Matt Watt proposed studying Ken Wheeler's book in depth and perhaps coming up
with a clearer understanding of this inner space or sub space. (Again, Steinmetz and Dollard discuss this concept at length)
It occurs to me I might be able to address this concept without trying to parse out
Wheeler's intent. He may have well covered the subject in depth and cogently.
I just haven't had time to read his book yet. The members here keep stimulating ideas
for me to cover. So let's have a go at this subspace.
In a separate thread I stated that R=k/c=30 ohms
where k is Coulomb's constant, c is the speed of light, and R is a constant resistance of space.
Exception was taken to my designating R as a constant resistance of space since it is known
that when measured the resistance (impedance) of space far exceeds this value.
Smudge, using some remarkable insight recognized that R factored by 4pi was the Zero Point
impedance of 120pi.
I then realized this makes sense since R is electrostatic and confined to the plane. When taken
to 3D we go from square area of a plane to the surface area of a sphere, 4pir. In this case
R is equivalent to r the distance.
Now if we wanted to compute how much charge occupies the sphere we would simply compute
4/3[pi(rrr)]. But we know that charges can't occupy the volume of a sphere only the surface.
This is where simple quaternion algebra comes to the fore.
Quaternion algebra says ii=jj=kk=ijk=-1.
rrr is actually xyz
and xyz is actually ijk which equals-1.
So to compute the volume of this sphere we have
Because when oriented orthonormally they take on the characteristics of vectors, or versor, not scalars and behave accordingly.
Therefore the volume of this sphere is -4/3(pi).
Note the negative sign. Also note this is a scalar in the sense that -1 is a directed scalar.
Ostensibly it would seem to be a tensor but the factoring by -1 makes it a scalar.
This inner space, this -4/3(pi) is a pseudo volume. A pseudo volume because it has no units of volume and yet is comprised of 3D components.
Given the negative sign it is a space that rejects the presence of versors, of spinors, of electrons, of charges.
It acts similarly to the Meisener effect where the Meisner effect rejects magnetic fields this pseudo volume rejects electric fields.
It is a null space that separates conjugates thus the formation of the atom and its nucleus
Again. The empty space in an atom is not just empty space. It is this innerspace. A quaternion space predicated on scalar components.
This is my take on innerspace. A very simple concept, at least algebraically.
Physically, it is a difficult concept to conceptualize. This is because our perception of the world is vector.
It takes a bit of getting used to looking at things from a scalar perspective.