Introduction
The local sun (Sol aka Rahsol) is a typical star of spectral class G2V on the Hertzsprung-Russell diagram.
It is a
'garden variety' yellow main sequence dwarf star consisting of about 70% hydrogen and 28% helium and a 2%
remainer of mainly oxygen and carbon.
Its mass is about 2x1030 kg and its average radius 7x108
m with a core radius of so 2x108 meters.
At the center, the temperature is estimated to be about
14 million Kelvin, differentiating to a surface (photosphere) temperature of about 5700 Kelvin.
Above the Photosphere,
the Chromosphere increases the surface temperature into the Corona to a order of 100,000 Kelvin, about 10,000 km above the
surface.
The outermost layer of the Sun's atmosphere, the Corona extends for millions of km into extrasolar space
and harbours the Solar Wind with temperatures characterised in the 1-2 Million Kelvin range.
Rahsol is the gravitational
center for a typical solar system from the central star to the outermost planets (Neptune at about 30 AUs and Pluto at
so 40 AUs).
Just as Jupiter dominates the Asteroid Belt; Neptune dominates the (trans-Neptunian) Kuiper Belt (asteroids
found mainly between 2.2-3.3 AUs with a center of mass at Ceres at 2.8 AU) up to about 55 AUs.
A doughnut-disc-shaped
Inner Oort-Cloud (aka Hills Cloud) harbours long-period Comets as an inner comet distribution up to a lower
boundary of so 2,000-20,000 AUs extending out to 100,000-200,000 AUs as a spherical Outer Oort-Cloud as the gravitational
upper boundary for the selfinteracting local solar starsystem.
.
One Astronomical Unit or 1 AU is about 150 million
kilometers as the distance of the planet earth from the local star Sol. One lightyear 1 ly~63,000 AUs or 9.47x1012
km or 0.307 parsec (pc).
The local star Rahsol is one of about 400 billion suns in the local galaxy called the
Milky Way.
The Milky Way is a 'Barred Spiral Galaxy' (type SBbc) and has a mean radius of 50,000 lightyears or
about 4.8x1017 km, incorporating a central bar of radius so 13,000 lightyears or 1.2x1017 km. The length
of this bar at 26,000 ly is about the same as the distance of the star Sol from the galactic center, where a 'Radio
Source Sagittarius A* occupies a core galactic region encompassing a star-accreting region of radius about the size of the
Inner Oort-Cloud or the Hills Belt.
Sagittarius A* is resolved at the displacement scale of D=26,000 ly at 1/3600
arcseconds (as) per degree for 2πD/(360.3600)~1.2x1015 as and observed as occupying an angular area of so 400
microas2 (μas)2.
This infers a SuperMassive Black Hole (SMBH) Mass of 4 million solar masses
(8x1036 kg) for a (not gravitationally lensed) area with Schwarzschild radius RS=2x1010
meters (which is within the orbit of Mercury about the sun at 0.39 AUs or so 5.8x1010 meters).
About
this SMBH at the galaxy's core is found an accretion disk of (relatively) young stars to a distance of so 10 lightdays
(2.6x1014 meters or 1800 AUs). This star distribution obeys the orbital laws expected by objects orbiting a 'central
pointmass', such as a SMBH.
The extended 'Halo-DarkMatter' scale of the Milky Way then increases the galactic
neighbourhood interaction radius to about 300,000 lightyears (3x1021 meters) as the displacement scale for the
'Local Group' and becomes 'Group-Galactic' at 6 million lightyears (6x1022 meters) for the interaction
between large galaxies, such as the Milky Way and Andromeda aka M31 (type SB) about 2.6 million ly apart and approaching each
other at so 130 km/s.
1. Hypersphere volumes and the mass of the
Tau-neutrino
Consider the universe's thermodynamic expansion to proceed at an initializing time (and practically at lightspeed for the lightpath x=ct describing the hypersphere radii)
to from a single spacetime quantum with a quantized toroidal volume 2π²rw³ and where rw
is the characteristic wormhole radius for this basic building unit for a quantized universe (say in string parameters given in the Planck scale and its transformations).
At a time tG, say so 18.85 minutes later, the count of space time quanta
can be said to be 9.677x10102 for a universal 'total hypersphere radius' of about rG=3.39x1011 meters and for a G-Hypersphere volume of so 7.69x1035cubic
meters.
{This radius is about 2.3 Astronomical Units (AUs) and about the distance of the Asteroid Belt from the star Sol in a typical (our) solar system.}
This modelling of a mapping of the quantum-microscale
onto the cosmological macroscale should now indicate the mapping of the wormhole scale onto the scale of the sun itself.
rw/RSun(i)=Re/rE for RSun(i)=rwrE/Re=1,971,030
meters. This gives an 'inner' solar core of diameter about 3.94x106 meters.
As the classical
electron radius is quantized in the wormhole radius in the formulation Re=1010rw/360, rendering
a finestructure for Planck's Constant as a 'superstring-parametric': h=rw/2Rec3;
the 'outer' solar scale becomes RSun(o)=360RSun(i)=7.092x108 meters as the observed
radius for the solar disk.
19 seconds later; a F-Hypersphere radius is about rF=3.45x1011
meters for a F-count of so 1.02x10103 spacetime quanta.
We also define an E-Hypersphere radius at rE=3.44x1014
meters and an E-count of so 10112 to circumscribe this 'solar system' in so 230 AU.
We so have
4 hypersphere volumes, based on the singularity-unit and magnified via spacetime quantization in the hyperspheres defined
in counters G, F and E. We consider these counters as somehow fundamental to the universe's expansion, serving as boundary
conditions in some manner. As counters, those googol-numbers can be said to be defined algorithmically and independent on mensuration physics of any kind.
2. The mapping of the atomic nucleus onto the thermodynamic universe of the hyperspheres
Should we consider the universe to follow some kind of architectural blueprint; then we might attempt to
use our counters to be isomorphic (same form or shape) in a one-to-one mapping between the macrocosmos and the microcosmos. So we define a quantum geometry
for the nucleus in the simplest atom, say Hydrogen. The hydrogenic nucleus is a single proton of quark-structure udu and which
we assign a quantum geometric template of Kernel-InnerRing-OuterRing (K-IR-OR), say in a simple model of concentricity.
We set the up-quarks (u) to become the 'smeared out core' in say a tripartition uuu so allowing a substructure for
the down-quark (d) to be u+InnerRing. A down-quark so is a unitary ring coupled to a kernel-quark. The proton's quark-content
so can be rewritten and without loss of any of the properties associated with the quantum conservation laws; as proton→udu→uuu+IR=KKK+IR.
We may now label the InnerRing as Mesonic and the OuterRing as Leptonic.
The OuterRing is so definitive for the strange
quark in quantum geometric terms: s=u+OR.
A neutron's quark content so becomes neutron=dud=KIR.K.KIR with a 'hyperon
resonance' in the lambda=sud=KOR.K.KIR and so allowing the neutron's beta decay to proceed in disassociation from
a nucleus (where protons and neutrons bind in meson exchange); i.e. in the form of 'free neutrons'. The neutron decays
in the oscillation potential between the mesonic inner ring and the leptonic outer ring as the 'ground-energy' eigenstate.
There actually exist three uds-quark states which decay differently via strong, electromagnetic and weak decay rates in the uds (Σo* =Sigmao Resonance); usd (Σo=Sigmao) and the sud (Λo=Lambdao)
in increasing stability. This quantum geometry then indicates the behaviour of the triple-uds decay from first principles,
whereas the contemporary standard model does not, considering the u-d-s quark eigenstates to be quantum geometrically undifferentiated.
The nuclear interactions, both strong and weak are confined in a 'Magnetic Asymptotic Confinement Limit' coinciding with the Classical Electron radius Re=ke²/mec² and in a scale of so 3 Fermi or 2.8x10-15 meters. At a distance further
away from this scale, the nuclear interaction strength vanishes rapidly. The wavenature of the nucleus is given in the Compton-Radius Rc=h/2πmc with m the mass of the nucleus, say a proton; the latter so having Rc=2x10-16
meters or so 0.2 fermi.
The wave-matter (after de Broglie generalising wavespeed vdB from c in Rc) then relates the classical electron radius as the 'confinement
limit' to the Compton scale in the electromagnetic finestructure constant in Re=Alpha.Rc.
The
extension to the Hydrogen-Atom is obtained in the expression Re=Alpha².RBohr1 for the first Bohr-Radius as the 'ground-energy' of so 13.7 eV at a scale of so 10-11 to 10-10 meters (Angstroems).
These 'facts of measurements' of the standard models now allow our quantum geometric correspondences to assume cosmological
significance in their isomorphic mapping. We denote the OuterRing as the classical electron radius and introduce the InnerRing
as a mesonic scale contained within the geometry of the proton and all other elementary baryonic- and hadronic particles.
Firstly, we define a mean macro-mesonic radius as: rM=½(rF+rG)~ 3.42x1011
meters and set the macro-leptonic radius to rE=3.44x1014 meters.
Secondly, we map the macroscale
onto the microscale, say in the simple proportionality relation, using
(de)capitalised symbols: Re/Rm=rE/rM.
We can so solve for the micro-mesonic scale Rm=Re.rM/rE ~ 2.76x10-18
meters.
So reducing the apparent measured 'size' of a proton in a factor about about 1000 gives the scale of
the subnuclear mesonic interaction, say the strong interaction coupling by pions.
The Higgsian Scalar-Neutrino
The (anti)neutrinos are part of the electron
mass in a decoupling process between the kernel and the rings. Neutrino mass is so not cosmologically significant and cannot
be utilized in 'missing mass' models'.
We may define the kernel-scale as that of the singular spacetime-quantum
unit itself, namely as wormhole radius rw=10-22/2π meters.
Before the decoupling between
kernel and rings, the kernel-energy can be said to be strong-weakly coupled or unified to encompass the gauge-gluon of the strong interaction and the gauge-weakon of the weak interaction defined in a coupling between the OuterRing and the Kernel and bypassing the mesonic InnerRing.
So for matter,
a W-Minus (weakon) must consist of a coupled lepton part, yet linking to the strong interaction via the kernel part. If now the colour-charge
of the gluon transmutates into a 'neutrino-colour-charge'; then this decoupling will not only define the mechanics
for the strong-weak nuclear unification coupling; but also the energy transformation of the gauge-colour charge into the gauge-lepton
charge.
There are precisely 8 gluonic transitive energy permutation eigenstates between a 'radiative-additive'
Planck energy in W(hite)=E=hf and an 'inertial-subtractive' Einstein energy in B(lack)=E=mc2, which describe
the baryonic- and hyperonic 'quark-sectors' in: mc2=BBB, BBW, WBB, BWB, WBW, BWW, WWB and WWW=hf. The permutations
are cyclic and not linearly commutative. For mesons (quark-antiquark eigenstates), the permutations are BB, BW, WB and WW
in the SU(2) and SU(3) Unitary Symmetries.
So generally, we may state, that the gluon is unfied with a weakon before decoupling; this decoupling 'materialising'
energy in the form of mass, namely the mass of the measured 'weak-interaction-bosons' of the standard model (W- for
charged matter; W+ for charged antimatter and Zo for neutral mass-currents say).
Experiment
shows, that a W- decays into spin-aligned electron-antineutrino or muon-antineutrino or tauon-antineutrino pairings under
the conservation laws for momentum and energy.
So, using our quantum geometry, we realise, that the weakly decoupled
electron must represent the OuterRing, and just as shown in the analysis of QED (Quantum-Electro-Dynamics). Then it can be inferred, that the Electron's Antineutrino represents a transformed and materialised gluon via its colourcharge,
now decoupled from the kernel.
Then the OuterRing contracts (say along its magnetoaxis defining its asymptotic confinement); in effect 'shrinking the electron' in its inertial and charge- properties to
its experimentally measured 'point-particle-size'. Here we define this process as a mapping between the Electronic
wavelength 2πRe and the wormhole perimeter λw=2πrw.
But in this process
of the 'shrinking' classical electron radius towards the gluonic kernel (say); the mesonic ring will be encountered
and it is there, that any mass-inductions should occur to differentiate a massless lepton gauge-eigenstate from that manifested
by the weakon precursors.
{Note: Here the W- inducing a lefthanded neutron to decay weakly into a lefthanded proton,
a lefthanded electron and a righthanded antineutrino. Only lefthanded particles decay weakly in CP-parity-symmetry violation,
effected by neutrino-gauge definitions from first principles}.
This so defines a neutrino-oscillation potential
at the InnerRing-Boundary. Using our proportions and assigning any neutrino-masses mυ as part of the electronmass
me, gives the following proportionality as the mass eigenvalue of the Tau-neutrino:
mυ=meλw.rE/(2πrMRe)
~ 5.4x10-36 kg or 3.0 eV.
So we have derived, from first principles, a (anti)neutrinomass
eigenstate of 3 eV.
This confirms the Mainz, Germany Result as the upper limit for neutrino masses resulting from
ordinary Beta-Decay and indicates the importance of the primordial beta-decay for the cosmogenesis and the isomorphic scale
mappings stated above.
The hypersphere intersection of the G- and F-count of the thermodynamic expansion of the
mass-parametric universe so induces a neutrino-mass of 3 eV at the 2.76x10-18 meter marker.
The more
precise G-F differential in terms of eigenenergy is 0.052 eV as the mass-eigenvalue for the Higgs-(Anti)neutrino (which is
scalar of 0-spin and constituent of the so called Higgs Boson as the kernel-Eigenstate). This has been experimentally verified
in the Super-Kamiokande (Japan) neutrino experiments published in 1998 and in subsequent neutrino experiments around the globe, say Sudbury, KamLAND,
Dubna, MinibooNE and MINOS.
This Higgs-Neutrino-Induction is 'twinned' meaning that this energy can be related
to the energy of so termed 'slow- or thermal neutrons' in a coupled energy of so twice 0.0253 eV for a thermal equilibrium at so 20° Celsius and a rms-standard-speed of so 2200 m/s from the Maxwell statistical distributions for the kinematics.
Neutrinomasses
The Electron-(Anti)Neutrino is massless as base-neutrinoic weakon eigenstate.
The Muon-(Anti)Neutrino is
also massless as base-neutrinoic weakon eigenstate.
The Tauon-(Anti)Neutrino is not massless with inertial eigenstate
meaned at 3.0 eV.
The weakon kernel-eigenstates are 'squared' or doubled (2x2=2+2) in comparison with the gluonic-eigenstate
(one can denote the colourcharges as (R²G²B²)[½] and as (RGB)[1] respectively say and with the [] bracket
denoting gauge-spin and RGB meaning colours Red-Green-Blue).
The scalar Higgs-(Anti)Neutrino becomes then defined in: (R4G4B4)[0].
The twinned neutrino
state so becomes MANIFESTED in a coupling of the scalar Higgs-Neutrino with a massless base neutrino in a (R6G6B6)[0+½])
mass-induction template.
The Higgs-Neutrino is bosonic and so not subject to the Pauli Exclusion Principle; but quantized in the form of the FG-differential of the 0.052 Higgs-Restmass-Induction.
Subsequently all experimentally
observed neutrino-oscillations should show a stepwise energy induction in units of the Higgs-neutrino mass of 0.052 eV. This
was the case in the Super-Kamiokande experiments; and which was interpreted as a mass-differential between the muonic and tauonic neutrinoic forms.
3.
The first stars in the Ylemic Universe
The stability of stars is a function of the
equilibrium condition, which balances the inward pull of gravity with the outward pressure of the thermodynamic energy or
enthalpy of the star (H=PV+U). The Jeans Mass MJ and the Jeans Length RJ a used to describe
the stability conditions for collapsing molecular hydrogen clouds to form stars say, are well known in the scientific data
base, say in formulations such as:
MJ=3kTR/2Gm for
a Jeans Length of: RJ=√{15kT/(4πρGm)}=√(kT/Gnm²). Now the Ideal Gas
Law of basic thermodynamics states that the internal pressure P and Volume of such an ideal gas are given by PV=n.RIG.T=NkT
for n moles of substance being the Number N of molecules (say) divided by Avogadro's Constant L in n=N/L .
Since the Ideal Gas Constant RIG divided by Avogadro's Constant L and defines Boltzmann's Constant k=RIG/L.
Now the statistical analysis of kinetic energy KE of particles in motion in a gas (say) gives a root-mean-square velocity
(rms) and the familiar 2.KE=mv²(rms) from the distribution of individual velocities v in such a system. It is
found that PV=(2/3)N.KE as a total system described by the v(rms). Now set the KE equal to the Gravitational PE=GMm/R
for a spherical gas cloud and you get the Jeans Mass. (3/2N).(NkT)=GMm/R with m the mass of a nucleon or Hydrogen atom
and M=MJ=3kTR/2Gm as stated. The Jeans' Length is the critical radius of a cloud (typically a
cloud of interstellar dust) where thermal energy, which causes the cloud to expand, is counteracted by gravity, which causes
the cloud to collapse. It is named after the British astronomer Sir James Jeans, who first derived the quantity; where k is Boltzmann's constant, T is the temperature of the cloud, r is the radius of the cloud, μ is the mass per particle in the cloud, G is the
Gravitational Constant and ρ is the cloud's mass density (i.e. the cloud's mass divided by the cloud's volume).
Now
following the Big Bang, there were of course no gas clouds in the early expanding universe and the Jeans formulations are
not applicable to the mass seedling Mo; in the manner of the Jeans formulations as given.
However,
the universe's dynamics is in the form of the expansion parameter of GR and so the R(n)=Rmax(n/(n+1))
scalefactor of Quantum Relativity.
So we can certainly analyse this expansion in the form of the Jeans Radius
of the first protostars, which so obey the equilibrium conditions and equations of state of the much later gas clouds, for
which the Jeans formulations then apply on a say molecular level.
This analysis so defines the ylemic
neutron stars as protostars and the first stars in the cosmogenesis and the universe.
Let the thermal internal
energy or ITE=H be the outward pressure in equilibrium with the gravitational potential energy of GPE=Ω.
The Nuclear
Density in terms of superbrane parameters is ρcritical=mc/Vcriticalwith mc
the base nucleon (ylemic neutron) mass and Vcritical=4πRe3/3 as the volume of the ylemic
neutron as given by the classical electron radius as superbrane quantisation/magnification and for Re=1010λw/360=e*/2c2.
H=(molarity)kT for molarity in volumes as N=(R/Re)3 for dH=3kTR2/Re3.
Ω(R)= -∫GMdm/R = -{3Gmc²/(Re³)²}∫R4dR= -3Gmc².R5/Re6 for
dm/dR=d(ρV)/dR=4πρ.R²
and for ρ=3mc/4πRe³.
So dΩ(R)=-3Gmc².R4/(Re³)²=-16π²ρ²G.R4/3.
For equilibrium the condition is that dH=dΩ as the minimum integral dH+dΩ=0.
This gives:
dH+dΩ=3kTR2/Re5-16Gπ2ρ2R4/3=0 and the ylemic
radius as:
Rylem
=√(kT.Re³/Gomc²) as the Jeans Length
precursor or progenitor.
The ylemic (Jeans)
radii are all independent of the mass of the star as a function of its nuclear generated temperature. Applied to
the protostars of the neutron matter or ylem, the radii are all neutron star radii and define a specific range of radii
for the range of gravitational collapse.
This spans from the 'First three
minutes' scenario of the cosmogenesis to 1.1 million seconds or about 13 days and encompasses the ordinary beta decay
of the neutron (underpinning radioactivity). The upper limit defines a trillion degree temperature and
a radius of over 40 km, the typical Schwarzschild solution defines a typical ylem radius of so 7.4 km and the lower limit
defines the 'mysterious' planetesimal limit as 1.8 km.
For long a cosmological conundrum, it
could not be modelled just how the molecular and electromagnetic forces applicable to conglomerate matter particles (say
hydrogen gas as dust) on the quantum scale of molecules could become strong enough to form say 1km mass concentrations,
required for 'ordinary' gravity to assume control. The ylem radii's lower limit defined in this
cosmology show, that it is the ylemic temperature of then 1.2 billion degrees K, which performs the trick under the Ylem-Jeans
formula, which is then applied to the normal collapse of hydrogenic atoms in summation.
The
stellar evolution from the ylemic(dineutronic) templates is well established in QR and confirms most of the Standard Model's
ideas of nucleosynthesis and the general Temperature cosmology. The standard model is correct in the temperature assignment,
but is amiss in the corresponding 'size-scales' for the cosmic expansion. The Big Bang cosmogenesis describes
the universe as a Planck-Black Body Radiator, which sets the Cosmic-Microwave-Black Body Background Radiation Spectrum (CMBBR)
as a function of n as T4=18.2(n+1)²/n³ and derived from the Stefan-Boltzmann-Law and the related statistical
frequency distributions.
We have the GR metric for Schwarzschild-Black Hole Evolution as RS=2GM/c²
as a function of the star's Black Hole's mass M and we have the ylemic Radius as a function of temperasture only as:
Rylem=√(kT.Re³/Gomc²).
The
nucleonic mass-seed mc=Planck-Mass(mP).Alpha9 and Gomc² is
constant in the partitioned n-evolution of mc(n)=Yn.mc with G(n)=Go.Xn.
Identifying
the ylemic Radius with the Schwarzschild Radius then indicates a specific mass a specific temperature and a specific radius.
Those we call the Chandrasekhar Parameters:
MChandra=1.5 solar Masses=3x1030
kg and RChandra=2GoMChandra/c² or 7407.40704..metres, which is the typical neutron star
radius inferred today.
TChandra=RChandra².Gomc²/kRe³
=1.985x1010 K for Electron Radius Re and Boltzmann's Constant k.
Those Chandrasekhar
parameters then define a typical neutron star with a uniform temperature of 20 billion K at the white dwarf limit of ordinary
stellar nucleosynthetic evolution (Hertzsprung-Russell or HR-diagram).
The Radius for the massparametric Universe
is given in R(n)=Rmax(1-n/(n+1)) correlating the ylemic temperatures as the 'uniform' CMBBR-background
and we can follow the evolution of the ylemic radius via the approximation:
Rylem=0.05258..√T=(0.0753).[(n+1)²/n³][1/8]
Rylem(npresent=1.1324..)=0.0868 m* for a Tylem(npresent)=2.73
K for the present time tpresent=npresent/Ho.
What is nChandra?
This would describe the size of the universe as the uniform temperature CMBBR today manifesting as the largest
stars, mapped however onto the ylemic neutron star evolution as the protostars (say as nChandra'), defined
not in manifested mass (say neutron conglomerations), but as a quark-strange plasma, (defined in QR as the Vortex-Potential-Energy
or VPE).
R(nChandra')=Rmax(nChandra'/(nChandra'+1))=7407.40741..
for nChandra'=4.64x10-23 and so a time of tChandra'=nChandra'/Ho=nChandra'/1.88x10-18=2.47x10-5
seconds.
QR defines the Weyl-Temperature limit for Bosonic Unification as 1.9 nanoseconds at a temperature
of 1.4x1020 Kelvin and the weak-electromagnetic unification at 1/365 seconds at T=3.4x1015 K.
So
we place the first ylemic protostar after the bosonic unification (before which the plenum was defined as undifferentiated
'bosonic plasma'), but before the electro-weak unification, which defined the Higgs-Bosonic restmass induction via
the weak interaction vector-bosons and allowing the dineutrons to be born.
The universe was so
15 km across, when its ylemic 'concentrated' VPE-Temperature was so 20 Billion K and we find the CMBBR in the Stefan-Boltzmann-Law
as T4=18.20(n+1)²/n³ =1.16x1017 Kelvin.
So the thermodynamic temperature for
the expanding universe was so 5.85 Million times greater than the ylemic VPE-Temperature; and implying that no individual
ylem stars could yet form from the mass seedling Mo. The universe's expansion however cooled the CMBBR background and
we to calculate the scale of the universe corresponding to this ylemic scenario; we simply calculate the 'size' for
the universe at TChandra=20 Billion K for TChandra4 and we then find nChandra=4.89x10-14
and tChandra=26,065 seconds or so 7.24 hours.
The Radius R(nChandra)=7.81x1012
metres or 7.24 lighthours.
This is about 52 Astronomical Units and an indicator for the largest possible star
in terms of radial extent and the 'size' of a typical solar system, encompassed by supergiants on the HR-diagram.
We
so know that the ylemic temperature decreases in direct proportion to the square of the ylemic radius and one hitherto
enigmatic aspect in cosmology relates to this in the planetesimal limit. Briefly, a temperature of so 1.2 billion degrees
defines an ylemic radius of 1.8 km as the dineutronic limit for proto-neutron stars contracting from so 80 km down to this
size just 1.1 million seconds or so 13 days after the Big Bang.
This then shows why chunks of matter
can conglomerate via molecular and other adhesive interactions towards this size, where then the accepted gravity is strong
enough to build planets and moons. It works, because the ylemic template is defined in subatomic parameters reflecting the
mesonic-inner and leptonic outer ring boundaries, the planetesimal limit being the leptonic mapping. So neutrino- and
quark blueprints micromacro dance their basic definition as the holographic projections of the spacetime quanta.
Now
because the Electron Radius is directly proportional to the linearised wormhole perimeter and then the Compton Radius via
Alpha in Re=1010.λw/360=e*/2c2=Alpha.Re, the Chandrasekhar hite
Dwarf Limit should be doubled to reflect the protonic diameter mirrored in the classical electron radius.
Hence any star experiencing electron degeneracy is actually becoming YLEMIC or DINEUTRONIC, the boundary for this process
being the Chandrasekhar mass. This represents the subatomic mapping of the first Bohr orbit collapsing onto the leptonic
outer ring in the quarkian wave-geometry.
But this represents the Electron Radius as a Protonic Diameter and
the Protonic Radius must then indicate the limit for the scale where proton degeneracy would have to enter the scenario. As
the proton cannot degenerate in that way, the neutron star must enter Black Hole phasetransition at the Re/2 scale,
corresponding to a mass of 8MChandra=24x1030 kg* or 12 solar masses.
The maximum ylemic
radius so is found from the constant density proportion ρ=M/V:
(Rylemmax/Re)³=MChandra/mc
for Rylemmax=40.1635 km.
The corresponding ylemic temperature is 583.5 Billion K for a CMBBR-time
of 287 seconds or so 4.8 minutes from a n=5.4x10-16, when the universe had a diameter of so 173 Million
km.
But for a maximum nuclear compressibility for the protonic radius, we find:
(Rylemmax/Re)³=8MChandra/mc
for Rylemmax=80.327 km, a ylemic temperature of 2,334 Billion K for a n-cycletime of 8.5x10-17
and a CMBBR-time of so 45 seconds and when the universe had a radius of 13.6 Million km or was so 27 Million km
across.
The first ylemic protostar vortex was at that time manifested as the ancestor for all neutron star
generations to follow. This vortex is described in a cosmic string encircling a spherical region so 160 km across and within
a greater universe of diameter 27 Million km which carried a thermodynamic temperature of so 2.33 Trillion Kelvin at
that point in the cosmogenesis.
This vortex manifested as a VPE concentration after the expanding universe
had cooled to allow the universe to become transparent from its hitherto defining state of opaqueness and a time known as
the decoupling of matter (in the form of the Mo seedling partitioned in mc's) from the radiation pressure of the CMBBR
photons.
The temperature for the decoupling is found in the galactic scale-limit modular dual to the wormhole
geodesic as λw=1022 metres or so 1.06 Million ly and its luminosity attenuation in the 1/e proportionality
for then 388,879 lightyears as a decoupling time ndc. A maximum galactic halo limit is modulated in 2πλw
metres in the linearisation of the Planck-length encountered before in an earlier discussion.
R(ndc)=Rmax(ndc/(ndc+1))=1022
metres for ndc=6.26x10-5 and so for a CMBBR-Temperature of about T=2935 K for a galactic protocore then
attenuated in so 37% for ndcmin=1.0x10-6 for R=λw/2π and ndcmax=3.9x10-4
for R=2πλw and for temperatures of so 65,316 K and 744 K respectively, descriptive of the temperature
modulations between the galactic cores and the galactic halos.
So a CMBBR-temperature of so 65,316 K at
a time of so 532 Billion seconds or 17,000 years defined the initialisation of the VPE and the birth of the first ylemic protostars
as a decoupling minimum. The ylemic mass currents were purely monopolic and known as superconductive cosmic strings,
consisting of nucleonic neutrons, each of mass mc.
If we assign this timeframe to the maximised ylemic radius
and assign our planetesimal limit of fusion temperature 1.2 Billion K as a corresponding minimum; then this planetesimal
limit representing the onset of stellar fusion in a characteristic temperature, should indicate the first protostars at a
temperature of the CMBBR of about 744 Kelvin.
The universe had a temperature of 744 K for ndcmax=3.9x10-4
for R=2πλw and this brings us to a curvature radius of so 6.6 Million lightyears and an 'ignition-time'
for the first physical ylemic neutron stars as first generation protostars of so 7 Million years after the Big Bang.
The
important cosmological consideration is that of distance-scale modulation.
The Black Hole Schwarzschild metric
is the inverse of the galactic scale metric.
The linearisation of the Planck-String as the Weyl-Geodesic and so
the wormhole radius in the curvature radius R(n) is modular dual and mirrored in inversion in the manifestation of galactic
structure with a nonluminous halo a luminous attenuated diameter-bulge and a superluminous (quasar or White Hole Core).
The
core-bulge ratio will so reflect the eigenenergy quantum of the wormhole as heterotic Planck-Boson-String or as the magnetocharge
as 1/500, being the mapping of the Planck-Length-Bounce as e=lP.c²√Alpha onto the electron radius in
e*=2Re.c².
4.The Elementary Cosmic Ray Spectrum
The elementary Cosmic Ray Spectrum derives from the transformation of the Planck-String-Boson at the birth of the universe.
The following tabulation relates those transformation in energy and the modular duality between the distance
parameters of the macrocosm of classical spacetime geometry and the microcosm of the quantum realm.
String-Boson...........Wavelength(λ)......Energy (hc/λ)............Modular Wavelength....Significance
1. Planck-Boson........1.2x10-34 m...1.6 GJ
or 9.9x1027 eV....8.0x1033 m...Outside Hubble Horizon Limit
2. Monopole-Boson...4.6x10-32
m...4.3 MJ or 2.7x1025 eV....2.2x1031 m...Outside Hubble Horizon Limit
3. XL-Boson............6.6x10-31
m...303 kJ or 1.9x1024 eV....1.5x1030 m....Outside Hubble Horizon Limit
4. X-K-Boson transit...8.8x10-28 m....227 J or 1.6x1021 eV...1.1x1027
m....2πRHubble11D
5 .X-K-Boson transit...1.0x10-27 m....201 J or 1.2x1021
eV...1.0x1027 m....2πRHubbleHorizonLimit
6. CosmicRayToe.......1.9x10-27 m....106
J or 6.6x1020 eV..5.3x1026 m......2πRHubble10D
7. CosmicRayAnkle....2.0x10-25 m...1.0J or 6.2x1018 eV.....5.0x1024
m......Galactic Supercluster Scale
8. CosmicRayKnee(+)..1.0x10-22 m...0.002J or 1.24x1016
eV..1.0x1022 m.....Galactic Halo Scale
9. CosmicRayKnee(-)...6.3x10-22 m...0.0003J or 2.0x1015
eV..1.6x1021 m......Galactic Disc Scale
Lower Cosmic Ray energies then become
defined in standard physics, such as supernovae, neutron stars and related phenomena, engaging electron accelerations and
synchrotron radiation.
7. represents the ECosmic-Boson and 8. the Weyl-Boson of the Big Bang Planck-singularity
of the Weyl-Geodesic of relativistic spacetime. 9 modulates the experimentally well measured 'knee' energy for Cosmic
Rays as the distribution flux of high-energy protons as the primary particle in the 2π-factor. The wormhole radius is 10-22
m/2π for a Halo-(DarkMatter)-Radius of 2πx1022 metres.
The SciAm article below from
1998 links to the above in clarification of the questions raised.
http://auger.cnrs.fr/presse/ScAm_jan97.html
Cosmic Rays at the Energy Frontier
These particles carry more energy than any others in the universe.
Their origin is unknown but may be relatively nearby
by James W. Cronin, Thomas K. Gaisser and Simon P. Swordy