Consider first ZEO.

- In ZEO zero energy states are superpositions of space-time surfaces inside causal diamond (CD) identified as preferred extremals of the basic action principle of TGD. CD is cartesian product of causal diamond cd of M
^{4}and of CP_{2}. The preferred extremals analogous to Bohr orbits have boundaries - ends of space-time - at the light-like boundaries of CD. There is a fractal hierarchy of CDs and given CD is an imbedding space correlate for a conscious entity - self - consciousness is universal.

- Zero energy states can be seen as superpositions of state pairs with members assigned to the opposite boundaries of CD. ZEO predicts that in ordinary or "big" state function reductions (BSFRs) the arrow of time of system changes and remains unaffected in "small" state functions (SSFRs), which are TGD counterpart for "weak" measurements and associated with a sequence of unitary evolution for the state assignable to the active boundary CD, which also shifts farther from the passive boundary. Passive boundary is unaffected as also members of state pairs at it.

- Subjective time is identified as a sequence of SSFRs and correlates strongly with clock time identifiable as the distance between the tips of CD and increasing in statistical sense during the sequences of SSFRs.

- BSFR corresponds to state function reduction at active boundary of CD which becomes passive. This forces the state at passive boundary to change. Passive boundary becomes active. BSFR means the death of self and reincarnation with an opposite arrow of time. Thus the notion of life cycle is universal and life can be lieved in both directions.

- What happens to CD in long run? There are two options.

- The original assumption was that the location of formerly passive boundary is not changed. This would mean that the size of CD would increase steadily and the outcome would be eventually cosmology: this sounds counter-intuitive. Classically energy and other Poincare charges are conserved for single preferred extremal could fail in BSFRs due to the fact that zero energy states cannot be energy eigenstates.

- The alternative view suggested strongly M
^{8}-H duality (see this) is that the size of CD is reduced in BSFR so that the new active boundary can be rather near to the new passive boundary. One could say that the reincarnated self experiences childhood. In this case the size of CD can remain finite and its location in M^{8}more or less fixed. One can say that the self associated with the CD is in a kind of Karma's cycle living its life again and again. Since the extension of rationals can change in BSFR and since the number of extensions larger than given extension is infinitely larger than those smaller than it, the dimension of extension identifiable in terms of effective Planck constant increases. Since n= h_{eff}/h_{0}serves as a kind of IQ, one can say that the system becomes more intelligent.

- The original assumption was that the location of formerly passive boundary is not changed. This would mean that the size of CD would increase steadily and the outcome would be eventually cosmology: this sounds counter-intuitive. Classically energy and other Poincare charges are conserved for single preferred extremal could fail in BSFRs due to the fact that zero energy states cannot be energy eigenstates.

**Cosmic redshift but no expansion of receding objects: one further piece of evidence for TGD cosmology**

"Universe is Not Expanding After All, Controversial Study Suggests" was the title of very interesting Science News article (see this) telling about study, which forces to challenge Big Bang cosmology. The title of course involved the typical exaggeration.

The idea behind the study was simple. If Universe expands and also astrophysical objects - such as stars and galaxies - participate the expansion, they should increase in size. The observation was that this does not happen! One however observes the cosmic redshift so that it is too early to start to bury Big Bang cosmology. This finding is however a strong objection against the strongest version of expanding Universe. That objects like stars do not participate the expansion was actually known already when I developed TGD inspired cosmology for quarter century ago, and the question is whether GRT based cosmology can model this fact naturally or not.

The finding supports TGD cosmology based on many-sheeted space-time. Individual space-time sheets do not expand continuously. They can however expand in jerk-wise manner via quantum phase transitions increasing the p-adic prime characterizing space-time sheet of object by say factor two of increasing the value of h_{eff}=n× h for it. This phase transition could change the properties of the object dramatically. If the object and suddenly expanded variant of it are not regarded as states of the same object, one would conclude that that astrophysical objects do not expand but only comove. The sudden expansions should be observable and happen also for Eart. I have proposed a TGD variant of Expanding Earth hypothesis along these lines (see this).

**Stars as reincarnating conscious entities**

One can apply ZEO to the evolution of stars. The basic story (see this) is that the star is formed from he interstellar gas cloud, evolves and eventually collapses to a white dwarf, degenerate carbon-oxygen core, supernova or even blackhole if the mass of the remnant resulting in explosion throwing outer layers of the star away is in the range of 3-4 solar masses. Only very massive stars end up to supernovas. The type of the star depends on the abundances of various elements in the interstellar gas from which they formed and believed to contain heavier elements produced by earlier supernovas.

There are however several anomalies challenging the standard story. There are stars older than Universe (see this)). There is also evidence that the abundances of heavier elements in the early cosmology are essentially the same as for modern stars (see this). TGD based explanation is discussed earlier.

Karma's cycle option for the stellar evolution could explain these anomalies.

- Stars would be selves in Karma's cycle with their magnetic bodies reincarnating with a reversed arrow of time in a collapse to blackhole/white hole like entity (BHE/WHE) - depending on the arrow of time. This would follow by a stellar evolution leading to an asymptotic state BHE/WHE corresponding to maximum size of CD followed by a collapse to BHE or WHE. Also ordinary stars would correspond to BHEs/WHEs characterized by p-adic length scale L(k) longer than L(107) assignable to GRT blackholes. In standard time direction WHE would look like blackhole evaporation.

- This would allow stars older than the Universe and suggests also universal abundances. Note however that the abundances would strongly depend on the abundances of the interstellar gas and matter produced by the magnetic energy of flux tube. "Cold fusion" as dark fusion could produce elements heavier than Fe and light elements Li, Be, B, whose abundances for fusion in stellar core is predicted to be much much smaller than the observed abundances in the case of old stars. The lifetimes of stars depend on their type. Also a universal age distribution of stars in stellar clusters not depending appreciably on cosmic time is highly suggestive. I remember of even writing about this. Unfortunately I could not find the article.

- One could perhaps say that also quantum non-determinism has classical correlates. CDs would be the units for which time-reversing BSFRs are possible. Also SSFRs affecting CDs could have classical space-time correlates. M
^{8}-H duality predicts that the time evolution for space-time surface inside CDs decomposes to a sequence of deterministic evolutions glued together along M^{4}time t=r_{n}hyperplanes of M^{4}defining special moments in the life of self at which the new larger CD receives a new root t=r_{n}. The non-deterministic discontinuity could be localized to the 2-D vertices represented by partonic 2-surfaces at which the ends of light-like partonic orbits meet.

- The M
^{4}hyperplanes t=r_{n}correspond to the roots of a real polynomial with rational coefficients defining the space-time surfaces at the level of M^{8}as roots for the real or imaginary part in quaternionic sense for the octonionic continuation of the polynomial. These moments of time could correspond to SSFRs.

- The finite classical non-determinism is in accordance with the classical non-determinism predicted at the limit of infinitely large CD and vanishing cosmological constant at which classical action reduces to Kähler action having a huge vacuum degeneracy due to the fact than any space-time surface having Lagrangian manifold (vanishing induced Kähler form) as CP
_{2}projection is a vacuum extremal. The interpretation of this degeneracy interpreted in terms of 4-D spin glass degeneracy would be that at the limit of infinitely large CD the extension of rationals approaches to algebraic numbers and the roots t=r_{n}becomes dense and the dynamics becomes non-deterministic for vacuum extremals and implies non-determinism for non-vacuum extremals.

**No time dilation for the periods of processes of quasars**

There are strange findings about the time dilation of quasar dynamics challenging the standard cosmology . One expects that the farther the object is the slower its dynamics looks as seen from Earth. 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 and 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.

In GRT the redshift violates conservation of four-momentum. In TGD cosmic redshift reduces to the fact that the tangent spaces of the space-time surface for target and receiver differ by a Lorentz boost. Redshift does not mean non-conservation of four-momentum but only that the reference frames are different for target and observer. The size for the space-time sheets assignable to the systems considere must be large, of the order of the size scale L defined by the size of the recent cosmology to which one assigns the Hubble constant. In the flux tube picture this means that the flux tubes have length of order L but thickness would be about R=10^{-4 } meters - the size scale of large neuron. Photons arrive along flux tubes connecting distant systems. Note that CMB corresponds to 10 times longer peak wavelength.

I have already earlier discussed this time anomaly but what I have written is just the statement of the problem and and some speculations about its solution in terms of ZEO. A valuable hint is that the time anomaly appears for quasars- very heavy objects - but not for supernovae - much lighter objects. This suggests that the redshift depends on the masses of the objects considered.

- One considers an approximately periodic process. It is quite possible that this process is not classical deterministic process at space-time level but that one has sequence of SSFRs (weak measurements) or even BSFRs for a subsystem of the target. These processes replace quantum superposition of space-time surfaces inside CD with a new one and SSFR also increases its size in statistical sense. A natural Lorentz invariant "clock time" for the target is the distance between the tips of CD - light-cone proper time. Both M
^{4}linear coordinates and light-cone Robertson-Walker coordinates are natural coordinates for space-time sheets with 4-D M^{4}projection.

"Clock time" must be mapped to M

^{4}linear time for some space-time sheet. The Minkowski coordinates for the CD are determined only modulo Lorentz boost leaving the light-like boundary of CD invariant. In general the M^{4}coordinates of the target and observer are related by a Lorentz boost and this gives rise to cosmological redshift and also gravitational reshift.

- The information about SSFR or BSFR at the target must be communicated to the observer so that the space-time sheets in question must be connected by flux tubes carrying the photons. CD must contain both systems and naturally has cosmological size given by L so that flux tubes have thickness about R. The M
^{4}time coordinate must be common to both systems. The natural system to consider is center of mass system (cm) in which the sum of the momenta of two systems vanishes.

**Do quasars and galactic blackholes relate by time reversal in ZEO?**

This picture combined with zero energy ontology (ZEO) based view about ordinary state functions changing the arrow of time and occurring even in astrophysical scales leads to a tentative view about quasars and galactic blackholes as time reversals of each other.

- Quasars could be seen as analogs of white holes feeding the mass of cosmic string out to build the galactic tangle and part of the mass of thickening tangle would transform to ordinary matter. They would initiate the formation of galaxy meaning emergence of increasing values of h
_{eff}in the hierarchy of Planck constant. Cosmic string would basically feed the mass and energy liberated in the decay of magnetic energy at cosmic strings thickening to flux tubes to ordinary matter and serving in the role of metabolic energy driving self-organization.

- Galactic blackholes could be perhaps indeed analogs of blackholes as time reversals of quasars - "big" (ordinary) state function reduction would transform quasar as white hole to a galactic blackhole. Now the system would be drawing back the mass from the surroundings to the flux tube and maybe cosmic string. The process could be like breathing. In zero energy ontology breathing could indeed involve a sequence of states and their time reversals.

_{eff}would be reduced. The climax of his evolution would correspond to maximal values of h

_{eff}. The evolution of life would be certainly this kind of climax.

See the article Cosmic string model for the formation of galaxies and stars or the chapter of "Physics in many-sheeted space-time" with the same title.

For a summary of earlier postings see Latest progress in TGD.

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