is also a small constant density core around the center of galaxy behaving like rigid body rather than a density peak with maximum at the center. Also the attempts to detect various exotic particles proposed to serve as building bricks of dark matter have chronically failed. Quite recently very old galaxies which do not have dark matter have been found.
The latest trouble of the model, one might say a death blow, is that dark matter disks do not seem to exist at all (see this)! I am afraid that this means serious funding problems for the model builders.
The death of one idea is the victory of second one. I have been preaching for almost two decades that galactic dark matter along cosmic string containing galaxies like pearls in necklace: there would be no dark matter halo (see this, this, and this). The model predicts correct velocity profile for distant stars without furher assumptions: the value of string tension determines the value of the velocity. The model solvs a multitude of anomalies of halo model, and leads to a rather detailed model for evolution of galaxies and also provides insights to problems like matter-antimatter asymmetry.
See the the chapter TGD and astrophysics .
It has been found that long range magnetic fields in microgauss range exists at distance of about 5 billion light years (see this).
The presence of cosmic magnetic fields is one of the mysteries challenging not only the existing cosmological models but even the standard model itself. Due to high temperatures there are no long range currents and there should be no long range magnetic fields in early cosmology and also the mechanism for their emergence later has remained mystery.
The observations, in particular the observations described in the article, are in conflict with the standard model view. The TGD explanation is direct implication of the assumption space-time is surface in M4×CP2. CP2 has non-trivial homology: one can regard it as having 4-D space with Euclidian signature of metric and carrying as topological magnetic monopole flux. No magnetic charge but non-trivial magnetic flux over homologically non-trivial 2-surfaces.
At space-time level this implies the existence of cosmic strings carrying monopole flux and having huge magnetic energy per unit length: they are essentially objects with 2-D M4 projection obeying string dynamics (minimal surface) and having 2-D complex surface as CP2 projection. No currents are needed to create these magnetic fields and they are stable for purely topological reasons. The very early universe would consist of a gas or plasma like state of cosmic strings.
After that the TGD analog of inflationary period took place and the projections M4 of flux tubes became 4-D. Cosmic strings started to thicken and magnetic fields gradually weakened. The prediction that magnetic fields were strongest in the early universe conforms with the observations. Standard model predicts just the opposite and cannot even provide a plausible mechanism for how they could have got stronger.
Other predictions are a detailed model for galactic dark matter associated with thickening cosmic strings. No dark matter halo is predicted and automatically correct prediction for the velocity spectrum of distant stars follows.
See the the chapter Breaking of CP, P, and T in cosmological scales in TGD Universe .
The observation of GW170817 was perhaps the event of the year in astronomy. Both gravitational waves and electromagnetic radiation from the collision of two neutron stars fusing to single object were detected. The event occurred at distance of order 130 Mly (size scale of large voids). This was a treasure trove of information.
The first piece of information relates to the question about the synthesis of elements heavier than Fe. It is l assumed that the heavier elements are generated in so called r-process involving creation of neutrons fusing with nuclei. One option is that the r-process accompanies supernova explosions but SN1987A did not provide support for this hypothesis: the characteristic em radiation accompanying r-process was not detected. GW170817 generated also em radiation, so called kilonova (see this), and the em radiation accompanying r-process was reported. Therefore this kind of collisions would generate at least part of the heavier elements. In TGD framework also so called dark nucleosynthesis occurring outside stellar interiors and explaining so called nuclear transmutations, which are now rather well-established phenomenon, would also contribute to he generation of heavier elements (and also the lighter ones) (see this).
Second piece of information was that in GW170817 both gravitational waves and gamma ray signal were detected, and the difference between the arrival times was about 1.7 seconds: gamma rays arrived slightly after the gravitational ones. From this the difference between effective propagation velocities between gravitational and em waves is extremely small.
Note that similar difference between neutrino signal and gamma ray signal was measured for SN1987A. Even gamma rays arrived at two separate pulses from SN1987A. In this case the delay was longer and a possible TGD explanation is that the signals arrived along different space-time sheets (one can certainly tailor also other explanations).
Although this kind of models look hopelessly ad hoc (at least to me), they have right to be shown wrong and GW170817 did it (see this). The point is that the coupling to dark matter besides ordinary matter implies that gamma rays experience additional delay and arrive later than gravitons coupling only to the ordinary matter. This causes what is called Shapiro delay of about 1000 days much longer than the observed 1.7 seconds. Thus these models are definitely excluded. I do not know what this means fro MOND and Verlinde's model.
There is an amazing variety of MOND like models there to be killed and another article about what GW170817 managed to do can be found (see this). Theoretical physics is drowning to a flood of ad hoc models: this is true also in particle physics where great narratives have been dead for four decades now. GW170817 looks therefore like a godly intervention similar to what happened with Babel's tower.
There is a popular article titled "Seeing One Example Of Merging Neutron Stars Raises Five Incredible Question" (see this) telling that GW100817 seems to be very badly behaving guy challenging the GRT based models for the collisions of neutron stars. Something very fishy seems to be going on and this might be the change for TGD to challenge GRT based models.
For instance, our nearest neighbor, Alpha Centauri, is a triplet system. Explanation for this have been sought for for a long time. Does star capture occur leading to binaries or triplets. Or does its reverse process in which binary splits up to become single stars occur? There has been even a search for a companion of Sun christened Nemesis.
The new assertion is based on radio survey of a giant molecular cloud filled with recently formed sunlike stars (with age less than 4 million years) in constellation Perseus, a star nursery located 600 ly from us in Milky Way. All singles and twins with separations above 15 AUs were counted.
The proposed mathematical model was able to explain the observations only if all sunlike stars are born as wide binaries. "Wide" means that the mutual distance is more than 500 AU, where AU is the distance of Earth from Sun. After the birth the systems would shrink or split t within time about million years. It was found that wide binaries were not only very young but also tended to be aligned along the long axes of an egg-shaped dense core. Older systems did not have this tendency. For instance, triplets could form as binary captures a single star.
The theory says nothing about why the stars should born as binaries and what could be the birth mechanism. Could TGD say anything interesting about the how the binaries are formed?
One of the topics of discussion were the results related to supermassive blackholes at the centers of galaxies. Gareth gave a link to an article telling about correlations between supermassive blackhole in galactic center and the evolution of galaxy itself.
See the the chapter TGD and astrophysics or the article TGD view about universal galactic rotation curves for spiral galaxies.
The news about third gravitational wave detection managed to direct the attention of at least some of us from the doings of Donald J. Trump. Also New York Times told about the gravitational wave detection by LIGO, the Laser Interferometer Gravitational-Wave Observatory. Gravitational waves are estimated to be created by a black-hole merger at distance of 3 billion light years. The results are published in the article "Observation of a 50-Solar-Mass Binary Black Hole Coalescence at Redshift 0.2" in Phys Rev Lett.
Two black holes with masses 19× M(Sun) and 31× M(Sun) merged to single blackhole hole of with mass of 49× M(Sun) meaning that roughly one solar mass was transformed to gravitational radiation. During the the climax of the merger, they were emitting more energy in the form of gravitational waves than all the stars in the observable universe.
The colliding blackholes were very massive in all three events. There should be some explanation for this. An explanation considered in the article is that the stars giving rise to blackholes were rather primitive containing light elements and this would have allowed large masses. The transformation to blackholes could have occurred directly without the intervening supernova phase. There is indeed quite recent finding showing a disappearance of very heavy star with 25 solar masses suggesting that direct blackhole formation without super-nova explosion is possible for heavy stars.
It is interesting to take a fresh look to these blackhole like entities in TGD framework. This however requires brief summary about the formation of galaxies and stars in TGD Universe (see this and this).
The observed universality of rotation curves for spiral galaxies is a challenge for TGD inspired model of galaxy formation. In TGD universality reduces to scaling invariance of the rotation curves natural since TGD Universe is quantum critical. The study of mini spiral galaxies supports the conclusion that they have a dark matter core of radius of few parsecs - 2-3 times the optical radius. This is a problem in the halo models. The simplest TGD based explanation is that galaxies correspond to knots or even spaghetti like tangles of long dark strings defining a kind of necklace containing galaxies as pearls. The model also suggests that dark matter core gives rise to Fermi bubble. Dark cosmic ray protons from supermassive galactic black hole containing dark matter would scatter from dark matter and some fraction of the produced dark photons would transform to ordinary ones. This would take place only inside the dark matter sphere and double sphere structure would be due to the fact that cosmic rays would not proceed far in galactic plane.
See the the chapter Astrophysics in TGD or the article TGD view about universal galactic rotation curves for spiral galaxies.
Galactic blackholes (or blackhole like entities) could serve as a test for the proposal. Galactic blackholes are supermassive having masses measured in billions of solar masses. These blackhole like entities is thought to grow rapidly as matter falls into them. In this process light is emitted and makes the blackhole a quasar (see this), one of the most luminous objects in the Universe.
TGD based model predicts that the seed of galaxy would be formed in the reconnection of cosmic strings and consist of dark matter. If galaxies are formed in this manner, the blackhole like entity formed in the reconnection point would get its mass from cosmic strings as dark mass and visible galactic mass would result from dark matter "boiling" to ordinary particles (as in the decay of inflaton field to particles). Matter from cosmic strings could flow to the reconnection point and a fraction of antimatter would remain inside cosmic string as dark matter.
During the "boiling" period intense radiation is generated, which leads to ask whether an interpretation as a formation of a quasar makes sense. The flow of matter would be from the blackhole like object rather than into it as in the ordinary model of quasar. Quasar like objects could of course be created also by the standard mechanism as ordinary matter starts to fall into the galactic dark blackhole and transforms to dark matter. This would occur much later than the formation of galactic blackhole like objects and galaxies around them.
Now three odd-ball quasars have been discovered in the early universe (13 billion years in past, less than billion years after Big Bang) by Eilers et al (see this). The authors conclude that the most compelling scenario is that these quasars have been shining only about 105 years. This time is not enough to build the mass that they have. This challenges the standard mechanism for the formation of galactic blackholes. What about the situation in TGD Universe? Could the odd-balls quasars be quasars in the usual sense of the word being created as ordinary matter starts to fall to the galactic dark matter blackhole and transforms to dark matter? Quantum phase transition would be involved.
See the the chapter Breaking of CP, P, and T in cosmological scales in TGD Universe or the article with the same title.
The twistor lift of TGD forces to introduce the analog of Kähler form for M4, call it J. J is covariantly constant self-dual 2-form, whose square is the negative of the metric. There is a moduli space for these Kähler forms parametrized by the direction of the constant and parallel magnetic and electric fields defined by J. J partially characterizes the causal diamond (CD): hence the notation J(CD) and can be interpreted as a geometric correlate for fixing quantization axis of energy (rest system) and spin.
Kähler form defines classical U(1) gauge field and there are excellent reasons to expect that it gives rise to U(1) quanta coupling to the difference of B-L of baryon and lepton numbers. There is coupling strength α1 associated with this interaction. The first guess that it could be just Kähler coupling strength leads to unphysical predictions: α1 must be much smaller. Here I do not yet completely understand the situation. One can however check whether the simplest guess is consistent with the empirical inputs from CP breaking of mesons and antimatter asymmetry. This turns out to be the case.
One must specify the value of α1 and the scaling factor transforming J(CD) having dimension length squared as tensor square root of metric to dimensionless U(1) gauge field F= J(CD)/S. This leads to a series of questions.
How to fix the scaling parameter S?
How can one fix the value of U(1) coupling strength α1? As a guideline one can use CP breaking in K and B meson systems and the parameter characterizing matter-antimatter symmetry.
For ε=2-30 the value of lP2/R2(CP2) is lP2/R2(CP2)=(2π)2 × R2(S2)/R2(CP2) ≈ 3.7× 10-8. lP/R(S2) would be a transcendental number but since it would not be a fundamental constant but appear only at the QFT-GRT limit of TGD, this would not be a problem.
One can make order of magnitude estimates for the Jarlskog parameter J and the fraction r= n(B)/n(γ). Here it is not however clear whether one should use ε or α1 as the basis of the estimate
Quantal U(1) force must be also consistent with atomic physics. The value of the parameter α1 consistent with the size of CP breaking of K mesons and with matter antimatter asymmetry is α1= εαK = 2-30αK.
The twistor lift of TGD forces the analog of Kähler form for M4. Covariantly constant sef-dual Kähler form J(CD) depends on causal diamond of M4 and defines rest frame and spin quantization axis. This implies a violation of CP, P, and T. By introducing a moduli space for the Kähler forms one avoids the loss of Poincare invariance. The natural question is whether J(CD) could relate to CP breaking for K and B type mesons, to matter antimatter asymmetry and the large scale parity breaking suggested by CMB data.
The simplest guess for the coupling strength of U(1) interaction associated with J(CD) predicts a correct order of magnitude for CP violation for K meson and for the antimatter asymmetry and inspires a more detailed discussion. A general mechanism for the generation of matter asymmetry is proposed, and a model for the formation of disk- and elliptic galaxies is considered. The matter antimatter asymmetry would be apparent in the sense that the CP asymmetry would force matter-antimatter separation: antimatter would reside as dark matter (in TGD sense) inside magnetic flux tubes and matter outside them. Also the angular momenta of dark matter and matter would compensate each other.
See the new chapter Breaking of CP, P, and T in cosmological scales in TGD Universe or the article with the same title.
The discoveries related to galaxies and dark matter emerge with an accelerating pace, and from TGD point of view it seems that puzzle of galactic dark matter is now solved.
The newest finding is described in popular article This Gigantic Ring of Galaxies Could Bring Einstein's Gravity Into Question. What has been found that in a local group of 54 galaxies having Milky Way and Andromeda near its center the other dwarf galaxies recede outwarts as a ring. The local group is in good approximation in plane and the situation is said to look like having a spinning umbrella from which the water droplets fly radially outwards.
The authors of the article Anisotropic Distribution of High Velocity Galaxies in the Local Group argue that the finding can be understood aif Milky Way and Andromeda had nearly head-on collision about 10 billion light-years ago. The Milky Way and Andromeda would have lost the radially moving dwarf galaxies in this collision during the rapid acceleration turning the direction of motion of both. Coulomb collision is good analog.
There are however problems. The velocities of the dwards are quite too high and the colliding Milky Way and Andromeda would have fused together by the friction caused by dark matter halo.
What says TGD? In TGD galactic dark matter (actually also energy) is at cosmic strings thickened to magnetic flux tubes like pearls along necklace. The finding could be perhaps explained if the galaxies in same plane make a near hit and generate in the collision the dwarf galaxies by the spinning umbrella mechanism.
In TGD Universe dark matter is at cosmic strings and this automatically predicts constant velocity distribution. The friction created by dark matter is absent and the scattering in the proposed manner could be possible. The scattering event could be basically a scattering of approximately parallel cosmic strings with Milky Way and Andromeda forming one pearl in their respective cosmic necklaces.
But were Milky Way and Andromeda already associated with cosmic strings at that time? The time would be about 10 billion years. One annot exclude this possibility. Note however that the binding to strings might have helped to avoid the fusion. The recent finding about effective absence of dark matter about 10 billion light years ago - velocity distributions decline at large distances - suggests that galaxies formed bound states with cosmic strings only later. This would be like formation of neutral atoms from ions as energies are not too high! How fast the things develop becomes clear from the fact that I posted TGD explanation to my blog yesterday and replaced with it with a corrected version this morning!.
See the chapter TGD and Astrophysics of "Physics in Many-Sheeted Space-time" or the article TGD interpretation for the new discovery about galactic dark matter.
Sabine Hossenfelder gave a link to a popular article "Declining Rotation Curves at High Redshift" (see this) telling about a new strange finding about galactic dark matter. The rotation curves are declining in the early Universe meaning distances about 10 billion light years (see this). In other words, the rotation velocity of distant stars decreases with radius rather than approaching constant - as if dark matter would be absent and galaxies were baryon dominated. This challenges the halo model of dark matter. For the illustrations of the rotation curves see the article. Of course, the conclusions of the article are uncertain.
Some time ago also a finding about correlation of baryonic mass density with density of dark matter emerged: the ScienceDaily article "In rotating galaxies, distribution of normal matter precisely determines gravitational acceleration" can be found here. The original article can be found in arXiv.org (see this). TGD explanation (see this) involves only the string tension of cosmic strings and predicts the behavior of baryonic matter on distance from the center of the galaxy.
In standard cosmology based on single-sheeted GRT space-time large redshifts mean very early cosmology at the counterpart of single space-time sheet, and the findings are very difficult to understand. What about the interpretation of the results in TGD framework? Let us first summarize the basic assumptions behind TGD inspired cosmology and view about galactic dark matter.
The clocks distributed at the hyperboloids of light-cone assignable to CD can in principle be synchronized in Lorentz invariant manner (see this). But what about actual Lorentz invariant synchronization of the clocks? Could TGD say something non-trivial about this problem? I received an interesting link relating to this (see this). The proposed theory deals with fundamental uncertainty of clock time due to quantum-gravitational effects. There are of course several uncertainties involved since quantum theory of gravity does not exist (officially) yet!
See the chapter More about TGD inspired cosmology.
I participated an FB discussion with several anti-Einsteinians. As a referee I have expressed my opinion about numerous articles claiming that Einstein's special or general relativity contains a fatal error not noticed by any-one before. I have tried to tell that colleagues are extremely eager to find a mistake in the work of colleague (unless they can silence the colleague) so that logical errors can be safely excluded. If something goes wrong it is at the level of basic postulates. In vain.
Once I had a long email discussion with a professor of logic who claimed to have found logical mistake in the deduction of time dilation formula. It was easy to find that he thought in terms of Newtonian space-time and this was of course in conflict with relativistic view. The logical error was his, not Einstein's. I tried to tell this. In vain again.
At this time I was demanded to explain why the 2 page article of Stephen Crothers (see this). This article was a good example of own logical error projected to that of Einstein. The author assumed besides the basic formulas for Lorentz transformation also synchronization of clocks so that they show the same time everywhere (about how this is achieved see this).
Even more: Crothers assumes that Einstein assumed that this synchronization is Lorentz invariant. Lorentz invariant synchronization of clocks is not however possible for the linear time coordinate of Minkowski space as also Crothers demonstrates. Einstein was wrong! Or was he? No!: Einstein of course did not assume Lorentz invariant synchronization!
The assumption that the synchronization of clock network is invariant under Lorentz transformations is of course in conflict with SR. In Lorentz boosted system the clocks are not in synchrony. This expresses just Einstein's basic idea about the relativity of simultaneity. Basic message of Einstein is misunderstood! The Newtonian notion of absolute time again!
The basic predictions of SR - time dilation and Lorentz contraction - do not depend on the model of synchronization of clocks. Time dilation and Lorentz contraction follow from basic geometry of Minkowskian space-time extremely easily.
Draw system K and K' moving with constant velocity with respect to K. The t' and x' axis of K' have angle smaller than π/2 and are in first quadrant.
This however raises a question. Is it possible to find a system in which synchronization is possible in Lorentz invariant manner? The quantity a2=t2-x2 defines proper time coordinate a along time like geodesics as Lorentz invariant time coordinate of light-one. a = constant hyper-surfaces are now hyperboloids. If you have a synchronized network of clocks, its Lorentz boost is also synchronized. General coordinate invariance of course allows this choice of time coordinate.
For Robertson-Walker cosmologies with sub-critical mass time coordinate a is Lorenz invariant so that one can have Lorentz invariant synchronization of clocks. General Coordinate Invariance allows infinitely many choices of time coordinate and the condition of Lorentz invariant synchronization fixes the time coordinate to cosmic time (or its function to be precise). To my opinion this is rather intesting fact.
What about TGD? In TGD space-time is 4-D surface in H=M4×CP2. a2= t2-r2 defines Lorentz invariant time coordinate a in future light-cone M4+ ⊂ M4 which can be used as time-coordinate also for space-time surfaces.
Robertson-Walker cosmologies can be imbedded as 4-surfaces to H=M4×CP2. The empty cosmology would be just the lightcone M4+ imbedded in H by putting CP2 coordinates constant. If CP2 coordinates depend on M4+ proper time a, one obtains more general expanding RW cosmologies. One can have also sub-critical and critical cosmologies for which Lorentz transformations are not isometries of a= constant section. Also in this case clocks are synchronized in Lorentz invariant manner. The duration of these cosmologies is finite: the mass density diverges after finite time.
See the chapter More about TGD inspired cosmology.
Sabine Hossenfelder wrote about Bullet Cluster. Usually Bullet Cluster is seen to favor dark matter and disfavor MOND theory introducing a modification of Newtonian gravity. Sabine Hossenfeldersaw it differently.
Cold dark matter model (ΛCDM) and MOND are two competing mainstream models explaining the constant velocity spectrum of stars in galaxies.
What could be the interpretation in TGD?
In FB I was made a question about general aspects of TGD. It was impossible to answer the question with few lines and I decided to write a blog posting. I am sorry for typos in the hastily written text. A more detailed article Can one apply Occam’s razor as a general purpose debunking argument to TGD? tries to emphasize the simplicity of the basic principles of TGD and of the resulting theory.
A. In what aspects TGD extends other theory/theories of physics?
I will replace "extends" with "modifies" since TGD also simplifies in many respects. I shall restrict the considerations to the ontological level which to my view is the really important level.
B. In what sense TGD is simplification/extension of existing theory?
C. What is the hypothetical applicability of the extension - in energies, sizes, masses etc?
TGD is a unified theory and is meant to apply in all scales. Usually the unifications rely on reductionistic philosophy and try to reduce physics to Planck scale. Also super string models tried this and failed: what happens at long length scales was completely unpredictable (landscape catastrophe).
Many-sheeted space-time however forces to adopt fractal view. Universe would be analogous to Mandelbrot fractal down to CP2 scale. This predicts scaled variants of say hadron physics and electroweak physics. p-Adic length scale hypothesis and hierarchy of phases of matter with heff=n×h interpreted as dark matter gives a quantitative realization of this view.
D. What is the leading correction/contribution to physical effects due to TGD onto particles, interactions, gravitation, cosmology?
See the new chapter Can one apply Occam's razor as a general purpose debunking argument to TGD? or article with the same title.