The Early Universe
----------------
Home astronomers typicly terminate their inquiries after
cosmology at the moment the photosphere dissolved, when the matter and
energy densities crossed, when the universe switched from energy to
matter ruled. This is because the physics of the photospheric period
going back to the bigbang instant is not in the general education of
the home astronomer. In fact, the closer one approaches to the moment
of the bigbang the heavier the physics becomes! The temperatures and
densities increase as we roll back in time and there comes the
question: Is the physics already in hand really up to describing the
world at those early moments?
We can appreciate the concept of a breakdown in familiar physics
when confronted with unfamiliar circumstances. Consider an ordinary
liquid thermometer. The liquid expands in step with the temperature.
By surrounding the thermometer with known temperatures we can
calibrate it and thereafter use it to assay unknown temperatures. We
can plot a graph of temperature versus liquid volume, for instance.
We see that the volume varies linearly with temperature over the
limited range of temperatures we can present to the thermometer. We
generalize and say that for all temperatures the volume is
proportional to the temperature.
We get bold and extrapolate our experience to low temperatures and
find that our V(T) curve crosses the T axis (V = 0) at some particular
temperature. There is some cold point where the liquid attains zero
volume! This in fact is one definition of absolute zero. It's that
temperature at which the thermometer liquid shrinks to zero volume.
In maths this point of zero volume is called a singularity and there
are weird implications. Like, since the mass hasn't changed and
remains finite, the density of the liquid goes to infinity.
Then we continue our experiment. As we cool the thermometer the
liquid in deed contracts along the linear curve V(T). But at some one
temperature an astounding thing happens. The liquid freezes to a solid!
We can no longer apply the rule we developed for a liquid to
continue our experiment. We must turn to a new regime of physics, that
governing solids like crystals, polymers, amorphics, and so on. The
old physics of liquids is invalid and gives a false prediction.
In point of fact many physicists believe that the freezing of the
liquid to a solid, whose volume is almost invariant with temperature,
is nature's way to avoid the issue of a singularity.
The Singularity of the Bigbang
----------------------------
The Friedmann models, including the Einstein-deSitter or standard
model, start the universe from a singularity. The scalefactor is
identicly zero and swells into finite realms with increasing time. Is
this possible? Most cosmologists say it is allowable under the
Einstein physics that describe the expanding universe.
Others are not so sure. One of the prime motives for physicists to
build atom smashers of ever larger size [and higher cost] is to
duplicate the conditions of the bigbang and see what physics is
required to describe them. Did something happen to prevent the
singularity, like some phase change to make the universe start from a
nonzero volume? Was there really a time when the whole cosmos fit
inside a true geometric point?
We here can not explore the early universe too far back in time
because of the lack of the heavy physics. However, we can dip our toes
in the waters and see what sort of thinking cosmologists go thru.
Geometrical and Physical Cosmology
--------------------------------
Before World War II cosmology was essentially a geometric
construct. Altho leMaitre tried to impute physical reality to the
origin of the universe -- it exploded from a cosmic egg -- in his
model, he lacked a solid grounding in the physics of the day. What is
more important, the physics of atoms needed to deal with the origin of
the universe was only just born in the 1930s.
It was World War II that drove the development of this nascent
atomics in connection with the atom bomb project. All the major
factions in the war had supersecret schemes to build and deploy the
atom bomb. The workings of the bomb depended on the behavior of nuclei
under high temperature and density.
Many astronomers worked on the atom bomb as part of their military
duties and were introduced to this new physics. But with the wartime
secrecy they could not exchange ideas and thoughts nor apply them in
academic settings. After the war the restrictions were lifted and the
science of atomics (also called nuclear, particle, high-energy, and
quantum physics) moved into the regular curriculum of the astronomer.
No Antimatter?
------------
Despite our lack of heavy physics we can walk thru one example of
how cosmologists inquire after the goings-on in the period before the
photosphere dissolved. We look at matter and anitmatter. By all known
physics matter and antimatter must be of exactly equal amounts in any
interaction. Anitmatter is identical to matter except that it has the
opposite electric charge. For matter of zero charge the matter is its
own anti by identity. The anti of a proton is the antiproton, a proton
with one minus charge in the stead of the normal one plus charge. It
is also called the negatron.
When matter and antimatter meet, they annihilate and produce a
photon. The one can not vanish by itself and leave the other intact.
Note well that this photon marks the prior existence of two bodies,
the matter one and the anti one.
Now we saw that the energy and mass in the universe are today
virtually unchanged since the photosphere era. The photons we see
today in the form of the universal blackbody radiation proceded to us
directly from the time before the photosphere and are relics of the
bigbang. Of course, we also have the mass in the universe, itself
essentially unmodified in quantity since the bigbang.
If matter and antimatter must coexist in equal amounts, why then do
we have in our universe only matter? During the 50s and 60s we
believed the galaxies were each made of either matter or antimatter.
Their great separations kept them from contact and selfdestruction.
When we came onto an intense radiosource consisting of two colliding
galaxies, we presumed that they were of opposite types. They were
consuming themselves in annihilation and generating photons.
We now understand that the galaxies are not sitting in empty space
but are connected by fields of intergalactic gas. They are in contact
yet not self-destructing. Also we have other plausible means of
explaining the fierce radioemissions from colliding galaxies.
So since the 1970s we find our universe consists of only matter
and no antimatter. Why?
Matter-Antimatter Ratio
---------------------
Cosmologists think that the law of matter-antimatter equality was
'not in force' at the bigbang instant. It was 'enacted' some short
time later. Hence for a little while, microseconds, there was a
permissible imbalance of matter versus animiatter as an initial state
of the universe. When the equality law 'took effect' the preceding
matter-antimatter ratio was 'grandfathered. How all this actually
happened is part of the unified field theories and is not at all
certain. In due time the annihilation of matter and antimatter
occurred, leaving as survivor some residuum of matter. This is the
matter we now have around us in the universe.
Can we assess the severity of this initial imbalance? Amazingly we
can, even tho it occurred inside the photosphere. In a unit volume of
space we have photons and particles. The photons are almost all from
the relic Planck radiation and the particles are mostly protons. Being
that there was since the bigbang quite little alteration in the
amounts of photons or protons, their ratio today is the same as that
at the bigbang.
The photon/meter^3 comes from the photon-temperature law with tau
= 2.735K
N(tau) = (pi / 13) * (k / (h * c))^3 * tau^3
= (pi / 13) * ((1.381E-23j/K) / ((1.055E-34j.s)
* (2.998E8m/s)))^3 * tau^3
= (2.012E7/(K.m)^3) * (2.735K)^3
= 4.116E8/m^3
Now we find the proton/meter^3
N[proton] = rho0 / m[proton]
= (4E-28kg/m^3) / (1.673E-27kg/proton)
= 0.239 proton/m^3
Recall that each photon stands for two particles, say a proton and
a negatron, that once existed in the bigbang. So
N[orig] = (2 part/photon) * N(tau)
= (2 part/photon) * (4.116E8 photon/m^3)
= 8.232E8 part/m^3
N[prot] / N[orig] = 0.239 / 8.232E8
= 2.903E-10
This is an awesome conclusion! The universe really started out
with almost equal parts of matter and antimatter with an excess of one
part in 29 BILLION in favor of matter. We here today live with just
this left over grain of matter after all the rest annihilated itself
in the bigbang!
Abundance of the Elements
-----------------------
Until the 1920s the mix of chemical elements in the universe
escaped notice by astronomers. By spectrometry they assayed the stars,
planets, &c were mainly concerned with the mere presence or absence of
a given element. For example, we assumed the Sun was made of a
substantial portion of the heavy elements which produced prominent
spectral lines.
Payne-Gaposchkin in the 1920s accumulated sufficient evidence and
applied the new quantum physics to it to realize that the sun and
stars are overwhelmingly made of hydrogen, up to 3/4 by mass.
Astronomers were not happy with this finding and generally ignored it
until the late 1930s, when it was confirmed by later assays.
The definite census of the universe was done by Urey in 1954,
showing that hydrogen was 75% (by mass); helium, 24%; and all the
other elements from lithium thru uranium were present in traces.
Helium in the Universe
--------------------
By the mid 1930s astronomers were exploring crude models of the
stars and they hit on the fusion of hydrogen into helium and heavies
with the consequent release of energy. This is how the stars shine, a
mystery for all prior time.
The stellar energy processes yield about the correct portions of
the heavy elements but wildly too low ratios for helium. In astronomy
'heavy elements' are all elements other than hydrogen and helium; it
has the unofficial symbol 'Hv'. It seems that the stars start off with
a large portion of helium and then produce only a little additional
amount.
The amount of helium, and other elements, in the universe is not
easy to assess. There is no representative place to take a sample of.
In the solar system the original mix of elements is far too massaged
by planetological processes to be a fair sample. Ongoing creation of
the elements in the stars distorts the mixture. The interstellar dust
and gas seem too nonhomogeneous for good sampling.
In spite of everything we feel confident that the universe at
large is comprised of 75%, by mass, hydrogen, 24% helium, and quite
one percent heavies. Contrast this against the Earth which is all
heavies with almost no hydrogen and helium.
Origin of the Helium
------------------
The mass converted into energy by the stars is order 1E-4 of the
total mass of the universe and the energy emitted by the stars added
only a few percent to the energy coming from the bigbang. Hence the
amount of mass converted into helium in the stars is negligible and
the huge helium portion must have existed before the stars. `
Plausibly it was created in the photospheric era soon after the
bigbang.
Alpher, Bethe, Herman, and Gamow were among the first, in 1948, to
calculate the creation of hydrogen and helium out of the bigbang. To
do so they had to add thermodynamics to the standard model, thus
introducing mainline physics into cosmology. There were several
earlier attempts, such as that of Weizsacker in 1937, to explain the
abundance of the various elements in the universe but they suffered
from the prevailing weak theory of atomics.
To them the universe started off indefinitely hot. As it expanded
it cooled. Gamow further noted that the radiation from the time of
initial high temperature should be cooled by now to a few Kelvin. In
fact this is the 2.7K microwave background, the relic radiation from
the photospheric period.
Nucleogenesis
-----------
The team of Alpher-Bethe-Herman-Gamow banked their calcs on the
newly emerging atomics. The team's original scheme has long since been
supplanted for it originally made all the elements out of the bigbang,
ignoring the role of the stars.
With the Urey assay in hand Gamow, Burbidge, &a in 1957 divvied up
the element creation regimes. Gamow demonstrated that essentially only
hydrogen and helium are made in the bigbang while Burbidge's team
showed that the rest (including some additional helium) was produced
in the stars.
Gamow assumed that at some point in the expansion and cooling the
universe was populated only by neutrons. There were the several
'classical' atomic particles to work with: neutron, proton, electron,
neutrino, and photon. As an aside, the neutrino was theorized partly
out of the prewar work on stellar evolution but it was not discovered
in nature until 1954.
Today physicists postulate that neutrons came from some other more
elemental particles in a prior hotter denser stage of the universe. We
start with the neutrons already in place. This is believed to occur at
a temperature of order one billion Kelvin and time of order one
hundred seconds after the bigbang instant.
Gamow showed that from this sea of neutrons hydrogen and helium
derived in close to the observed ratios. The heavies ratio was badly
too low but he figured the element creation in the stars made up the
deficit.
The theory of the creation of the elements in the bigbang is
called nucleogenesis, as sexy a term in astronomy as ever there was
one. The creation of elements in the stars, aeons after the bigbang
and in our own era, is called nucleosynthesis, an other sexy term..
Regimes of Element Creation
-------------------------
Today we recognize five regimes under which elements are created
in the universe. These regimes divide the elements into five groups
ordered by their atomic number (count of protons). The first, the
nucleogenesis explored in this treatise, produced the initial hydrogen
and helium. All subsequent elements were generated by the other four
processes from this primary reservoir of hydrogen and helium.
The hydrogen is then burned by the stars on the Main Sequence to
produce more helium. This extra helium is a small addition to the
initial helium already in the star.
When the star leaves the Main Sequence to live out its life as a
redgiant and beyond it burns some of its helium into heavies. This
process generates the elements up to iron.
Later the more massive stars supernovate and crush the heavies
into still larger heavies up to uranium. The ejecta from the supernova
dissipate into the interstellar regions as nebulae.
This material is laced with all the elements hydrogen thru uranium
and from it a new generation of stars is created. That is, stars are
born with a preexisting mix of elements reflecting the deaths of the
last generation.
In time the last generation of supernova ejecta will be laced with
too much heavies and too little hydrogen. This stuff will not burn in
a main sequence star and the creation of new stars ceases.
The final regime began in WW II, the production of elements
heavier than uranium. These ultrauranium elements are not found in
nature but exist only because of human intervention. Of course, the
quantity of these artificial elements is minuscule even within the
solar system. They have no cosmological importance except as specimina
for experimentation in atomics.
We summarizes the regimes here:
--------------------------------------
elements how produced
-------- ------------
hydrogen and helium in the bigbang thru nucleogenesis
helium in Main Sequence stars (minor amounts)
helium thru iron in post Main Sequence stars
iron thru uranium in supernovae
transuranium elements ny humans
---------------------------------------------------
Table of Particles
---------------
We need from an atomics reference the properties of the various
particles and the reactions they can undergo among themselfs. Here are
a few concepts to understand. Much of these are jargon terms.
The mass number, A, of a particle is the sum of the protons and
neutrons in it. More properly it is the mass of the particle expressed
in units of the neutron or proton mass. The proton and neutron have
almost equal mass. In comparison the electron has very little mass,
the neutrino has probably a;most with no mass, and the photon has no
mass at all.
The atomic, or element, number, Z, is the number of protons in the
particle and this number determines what element the particle is. A
particle with no protons has atomic number zero and is not an element.
Often if the particle is named as an element the atomic number is left
out. For each element has its unique and proper atomic number.
The neutron number, N, is the number of neutrons in the particle.
Note well that A = Z+N. The neutron number is rarely stated because it
can be derived from the atomic and mass numbers, N = A-Z. In deed the
neutron number is sometimes called the 'A minus Z' number.
The decay of a particle refers to its spontaneous mutation into
other particles without outside stimulus. Altho we are dealing with
particles, a decay will generally yield a photon, which radiates away.
The halflife, tau, of a particle is the time it takes for the
particle to decay, disintegrate, transmutate into other particles with
a 50-50 probability. For a multitude of the particle this is the time
for half of it to decay, leaving half as yet in its original state.
Many particles are stable; they remain unchanged for an indefinitely
long time.
An isotope is one of several particles with the same atomic number
but different mass numbers. Or the same number of protons but different
numbers of neutrons.
The anti of a particle is the very particle with the electric
charge of opposite signum. A particle with no charge is its own
antiparticle. The anti of the electron, e-, is the antielectron, e+,
which is an electron with a positive charge in the place of a negative
charge. We also call it the positron.
Among atomicists there grew a nomenclature for particles as arcane
as star nomenclature. A few are noted here.
An alpha [particle] is the nucleus of helium. It contains two
protons and two neutrons. Occasionally this is referred to as a
helion.
A beta [particle] is the electron. It is often written as 'beta-'
to emphasize that it has the negative electric charge associated with
the electron. By parallel construct the antielectron is sometimes
written as 'beta+'.
A gamma [ray] is the photon, the quantum of electromagnetic
radiation. It does not have to be visible light but may have any
wavelength, as appropriate for the particle e's reaction.
A deuteron is a particle of one proton and one neutron. It is also
called heavy hydrogen or hydrogen2. Its symbol is d or H2.
A triton is a particle of one proton and two neutrons. It is also
called double-heavy hydrogen and is symboled as t or H3.
Proton, deuteron, and triton are isotopes of hydrogen. They all
have one proton but no, one, or two neutrons. The names 'deuteron' and
'triton' imply the existence of actual elements called 'deuterium' and
'tritium'. These are not separate elements but traditional names for
isotopes of hydrogen when treated as chemical agents. All three are
chemicly the same.
The symbol of a particle is letters followed by digits. The
letters are the name of the particle and carry its associated atomic
number. The atomic number itself is rarely explicitly written.. The
number is the mass number. He4 is the helion (helium nucleus, alpha)
with mass number 4. The atomic number is not specified because helium
must have two protons. To fill up to mass number 4 the particle must
have two neutrons.
The properties of many cosmologicly important particles is set out
in the table here. Several particles are repeated under their different
names; this saves time in looking up aliases.
---------------------------------------------------------
name symb Z N A decays halflife comments
---- ---- - - - -------- -------- --------
gamma gamma 0 0 0 stable = photon
photon gamma 0 0 0 stable = gamma
neutrino nu 0 0 0 stable
anitneutrino nu' 0 0 0 stable
beta beta- 0 0 0 stable = electron
electron e- 0 0 0 stable = beta
antielectron e+ 0 0 0 stable = positron
positron beta+ 0 0 0 stable = anitelectron
neutron n 0 1 1 p,e-,nu' 1.05E1m
proton p 1 0 1 stable = hydrogen 1
hydrogen 1 H1 1 0 1 stable = proton
deuteron d 1 1 2 stable = hydrogen 2
hydrogen 2 H2 1 1 2 stable = deuteron
triton t 1 2 3 He3,e- 1.23E1y = hydrogen 3
hydrogen 3 H3 1 2 3 He3,e- 1.23E1y = triton
helium 3 He3 2 1 3 stable
helium 4 He4 2 2 4 stable = helion, alpha
alpha alpha 2 2 4 stable = helion, helium 4
helion He4 2 2 4 stable = alpha, helium 4
helium 5 He5 2 3 5 He4,n 2.0E-21s instant decay
lithium 5 Li5 3 2 5 He4,p 1.0E-21s instant decay
helium 6 He6 2 4 6 Li6,e- 8.05E-1s
lithium 6 Li6 3 3 6 stable
beryllium 6 Be6 4 2 6 He4,p,p 3.0E-21s
lithium 7 Li7 3 4 7 stable
beryllium 7 Be7 4 3 7 Li7 5.33E0d electron capture
helium 8 He8 2 6 8 Li8,e- 1.19E-1s
lithium 8 Li8 3 5 8 Be8,e- 8.44E-1s
beryllium 8 Be8 4 4 8 He4,He4 1.0E-16s instant decay
boron 8 B8 5 3 8 Be8,e+ 7.70E-3s positron decay
lithium 9 Li9 3 6 9 Be9,e- 1.77E-1s
beryllium 9 Be9 4 5 9 stable
boron 9 B9 5 4 9 Be8,p 8.0E-19s
carbon 9 C9 6 3 9 B9,e+ 1.27E-1s positron decay
beryllium 10 Be10 4 6 10 B10,e- 1.6E6y
boron 10 B10 5 5 10 stable
carbon 10 C10 6 4 10 B10,e+ 1.93E0s positron decay
lithium 11 Li11 3 8 11 Be11,e- 8.7E-3s
beryllium 11 Be11 4 7 11 B11,e- 1.38E1s
boron 11 B11 5 6 11 stable
carbon 11 C11 6 5 11 B11,e+ 2.03E1m positron decay
beryllium 12 Be12 4 8 12 B12,e- 2.4E-2s
boron 12 B12 5 7 12 C12,e- 2.02E-2s
carbon 12 C12 6 6 12 stable
nitrogen 12 N12 7 5 12 C12,e+ 1.1E-2s positron decay
---------------------------------------------------------------
A positron decay is where a proton emits a positron and turns into
a neutron. An electron capture is where a proton sucks in a nearby
external electron and turns into a neutron. The electrons are
captured from the surrounding space.
In the halflife column s = seconds, m = minutes, d = days, y =
years. Note that triton and beryllium 10 have long halflifes and are
found natively on Earth as radioactive isotopes. All the others are
either long gone or must be continuously created from other particles.
Every mass number has at least one stable isotope, EXCEPT FOR A =
5 AND 8. This is a circumstance of crucial importance in the
nucleogenesis theory.
Table of Interactions
-------------------
Besides natural decay, a particle can mutate by capturing certain
particles and ejecting others. Of the many thousands of possible
interactions, the ones here are germane to nucleogenesis right after
the bigbang. All of these are two-particle interactions. We think that
the conditions in the first moments after the bigbang allowed only
two-particle reactions.
Many reactions are labelled '[not poss]'. The supposed outputs for
them are either unknown at this time or are so rapidly self-decaying
that it looks as if the reaction never occurred.
The reactions are listed both ways to ease searching for them.
--------------------+-----------------------+----------------
input output | input output | input output
----- ------ | ----- ------ | ----- ------
n p,e-,nu' | |
--------------------+-----------------------+---------------------
n,nu p,e- | n,e+ p,nu' | n,n [not poss}
n,p d,gamma | n,d t,gamma | n,t [not poss]
n,He3 t,p | n,He3 alpha,gamma | n,alpha [not poss]
--------------------+-----------------------+---------------------
p,n d,gamma | p,d He3,gamma | p,t alpha,gamma
p,He3 [not poss] | p,alpha [not poss] |
--------------------+-----------------------+---------------------
d,n t,gamma | d,p He3,gamma | d,d t,p
d,d He3,n | d,t alpha, n | d,He3 alpha,p
d,alpha Li6,gamma | |
--------------------+-----------------------+----------------------
t,n [not poss] | t,p alpha,gamma | t,d alpha,n
t,t [not poss] | t,He3 Li6,gamma | t,alpha Li7,gamma
--------------------+-----------------------+----------------------
He3,n t,p | He3,n alpha,gamma | He3,p [not poss]
He3,d alpha,p | He3,He3 alpha,p,p | He3,alpha Be7,gamma
--------------------+-----------------------+-----------------------
alpha,n [not poss] | alpha,p [not poss] | alpha,d Li6,gamma
alpha,t Li7,gamma | alpha,He3 Be7,gamma | alpha,alpha [not poss]
---------------------+----------------------+-----------------------
Initial Conditions
----------------
The above reactions procede at various rates (reactions/second)
and probabilities (based on the cross-section of the particles when
they collide in their interaction). The rates and probabilities are
functions of temperature and density, which in turn are functions of
time. The universe steadily cools and dilates with its expansion.
At some moment after the bigbang instant the universe cooled and
expanded enough to allow the precipitation of neutrons. Neutrons, by
modern atomic theory, came from more elemental particles under hotter
denser conditions. Here we wait until the neutrons are in full bloom
and then start our nucleogenesis simulation.
We must ignore the rates and probabilities of the interactions
being that they involve an order of physics much outside the home
astronomer. The neglect of the reaction kinetics compromises the
numerical results of our simulations. Yet the qualitative results end
up being very enlightening.
The universe at the start of our study consisted all of neutrons,
no other particles, and gamma rays (photons) from other earlier
reactions. A free neutron is not a stable particle. It spontaneously
decays into a proton, electron, and antineutrino. The neutrons are not
yet joined into nuclei, where they turn into stable particles.
Soon, after many of the neutrons self-decayed, there is a sea of
loose native neutrons and newborn protons. The leftover neutrons and
new protons combine among themselfs, in pairs, to create deuterons
plus more gamma rays. The deuterons combine in pairs to yield tritons
and newly released protons. These new protons are of a second
generation, not from the decay of the original neutrons.
Tritons and deuterons combine to produce alpha particles (helions,
helium nuclei) and ejected neutrons. These neutrons partly replenish
the original supply and decay into protons of the third generation,
after the initial neutron decay and the deuteron-deuteron reactions.
We have, then, the following interactions to work with:
n -> p,e-,nu'
|
p,n -> d,gamma
|
d,d -> t,p
|
t,d -> alpha,n
Some egredients of these reactions become ingredients while others
remain: proton, al[ha, gamma. With more familiar names: hydrogen,
helium, radiation
Conservation Rules
----------------
There are, from atomics, various conservation rules that govern
the way we can work these reactions against each other. The number of
neutrons and protons on both sides of the reaction must be equal. This
is the baryon number, a baryon being a neutron or a proton, both being
nearly equal in mass. A baryon counts as +1; an antibaryon, -1.
The number of electrons and neutrinos must be equal across the
interaction. This, the lepton number, counts particles as +1 and the
antis as -1.
The electric charge must be equal on both sides. Positive charges
are +1; negative, -1. This number has no fancy name; it's just the
charge number.
There is an energy conservation rule for gamma rays which we do
not employ here. We let gamma rays be taken in or given out as necessary
to make the total energy on both sides balance. In general whenever a
single particle is the output of a reaction we allow for a gamma ray
emission with the particle.
Interaction Flowchart
-------------------
It is a lot easier to picture what is going on by diagramming the
reactions in a flowchart. We start with six initial neutrons and end up
with one helion (plus some other stuff).
In the flowchart boxes enclose the reactions, square brackets
enclose the initial particles, angle brackets enclose the final
particles, and vertical arrows flow from the earlier (upper) to later
(lower) reaction.
[n] [n] [n] [n] [n] [n]
| | | | | |
| \|/ | \|/ | \|/
| +---------------+ | +---------------+ | +---------------+
| | n -> p,e-,nu' | | | n -> p,e-,nu' | | | n -> p,e-,nu' |
| +---------------+ | +---------------+ | +---------------+
| \|/ \|/ \|/ | \|/ \|/ \|/ | \|/ \|/ \|/
| p <e-> <nu'> | p <e-> <nu'> | p <e-> <nu'>
\|/ \|/ \|/ \|/ \|/ \|/
+----------------+ +----------------+ +----------------+
| p,n -> d,gamma | | p,n -> d,gamma | | p,n -> d,gamma |
+----------------+ +----------------+ +----------------+
| \|/ \|/ \|/ | |
\|/ d d \|/ | \|/
<gamma> \|/ \|/ <gamma> | <gamma>
+------------+ \|/
| d,d -> t,p | d
+------------+ |
| \|/ |
\|/ t |
<p> \|/ \|/
+--------------------+
| t, d -> alpha, n |
+--------------------+
| \|/
\|/ n
,<alpha> \|/
+---------------+
| n -> p,e-,nu' |
+---------------+
| | |
\|/ \|/ \|/
<p> <e-> <nu'>
The net transformation is
6 n -> alpha, 2 p, 4 gamma, 4 e-, 4 nu'
Test this for balance against the conservation rules:
Baryon number: In = 6 = 6 initial neutrons
Out = 6 = 4 in the alpha and 2 protons
Lepton number: In = 0 = 0 initially
Out = 0 = 4 electrons cancelling 4
antineutrinos
Charge number: In = 0 = 0 initially
out = 0 = 4 electrons cancelling 2 protons in
the helion and 2 free protons
Other Reaction Chains
-------------------
By studying the 'Table of Interactions' we can find other chains
of reactions to work with. One such is the d,d -> He3,n followed by
He3,He3 -> alpha,p,p. We have the set of interactions
n -> p,e-,nu'
|
p,n -> d,gamma
|
d,d -> He3,n
|
He3,He3 -> alpha,p,p
Working with this set we get the flowchart below:
[n] [n] [n] [n] [n] [n] [n] [n]
| | | | | | | |
| \|/ | \|/ | \|/ | \|/
| +------------+ | +------------+ | +------------+ | +------------+
| | n -> p,... | | | n -> p,... | | | n -> p,... | | | n -> p,... |
| +------------+ | +------------+ | +------------+ | +------------+
| | | | | | | | | | \|/ \|/ | \|/ | \|/
| p <e-> <nu'> | p <e-> <nu'> | p <e-> <nu'> | p <e-> <nu'>
| | | | | | | \|/
+--------------+ +--------------+ +--------------+ +--------------+
| p,n -> d,... | | p,n -> d,... | | p,n -> d,... | | p,n -> d,... |
+--------------+ +--------------+ +--------------+ +--------------+
| \|/ \|/ \|/ \|/ \|/ | |
\|/ d d <gamma> <gamma> d d \|/
<gamma> \|/ \|/ \|/ \|/ <gamma>
+--------------+ +--------------+
| d,d -> He3,n | | d,d -> He3,n |
+--------------+ +--------------+
| \|/ \|/ |
\|/ He3 He3 \|/
|n \|/ \|/ n
| +----------------------+ |
| | He3,He3 -> alpha,p,p | |
\|/ +----------------------+ \|/
+---------------+ | | | +---------------+
| n -> p,e-,nu' | \|/ | | | n -> p,e-,nu'
| <alpha> \|/ \|/
+---------------+ <p> <p> +---------------
+ | | | |
\|/ | \|/ | | |
<p> <e-> <nu'> <p> <e-> <nu'>
The net transformation is
8 n -> alpha, 4 p, 4 gamma, 8 e-, 8 nu'
Check with the conservation rules
Baryon number: In = 8 = 8 initial neutrons
Out = 8 = 4 in the alpha and 4 protons
Lepton number: In = 0 = 0 initially
Out = 0 = 8 electrons cancelling 8
antineutrinos
Charge number: In = 0 = 0 initially
Out = 0 = 8 electrons cancelling 4 protons in
the helion and 4 free protons
Limits of the Simulation
----------------------
Recall that we omitted any attempt to factor in the probability
and speed of the reactions. Some may procede so rapidly that there is
a huge excess of their output particles. Others may occur so rarely
that their output plays no significant role in further interactions.
To see how the numbers fail, look at the two chains here. In the
first one we end up with one alpha and two protons (plus other low-
mass stuff). The mass ratio of alpha and proton to the entire mass of
the system is
alpha ratio = 4 / (4 + 2) | proton ratio = 2 / (4 + 2)
= 4 / 6 | = 2/ 6
= 0.667 | = 0.333
We created a universe of 2/3 helium and 1/3 hydrogen! Of course this
disagrees with the observed ratio of hydrogen and helium. The other
chain yielded one alpha and four protons. So
alpha ratio = 4 / (4 + 4) | proton ratio = 4 / (4 + 4)
= 4 / 8 | = 4 / 8
= 0.5 | = 0.5
This is just as far off: a world half hydrogen and half helium.
Never the less, the qualitative broadbrush model is in fact dead
on target. We do with our analysis start with all neutrons in the
universe and do come up with a universe of just hydrogen, helium,
gammas, electrons, and antineutrinos. These are exactly the major
particles the advanced calcs derive.
Why Stop at Helium?
-----------------
We stopped the simulation with the production of helium4. Why?
If we went and continued the nucleogenesis in our crude system we
could have consumed all the helium, and probably a lot of the
hydrogen, into heavies. Our universe would contain all heavies with
little or no helium and hydrogen! There is nothing in our model that
naturally terminates at helium.
The main reason for us to stop at helium is to follow the
detailed model with its declining temperature and density. Under a
proper analysis while the nucleogenesis is in progress the universe
continues to cool and dilate. By the time helions are in place the
density and temperature had already fallen below those required for
further reactions of helion with other particles.
Amazingly, the entire nucleogenesis from the native neutrons all
the way into the hydrogen and helium (and other stuff) takes only one
half hour!! And the temperature at the end of the nucleogenesis is
down to about ten million kelvin.
The universe grows cooler and thinner as the end-product particles
no longer interact. They must wait for the next stage of element
production within stars. We once thought there was no more nuclear
activity for a couple million years while stars and galaxies were
slowly condensing. We called this no-activity period the 'dark ages'.
Recent observations suggest that galaxies sprang up only several
hundred million years after the bigbang. This allowed for the first
stars to begin element production much earlier in the life of the
universe.
The Neutron Decay
---------------
The particles in the early universe were almost all stable ones,
not self-disintegrating into other particles. Tritons and neutrons
aren't stab;e. They decay. The triton's halflife is some 20 years.
Once created near the bigbang it endures long enough to engage in other
reactions.
The neutron has two cases of life. Within a nucleus it is stable,
like the proton. As an unattached free particle it has a halflife pf
only 'a few minutes'. The vague halflife came from the preliminary
data released about atmoic research after World War II and most cited
a time of some 20 minutes.
The original neutrons after the bigbang were unattached into
nuclei. They were free particles. With a 20-minute halflife the
neutrons COULD stay intact until the end of the interaction era
without producing protons! When the neutrons do disintegrate their
daughter protons would be too cold to interact and we would not move
along with nucleogenesis. The bigbang cosmology would be discarded or
massive revised.
Our world would be a era of cold protons, never able to merge into
any other elements. We wouldn't be here to study such a universe.
Better data for the neutron came in the 1960s but even into the 2-
thous there was still some concern that the neutron halflife doesn't
quite fit into the bigbang model. In fact, the acceptance of the
bigbang model pushes inquiry into the properties of the neutron!
The current value for the neutron halflife is about 14.7 minutes.
This seems about right to sustain the nucleogenesis of the bigbang.
The Relics of the Bigbang
-----------------------
The cosmic microwave flux of 537K temperature is the relic of the
bigbang. In our model here this flux comes from the gamma rays emitted
by the nucleogenesis. At first they would have the ambient temperature
when they were created, from around one billion kelvin. These gamma
rays were constantly absorbed and reradiated all during the
photosphere time after the initial half-hour of nucleogenesis. During
this period they were dispersed into a Planck distribution and
exhibited a blackbody spectrum.
At last, at the dissolution of the photosphere they were freed
into space. At this moment they had cooled to around 2500K. The
surrounding materials were able to settle into atoms with electrons
attached to nuclei. This material no longer interacted with radiation
and was transparent.
There after the gamma radiation was virtually unmolested by any
further interactions and it is felt by us today. it cooled with the
Hubble expansion such that it has the observed temperature of 2.7
kelvin.
Our analysis shows an other possible relic: the antineutrinos.
Antineutrinos are essentially inert against any reaction once they are
created. They travel in straight lines from their origination point
out thru all space. For them there was never a photosphere and the
universe was always completely transparent.
Many cosmologists believe we should find relic antineutrinos all
around us today. There actually is an isotropic and homogeneous
background flux of antineutrinos that suggests a bigbang origin.
Antineutrinos, being so inert, just aren't easy to capture and
measure. Of the zillions of [possibly] primoidal antineutrinos per
second that pass thru our human bodies, perhaps one in a whole
lifetime may mutate a body cell away from its normal function..
Electrons and protons are also relics of the bigbang and we
certainly have lots of them around now in an uniform deployment over
the heavens. Because they carry electric charge they are easily
influenced by magnetic fields.
They exchange energy with these fields and with other particles.
By now they have just no vestige of their primoidal properties. We
can extract little intelligence about the early universe from them.
In addition to possible original protons, protons and electrons
are created by many astrophysical process since the bigbang. There
seems to be no way to tell the original ones from the newer ones.