This webpage provides the solution to one of the greatest enigmas of physics:

Where is antimatter in the universe?

Here, we first calculate the quantity of antimatter inside atoms.
Then, we will extend this calculation to the antimatter in the universe.

This webpage is the fourth part of the website
http://www.quarks-antimatter.com
It is strongly suggested to also read the first three pages.

Starting points

1 - Antimatter in atoms

If the electron-positron pairs were created at the same time and in the same place, positrons are necessarily
close to electrons.
We already know where the electrons are.
So, the positrons we are looking for are not far from electrons.
The only possible place is inside the nucleus.
These positrons can be associated in quarks or in any different form, it does not matter.
In other words, we can say: Search the electron, and you will find its companion, the positron,
which, by necessity, is close to it (*).
If at a given time, an electron was created in the universe,
its counterpart, the positron, is certainly not 14 billion light-years from the event.
It is an evidence.

2 - b^{+} radioactivity

We expect that we have a large amount of helium in the universe, but we do not know where.
At the bottom of universe? In extra-dimensions (M-theory)?
On the other hand, imagine that each nucleus is a type of balloon filled with helium.
After accurate investigations, we note that one part per million of helium flows out of each balloon.
What should we think?
Of course, the immediate thought is:

"The little amount of helium that flows out of the balloons leads us
to suppose that the balloons are
filled with the helium we are looking for".

In physics, we are faced with the same problem.
We know that a very small amount of antimatter flows out from the nucleus by the way of beta+ radioactivity.
Whatever the name given to the internal particles, bosons, gluons, X, Y or Z... we can strongly
suppose that antimatter we are looking for is enclosed inside the nucleus.
This means that we must undertake our investigations within the nucleus
...and not in the deep universe.
It is also an evidence.

So, we can conclude that

We have a strong probability of finding
antimatter inside the nucleus, not at
14.5 billions light-years from Earth

(*) As on Earth, search the woman, and you will find her companion, the man.
It is obvious that women and men necessarily live on the same planet.
It would be strange to consider that women live on Earth, whereas men live on a planet located 14 billion
light-years away from the Earth.
In the same way in Physics, it would be strange to have matter on the Earth and antimatter located 14 billion
light-years away from Earth, in the deep universe.

Homogeneity of the atom

Since we need 3 positrons to make an u quark (see the previous page), and by adding an electron we get a d quark,
it is easy to calculate the number of electrons and positrons inside any atom.

If we take into account the number of electrons of the atom, Z, we get:

In other words, whatever the chemical element is, this calculation indicates that, in any atom, we have exactly the same number
of positrons as electrons: 2A (A = atomic number).
Therefore, the amount of antimatter in the universe is strictly equal to that of the matter.
This conclusion is in accordance with Feynman's Formalism (Nobel Prize 1965) and QED in which the electron and
positron have exact symmetrical roles in quantum mechanics.

Inside any atom, the number of electrons N_{e-}
is strictly equal to the number of positrons N_{e+}
N_{e+} = N_{e-} = 2A

Antimatter in the nucleus

The table below shows some isobars A = 16.

Each column of the table must be read as follow:

u_{N}: The number of u quarks in neutrons (= N)

d_{N}: The number of d quarks in neutrons (= 2N)

u_{Z}: The number of u quarks in protons (= 2Z)

d_{Z}: The number of d quarks in protons (= Z)

U_{total}: Since each d quark contains an u quark, the total of u quarks is:
U_{total} = u_{N} + d_{N} + u_{Z} + d_{Z}

Positrons: Since three u quarks are made up of two positrons, the number of positrons is
2/3 of U_{total}. This number is e+.

Electrons: Each d quark contains one electron. Moreover, we have Z atomic electrons around the nucleus.
The total of electrons is therefore: d_{N} + d_{Z} + Z

This table can be extended to all atoms of the universe.
In any case, we have exactly the same number of positrons as electrons whatever the atom.
Matter strictly equals antimatter.
The number of electrons and positrons, in any case and in any atom, is the double of the mass number A.
This means that antimatter is located into the quarks inside the protons and neutrons.

We obtain the same result with any atom or isotope.

This rule is verified within
the 2930 known isotopes

Note
The "exotic" Li_{3} is the only exception but its existence is not proven and depends on published works.
This means that this exception can not be retained as a valid objection.
The problem of the Li_{3} comes from the lack of a neutron.
In the Spacetime Model, as we shall see further, each nucleus needs at least one neutron.
The Li_{3} does not have any.
If this isotope does exist, it should decay immediately into three protons.
This problem of neutron also exists in atoms with a halo which must have at least one neutron.
This tends to confirm the theory presented here.

Antimatter in the universe

The main elements in the universe are neutrons, hydrogen, and various atoms resulting from the Bethe Cycle or others.
Black holes and dark matter are not taken into account since we do not know the exact the constitution of these elements.

Neutrons

We have shown that we have a perfect equivalence of matter and antimatter in the neutron.

Hydrogen and various atoms

We simply apply the above equation.
For hydrogen, since A=1, we have two positrons and two electrons (= 2A).
To summarize, the formula of the antimatter in the universe is:

where:

ke-, ke+: Number of electrons or positrons in the universe

n_{n}: Number of neutrons in various elements.
The "2" factor comes from the above formula ne+ = ne- = 2A.

N_{H}: Number of hydrogen atoms in the universe.
As in the neutron calculation, the "2" factor comes from the above formula.

Index A: Atomic number of the various atoms in the universe.
The limit "m" is the maximum atomic number supposed in the universe.
"A" serves as an index too.
It starts from 2 since we have already taken hydrogen into account.

N_{A}: Number of atoms, of index A, in the universe.

2A: Number of electrons or positrons of the atom of index A.
The "2" factor comes from the same formula

e: Free particles in various forms in the universe such as muons/anti-muons.
This, quantity is negligible when compared to the other terms.
Since the neutrinos are not basic particles but sub-products, they are not taken into account in this formulae.

The begining of the universe

The following figure shows that the universe probably began with only sCells.
Electrons, positrons, u quarks, d quarks... can be made with only this "particle": sCell.
The creation of the universe is covered in Part 5.