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Pitkänen, M., Cosmic String Model for Formation of Galaxies, & DNA Structure

Article

Cosmic String Model for Formation of Galaxies, & DNA Structure

Matti Pitkänen 1

Abstract

The view about the role of new nuclear physics predicted by TGD in the model of solar interior
gives excellent guidelines for attempts to develop a more detailed understanding about TGD counter-
parts of blackholes as volume filling flux tube tangles. One ends up to rather detailed picture making
correct predictions about minimum radii of blackholes and neutron stars. The idea about ordinary
stars as blackhole like objects emerges. The standard blackhole thermodynamics is replaced by two
thermodynamics. The first thermodynamics is assignable to the flux tubes as string like entities hav-
ing Hagedorn temperature TH as maximal temperature. The second thermodynamics is assignable
to gravitational flux tubes characterized by the gravitational Planck constant hgr. Cosmic strings
are assumed to form a fractal hierarchy and that in TGD inspired biology cosmic strings thickened
to monopole flux tubes are behind various linear biomolecules organized around them as ordinary
matter. This leads to ask whether DNA double strand and the organization of DNA double strands
to chromosomes might be more general phenomenon. Chromosomes consist of 4 strands, which allows
to ask whether something similar happens even at the level of superclusters and that the topology of
quadrupole field is involved.

Keywords: Cosmic string model, galaxy, formation, DNA strand, TGD framework.

1 Introduction

The view about the role of new nuclear physics predicted by TGD in the model of solar interior [25] gives
excellent guidelines for attempts to develop a more detailed understanding about TGD counterparts of
blackholes as volume filling flux tube tangles.

1.1 Brief description of the model for for the formation of galaxies and stars

TGD based cosmology predicts that the primordial cosmology was dominated by cosmic strings identified
as 4-surfaces having 2-D M4 projection in H = M4xCP2. CP2 projection is a complex surface of CP2.
The dimension of M4 projection is unstable against perturbations and during cosmological evolution the
M4 projection thickens. This leads to a model for the formation of galaxies as tangles along cosmic strings
in turn containing stars and even planets as sub-tangles.

1. Twistor lift of TGD [15] predicts that cosmological constant at the level of space-time surface (to be
distinguished from that associated with GRT limit of TGD) is length scale dependent. This solves
the basic problem caused by the huge value of cosmological constant in the very early Universe. In
zero energy ontology length scale dependent Λ having spectrum coming in some negative powers of
2 characterizes the space-time sheets assignable to individual system and the corresponding causal
diamond (CD) and is determined by its p-adic length scale.

For instance, Sun has its own cosmological constant predicted by the model solving the puzzle
due to larger abundances obtained in solar-seismological determinations than in spectroscopic and
meteoritic determinations. Dark nuclear states of nuclei inside solar core contribute also to the
nuclear abundances [25].

1Correspondence: Matti Pitkänen http://tgdtheory.fi/. Address: Rinnekatu 2-4 8A, 03620, Karkkila, Finland. Email:
matpitka6@gmail.com.

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Pitkänen, M., Cosmic String Model for Formation of Galaxies, & DNA Structure

2. The energy of flux tubes consists of Kähler magnetic energy and volume energy. Quantum classical
correspondence strongly suggests that this energy is identifiable as dark matter even for minimal
value of heff .

3. Phase transitions reducing the value of cosmological constant are possible. Cosmic strings (or rather
their M4 projections) start to thicken and lose magnetic energy by transforming to ordinary matter.
This is analogous to the decay of the inflaton field to matter. This generates Einsteinin space-time
with space-time surfaces having large and increasing 4-D M4 projection. Flux tubes and cosmic
strings are however still present.

The expansion of flux tubes in phase transitions reducing Λ gives rise to a jerk-wise accelerated
expansion at the level of astrophysical objects. For given phase transition the accelerated expansion
eventually stops since the expansion increases volume energy. The expansion periods however repeat
being induced by phase transitions reducing length scale dependent quantized cosmological constant
Λ associated with the volume action coming as powers of 2 and making flux tubes unstable against
thickening and transformation of magnetic energy to ordinary matter. The recent accelerated
expansion corresponds to this kind of period being thus analogous to inflation and is predicted to
stop since volume energy increases. The expansion rate is predicted to oscillate so that the expansion
takes place as jerks and there is evidence for this [2] (see (http://tinyurl.com/oqcn2hp) discussed
from TGD point of view in [13].

4. In particular, the TGD counterpart of inflation would have led from cosmic string dominated primor-
dial cosmology in which Einsteinian space-time does not make sense to a radiation dominated phase
in which Einsteinian space-time makes sense. Expanding Earth model [21] allowing to understand
Cambrian Explosion is one application of TGD based quantum cosmology.

1.2 The notion of length scale dependent cosmological constant

In this section the notion of length scale dependent cosmological constant is considered in more detail.
TGD predicts that cosmological constant Λ characterizing space-time sheets is length scale dependent
and depends on p-adic length scale. Furthermore, expansion would be fractal and occur in jerks. This is
the picture that twistor lift of TGD leads to [15].

Quite generally, cosmological constant defines itself a length scale R = 1/Λ1/2. r = (8π)1/4
√
RlP -

essentially the geometric mean of cosmological and Planck length - defines second much shorter length
scale r. The density of dark energy assignable to flux tubes in TGD framework is given as ρ = 1/r4.

In TGD framework these scales corresponds two p-adic length scales coming as half octaves. This
predicts a discrete spectrum for the length scale dependent cosmological constant Λ [15] . For instance,
one can assign to ..., galaxies, stars, planets, etc... a value of cosmological constant. This makes sense in
many-sheeted space-time but not in standard cosmology.

Cosmic expansion is replaced with a sequence of fast jerks reducing the value of cosmological constant
by some power of 2 so that the size of the system increases correspondingly. The jerk involves a phase
transition reducing Λ by some negative power of 2 inducing an accelerating period during which flux tube
thickness increases and magnetic energy transforms to ordinary matter. Thickening however increases
volume energy so that the expansion eventually halts. Also the opposite process could occur and could
correspond to a ”big” state function reduction (BSFR) in which the arrow of time changes.

An interesting question is whether the formation of neutron stars and super-novas could involve BSFR
so that these collapse phenomena would be kind of local Big Bangs but in opposite time direction. One
can also ask whether blackhole evaporation could have as TGD analog BSFR meaning return to original
time direction by a local Big Bang. TGD analogs of blackholes are discussed in [22].

Evidence for the anisotropy of the acceleration of cosmic expansion has been reported (see http:

//tinyurl.com/rx4224f). Thanks to Wes Johnson for the link. Anisotropy of cosmic acceleration
would fit with the hierarchy of scaled dependent cosmological constants predicting a fractal hierarchy

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Pitkänen, M., Cosmic String Model for Formation of Galaxies, & DNA Structure

of cosmologies within cosmologies down to particle physics length scales and even below. The phase
transitions reducing the value of Λ for given causal diamond would induce accelerated inflation like period
as the magnetic energy of flux tubes decays to ordinary particles. This would give a fractal hierachy of
accelerations in various scales.

Consider now some representative examples to see whether this picture can be connected to empirical
reality.

1. Cosmological constant in the length scale of recent cosmology corresponds to R ∼ 1026 m (see
http://tinyurl.com/k4bwlzu). The corresponding shorter scale r = (8π)1/4

√
RlP is identified

essentially as the geometric mean of R and Planck length lP and equals to r ∼ 4 × 10−4 m: the
size scale of large neuron. This is very probably not an accident: this scale would correspond to the
thickness of monopole flux tubes.

2. If the large scale R is solar radius about 7 × 108 m, the short scale r ' 1012 m is about electron
Compton length, which corresponds to p-adic length scale L(127) assignable to Mersenne prime
M127 = 2127− 1. This is also the size of dark proton explaining dark fusion deduced from Holmlid’s
findings [16, 17]: this requires heff ∼ 212!

Remark: Dark proton sequences could be neutralized by a sequence of ordinary electrons locally.
This could give rise to analogs of atoms with electrons being very densely packed along the flux
tube.

The prediction of the TGD based model explaining the 10 year old puzzle related to the fact
that nuclear abundances in solar interior are larger than outside [25] (see http://tinyurl.com/

y38m54ud) assumes that nuclear reactions in Sun occur through intermediate states which are dark
nuclei. Hot fusion in the Sun would thus involve the same mechanism as ”cold fusion”. The view
about cosmological constant and TGD view about nuclear fusion lead to the same prediction.

3. If the short scale is p-adic length L(113) assignable to Gaussian Mersenne MG,113 = (1 + i)113 − 1
defining nuclear size scale of r ∼ 10−14 m, one has R ∼ 10 km, the radius of a typical neutron star
(see http://tinyurl.com/y5ukv2wt) having a typical mass of 1.4 solar masses.

A possible interpretation is as a minimum length of a flux tube containing sequence of nucleons or
nuclei and giving rise to a tangle. Neutron would take volume of about nuclear size - size of the
magnetic body of neutron? Could supernova explosions be regarded as phase transitions scaling the
stellar Λ by a power of 2 by making it larger and reducing dramatically the radius of the star?

4. Short scale r ∼ 10−15 m corresponding to proton Compton length gives R about 100 m. Could
this scale correspond to quark star (see http://tinyurl.com/y3n78tjs)? The known candidates
for quark stars are smaller than neutron stars but have considerably larger radius measured in few
kilometers. Weak length scale would give large radius of about 1 cm. The thickness of flux tube
would be electroweak length scale.

Starting from this picture, one ends up to rather detailed picture making correct predictions about
minimum radii of blackholes and neutron stars. The idea about ordinary stars as blackhole like objects
emerges naturally since flux tubes are universal objects in TGD Universe and could be also inspired by
the fashion of dualizing everything to blackholes.

The standard blackhole thermodynamics is replaced by two thermodynamics. The first thermody-
namics is assignable to the flux tubes as string like entities having Hagedorn temperature TH as maximal
temperature. The second thermodynamics is assignable to the gravitational flux tubes characterized by
the gravitational Planck constant hgr: Hawking temperature TB is scaled up by the ratio ~gr/~ to TB,D

and is gigantic as compared to the ordinary Hawking temperature but the intensity of dark Hawking
radiation is extremely low.

The condition TH = TB,D for thermodynamical equilibrium fixes the velocity parameter β0 = v0/c
appearing in the Nottale formula for ~gr and suggests β0 = 1/heff for the dark nuclei at flux tubes

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defining star as blackhole like entity in TGD sense. This also predicts the Hagedorn temperature of the
counterpart of blackhole in GRT sense to to be hadronic Hagedorn temperature assignable to the flux
tube containing dark nuclei as dark nucleon sequences so that there is a remarkable internal consistency.
In zero energy ontology (ZEO) quasars and galactic blackholes can be seen as time reversals of each other.

The cosmological time anomalies such as stars older than the Universe can be understood. In ZEO
the time evolution for the zero energy states associated with causal diamonds (CDs) by sequences of
small state function reductions (weak measurements) gives rise to conscious entity, self. Self dies and re-
incarnates with an opposite arrow of time in big (ordinary) state function reduction reversing the arrow
of time. These reincarnations define kind of universal Karma’s cycle. If the Karma’s cycle leaves the sizes
of CDs bounded and their position in M4 unaffected, quantum dynamics reduces to a local dynamics
inside CDs defining sub-cosmologies. In particular, the age distributions and properties of stars depend
only weakly on the value of cosmic time - stars older than the Universe become possible in standard view
about time.

The flux tube picture about galaxies and larger structures is discussed with application to some
anomalies strongly suggesting the presence of coherence in scales of even billion light years. Also ”too”
fast spinning galaxies are discussed. The local galaxy supercluster Laniakea is discussed in the flux tube
picture as a flux tube tangle in scale of .5 Gly.

2 Blackholes, quasars, and galactic blackholes

I have discussed a model of quasars in [22] (see http://tinyurl.com/y2jbru4k) . The model is inspired
by the notion of MECO and proposes that quasar has a core region analogous to black hole in the sense
that the radius is apart from numerical factor near unit rS = 2GM . This comes from mere dimensional
analysis.

2.1 Blackholes in TGD framework

In TGD the metric of blackhole exterior makes sense and also part of interior is embeddable but there
is not much point to consider TGD counterpart of blackhole interior, which represents failure of GRT
as a theory of gravitation: the applicability of GRT ends at rS . The following picture is an attempt to
combine ideas about hierarchy of Planck constant and from the model of solar interior [25] deriving from
the 10 year old nuclear physics anomaly [4, 6].

1. The TGD counterpart of blackhole would be maximally dense spaghetti formed from monopole flux
tube. Stars would not be so dense spaghettis. A still open challenge is to formulate precise conditions
giving the condition rS = 2GM . The fact that condition is ”stringy” with T = 1/2G taking
formally the role of string tension encourages the spaghetti idea with length of cosmic string/flux
tube proportional to rS .

2. The maximal string tension allowed by TGD is determined by CP2 radius and estimate for Kähler
coupling strength as 1/αK ' 1/137 and is roughly Tmax ∼ 10−7.5/G suggesting that in blackhole
about 107.5 parallel flux tubes with maximal string tension and with length of about rS give rise
to blackhole like entity. Kind of dipole core consisting of monopole flux tubes formed by these flux
tubes comes in mind. The flux tubes could close to short flux tubes or flux tubes could continue
like flux lines of dipole magnetic field and thicken so that the energy density would be reduced.

3. This picture conforms with the proposal that the integer n appearing in effective Planck constant
heff = n × h0 can be decomposed to a product n = m × r associated to space-time surface which
is m-fold covering of CP2 and r-fold covering of M4. For r = 1 m-fold covering property could be
interpreted as a coherent structure consisting of m almost similar regions projecting to M4: one

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could say that one has field theory in CP2 with m-valued fields represented by M4 coordinates. For
r = 1 each region would correspond to r-valued field in CP2.

This suggests that Newton’s constant corresponds apart from numerical factors 1/G = m~/R2,
where R is CP2 radius (the radius of geodesic circle). This gives m ∼ 107.5 for gravitational flux
tubes. The deviations of m from this value would have interpretation in term of observed deviations
of gravitational constant from its nominal value. In the fountain effect of super-fluidity the deviation
could be quite large [11].

Smaller values of heff are assigned in the applications of TGD with the flux tubes mediating
other than gravitational interactions, which are screened and should have shorter scale of quantum
coherence. Could one identify corresponding Planck constant in terms of the factor r of m: heff =
r~0? TGD leads also to the notion of gravitational Planck constant ~gr = GMm/v0 assigned to the
flux tubes mediating gravitational interactions - presumably these flux tubes do not carry monopole
flux.

4. Length scale dependent cosmological constant should characterize also blackholes and the natural
first guess is that the radius of the blackhole corresponds to the scaled defined by the value of
cosmological constant. This allows to estimate the thickness of the flux tube by a scaling argument.
The cosmological constant of Universe corresponds to length scale L = 1/

√
Λ ∼ 1026 m and the

density ρ of dark energy corresponds to length scale r = ρ−1/4 ∼ 10−4 m. One has r = (8πr)1/4
√
LlP

giving the scaling law (r/r1) = (L/L1)1/2. By taking L1 = rs(Sun) = 3 km one obtains r1 =
.7×10−15 m rather near to proton Compton length 1.3×10−15 m and even nearer to proton charge
radius .87××10−15 m. This suggests that the nuclei arrange into flux tubes with thickness of order
proton size, kind of giant nucleus. Neutron star would be already analogous structure but the flux
tubes tangled would not be so dense.

Denoting the number of protons by N , the length of flux tube would be L1 ' Nlp ≡ xrS (lp denotes
proton Compton length) and the mass would be Nmp. This would give x as x = (lp/lPl)

2 ∼ 1038.
Note that the ratio of the volume filled by the flux tube to the M4 volume VS defined by rS is

Vtube
VS

=
3

8
(
lP
lPl

)2 × (
lp
rS

)2 ∼ 10(
rS(Sun)

rS
)2 . (2.1)

The condition Vtube/VS < 1 gives a lower bound to the Schwartschild radius of the object and
therefore also to its mass: rS >

√
10rS(Sun) and M >

√
10M(Sun). The lower bound means that

the flux tube fills the entire M4 volume of blackhole. Blackhole would be a volume filling flux tube
with maximal mass density of protons (or rather, neutrons -) per length unit and therefore a natural
endpoint of stellar evolution. The known lower limit for the mass of stellar blackhole is few stellar
masses (see http://tinyurl.com/ycd4w4m4) so that the estimate makes sense.

5. An objection against this picture are very low mass stars with masses below .5M(Sun) (see http:

//tinyurl.com/ceoo6sj) not allowed for k ≥ 107. They are formed in the burning of hydrogen
and the time to reach white dwarf state is longer than the age of the universe. Could one give up
the condition that flux tube volume is not larger than the volume of the star. Could one have dark
matter in the sense of n2-sheeted covering over M4 increasing the flux tube volume by factor n2.

6. This picture does not exclude star like structure realized in terms of analogs of protons for scaled up
variants of hadron physics M89 hadron physics would have mass scale scaled up by a factor 512 with
respect to standard hadron physcs characterized by Mersenne prime M107. The mass scale would
correspond to LHC energy scale and there is evidence for a handful of bumps having interpretation
as M89 mesons. It is of course quite possible that M89 baryons are unstable against transforming
to M107 baryons.

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7. The model for star [25] inspired by the 10 year old nuclear physics anomaly led to the picture that
protons form at least in the core dark proton sequences associated with the flux tube and that the
scaled up Compton length of proton is rather near to the Compton length of electron: there would
be zooming up of proton by a factor about 211 ∼ mp/me. The formation of blackhole would mean
reduction of heff by factor about 2−11 making dark protons and neutrons ordinary.

2.2 Can one see also stars as blackhole like entities?

The assignment of blackholes to almost any physical objects is very fashionable, and the universality of
the flux tube structures encourages to ask whether the stellar evolution to blackhole as flux tube tangle
could involve discrete steps involving blackhole like entities but with larger Planck constant and with
larger radius of flux tube.

1. Could one regard stellar objects as blackholes labelled by various values of Planck constant heff?
Note that heff is determined essentially as the dimension n of the extension of rationals [12, 18].
The possible p-adic length scales would correspond to the ramified primes of the extension. p-Adic
length scale hypothesis selects preferred length scales as p ' 2k, with prime values of k preferred.
Mersennes and Gaussian Mersennes would be in favoured nearest to powers of 2.

The most general hypothesis is that all values of k in the range [127, 107] are allowed: this would
give half-octaves spectrum for p-adc length scales. If only odd values of k are allowed, one obtains
octave spectrum.

2. The counterpart of Schwartchild radius would be rS(k) = (L(k)/L(107))2rS corresponding to the
scaling of maximal string tension proportional to 1/G by L(107)/L(k)2, where k is consistent with
p-adic length scale hypothesis.

The flux tube area would be scaled up to L(k)2 = 2k−107L(107)2, and the constant x ≡ x(107)
would scale to x(k) = 2k−107x. Scaling guarantees that condition V (tube)/VS does not change at
all so that the same lower bound to mass is obtained. Note that the argument do not give upper
bound on the mass of star and this conforms with the surprisingly large masses participating in the
fusion of blackholes producing gravitational radiation detected at LIGO.

3. The favoured p-adic length scales between p-adic length scale L107 assignable to black hole and
L(127) corresponding to electron Compton length assignable to solar interior are the p-adic length
scale L(113) = 8L(127) assignable to nuclei, and the length scale L(109), which corresponds to p
near prime power of two.

(a) For k = 109 (assignable to deuteron) the value of the mass would be scaled by factor 4 to a
lower about 12 km to be compared with the typical radius of neutron star about 10 km. The
masses of neutron stars around about 1.4 solar masses, which is rather near to the lower bound
derived for blackholes. Neutron star could be seen the last phase transition in the sequence of
p-adic phase transition leading to the formation of blackhole.

(b) Could k = 113 phase precede neutron stars and perhaps appear as an intermediate step in
supernova? Assuming that the flux tubes consist of nucleons (rather than nuclei), one would
have rS(113) = 64rS giving in the case of Sun rS(113) = 192 km.

(c) For k = 127 the p-adic scaling from k = 107 would give Schwartschild radius rS(127) ∼ 220rS .
For Sun this would give rS(127) = 3 × 109 m is roughly by factor 4 larger than the radius of
the solar photosphere radius 7× 108 meters. k = 125 gives a correct result. This suggests that
k = 127 corresponds to the minimal value of temperature for ordinary fusion and corresponds
to the value of dark nuclear binding energy at magnetic flux tubes.

The evolution of stars increases the fraction of heavier elements created by hot fusion and also
temperatures are higher for stars of later generations. This would suggest that the value of

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k is gradually reduced in stellar evolution and temperature increases as T ∝ 2(127−k)/2. Sun
would be in the second or third step as far the evolution of temperature is considered. Note
that the lower bound on radius of star allows also larger radii so that the allowance of smaller
values of k does not lead to problems.

2.3 What about blackhole thermodynamics?

Blackhole thermodynamics is part of the standard blackhole paradigm? What is the fate of this part of
theoretical physics in light of the proposed model?

Consider first the natural picture implied the vision about blackhole as space-filling flux tube tangle.

1. The flux tubes are deformations of cosmic strings characterized by cosmological constant which
increases in the sequence of increasing the temperature of stellar core. The vibrational degrees
of freedom are excited and characterized by a temperature. The large number of these degrees
of freedom suggests the existence of maximal temperature known as Hagedorn temperature at
which heat capacity approaches to infinity value so that the pumping of energy does not increase
temperature anymore.

The straightforward dimensionally motivated guess for the Hagedorn temperature is suggested by
p-adic length scale hypothesis as T = x~/L(k), where x is a numerical factor. For blackholes as
k = 107 objects this would give temperature of order 224 MeV for x = 1. Hadron physics giving
experimentally evidence for Hagedorn temperature about T = 140 MeV near to pion mass and near
to the scale determined by ΛQCD, which would be naturally relate to the hadronic value of the
cosmological constant Λ.

The actual temperature could of course be lower than Hagedorn temperature and it is natural to
imagine that blackhole cools down. The Hagedorn temperature and also actual temperature would
increase in the phase transition k → k − 1 increasing the value of Λ(k) by a factor of 2.

2. The overall view about the situation would be that the thermal excitations of cosmic string die out
by emissions assignable perhaps to black hole jets and also going to the cosmic string until a state
function reduction decreasing the value of k occurs and the process repeats itself.

The naive idea is that this process eventually leads to ideal cosmic string having Hagedorn temper-
ature T = ~/R and possible existing at very low temperature: this would conform with the idea
that the process is the time reversal of the evolution leading from cosmic strings to astrophysical ob-
jects as tangles of flux tube. This would at least require a phase transition replacing M107 hadron
physics with M89 hadron physics and this with subsequent hadron physics. One must of course
consider also all values of k as possible options as in the case of the evolution of star. The hadron
physics assignable to Mersenne primes and their Gaussian counterparts could only be especially
stable against a phase transition increasing Λ(k).

2.3.1 What happens to blackhole thermodynamics in TGD?

Blackhole thermodynamics (see http://tinyurl.com/y7pvj23x) has produced admirable amounts of
literature during years. What is the fate of the blackhole thermodynamics in this framework? It turns
out that the the dark counterpart of of Hawking radiation makes sense if one accepts the notion of
gravitational Planck constant assigned to gravitational flux tube and depending on masses assignable to
the flux tube. The condition that dark Hawking radiation and flux tubes at Hagedorn temperature are
in thermal radiation implying TB,dark = TH . The emerging prediction TH is consistent with the value of
the hadronic Hagedorn temperature.

1. In standard blackhole thermodynamics the blackhole temperature TB identifiable identifiable as the
temperature of Hawking radiation (see http://tinyurl.com/md6mmvg) is essentially the surface

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gravity at horizon and equal to TB = κ/2π = ~/4πrS is analogous to Hagedorn temperature as far
as dimensional analysis is considered. One could think of assigning TB to the radial pulsations of
blackhole like object but it is very difficult to understand how the thermal isolation between stringy
degrees of freedom and radial oscillation degrees of freedom could be possible.

2. The ratio TB/TH ∼ Lp/4πrS would be extremely small for ordinary value of Planck constant.
Situation however changes if one has

TB =
~eff
4πrS

, (2.2)

with ~eff = n~0 = ~gr, where ~gr is gravitational Planck constant.

The gravitational Planck constant ~gr was originally introduced by Nottale [1] [10, 9] assignable to
gravitational flux tube (presumably non-monopole flux tube) connecting dark mass MD and mass
m (M and m touch the flux tubes but do not define its ends as assumed originally) is given by

~gr =
GMDm

v0
, (2.3)

where v0 < c is velocity parameter. For the Bohr orbit model of inner planets Nottale assumes
MD = M(Sun) and β0 = v0/c ' 2−11. For blackholes one expects that one has β0 < 1 is not too
far from β0 = 1.

The identification of MD is not quite clear. I have considered the problem how v0 and MD are
determined in [20, 19] [14]. For the inner planets of Sun one would have β0 ∼ 2−11 ∼ me/mp. Note
that the size of dark proton would be that of electron, and one could perhaps interpret 1/β0 as
the heff/~ assignable to dark protons in Sun. This would solve the long standing problem about
identification of β0.

3. One would obtain for the Hawking temperature TB,D of dark Hawking radiation with heff = hgr

TB,D =
~gr
~
TB =

1

8πβ0
× MD

M
×m . (2.4)

For k = 107 blackhole one obtains

TB,D

TH
=

~gr
~
× TB ×

L(107)

x~
=

1

8πβ0(107)
× MD

M
× L(107)m

x~
. (2.5)

For m = mp this gives

TB,D

TH
=

~gr
~
TB ×

L(107)

x~
=

1

8πxβ0(107)
× MD

M
× mp

224 MeV
. (2.6)

The order of magnitude of thermal energy is determined by mp. The thermal energy of dark
Hawking photon would depend on m only and would be gigantic as compared to that of ordinary
Hawking photon.

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4. Thermal equilibrium between flux tubes and dark Hawking radiation looks very natural physically.
This would give

TB,D

TH
= 1 (2.7)

giving the constraint

~gr
~
TB ×

L(107)

x~
=

1

8πxβ0
× MD

M

mp

224 MeV
= 1 . (2.8)

on the parameters. For M/MD = 1 this would give xβ0 ' 1/6.0 conforming with the expectation
that β0 is not far from its upper limit.

5. If ordinary stars are regarded as blackholes in the proposed sense, one can assign dark Hawking
radiation also with them. The temperature is scaled down by L(107)/L(k) and for Sun this would
give factor of L(107)/L(125) = 2−9 if one requires that rS(k) corresponds to solar radius. This
would give

TB(dark, k)→ ~gr
~
× L(107)

L(k)
TB =

2(k−107)/2

8πβ0
× MD

M
×m . (2.9)

For k = 125 and MD = M this would give TB(dark, 125) = m/2π.

The condition TB,D = TH for k = 125 would require scaling of β0(107) to β(125) = 2−9β0(107) '
2−11. This would give β0(107) ' 1/4 in turn giving x ' .66 implying TH ' 149 MeV. The
replacement of mp = 1 GeV with correct value mp = .94 GeV improves the value. This value is
consistent with the value of hadronic Hagedorn temperature so that there is remarkable internal
consistency involved although a detailed understanding is lacking.

6. The flux of ordinary Hawking thermal radiation is T 4
B/~3. The flux of dark Hawking photons would

be T 4
B,dark/~3gr = (~gr/~)T 4

B and therefore extremely low also now also. In principle however the
huge energies of the dark Hawking quanta might make them detectable. I have already earlier
proposed that TB(hgr) could be assigned with gravitational flux tubes so that thermal radiation
from blackhole would make sense as dark thermal radiation having much higher energies.

One can however imagine a radical re-interpretation. BHE is not the thermal object emitting
thermal radiation but BHE plus gravitational flux tubes are the object carrying thermal radiation
at temperature TH = TB . For this option dark Hawking radiation could play fundamental role in
quantum biology as will be found.

7. What about the analog of blackhole entropy given by

SB =
A

4G
= π

l2Pl

T 2
B

, (2.10)

where A = 4πr2S is blackhole surface area. This corresponds intuitively to the holography inspired
idea that horizon decomposes to bits with area of order l2P ?

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The flux tube picture does not support this view. One however ask whether the volume filling
property of flux tube could effectively freeze the vibrational degrees of flux tubes. Or whether these
degrees of freedom are thermally frozen for ideal blackhole. If so, only the ends of he flux tubes
at the surface or their turning points (in case that they are turn back) can oscillate radially. This
would give an entropy proportional to the area of the surface but using flux tube transversal area
as a unit. This would give apart from numerical constant

SB =
A

4L(k)2
. (2.11)

2.3.2 Constraint from ~gr/~ > 1

What values of mass m can interact quantum gravitationally and are thus allowed in hgr for given MD?

1. The notion of hgr makes sense only for hgr > h. If one has hgr < h assume hgr = h. An alternative
would be hgr =→ h0 = h/6 for hgr < h0. This would given GMDm/v0 > ~min (~min = ~ or ~/6)
leading

m >
β0~

2rS(MD)
× ~min

~
. (2.12)

This condition is satisfied in the case of stellar blackholes for all elementary particles.

2. One can strengthen this condition so that it would satisfied also for gravitational interactions of
two particles with the same mass (MD = m). This would give

m

mPl
>

√
β0 . (2.13)

For β0 = 1 this would give m = mPl, which corresponds to a mass scale of a large neuron and
to size scale 10−4 m. β0(125) = 2−11 gives mass scale of cell and size scale about 10−5 meters.
β0(127) ' 2−12 corresponding to minimum temperature making hot fusion possible gives length
scale about 10−6 m of cell nucleus. A possible interpretation is that the structure in cellular length
scale have quantum gravitational interaction via gravitational flux tubes. Biological length scales
would be raised in special position from the point of view of quantum gravitation.

3. Also interactions of structures smaller than the size of cell nucleus with structures with size larger
the size of cell nucleus are possible. By writing the above condition as (m/mPl)(MD/mpl) > β0,
one sees that from a given solution to the condition one obtains solutions by scaling m→ xm and
MD →MD/x. For β0(127) ' 2−11 corresponding to the scale of cell nucleus the atomic length scale
10−10 m and length scale 10−4 m of large neuron would correspond to each other as ”mirror” length
scales. There would be no quantum gravitational interactions between structures smaller than cell
nucleus. There would be master-slave relationship: the smaller the scale of slave, the larger the
scale of the master.

2.3.3 Quantum biology and dark Hawking radiation

The scaling formula β0(k) ∝ 1/L(k) with flux tube thickness scale given by L(k) allows to estimate β0(k).
In this manner one obtains also biologically interesting length scales. An interesting question is whether
the scales for the velocities of Ca waves (see http://tinyurl.com/qs3j5cp) and nerve pulse conduction
velocity could relate to v0.

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1. The tube thickness about 10−4 m, which corresponds to ordinary cosmological constant being in
this sense maximal corresponds to the p-adic length scale k = 171. The scaling of β0 ∝ 1/L(k) gives
v0(171) ∼ 4.7 µm/s In eggs the velocity of Ca waves varies in the range 5-14 µm/s, which roughly
corresponds to range k ∈ {171, 170, 169, 168}.
In other cells Ca wave velocity varies in the range 15-40 µm/s. k = 165 corresponds to 37.7
µm/s near the upper bound 40 µm/s. The lower bound corresponds to k = 168. k = 167, which
corresponds to the larges Gaussian Mersenne in the series assignable to k ∈ {151, 157, 163, 167} the
velocity is 75 µm/s.

2. For k = 127 gives v0 ∼ 75 m/s. k = 131 corresponds to v0 = 18 m/s. These velocities could
correspond to conduction velocities for nerve pulses in accordance with the view that the smaller
the slave, the larger the master.

I have already earlier considered that dark Hawking radiation could have important role in living
matter. The Hawking/Hagedorn temperature assuming x = 1/6.0 k = L(171) has peak energy 38
meV to be compared with the membrane potential varying in the range 40-80 meV. Room temperature
corresponds to 34 meV. For k = 163 defining Gaussian Mersenne one would have peak energy about .6
eV: the nominal value of metabolic energy quantum is .5 eV. k = 167 corresponds to .15 eV and 8.6 µm -
cell size. Even dark photons proposed to give bio-photons when transforming to ordinary photons could
be seen as dark Hawking radiation: Gaussian Mersenne k = 157 corresponds to 4.8 eV in UV. Could
CMB having peak energy of .66 meV and peak wavelength of 1 mm correspond to Hawking radiation
associated with k = 183? Interestingly, cortex contains 1 mm size structures.

To sum up, these considerations suggest that biological length scales defined by flux tube thickness
and cosmological length scales defined by cosmological constant are related.

2.4 Zero energy ontology, cosmology, and astrophysics

Zero energy ontology replaces ordinary ontology in TGD based view about quantum states and quantum
jump [26].

1. 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 M4 and of CP2. 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.

2. 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.

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

4. 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.

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

(a) 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.

(b) The alternative view suggested strongly M8 −H duality [12] 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 M8 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 = heff/h0 serves as a kind of IQ, one can say
that the system becomes more intelligent.

2.4.1 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 http://tinyurl.com/o6vyb9g) 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 heff = 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 Earth. I have proposed a TGD variant of Expanding Earth hypothesis
along these lines [21].

2.4.2 Stars as reincarnating conscious entities?

One can apply ZEO to the evolution of stars. The basic story (see http://tinyurl.com/ceoo6sj) 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 http://tinyurl.com/s698l86). There is also evidence that the abundances of heavier

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elements in the early cosmology are essentially the same as for modern stars [3] (see http://tinyurl.

com/qkk26dv). TGD based explanation is discussed in [25].
Karma’s cycle option for the stellar evolution could explain these anomalies.

1. Stars would be selves in Karma’s cycle with their magnetic bodies reincarnating with a reversed ar-
row 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 corre-
sponding 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.

2. 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.

To put it more generally, the hierarchy of CDs implies that the Universe decomposes effectively to
sub-Universes behaving to some degree independently. The view about Karma’s cycles provides a more
precise formulation of the pre-ZEO idea that systems are artists building themselves as 4-D sculptures.
In particular, this applies to mental images in TGD based view about brain.

1. 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. M8 −H duality [12] predicts that the time evolution for space-time
surface inside CDs decomposes to a sequence of deterministic evolutions glued together along M4

time t = rn hyperplanes of M4 defining special moments in the life of self at which the new larger
CD receives a new root t = rn. 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.

2. The M4 hyperplanes t = rn correspond to the roots of a real polynomial with rational coefficients
defining the space-time surfaces at the level of M8 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.

3. The finite classical non-determinism is in accordance with the classical non-determinism is 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 CP2 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 = rn becomes dense and the dynamics becomes non-deterministic for
vacuum extremals and implies non-determinism for non-vacuum extremals.

2.4.3 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
[7]. 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

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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 [8]. 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 [13] 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.

1. 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 M4 linear coordinates and light-cone Robertson-Walker coordinates
are natural coordinates for space-time sheets with 4-D M4 projection.

”Clock time” must be mapped to M4 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 M4 coordinates of the target and observer are related by a Lorentz
boost and this gives rise to cosmological redshift and also gravitational reshift.

2. 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 M4 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.

2.4.4 Did cosmology have any ”Dark Ages”?

A further potential time anomaly of the recent cosmology relates to theDark Agesof the Universe. Between
the decoupling of CMB radiation from matter and the formation of stars there should have been aDark
Agesduring which there was only neutral hydrogen. Star formation generated radiation at energies high
enough to ionize hydrogen and the ionized interstellar gas started to produce radiation.

The 21 cm line of neutral hydrogen serves as a signature of neutral hydrogen. This line is redshifted
and from the lower bound for the redshift one can deduce the time when ”Dark Ages” ended. The popular
article tells (see http://tinyurl.com/wzegzxk) that the recent study using Murchison Widefield Array
(MWA) radio telescope by Jonathan Pober and collaborators gave an unexpected result. Only a new
lower upper bound for this redshift emerged: the upper bound corresponds to about 2 meters [5] (see
http://tinyurl.com/qttq3gl). The conclusion of the experimenters is optimistic: soon the upper bound
for the redshift should be brought to light.

In TGD based view about cosmology and astrophysics (http://tinyurl.com/tkkyyd2) one can for-
mulate two questions.

1. One can ask whether there were any ”Dark Ages” at all!

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2. An alternative question is whether the ”Dark Ages” in distant geometric past are prevailing anymore!
This would be like asking whether the Hitler of thirties is the Hitler we know anymore. The point
is that in TGD framework one must distinguish between subjective time and geometric time and
this leads to some rather dramatic modifications of the prevailing view about time. The following
arguments encourage a positive answer to the first question and negative answer to the second
question.

The following arguments encourage positive answer to the first question and negative answer to the
second question.

The answer to the first question relies of TGD based view about nuclear physics solving anomalies of
standard nuclear physics and leading to a new view about stellar evolution.

1. In TGD framework the formation of stars could have preceded by a pre-stellar period during which
dark fusion giving rise to dark proton sequences - dark nuclei - at monopole flux tubes happened:
this is Pollack effect in biology. This would have been ”cold fusion” period in the stellar evolution
and would have occurred spontaneously at low temperatures. It would have already produced abun-
dances, which are not far from modern ones and one of the recent surprises is that the abundances
at very early period are already near to modern ones.

2. The model predicts also the possibility of neutral states for which electrons are at flux tubes parallel
to dark proton flux tubes and have the same scaled up size (due to non-standard value of heff = nh0,
which is smaller by factor about 1/2000) as dark protons. In solar interior dark protons would have
Compton size of electron so that heff for them would be about 2000 times higher H = M4 × CP2

than h. Also smaller and larger value of heff are possible. For blackholes the protons at flux tubes
would be ordinary: heff = h.

3. The transformation of dark nuclei having much smaller binding energy would have liberated nuclear
binding energy and the resulting photons having energy up to gamma ray energies would have ionized
the neutral hydrogen.

Zero energy ontology (ZEO) leads to a negative answer to the question whetherDark Ages still prevail
in distant past.

1. In ZEO Universe consists at the level of imbedding space H = M4 × CP2 of a fractal hierarchy of
CD = cd × CP2, where cd is causal diamond of M4. CDs have interpretation as a hierarchy of
sub-cosmologies. Each CD defines a correlate for a conscious entity and increases in size in each
”small” state function reduction (SSFR) defining a counterpart of weak measurement. The flow of
experienced time corresponds to the increase of distance between tips of CD. Second boundary of
CD is however fixed - passive - as also members of state pairs at it defining zero energy states. The
active boundary recedes farther away from the passive one. This gives rise to the arrow of time for
given life of CD.

2. In a ”big” (ordinary) state function reduction (BSFR) the roles of boundaries of CD change. Active
becomes passive and vice versa. The arrow of time changes. Self dies and reincarnates with opposite
arrow of time. The simplest possibility is that the size of CD can decrease in BSFR meaning that
the formerly passive boundary becomes much nearer to active. In this case CD begins to grow from
a small size: self has ”childhood”. In this case it can happen that self never reaches a size larger
than some upper bound and lives again and its life. Each life is more evolved since the extension
of rationals involved with space-time surface increases in statistical sense in BSFR. This is nothing
but Karma’s cycle but in all scales.

3. At the level of stars this would mean that star could undergo evolution as Karma’s cycle also in
cosmological remote past as an object located at fixed point of H. The abundances would be more or

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less the same as for modern stars. This would explain the mystery of stars older than the Universe
and solve also other time anomalies of the standard cosmology. This explanation is consistent with
the first one and actually the first one is needed to explain abundances of nuclei heavier than Fe
and the light nuclei Li, B, Be much higher than predicted by standard model. Thus both questions
would have positive answer.

2.4.5 Observation of a time reversal of a blackhole like object?

A very strange object behaving like time reversal of blackhole has been observed (http://tinyurl.com/
umzxaoe). Usually blackhole eat the surrounding matter and also prevent the formation of stars since they
are powerful emitters of gamma rays - this is not in accordance with the naive view about blackholes. The
weird blackhole does not emit gamma rays and the environment around it cools and this makes possible
star formation. Instead of eating the surrounding matter it should feed matter to surroundings making
possible the star formation.

The most obvious TGD identification of the mystery object relies on zero energy ontology allowing
both arrow of time. The arrow of time chances in ordinary state function reduction - the ”big” one as
opposed to ”small” one corresponding to weak measurement. This predicts time reversed blackhole like
objects (BHEs) analogous to white holes: white hole like objects (WHEs).

WHEs could appear in the very early states of the galactic evolution. They could feed the magnetic
energy of monopole flux tubes to environment transformed to ordinary matter in turn forming galaxies.
As a matter of fact, monopole flux tubes portions emanating it much lines of magnetic field would be
formed and their local thickening and formation of tangles would give rise to stars.

If the time reversal idea is taken very seriously WHEs should suck gamma rays from environment
inducing cooling making the star formation easier. This would be dissipation in non-standard direction of
time identifiable as the basic metabolic mechanism associated with all kinds of self-organization process:
quantum coherence at the level of magnetic body would be essential and induce long range coherence of
ordinary matter as forced coherence.

WHE could be also created in BSFR for a BHE.

2.4.6 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 chang-
ing 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.

1. 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 heff 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.

2. 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.

This raises also the question whether the evolution of stars could be seen as a time reverse for the
formation of blackholes: kind of growth followed by a decay perhaps since the values of Planck constant
heff would be reduced. The climax of his evolution would correspond to maximal values of heff . The
evolution of life would be certainly this kind of climax.

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2.5 Objections against GRT blackholes

The basic theoretical objection against blackholes was due to Einstein himself. The collapse of matter to
single point is simply impossible. This objection has been however forgotten since doing calculations is
much more pleasant activity than hard thinking, and an enormous literature have been produced based on
this idealization. There is no doubt that blackhole like entities (BHEs) with about Schwartschild radius
exist, but general relativity does not allow to say anything about the situation inside possibly existing
horizon.

2.6 Badly behaving blackholes

There is an excellent video (thanks to Howard Lipman for a link) challenging the standard view about
blackholes. In the sequel list some arguments that I remember.

TGD was born as a solution to the fundamental difficulty of GRT due to the loss of classical conser-
vation laws. In TGD framework BHEs correspond to volume filling flux tube tangles. Also galactic BHEs
would correspond to a volume filling flux tube tangles.

In TGD framework also stars could be seen as BHEs having the flux tube thickness characterized by
p-adic length scale as an additional parameter. GRT blackholes correspond to flux tube thickness about
proton Compton length. For instance, Sun can be seen as a BHE and the size is predicted correctly.

The model for BHEs makes large number of correct predictions.

1. The minimal radii/masses of GRT blackholes and neutron stars are predicted correctly.

2. Ordinary blackhole thermodynamics is replaced with the thermodynamics associated with monopole
flux tubes carrying galactic dark mass characterized by Hagedorn temperature and the thermody-
namics gravitational flux tubes characterized by Hawking temperature but for gravitational Planck
constant hgr so that it is gigantic as compared to the ordinary Hawking temperature.

In thermal equilibrium these temperatures are same and this predicts hadronic string tension cor-
rectly.

Consider now the empirical objections against BH paradigm in light of TGD picture.

1. The observations by ALMA telescope show that stars can be formed surprisingly near to galactic
BHEs (see http://tinyurl.com/ry746pg). For instance, 11 young stars just forming have been
found at distance of 3 ly from galactic BHE of Milky Way. This is impossible since the intense
tidal forces and UV and X ray radiation should make impossible the condensation of stars from gas
clouds.

TGD explanation: Galaxies are formed as tangles on long thickened cosmic string responsible for
galactic dark matter as dark energy. Same mechanism give rise to stars as sub-tangles generating
at least part of the ordinary matter as decay of the magnetic energy of the flux tube as it thickens.
Ordinary matter already present could concentrate around the tangle.

One learns from the discussion in the above link that star formation involves bipolar flow consisting
two jets in opposite directions believed to take care of angular momentum conservation: the star
formed is thought to be formed from a rotating gas cloud (rotation would be around flux tube)
having much larger angular momentum and part of must be carried out by jets naturally parallel
to the flux tube. Also this gives support for the view that stars are tangles along flux tube. There
are also hundreds of massive and much older stars in the vicinity of galactic BHE.

Note that in TGD also these stars could be seen as BHEs but with different p-adic length scale
characterizing the thickened flux tube. The reason why galactic BHE does not swallow these objects
could be that they are bound states around flux tube (or even cosmic string outside the star), which
is rather rigid by its string tension.

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2. ”Non-hungry” BHEs are found.

TGD explanation: In zero energy ontology to which quantum TGD relies, one must distinguish
between BHEs and their time reversals, white hole like objects (WHEs), analogous to white holes.
WHEs would not be ”hungry” but feed matter into environment. The counterparts or jets would
flow into WHE and matter would flow out from WHE.

3. The standard theoretical belief is that in a dense star cluster only single blackhole can exist. If
there are several blackholes, they start to rotate around each other and fuse to a larger blackhole.
A case with two blackholes have been however observed.

TGD explanation: A possible explanation is that the objets are WHEs and their behavior is time
reversal of BHEs.

4. The velocities of particles in the jets associated with a galactic BHEs are near light velocity and
require extremely high energies and thus strong magnetic fields. No strong magnetic field has been
however observed.

TGD explanation: In TGD Maxwellian magnetic fields are replaced with flux tubes carrying
quantized monopole flux not possible in Maxwellian world. Their existence allows to understand
the presence of magnetic fields in even cosmological scales, the maintenance problem of Earth’s
magnetic field, and the recent findings about the magnetic field of Mars [24]. Ordinary magnetic
fields correspond to vanishing total flux and are indeed weak: it is these magnetic fields outside the
jet which would have been measured. Galaxies are tangles in monopole flux tube and this is the
carrier of very strong magnetic field associated with jets parallel to the flux tube.

5. Very distant galactic blackholes with distances in scale of million light years have radio jets in the
same direction. This is very difficult to understand in the standard view about cosmology.

TGD explanation: The galactic BHEs would be associated with the same long cosmic string
forming galaxies as tangles.

2.6.1 Too heavy blackhole in Milky Way

The standard model for blackhole formation predicts an upper bound on the mass of blackhole depending
also on environment since the available amount of matter in environment is bounded. In the case of Milky
Way the bound is about 20 solar masses. Now however a blackhole like entity (BHE) with mass about
70 solar masses has been discovered (see http://tinyurl.com/w7xlb78). I am grateful for Wes Johnson
for the link. Also the masses of BHEs producing the gravitational radiation in their fusion have been also
unexpectedly high, which suggets that standard view about BHEs is not quite correct.

The proposed model for BHEs as a volume filling flux tube gives correct lower bounds for masses
of neutron star and TGD counterpart of blackhole but does not give upper bound for the mass. For
time reversed BHEs - analogs of white holes (WHEs) possibly identifiable as quasars - the mass of WHE
comes from a tangling long cosmic string and there is no obvious upper bound. Even galactic BHEs could
correspond to WHEs, which have made quantum jump to BHEs at the level of magnetic body: in this
state the flux tube forming the counterpart of Maxwellian magnetic field is fed back from environment.
A breathing spaghetti would be in question.

In standard model the mechanism for the formation of blackhole is different since there is no flux tube
giving the dominant dark energy/dark matter contribution to the mass. Therefore the upper bound for
mass - if there exists such - is expected to increase. In TGD framework the dominant contribution would
come from the monopole flux tubes giving rise TGD counterpart of magnetic field which extends at least
over the region containing stars assumed to correspond sub-tangles of the galactic flux tangle. Intuitively
it seems clear that the upper bound is higher than in GRT. If the spaghetti straightens - the tangled flux
tube would untangle - one could have upper bound.

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The simplest model predicts that only the flux tube mass contributes to the mass of BHE. The mass
of the ordinary matter going to BHE would transform back to dark energy/mass of the flux tube. The
process would be time reversal of the process making sense in zero energy ontology [26] in which the
magnetic energy of flux tube transforms to ordinary matter: time reversal for the TGD counterpart of
inflation.

3 Anomalies related to galactic dynamics

Wes Johnson sent also two links related to the long range correlation between the dynamics of quasars
and galaxies. The first result was about correlations of quasar spins in billion light-year scale. Second
result was about coherence between the galactic spin and motions of surrounding galaxies at least up to
6 Mly. The explanation of both findings is in terms of cosmic strings thickened to flux tubes, which are
the basic element in the TGD based model for the formation of quasars and galaxies. Third anomaly
relates to ”too” fast spinning galaxies.

3.1 Correlated galactic spins in billion light-year scale

The first link is to a popular article ”Alignment of quasar polarizations with large-scale structures (see
http://tinyurl.com/rcoam7g) telling about alignment of quasar polarization with large scale structure
in scale of Gly, which is a really huge scale. This suggests that the quasar spin axes are aligned with a
linear structure connecting the quasars.

The correlations between spin directions of quasars over distances of billion light-years have been
observed. These correlations have been observed earlier over much shorter distances for quasars/galaxies
along the well-known linear structures. This suggests that the linear structures are much longer than
previously thought.

This is what I have been preaching for decades. There would exist a fractal tensor network of cosmic
string/monopole flux tubes over entire cosmos having local flux tube tangles as nodes. Networks inside
networks inside.... The flux tubes would carry dark matter in TGD sense making possible quantum
coherence in arbitrarily long length scales.

1. TGD predicts a fractal hierarchy of flux tubes formed from cosmic strings: 4-D surfaces in M4×CP2

having 2-D strings world sheet as M4 projection.

2. Galaxies reside along linear structures which would correspond to what I call cosmic strings: galaxies
would be tangles along these strings thickened locally to monopole flux tubes: part of their magnetic
energy would have transformed partially to matter and formed the visible part of galaxy. Volume
energy would correspond to length scale dependent cosmological constant. They would explain also
flat velocity spectra associated with spiral galaxies. There would be no dark matter halo.

Cosmic strings and their monopole flux tube portions would be remnant from cosmic string dom-
inated period, which transformed to GRT type cosmology via an inflation type period as cosmic
strings thickened to flux tubes. These strings containing the galaxies as tangles would form a net-
work correlating the dynamics of individual galaxies and making possible correlations and synchrony
even over distances of about 1 billion ly.

3. The correlations between spin directions of galaxies is what has been been could be inherited
from past when the galaxies along strings were much closer to each other. Angular momentum
conservation would take care that correlation are preserved.

4. Macroscopic quantum coherence even in cosmological scales is however possible by hierarchy of
Planck constants explaining dark matter as heff = n× h0 phases of ordinary matter. We could be
seeing quantum coherence of dark matter inducing ordinary coherence of matter in cosmic scales.

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Remark: I have asked whether all self-organization phenomena involving energy feed (needed to
increase heff responsible for quantal long range correlations at dark level) could be induced by dark matter
at magnetic flux tubes [23]. A further interesting question is whether self-organization is dissipation in
reversed time direction so that also it would be due to second law but in generalized sense required by
ZEO.

3.2 Mysterious coherence in several-megaparsec scales between galaxy rota-
tion and neighbor motion

Second link was to article ”Mysterious Coherence in Several-megaparsec Scales between Galaxy Rotation
and Neighbor Motion” by Lee et al (see http://tinyurl.com/sbmcn6g). The article states that there is
a ”mysterious” coherence between the rotational direction of galaxy and the average motion of its nearest
neighbours within 6 MPc, possibly even up to 11 MPc. This coherence cannot result from collisions with
nearby galaxies like coherence below 1 MPc and is proposed to originate from the collective motion of a
structure containing the galaxies affecting the directions of angular momenta of galaxies: the coherence
would be induced from that of the collective motion.

In TGD framework the natural identification for the collective structure would be as a long monopole
flux tube containing the galaxies or at least a subset of them as tangles. There could be of course several
monopole flux tubes in the sample studied. It was indeed found that the coherence was especially strong
when neighbors of the galaxy at center were restricted to red galaxies. Red galaxies could correspond
to the same flux tube. Alternatively, the collective motion affects them less than other galaxies as the
article suggests.

3.3 Galaxies spinning ”too” fast

The anomalous findings relating to cosmology and astronomy are proliferating I am grateful for Wes
Johnson for a flow of links. This particular link (see http://tinyurl.com/qv2vpw3) gives pictures
provided by NASA about spiral galaxies spinning ”too” fast. The problem is that centrifugal acceleration
destabilizes the system spinning too fast. This suggests that the structure of galaxy is not what our
models involving ordinary matter and dark matter halo are somehow wrong. TGD suggests an improved
view allowing to understand also ”too” fast spinning rates.

Suppose that galaxies are tangles along monopole cosmic string such that string has thickened to
flux tube. Monopole cosmic string would be rotating. These monopole tangles would serve as TGD
counterparts for the magnetic field of galaxy which has no Maxwellian counterpart. No currents are
needed for their maintenance.

1. Monopole flux tube has closed cross section, which is non-contractible 2-surface, pinch is impossible.
In other words, the conservation of monopole flux prevents its splitting so that centrifugal acceler-
ation cannot break the flux tube even at the highest spinning velocities. Only radial deformation
increasing the size is possible.

2. Ordinary matter - generated as the magnetic energy of the flux tubes has transformed to ordinary
matter in process analogous to inflation - in turn is gravitationally bound with the flux tube so that
the galaxy manages to keep also the ordinary matter.

3.4 Galaxy which existed 1 billion years after Big Bang

Galaxy GN-z11 (see http://tinyurl.com/tg7sscu) existed 1 billion years after the Big Bang and gave
rise to stars with a rate much faster than Milky Way. There should have been any stars giving rise to the
galaxies by the usual mechanism of gravitational condensation.

TGD explanation is simple. Galaxies formed as tangles to long cosmic string, which thickened and
liberated part of its magnetic energy to ordinary matter, which formed the stars of the galaxy as local

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tangles inside tangle. The formation of stars was faster because local cosmological constant was larger
and the rate for the transformation of magnetic energy to ordinary matter was higher. The periods of
star formation should correspond to the phase transitions decreasing the local cosmological constant.

Also in younger galaxies the star formation is highest near the galactic blackhole, even at distances
smaller than 3 ly, where it should not happen at all. The mechanism would be the same. For the flux
tubes extending farther from galactic center the local cosmogical constant is smaller and the rate for the
formation of stars is slower.

4 Local super-cluster Laniakea as flux tube structure

In the following I try to concretize the ideas about monopole flux tube network as a basic structure
behind formation of astrophysical structures by discussing the supercluster Laniakea in this framework
(the idea came from the question of Wes Johnson about how I understand Laniakea in TGD framework).
There are two excellent videos about Laniakea (see https://www.youtube.com/watch?v=rENyyRwxpHo

and http://tinyurl.com/ufvw6v5).
Consider first the structure of Laniakea.

1. Wikipedia contains a nice article about Laniakea (see http://tinyurl.com/zfphldm). Laniakea is a
local supercluster containing also Milky Way so that it is own home supercluster. Local supercluster
is defined as a basin of a local flow of galaxies directed to the center of the super-cluster.

There is a video giving view about the structure and dynamics of Laniakea is warmly recommended
(see https://vimeo.com/104910552). Laniakea contains about 105 galaxies, decomposes to four
smaller super-cluster like entities and contains about 500 galaxy clusters.

2. The general picture supports the idea about fractal spaghetti formed by monopole flux tube or
several of them. The presence of four smaller super-cluster type entities suggests quadrupole field
as a rough starting point as one tries to gues the analog as field line topology. The first very naive
guess is that the tangle defining the supercluster represents roughly the topology of quadrupole
magnetic field in the first approximation: there would be pair of dipoles. One cannot of course fix
the number of cosmic strings.

The simplest starting point hypothesis is that there is just single closed cosmic string forming a
structure analogous to that of quadrupole magnetic field. Reconnection can split smaller closed
cosmic string from a closed cosmic string and this could correspond to a decay of galaxy to smaller
galaxies. Therefore single cosmic string is certainly an approximation.

Remark: Recall that cosmic strings are closed and one can have for instance helical structures: say
two closed cosmic strings analogous to DNA double strands or single closed single having strands
as pieces of it.

Remark: Also non-monopole flux tubes are involved and the proposal is that gravitational interac-
tions are mediated along these flux tubes emanating radially from the source. The flux for them is
vanishing and there is no current needed to create the field. These flux tubes are not topologically
stable against splitting.

3. Cosmic strings are assumed to form a fractal hierarchy and that in TGD inspired biology cosmic
strings thickened to monopole flux tubes are behind various linear biomolecules organized around
them as ordinary matter. This leads to ask whether DNA double strand and the organization of
DNA double strands to chromosomes might be more general phenomenon. Chromosomes consist of
4 strands, which allows to ask whether something similar happens even at the level of superclusters
and that the topology of quadrupole field is involved.

Interestingly, also Milky Way consists of four arms assignable spiral density waves for ordinary
matter so that it is not clear whether the arms can be assigned with four poles of quadrupole.

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Fermi spheres are a peculiarity Milky Way possibly possibly related to a quadrupole structure of
monopole flux tube topology suggesting two cosmic strings meeting at the nucleus of galaxy. There
is evidence that Milky Way could be seen as being formed in a kind of cosmic collision. I have
asked whether this is due to a cosmic highway accident at crossroad at which two cosmic string are
pass by very near to each other is in question. This could make sense if tangle as a quadrupole
corresponds to two dipoles.

Consider next the dynamics of Laniakea. Reader can build his/her own views with the help of
the beautiful videos (see https://www.youtube.com/watch?v=rENyyRwxpHo and http://tinyurl.com/

ufvw6v5) demonstrating the velocity flow of visible parts of galaxies, which would be associated with
tangles moving along cosmic strings.

1. Wikipedia mentions that Laniakea is not gravitationally bound. Also this suggests that the galaxies
associated with it are tangles of one or more cosmic strings. The dynamics would correspond to s
motion in gravitational field with constraint forcing the galaxy to move along the cosmic string.

2. The motion of galactic tangles and that of ordinary matter formed from it along cosmic string is free
in absence of external forces: this distinguishes TGD from halo model having a spherical symmetry.
This would mean rather lose binding but strong correlation produced by the cosmic string. Most
galaxy motions are directed inward towards Great Attractor: this would have explanation in terms
of gravitational attraction. A good guess is that motion are along flux tube/cosmic string.

References

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Published by QuantumDream, Inc.

https://www.youtube.com/watch?v=rENyyRwxpHo
http://tinyurl.com/ufvw6v5
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Published by QuantumDream, Inc.

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	Introduction
	Brief description of the model for for the formation of galaxies and stars
	The notion of length scale dependent cosmological constant

	Blackholes, quasars, and galactic blackholes
	Blackholes in TGD framework
	Can one see also stars as blackhole like entities?
	What about blackhole thermodynamics?
	What happens to blackhole thermodynamics in TGD?
	Constraint from gr/>1
	Quantum biology and dark Hawking radiation

	Zero energy ontology, cosmology, and astrophysics
	Cosmic redshift but no expansion of receding objects: one further piece of evidence for TGD cosmology
	Stars as reincarnating conscious entities?
	No time dilation for the periods of processes of quasars
	Did cosmology have any "Dark Ages"?
	Observation of a time reversal of a blackhole like object?
	Do quasars and galactic blackholes relate by time reversal in ZEO?

	Objections against GRT blackholes
	Badly behaving blackholes
	Too heavy blackhole in Milky Way


	Anomalies related to galactic dynamics
	Correlated galactic spins in billion light-year scale
	Mysterious coherence in several-megaparsec scales between galaxy rotation and neighbor motion
	Galaxies spinning "too" fast
	Galaxy which existed 1 billion years after Big Bang

	Local super-cluster Laniakea as flux tube structure

