Figure 1: Penrose Spacetime.
Previously we mentioned the special relativity interval. However we must also now show all
four rotational copies relating to ± ct, ± ict, ± jct
and ± kct as we will define all dimensions as ℍ of which only
the ± ict and ± ct component is shown in Figure 1.
This will give us a central single time dimension as being complete and four dimensional with
one ℜ and three ℑ parts. The reason to do this is the ℜ
time part will represent spacetime from the view of electromagnetism, our observable domain and
the ℑ time parts will represent the three colours of the strong force. Thus not
only showing the connectivity between electrons and quarks, but also between matter and
This is where can see that for each quark or electron, spcetime looks like that described with
flat Minkowski spacetime however when we add everything together it starts to look more like
it has negative curvature (saddle shaped) which is a anti-de Sitter spacetime. Most crucially
we can see that because electromagnetism is ℜ part of spacetime it must be commutative
however interactions between the various strong force parts being ℑ must be
anticommutative as the order of operation now matters.
The concept of the big bang is now obvious to see as it represents a moment when T0
had zero radius, just like a ripple in a pond doesn't exist before a stone is thrown in, as there
is no concept of before or negative radius. Expanding spacetime is when the trough of
T0 and peaks of Sα and Sβ are
increasing in seperation which would have the effect of driving matter and antimatter apart as
well as forcing electromagnetism and strong forces apart (greater mass seperation).
Electrons (e−) would sit in the + ℍ part,
positrons (e+) in the − ℍ part and
quarks in the +i ℍ, +j ℍ and
+k ℍ parts respectively. The
antiquarks in the −i ℍ, −j ℍ
and −k ℍ parts respectively.
You may also see that when time T0 is created we must also have the seperation
of matter and antimatter space Sα and Sβ. We can
now also define three categories of matter:
- Matter: Share both common space and time dimensions.
- Dark Matter: Share only common space dimension.
- Dark Energy: Share only common time dimension.
As you can see in Figure 1, the electrons and positrons only share the same common time,
so positrons created at the big bang would count as some of the total dark energy. But from the
perspective of quarks or antiquarks, positrons and electrons share common space and time so would
be seen as matter. Mesons being the only solution using ℂ spacetime, atoms of
one colour electron and three coloured quarks the only solution using ℍ spacetime.
It is also important to note that Sα and Sβ do not
wrap around but instead connect to a different universe (as defined by its own central
T0), as we must define the overall multiverse as continuous with no hard edges.
Last point to note is that with penrose diagrams the origin or destination for light must always
be the diagonal edges, and matter moves from the central time area outward in each direction. For
spacelike ℜ mass must stay within the red areas, and for timelike ℑ mass
within the blue areas. Electromagnetic force (γ) must stay within the electron area, and the
strong force (g) in the quark areas. Only the weak bosons (W±, Z0)
can cross between quark and electron areas and will be made of part ℜ momentum and
ℑ momentum, which is why they must have mass and be commutative in nature.