The absolutely first to state:
The material property of some things is only a question
of relative complication and directions of structures 
when all building stones of Universe are seen as dimensions.
There is no such thing as the old fix
border between a "material" nature and an "abstract"
or "spiritual" world.
Fields  Mass/MatterCharges  Waves:
Elementary, according to the dimension model here, the concepts
"fields"  "matter"  "waves"
should be possible to connect with dimension degree steps
4 → 3 → [2
→ 1 → 0/00] respectively.
Matter is then seen as 3dimensional in relation to 4dimensional
fields, as 3dimensional superpositions to fields.
Waves, in relation to matter (in a prede
Brogliesense!), can structurally be described in terms
of dimension degree steps 2 → 1
→ 0/00, or (3) → 2 →
1 → 0/00. In these viewpoints we among other
things pay attention to the direction outwards towards the
ddegree of motion, the increasing number of external motion
moments.
We take as starting point the external
form of aggregated masses and material bodies as obeying
the Euclidean geometry for volumes proportional to r^{3}.
Mass and Matter?
There are two concepts: Mass and Matter:
a) "Mass" is a property equivalent with or part
in the expression for energy (E=mc^{2}) and is connected
with the gravitational force.
"Inertia" as a quality is associated
or equivalent with "mass" in this sense.
b) "Matter" is associated with relative "impermeability",
with surface structures, uphold through the property of
Charges.
Collapses when gravitation is too strong.
Hence, we assume here that Mass is the property created
in ddegree step 4 → 3,
(closer to the field level, and Matter the word for the
property created in ddegree step 3→2,
close to the differentiation of Charge.
Mass as "inversion" of fields:
Gravitation is seen as an answer from anticenter,
the 00pole, to the FAforce, the
outward acceleration force, on the field level, ddegree
4.
(About forces here:)
Here is assumed that Mass as property is the result of "inversion"
of fields from 4th ddegree to the 3rd, dominated by gravitation.
Some kind of "inversion". In three respects perhaps:
 "Inversion" as inward direction, interpreted
as "negative" direction versus outward acceleration
(FAforce), meaning a building
in of fields*,
 "Inversion" as the mathematical operation y
= x inverted to y = 1/x, a straight line translated
to curves.
 Geometrically through angle steps forming one pole with
enclosed center, ("the circular" pole) versus
the excluded pole of the surroundings, (the" radial"
pole).
* Compare, if superposition can be
viewed as addition, the 4 dimensional fields
plus 3dimensional mass structure, forming the 7 dimensions
that the string
theory talks about as underlying, "not
developed" ones.
Compare the inversion of numbers too, all numbers ›
+1 or
‹ 1, giving fractional numbers near the origin, the
Zero.
In old classical physics we have F = m x a, a Force is
Mass times Acceleration. That gives:
Mass = Force x 1/a, inversion of acceleration,
(s^{2}/m).
If we regard Forces as 4dimensional and Time as 0dimensional,
we get the Mass as 3dimensional. (With Time seen as 1dimensional,
Mass will be 5dimensional.).
According to first postulates in this model, the concept
Velocity is identified with the quantum jumps, (along
the main axis of a dimension chain).
Hence, the Einstein formula E = mc^{2},
where E designates energy, c the light velocity,
m the mass, the energy becomes 5dimensional, which
sounds reasonable, if Time is viewed as 0dimensional.
It could be interpreted as an expression
for a 5dimensional relation: Mass as a 3dimensional structure,
and c^{2} interpreted as the expression for the
2 quantum steps from ddegree 5 to the Mass degree 3, representing
the binding energy in underlying steps.
Mass as inertia:
Mass  Inertia  Heaviness  Gravitation: what difference?
1) It has been said  within the frames of
mechanical physics  that Mass as a property is more or
less equivalent with "inertia". Inertia as resistance
to changes in velocity or motion, when an outer force is
applied to it, is an aspect from outside.
A hypothesis in this model is that Mass
in this sense  but as an inner property  has its root
in what the concept of "center displacement"
stands for. (Compare in macrocosm the difference between
gravitation centers and mass centers.) First origin of Mass
should be found at the anticenter pole. With growing complexity
anticenter of units become centers of superposed units:
we get a stepwise center displacement as a eoretical foundation
during development of dimension chains....
Mass then should be Mass in force of
its "strangeness" to use a word from elementary
particle physics. (And compare perhaps a flywheel, the inertia
of which reasonably grows outwards with bigger radius.)
To compel a unit of an inward directed acceleration, even
if inverted, to accelerate outwards, is naturally against
its will!
Heaviness, in opposition to Inertia, could be described
as a concept for relations between two bodies, as between
the human body and the gravitation of earth.
There is a mess of loosely formulated statements about
these things. Physicists don't seem to care about congruence
between concepts in "classical" physics nowadays.
An example: Two statements seem difficult to unite:
It's said that gravitation is strongest
at the surface of an aggregated mass. This is rather simple
to understand: On a particle at the surface the gravitational
forces are acting only from particles besides and inwards.
For a particle deeper in the mass, gravitational forces
from others cancel each others.
At the same time we have the statement that
gravitation falls off proportional to 1/r inside an aggregated
mass, strongest in the center then, This means we have a
factor in gravitation as the inversion of the quality Distance,
as in inverted acceleration, see above.
The two statements must be a mix of essentially
opposite views, for instance from the single particle as
0pole and the aggregated mass as 00pole. Or a "reading"
of the gravitational force along two perpendicular coordinate
axes when the angle 180° of 4th ddegree is transformed
to the 90° of 3rd ddegree,
0 and 00poles along straight angles.
center and surface. What could that say about the structure
of Mass and aggregated masses  and the reason for rotation
of celestial bodies !? (Figure source: Sawyer 1961.
v = 1/t^{2})
Another problem is how to interpret the Einstein's (Lorentz')
formulas, which says that mass grows to infinity when the
velocity of a particle or body goes to the light velocity
c. And at the same time looses its length dimension, becomes
2dimensional.
The problem of the first formula arises
when the 0 or Zeropole shows itself as denominator, which
it really is in this model, mathematically giving the numerator
the role of 00pole and "infinity", more properly
the role of whatsoever. The relation becomes an undefined
"infinity". If we allow ourselves to multiply
both terms with with denominator zero, we get that Mass
in light velocity x 0 = the rest mass. This rest mass becomes
zero,
Without penetrating the equations behind, we
could assume here that the formula concerns mass as inertia,
and that velocity, reaching c, implies a transformation
to another coordinate axis  and ddegree 2 according to
the second formula (compare the figure above). The
Mass concept will then get another meaning.
Lower ddegrees always represent an infinity
 and "anticenter"  in relation to higher ddegrees.
(There are an infinity of surfaces in a volume, e.g.)
We have also in first formula a complex relation
(as "division") between the "rest mass"
as numerator and velocity in the denominator, both rest
and motion. In the model here the quantum jumps between
ddegrees are identified as the concept Velocity. They represent
then happenings between structures and motions.
Figuratively Mass could be called a dimension
fountain  of inversions,  or a "matter flower
" out of underlying fields and dimensional networks
of branches. A converted maelstrom.
(The Mass more like a source of unrest. As
builtin energy:
As the spring in a winded up watch. As the aviation
force in a bumblebee. As the spider when it spins
the thread of its path. Mass in itself just that
"being winded up" in a spring.)
Matter:
Matter as a concept is  in a certain contrast
to "mass"  connected with a more "material",
"particle" like structure, generally speaking:
particles with enclosed centers, with surfaces.
It is an aspect on the relative impermeability of
quanta, associated with this physical quality. .
It can be interpreted as a certain degree of complexity
in the structure, of "substantiation".
With the inwards / outwards development
of dimension chains, the particle character in the structure
increases. Hence, for matter as the property of being material
there are differences in degrees.
Matter is also connected with the charge concept, with
the charges of quarks, even if zero charged as some mesons
and the neutrons.
Charge
is in this model assumed to be a property of ddegree 2
(in relation to Mass analysed as a property of ddegree
3). That's a reason to see "matter" here as a
concept in ddegree 32:
Protons, e.g., as a pole 3a of 3 dimensions
curled and rolled up into them selves
in inward direction (compare
the String
theory).
We know that electromagnetic waves, outward directed as
waves, in inward direction* can create / transform to pairs
of charges as electrons/positrons (e+/e) momentarily.
* Interpretation in this model, more
here.
Since the level of analysis is optional, the structure
of matter as tiedup energy should alternatively be possible
to describe
 as stratified shells,
 as stabilised , relatively closed processes (of polarizations/
depolarizations), à la "standing
waves",
 as conglomerated, curly lines,
 as builtin movements, more or less stabilised.
This seen from lower dimension degrees 2←1←0/00.
Spin:
Matter particles are "fermions", are composed
by quarks according to assumptions in the standard model.
They have mass, and spin 1/2.
Spin 1/2 means, according to Hawking,
that the particle has to be turned twice (!) round for appearing
the same again, (in opposition to quanta of forces, which
only have to be turned one round).
A suggestion here is to think about a
band twisted once to an "8": The band has a 2dimensional
structure, an inside and an outside. Following the outside
we come to the inside and after two round to the outside
starting point again.
Generally speaking this indicates a more
complicated structure. More about spin on pages Charge
and Spin.)
Vacant Space:
Time has been called "an aspect on the relative motions
of bodies". Space could be seen as equal "relative",
an aspect on the relative positions of single units,
as quanta or material bodies.
Space is defined through distances relations
and direction relations of 1st degree and through motions.
Through surfaces as enclosing and excluding centers, through
material bodies and their movements.
The answer to the question how forces
can act over distances must be that it is the forces that
create distances and Space.
Vacant Space is here defined as the complementary pole
to Mass. It's seen as characterised by the outward acceleration,
the FAforce in ddegree 4, more
fundamentally
in the negative expression "E=mc^{2"}
in Dirac's hole theory, whose equations gave two results
+E = mc^{2}
 E = mc^{2}.
The first polarization of the Entirety
in ddegree 5 into the poles 0 and 00 is here presumed as
a polarization in +/ E for Energy.
According to first simple hypothesis in this model the opposite
poles of 3rd ddegree get the forms of "radial"
versus "circular" geometries. That is to say
that the radial structure of vector fields in ddegree 4
are preserved in ddegree 3 for the pole 3 representing
outward direction, while mass or matter as an "answer"
from the 00pole gets "circular" structure.(About
ddegree step 4→3, see here.)
Through a pole exchange Vacant space as
radial, open structure gets the role of anticenter to normal
mass  and matter of positive energy.
(Another aspect is to see mass and matter
as the result when a cosmos of "haploid" dimension
chains are "saturated" through meeting and combining
with another one  and see vacant space as the unsaturated
rest.)
Density, here chosen as concept for a primary physical
quantity (rather quality), between center and anticenter,
in ddegree step 5 →4, is
in outward direction imagined as polarized in e.g. Mass
per Volume unit in 3rd dimension degree.
Density is expressed too in quantities
(or qualities) as the strengths of vector fields and in
density of charge  as in Schrödinger's wave functions
 and is intrinsic in the concept of distance (closeness):
that is in lower ddegrees.
(In the same way as Forces are interpreted
as transformed into qualities of lower d degrees as Mass
 Distance  Time.)
The "negative" energy of vacant space should
not be interpreted as just lack of energy. It should be
understood as a world "below the E0line" (se
further down).
Different signs (+) and () are viewed
as representing complementary poles, at bottom opposite
directions.
If we presume that there are plus and minuspotentials
developed in matter, and have the multiplication of minusenergy
with minuspotentials (as in the expression for energy:
Force x Distance), we can get positive results, (the radial
ones, compare repulsion), and minusenergy on the pluspotentials,
(circular), of the nucleus, compare attraction). (Se some
notes about Energy.
Vacant space will be a working force,
giving both plus and minusenergy depending on the sign
(or direction) of that phenomenon which it is acting on,
etc.
The matter is not so simple:
According to the main geometrical
views in this model the anticenter pole as surrounding
is step by step built in into the counterpole units with
enclosed centers towards superposed levels.
This implies that we should expect mass/matter
and vacant space being complementary combinations of
both 0 and 00poles and FA and
FG , a complementary construction
of elements from the field level. Compare views on the nuclear
force here.
We could find "holes" or factors of "antimatter"
. (as earlier assumptions by physicists) in our ordinary
matter.
On the level of atomic structures there
are for instance the intervals between electron shells and
distances between electron shells and nuclei.
Compare too about Electromagnetic
waves.
If we accept the view about electromagnetic
waves, that the waves uphold their existence thanks to the
continuous access to vacant space as "nourishment",
then we could imagine Matter being
still more complicatedly dependant on vacant space for its
existence. Presumably we could say that Matter as atoms"is
breathing vacant space".
Hence, we see the particle like structures
as stabilised processes where matter, roughly interpreted
as plusenergy, all the time must be uphold through communication
with the original Entirety, via (+/)energies on underlying
levels, i.e. with that original Entirety which also is environment.
When for example
tremendously dense neutron stars implodes in so called gravity
collapses, and explodes into supernovas, the interpretation
could be that the access to "vacant space" in
the inner of the stars has been strangled to a certain density
limit. Matter  as just structure, is ruined (perishes)
or revolts.
Different degrees of Vacant Space
and Gravitation:
In more general terms we
could imagine that there in the neighbourhood of big celestial
bodies, where the field level so to say has been "used
up" at the inversion to mass, are another degree of
vacant space: gravitational fields as a sweating of vacant
space: the negative energy of vacant space sucked out, making
it extra or "collapsingly" empty, with losses
in its"radial force", curved towards circular
forms.
Masses are then depending on the outward acceleration force
and Vacant space. According to new information too it isn't
the galaxies that are flying outwards from us in cosmos
but the space that is expanding, "carrying" them
away.
Microcosm  macrocosm will then become 000poles
in a complex combination of matter and vacant space:
Matter builtin into vacant space in macrocosm,
and vacant space builtin into the matter in microcosm.
Motions
Motions could be called the communication between +E=mc^{2}
and E=mc^{2}
(Ddegree 0/00 of Motion
as the ultimate expression or translation for the Entirety
of 5th ddegree.)
Compare forces
as interactions, with quanta of forces which include
the complementary pole of vacant space.
The E0line:
With accepting the theory of "two worlds" of +/
E=mc^{2} we have to assume that the first Entirety
of ddegree 5 represents E0, 0 for Zero, a border line between
the regions, a kind of mirror.
Osmosis, the penetration into surroundings,
is a process generated by a Density difference. It doesn't
claim any energy. Big Bang as osmosis?!
Said in another way: the concept of Energy isn't yet defined.
According to the abstracts
of this model: first when we have a relation between between
derived ddegrees as force relative to structure (~Force
x potentials as Distance), there is a measurable "energy".
Still the border line or E0 will be the
real energy well.
In ddegree 4 we could see the lost ddegree, transformed
to motion, as this border line E0: expressed, say, in the
increasing/decreasing Density of longitudinal waves.
And then: Rotation as "E0" in
ddegree 3.
Mass  Vacant space in relation to Distance and Time:
Time (directions)
Distance
mass ————————›
space: frequencymodulating
mass ‹————————
space: amplitudemodulating
Time: inverted to frequencies outwards the space: waves
Distance: as wavelengths inverted to amplitudes inwards:
mass property.
Compare the same in the atom and in the
nervous
system.
A curious question seems to follow from first
postulates in this model. A 3dimensional space "should
have" movements in remaining 2 ddegrees, expressions
for the "lost" dimensions in steps 5 →
4→ 3.
Hence Space, analysed as 3dimensional
and an entity in its own right, should have some 2dimensional
motion. If we can see rotation as such a motion for its
complementary "circular" pole, for Matter. the
Vacant Space should have a motion of "radial"
character, perhaps possible to identify as negative curving
of surfaces in space? (Added here: As in some kind of hyperbolic
geometry?)
Is Vacant Space quantified?
Shall we think that the vacant space in itself is quantified
or only as a result of the quantified matter?
When, for instance, the positive energy
levels in the electron shells of atoms are quantified, the
space or the negative energies between the levels are by
that simultaneously quantified.
In terms of quantum jumps
versus continuum, the vacant space, in its role of a relative
00pole, should still correspond to continuum, in that sense
then be quantified by the counterpole, by matter.Yet, at
bottom, the principle should be the same as in longitudinal
waves: a simultaneous quantification through thinning 
condensation (motions "to/from each other").
According to the model here we should be able to find coresonances
in both "structures" , between matter and vacant
space, coupled through a joint, unpolarized underlying level.
See further
some notes on the experiments which became the foundation
of quantum mechanics.
Some critical notes here:
1) According to this model there should be a 3dimensional
structure, geometrically called Volume, still unpolarized
into Mass and Vacant Space. What should that be? It gets
very abstract and hard to imagine otherwise than in mathematical
terms, as 3dimensional functions or vector fields.
We could possibly imagine a 3dimensional,
Euclidean "room", polarized into an elliptical
and a hyperbolical geometry for mass and vacant space respectively?
(Or with positive and negative curvature.)
The concept Volume is a scalar, but imagined
as 3dimensional vector fields we have a much more dynamic
world.
2) How can such an abstract "volume" be interpreted
as the "binding force" between Mass and
Vacant Space? As their "inner connection"?
Simplest we could see the motions of material
units as an expression for this binding force. (It's not
least thanks to empty space that material bodies can move!)
In quantum mechanics we can think about
Feynman's "way integral", his interpretation
of behaviour and "path way" of electrons in quantum
experiments, the quanta taking "all ways" to a
split in a screen. The "way integral" seems to
just define the "Volume" concept.
Compare too forces as interactions and
their "carriers" in the standard model  as expressions
for this binding force.
3) Is it possible to state that the polarization between
mass and vacant space defines ddegree 2 as Surfaces  in
a more than a rather silly way? As a physical structure
"in its own right"? Possible to identify with
Charge as concept?
We leave the question to that chapter.
4) In which sense is it allowed, if at all so, to look
at Mass as a 3dimensional property?
Well, celestial bodies and atoms, even
nuclei?, occupy a 3dimensional Euclidean space. And perhaps
there is a connection with the physicists' statement that
the strong, nuclear force falls of proportional to 1/r^{3},
the cube of the radius.
Still, it should be possible in this model
to include the aspect on a 4dimensional "metaroom",
already defined on the vector field level, where one ddegree
is not yet transformed into external motion  not contradicting
the 4th ddegree of the room in Kaluza's calculations.
(About 11 dimensions, see some notes to
the String
Theory.)
Special notes in additional file here,
content:
 Waves before Mass?
 Matter as de Broglie waves
 Mass  transformed into other physical quantities
 Some numbers
 The lacking Mass or Matter in Universe
 Can new matter be created in our Universe?
 The splitting up or interference  diffraction of the Mass
 Vacant Space and the Future
Compare also file
The
ddegree step 4 → 3 and the
manyfold of masses
