In following files some problematic issues concerning
the dimension degree step 4 →
3 are discussed.
Headlines  different aspects:
I. Introduction
II. Rotation
III. Geometrical aspects
IV. Multiplicity of Mass and its Distribution
V. Mass as property  once again
VI. Step 4 → 3 in terms
of Forces
Introduction:
The start of Physics:
Physics starts at the border to metaphysics, or rather at
the triplepoint between metaphysics  mathematics/geometry
 and human concepts expressed in words.
The start of Universe:
Universe is proposed to be a "blown up singularity"
as in this model and there it starts. (But it doesn't seem
to be any consensus about the size of this "singularity.)
Inflationary or not, the Big Bang could
perhaps be described in terms of "osmosis" (!),
a scalar field of density, the derivation of which is vector
fields.
Compared with the model here, sketched in Presentation, scientists
seem to look at the creation of Universe backwards, from
the end of the 5dimensional chain: the first stage after
Big Bang is described as a Universe of "radiation"
only. Probably electromagnetic (EM) waves (?), referring to
the observed nearly homogeneous background microwave radiation.
This radiation should then in some way partly transform to
electrons, protons and atoms.
At the same time they imagine all forces
united at start and gravitation as the first one being "precipitated"
from the other ones. And, according to other books, the only
way one have observed "matter" created by EMradiation
is when energy rich photons create pairs of electrons/positrons
(e/e+), in the neighborhood of heavier masses or atoms (as
a condition).
It's not easy to unite these different aspects
in terms of established scientific data.
According to the 5dimensional chain of concepts in the model
here, reading it outwards towards lower dimension degrees:
5 →4 →3
→2 →1
→0/00,
forces or vector fields as Acceleration/Gravitation,
FA/ FG come first, in next step the EMforce, and the polarization
Mass — Space before Matter with polarization of Charge,
and waves in steps → 2 →1→0/00.
However, reading the chain as from a perpendicular
viewpoint, with debranched degrees in first steps meeting
the other way around, illustrated in the figure below, the
different proposals of the scientists seem more easily understandable.
What they imagine as purely radiation becomes in this interpretation
only the debranched degrees from first steps, but should be
complemented with the structures from vector fields in steps
4 →3 →(2).
It's very much that physicists don't know:
They don't know what Gravitation is and how it can act over
distances, just imagine a lot of small quanta as gravitons
gathering to a discontinuous "field" or the inverse,
a field quantified in those imagined quanta.
Some believe they can skip gravitation and
replace it with the curvature of space  but only half of
the curved way of light around the sun could be explained
by the curved space, the other half through "gravitation".
And they don't seem to know why big masses
are curving the space around them.
They don't know what Mass is, what is giving
matter the property of Mass, but particlehunting physicists
now are looking for the "Higgs' particle" that should
give this mass property.
They didn't know, at least forty years ago,
what Charge is and probably not yet.
They don't know what "Spin" is,
an invented property, it's neither this, nor that  but still
useful.
Not to mention quantum mechanics, which
they readily admit they don't understand but still have rules
and some words and mathematics to manage.
Yet, these concepts, forces, mass, charge and spin are the
main properties which they use in the "standard model"
to describe the realities, besides time and distances.
Such questions, what something "is", are by definition,
hard to answer: The answers have to be given in any of the
three areas meeting at the triplepoint. Words and mathematics
for the physicists' part. And there are a lot of concepts
and different mathematics to travel around in. Concepts have
to be defined through other concepts and these through others
again.
A force, for instance, was earlier defined
through its effect, as something that changes a motion, its
direction or speed. Now, in the "standard model",
forces are described similar to human talk: two persons as
"particles" throwing words as small field quanta,
photons or other things, on each other. Something like bacteria,
joining to exchange parts of their genetic code, just to describe
it on the superposed level of living societies.
One conclusion: If we want an understandable
description in words, it seems as we have rather much of a
free choice when it comes to which concepts to use.
The concept "Dimension":
A special problem is the different ways to define the concept
"Dimension".
In this model we have defined an outward
or inward directed vector field as 4dimensional. In which
sense isn't it 3dimensional  or representing an infinity
of dimensions as extensions in an infinity of directions?
 Physicists want one dimension for each independent variable.
Independent? Shall we believe that? According to the model
here nothing is really independent, at bottom. This "independence"
seems only to refer to elementary geometry and the usual coordinate
system and relations where the scalar product of vectors are
zero.
 Mathematicians as Hilbert creates an infinitydimensional
room for possible "states"...
 In ordinary speech of today there is often talk about this
and that as another dimension, usually referring to another
aspect, characterized through some kind of contrast or opposition.
 In elementary geometry we have the usual coordinate system
of 3 axes and they are indeed also characterized by opposite
directions from the origin, with signs plus and minus. One
says that the 3 axes are needed to completely define the position
of a point in space. However, this view disregards identification
of the origin, where the axes cross each other, and the "directions",
the "signs" (+/).
One definition concerns extension, actually
built on the basic concept Distance. A point has no extension,
represents dimension 0. The extensions are created first with
distances and space.
To this comes the little problem with a curved line or surface:
a curved line is 1dimensional in itself but needs 2 dimensions,
a curved surface 3 dimensions for its existence. What about
a curved space  ?  or a "curved" mass? * And in
the String theory a linear string needs 10 more dimensions
plus Time for its vibrations to express such things as mass
and charge and what else: still another definition of "Dimension"
as it seems.
*A point has in these days
been defined as something with an infinite radius
of curvature  a really selfabsorbed definition!
So, in which sense do we use the fundamental concept Dimension
in this model, when describing vector fields as 4dimensional
in relation to Masses and Vacant Space as 3dimensional? The
infinity of directions outwards from a point or inwards towards
the point is obviously not seen as different dimensions, just
as a property in this dimension degree (ddegree).
When talking about 4 dimensions we use the
kind of definition which concerns how many data that are needed
to identify a certain unit (3 for position in space, + 1 for
directions outwards/inwards. When talking about Mass and Space
as 3dimensional in relation to vector fields, we still keep
to the polarization concept of two complementary "structures"
but suddenly also enter into the definition of dimensions
as extensions, viewing Masses and Space very elementary, without
complex curvatures, only in their external form.
Do we use the same definition of dimensions
in these descriptions? What happens  in the "degradation"
of our viewpoint  or physically in the formation of enclosed
volumes as masses  when stepping from 4 to 3 dimensions?
How does an infinity of directions (vdiv
/ vcon) transform to an
ordinary 3dimensional form in the step 4 →3
according to the model here? In which sense could Mass be
interpreted as 3dimensional in relation to vector fields
as 4dimensional?
There are many questions connected with this one:
 Why do all masses of universe rotate?
 Why this manifolds of masses and unity of Space in cosmos?
 And again: What is Mass, how should Mass be interpreted
as created through this step 4 →3
→(2)?
See also a new suggestion about "GAwaves".
Rotation
Why do all celestial masses rotate, cosmic clouds and elementary
particles, even haploid eggs in the oviduct? It's an obvious
reality for celestial bodies in macrocosm and in microcosm,
but what is the best way to explain it?
In which sense do principally antiparallel
vectors (outwardsinwards) towards a center, in step 4→3,
change to perpendicular ones, an angular step proposed in
the model here? And what makes expansioncontraction transform
to rotational phenomena? It's difficult to find any convincing
explanation in the used literature behind this discussion.
The question is connected too with the problematic turbulence.
1. Rotation as a 2dimensional motion:
1a) In terms of the elementary 5dimensional conceptual
structure of our model:
We may ask: What is lost in the dimension
step 4→3? Ddegree 4 is
defined as vector fields, and a vector, according to the established
definition, is a physical quantity that besides numerical
values must be given a direction. So it has to be the character
of Direction that is lost in the structure in this step 
and translated to motion. A circular form has no direction
in the sense of inwards  outwards.
1b) In ddegree 3 two degrees should be viewed
as debranched and transformed to external motions. A 2dimensional
motion is rotation. (See files Presentation and Motion.)*
Hence, rotation is viewed as one expression for the polarization
of Direction in "poles 4a — 4b
There is also the general view on a dimension
chain as steps towards a more and more specified (crystallized)
direction towards "oneway" character. (From a chapter
on "chance", not yet on this site.)
The oneway direction in rotation could
be a Testimony of the rightness in the view of masses as one
"pole" or partial structure in relation to a complementary
one, the Vacant Space. (It may demand an excuse pointing out
the natural fact that Space "rotate" in the complementary
direction around celestial bodies.)
* Now it seems wrong to
state that a celestial body has only motions in 2 dimensions.
A planet like the Earth has its translation too, its pathway
motion (and a slow rotation of its rotational axis!). How
then justify the proposal? We could perhaps presume that it
is the orbital as a 2dimensional plane of each planet that
moves around the sun, not the 3dimensional planet (but not
the same as the very slow rotation of the orbit of Mercury
for instance, which Einstein explained). We could alternatively
see the linear motion in "geodesists" as expression
for the motion on an underlying 4dimensional level, not belonging
to a step in the same dimension chain?
2. Starting and end points of vectors as "stretched
out":
The starting points of vectors inwards   and target points
of vectors outwards  have positions "stretched out",
with a formulation from quantum mechanics, not defined  or
all possible...
The infinity of starting points of Direction
inwards as a virtual, circular structure may be interpreted
as transformed to Rotation with a factor of Time, that's Motion.
Compare the indeterminable principle: If
a particle has a certain moment, implying direction, (as inwards
from the 00pole towards a center in our model), this implies
that it has all possible positions. If it has a certain position
(as the 0pole in our model), it has all possible directions.
And here the 00pole is just defined as "anticenter".
Compare that the 00pole also represents multiplicity in our
model.
In a surface, the 3rd ddegree is indefinable,
and in 3rd ddegree the 4th ddegree should be likewise indefinable.
The higher ddegrees have the character of "superpositions"
(sooner "sub"positions).
Rotation, illustrating the "meeting
points" between targets of outward direction and starting
points of inward directions, may be regarded as expression
for the binding force between mass and empty space (E= +mc2/E=mc2)
 ultimately an expression for ddegree 5 as the binding force
between center and anticenter. This in accordance with our
description of ddegree 5 as step by step translated into
motion through the dimension chain.
Hence, rotation in ddegree 3 should be
interpreted as resulting from the combination of a radial
and circular geometry.
As to a higher ddegree as indefinable in rotation, a similar
description is given for quantum numbers of electron shells
in the atom: two of the quantum numbers (s l, x) are fixed,
defined, but the 3rd not: it is illustrated as a vector with
fix starting point but the arrow of which rotates around the
yaxis.
(The slow rotation of the "yaxis"
of the Earth seems to illustrate the same?)
3. How do physicists and astronomers explain Rotation?
The fact is that they don't seem to have any common explanation.
One vague suggestion is that rotation should result from some
irregularities in the surrounding gravitational field. If
so, we could compare with the general assumption in our model
that the 00pole as anticenter, ~ surroundings, represent
the polarizing force. Here in the step 4 →3.
Other sources refer more accurately to the
law of energy preservation: When a celestial cloud contracts
through gravitation, the potential energy of the outer areas
in the cloud decreases and the energy has to transform into
something else: rotation. To a certain degree it may transform
to temperature radiation outwards until the density becomes
too high. There is a change in the "quality" of
energy (a formulation attributed to Sarfatti).
If this view is an explanation or just a
description may be discussed. In any case it is in accordance
with the general proposal in our model that a) there is a
geometrical transformation from outwardsinwards to a radial
 circular one, b) it is in a certain sense the inward direction
from the anticenter that transforms into a circular geometry.
One author talks about "random motions which probably
show a little surplus in one direction" and with decreasing
radius develop to rotation in that direction. A rotation of
a star 17 times per second (!) is attributed to its collapse
to about 20 km radius, and to the law about preservation of
angular momentum.
Another formulation: the temperature ought
to increase when a celestial cloud is compressed, but the
clouds of gas have an effective way to get rid of the created
warmth: the energy is stored as rotation of the hydrogen atom.
(Hence, not only rotation of the big clouds, even the one
of individual atoms?!)
Compare the perpendicular relation between energy forms of
Frequency and Amplitude in electron shells (file EMwaves):
absorbed energy expressed in amplitude of electrons, outward
transmitted energy as "radial" radiation, expressed
in frequency.
4. Turbulence:
A corresponding transition from linear to 2dimensional, rotational
motion appears in the emergence of turbulence in gases and
liquids. Why has turbulence been such a mystery for the scientists?
(One of Heisenberg's questions to God: Why turbulence?)
How does a more or less rectilinear current
suddenly change to whirls and big whirls breed smaller whirls
etc.?
We could try the assumption that more substance
(as one form of energy) is poured into a water current for
instance than the outlet permits, in accordance with the description
of celestial clouds above, which should imply that the surplus
of energy had to be translated into rotation.
According to chaos research however, this
cannot explain why currents, like the Golf stream as an example,
here and there begin to wind and generate whirls or debranched
circular currents. Or the behavior of smoke from a cigarette.
We could probably add: the Rossby waves from the jet stream
of wind around the arctic pole, from which more or less circular
highpressure and lowpressure cells are debranched.
Could we assume that everything in the way
of a linear current, invisible perhaps, that can get the role
of a center, curves the linear motion as if activating one
pole of ddegree 4 and step 4 →3?
Perhaps a reality in some water streams but not a satisfying
assumption according to other examples.
Looking at our elementary dimension chain we have:
Ddegree of Structure: 5 →
4 → 3 →
2 → 1→
0/00
Ddegree of Motion: 0/00 1
2 3
4 5
Chemically, solid, liquid and gas phases have in another
part of this booklet series been characterized as 3, 2 and
1dimensional phases respectively on that higher, chemical
level. (Water for instance has molecules with a plane form.)
If our simple scheme above is possible to
apply to that level, we should find a 3dimensional motion
in liquids and a 4dimensional motion in gases: perhaps in
the form of spiraling (= translation + rotation)  with addition
of a motion inwards  outwards as expression for the 4th ddegree.
(Inwards?!. Do we eventually find such inward directed but
perhaps disregarded motions in gases?)
There are interesting experiments in the
literature showing how 3dimensional motions are appearing
in liquids (mentioned in a book about chaos):
A spot in a liquid was observed to twirl
east  west, up  down, inward  outward. And Theodore Schwenk
who studied currents in a watercourse found secondary streams
moving as in spirals, as one surface rolling around another.
Another example: studying liquid helium, there was observed
first the formation of two rotating cylinders of the liquid,
then, a bit later, also waves along these cylinders. Hence,
a 3dimensional motion.
Scientists also use the term "phase
transitions" when talking about such examples of turbulence,
which in our model should represent dimension steps.
The motion of a stream may represent a 4dimensional "vector
field" as it appears on that higher level of Matter.
"Direction" as structure. A liquid as a watercourse
 and a gas  has of course in its entirety also a mass and
a surface to the surrounding, possibly developing to internal
2dimensional "layers", and extensions as principally
1dimensional. (The step from linear motion to rotational
(2<1), corresponds in our dimension chain to the step
from the property Direction to volume, Mass, step 4→3→)
Hence, a stepwise increasing complexity
in the motional patterns could perhaps be reasonable from
this point of view, as expressions for how these different
properties of the stream manifest themselves?
Assuming such phase transitions, should we think of them
as endogenous or not? What causes the transitions?
One answer, in terms of abstract, general
postulates in our model, is that a unit whatever it is, here
a stream, always has a surrounding, corresponding to the anticenter
pole 00, representing the polarizing force. Compare the talk
about "external disturbances".
More concrete, a liquid has its borders, a cloud its emptier
surrounding. We could imagine that the difference at the border
 as defining a border in itself  is enough to represent
a polarization. Difference in velocities at the borders, through
friction perhaps, should be enough to create polarities.
The different properties in structure of
Direction and Mass (4 →3) seem
to manifest themselves stepwise, and this could depend on
a change in velocity. Velocity has in our model tentatively
been identified with the dimension steps as such, representing
the debranched ddegree, fundamentally expressed in the last
step 1 → 0/00.
About the splitting up of whirls to smaller and smaller
ones:
In a rigid body or a big whirl all parts or particles in the
whirl rotate with the same angle frequency, transverse the
same angle (as an area, 2dimensional) in the same time.
To get the same velocity, to pass the same
distance (1dimensional), the rigid body will have to crack,
the big whirl split in all kinds of angle frequencies like
frequencies in white noise. In this respect turbulence represents
a qualitative, geometrical step from ddegree 2 →1
in motional structure repeated. (Cf. perhaps Lev D. Landau
who has seen the turbulence as result of "competing frequencies",
mentioned in a book about Chaos.)
It also implies a step from rotation concerning
the radius to rotation concerning the circumference, poles
3b to 3a, (from radial to circular) as a repeated "pole
exchange".
To IIIIV:
Geometrical aspects
Multiplicity
of Mass and its Distribution
