1. Outwards - Inwards, and the "center" concept
2. Motions preexisting as structure
elements in higher dimensional degrees
3. The deflection of light around
the sun: gravitation, curved space
and/or influence of magnetic fields?
4. Can the curvature of space
or space-time replace the gravitational force?
reality of a centrifugal force?
Matter as a combination
of the opposite forces
How to interpret
the relation Mass - Mass?
5. Can forces act over distances
without mediation or not ?
6. E = -mc2 ; Einstein and the
imaginary world - and about EPR
7. The rotation of the elliptic
orbit of Mercury
8. Some books referred to.
This file as pdf here.
1. Outwards - Inwards, and the "center"
From the aspect of the model presented on this web
page it is rather confusing that Einstein in his books from 1916
or 1938 doesn't clearly differentiates between directions outwards
Acceleration as gravitation and as the opposite,
acceleration in a starting, lifting airplane is mentioned with
almost no distinction. (It's said to be one of Einstein's fundamental
experiences, the gravitational force he experienced in such an
Behind this lies the lack of a clear perception
of the concept "center", a concept not mentioned either.
Yet, the whole idea behind Einstein's relativity
theories and search for transformation rules between different
coordinate systems implies the concept of different centers as
origins in the coordinate systems. They are only implicit, not
mentioned or really observed, Einstein already soaring around
out in the three-dimensional space between the axes.
Concerning the directions outwards-inwards we have
a similar case: He had the good idea of a "cosmological constant"*
(A) for an expanding space of Universe, a repulsion mechanism,
which means the opposite direction to gravitation, even if he
later and wrongly abandoned it. (According to a rumor physicists
rather recently have found evidence for such an expansion of Universe.)
(Compare G/A-fields in the model here)
As it seems, Einstein didn't really recognize
the kernel of his own intuition.
(And the centrifugal force was still seen as
a fictitious force, only the effect of inertia of a mass, and
still seems to be viewed as such.)
(Einstein theorizes about gravitation as if it
comes into existence by acceleration - in an arbitrary direction
- without reference to any center. In comparison with the model
here we could put a question mark after the expression "comes
into existence". A force gives birth to an opposite force
according to Newton, all right. But they could eventually be
seen as born simultaneously, just revealing one another.)
2. Motions preexisting as structure elements
in higher dimensional degrees (d-degrees):
Einstein showed how Time, related motions, as a
4th dimension could be transferred to the same side of an equation
as the 3 space dimensions and thus make up - or be viewed as -
a 4th space dimension, a structure. He describes the 4-dimensional
space-time as the "being", the 3-dimensional space with
motions as the course (or process), the "becoming".
In another context in his books he also points out
and illustrates the simple fact that the motion of a falling stone
can be illustrated as a linear curve on a 2-dimensional surface
with coordinate axes for time and position. Einstein says: "Now
motion is expressed as something which is".
Once again, a structure element instead of a series of measure
points as a picture of motion.
Here as elsewhere it seems as if he missed what
the kernel in these views could imply. In the postulated assumptions
of the 5-dimensional model
presented on these pages we can say that this kernel is
made a very essential part, with structures transformed into motions
during steps towards lower dimensional degrees.
One reason why Einstein didn't developed these thoughts could
be that he saw "motion as such" ("in sich")
as a concept we cannot give any meaning. And one interpreter says:
"It has always been self-obvious that motion as we interpret
the concept must be perceived as relative motion".
But can we give any such concepts, as mass,
charge, distances, particles etc., any meaning in themselves,
without referring to other concepts, in their turn only possible
to define in third terms
In these more general statements about motions
and in the public's idea about "relativity" there is
Einstein himself took the fix velocity of light
as a postulate and an absolute reality - and how to count on a
velocity without something moving?
We can try to see motion as only a change in the
relative position between two bodies (as a derivative of a distance),
but if a jogger runs through the wood, which part will lose energy,
the jogger or the earth? There is something with energy too in
motions. Even if a uniform motion doesn't demand any force as
Newton said, something put the body on the track.
With three objects changing their relative positions,
it gets still more difficult. Imagine two persons separating walking
in different directions, and we choose to regard them as the fix
resting coordinate systems, the earth under their feet would be
seen cracking, wouldn't it?!
There is more in Motions
than the relative aspect. And it seems much easier to imagine
the planets circulating around the sun than seeing the sun circulating
around each individual planet.
3. The deflection of light around the sun:
gravitation, curved space and/or influence of magnetic fields?
Einstein's prediction about this deflection from
a straight line proved to be true. Only about a half of the deflection
could be explained by Newton's theories, so one says, the other
half depending on the curved space around the sun and Einstein's
interpretation of gravity in the general relativity theory.
Some physicists at that time, who had difficulties
with this theory, thought this deflection could depend on magnetic
Without knowing anything more about their arguments,
one can say that according to the model here there shouldn't necessary
be any contradiction between these different views:
Firstly, we have the assumption that magnetic and
electric fields, M/E, are
developed out of G/A, gravitational and outward acceleration
fields as more complex combinations of the first complementary
"poles". There is in that case a connection and relationship
(as between father and son?) between what gravitation represents
and the magnetic component of electromagnetic fields: a natural
assumption in its most general formulation.
The physicists' disagreement could just be different
aspects on the same thing, a question of analyses in different
Secondly, we have in this model assumed the view
that the propagation
of light waves depend on the "negative" form
of energy of vacant space. We have assumed that celestial bodies,
as long as they are matter and not collapsed to merely a mass
property and black holes, are depending on their "consumption"
of that negative energy too. In their neighborhood this "vacant
space" could be less satisfying nourishment for light beams
to keep to their straight course.
[Some physicists say the magnetic moment totally
depends on the motions of electrons. Oscar Klein, commenting on
Einstein's theory, says that the gravitational force, like the
magnetic one, should be caused by the motion of the bodies. We
cannot agree with the formulation "caused by".
Here we see the two complementary forms of energy
as with equal rights, and would sooner suggest to describe the
same thing (if true) in another way: When the more noticeable
bodies or particles move, the electrons for instance, the motion
plus the body represents a deeper, higher d-degree from which
the body and its complementary part were polarized (as E-
It connects the complementary poles and thus activates its counterpart.
The sun, one says, has a magnetic field divided
in sectors of alternating polarity. Is it really possible to
reduce such an example to only a relativistic effect of electrical
4. Can the curvature of space or space-time replace
the gravitational force?
It has been said that Einstein did - and thus explained
"gravitation". "There is no need for presumptions
of gravitational forces
The gravitational equations of the
general relativity theory are 'structure laws'" (Foster).
Firstly: It seems as if we have a false or unclear
opposition between the concepts of "structure" and "forces".
In the 5-dimensional model on this site here we have suggested
to see each dimensional
degree as a force in relation to higher or lower d-degree,
and most elementary vector fields of d-degree 4 as binding "forces"
in relation to mass.
Secondly: Why are big masses curving the space around
How explain that without using the illustrations of gravitational
heaviness of balls in 2-dimensional nets?
We could rather believe that centralized masses
and empty space are complementary structures born simultaneously
from polarizations into positive and negative curvature of structures
In compliance with this view and the model here Einstein denied
the existence of an independent "absolute Room" (Newton's
idea), which he found a "pre-scientific idea".
In reality, no physicists seem to have succeeded
in dismissing the gravitation concept, still mentioned as a force
in the standard model. (Remember too: the deflection of light
around the sun was said to depend only to one half on curved space,
to one half on Newton's laws for gravitation.)
For a body falling vertically from the sky towards
earth, it must also be difficult to think it as depending only
on a curved space.
Thirdly: In his general relativity theory, Einstein
let such forces slip in through the backdoor with the tensor
concept from mathematics, with the help of Gauss. Foster again:
"While scalar and vector fields are sufficient to formulate
Newton's theory of gravitation, tensor fields are an additional
requirement for Einstein's theory". "An elastic body
is placed under stress by body forces (such as gravity) acting
throughout its extent and by forces applied externally to its
surface". There we are again, with the gravity.
What Einstein studied was transformation rules for
celestial bodies in relative acceleration to each other, that
is in motion. This could be interpreted as studying the realities
in a lower d-degree.
Tensor fields, what is it: neither scalar fields
(as a density gradient) nor vector fields. They are also called
"vector fields of a second order". One example is mentioned:
when a material has different conductivity in different directions,
presumably as alongside and right across.
Hence, without being mathematicians we could
assume that these tensor fields introduces a more or less perpendicular
relation between directions - the one we in our model here have
presumed characterizing d-degree 3.
(Compare perhaps the presumed Higg's field,
in some way "horizontal" versus "vertical"
Rotation as a 2-dimensional motion is in our model
attributed to d-degree 3, and rotation is a form of acceleration.
We could see this motion as a result or transformation
of the binding force between the complementary "poles"
Mass - Vacant Space.
We could put the question in this way: Which
virtual motion as a built-in structural element in d-degree 4
is "precipitated" to motion in the d-degree step 4 →
3? It ought to be the vector character of direction inwards-outwards,
which more or less gets lost in rotation (compare elliptical orbits).
The conclusion could be that the gravity which Einstein
explored, could be the relation between these complementary poles
Mass and Vacant space, not (primarily) the one between 2 celestial
bodies, two masses which Newton was occupied with.
(This can have relevance for the question: How
can forces act over distances? See further down.)
With Motion realized as acceleration we get a relation
between Masses and Vacant space, between forces G and A, centripetal
and centrifugal forces, as a relation of (more or less?) 90°.
A curvature. The gravitational force is also said to be strongest
along the rotational axis, the centrifugal force along the equator
plane. And the strength depends on velocity too.
So much about the d-degree step 4 →
The reality of a centrifugal force?
Einstein wasn't ready to accept the reality of the centrifugal
force, as he abandoned the thought of "the cosmological constant"
(A) and "negative matter if it existed". Of the same
reason, surely, he denied Magnetism the property of a force in
its own right. He wanted to see electric and magnetic properties
as only a relativistic appearance of the same thing, from different
coordinate systems in relative motion. (In spite of the fact that
the expanding energy of Vacant space now appears to be acknowledged,
physicists still seem to keep to the same views on these "illusory"
(One says that the magnetic field in the sun
is divided in sectors with opposite polarities. It sounds
hard to interpret this as only a relativistic effect between
different coordinate systems in relative motion
Have these things something to do with the opposition
between heavy mass and mass as inertia? Renard writes:
"At rotation the inertia moment plays exactly the same role
as the ordinary (read "heavy") mass at translation".
Einstein showed in his relativity theory that
the heavy mass and the mass as inertia must be of the same size.
Is it just a question of analysis in different d-degrees - and
the difficulty to detect the "negative" energies?
Einstein found the two kind of masses over and under a fraction
line in his equations and thus possible to reduce away.
D-degree steps or complementary poles as inversions?
Two such examples:
Waves: A little wave, governed by surface tension,
propagates with a velocity inversely proportional to the square
root of its wave length, while a bigger wave, governed by gravitation,
propagates with a velocity directly proportional to the square
root of its wave length. (Thompson)
Celestial masses: The radius of white dwarfs
is inversely proportional to the cubic root of their masses, while
the radius of stars on the main series is directly proportional
to the cubic root of their masses.
Matter as a combination of the opposite forces:
We surely have to see non-collapsed Matter as a combination of
Space and Mass, of Acceleration and Gravitation. The A-factor
built-in into matter inside stars. We have "radiation"
keeping up the volume, we have stars expanding to big red giants,
we have exploding stars
And the big difference between atoms
with "emptiness" between electrons in the shells in
particle models, and the atom structure collapsed to neutrons.
Further, we have the disintegration force of weak interaction
inside elementary particles. Probably all of this can be thought
of as manifestations (in different d-degrees) of an elementary
In the direction towards microcosm Space built
into mass, in the direction towards macrocosm: Mass built
into "Vacant Space".
So why don't accept the centrifugal force
as a real force?
How to interpret the relation Mass - Mass, seemingly without
complementarity: as of higher or lower order or d-degree? As some
combination of two relations Mass -- Vacant Space, or what?
Between two M-fields we have attraction or repulsion,
repulsion if similar poles, attraction between opposite ones.
And the like between electrons with opposite spins in the atom
Newton's gravity theory needed only scalar and vector fields.
Vector fields are described as the derivative of scalar fields.
We have in our model suggested Density (a scalar fieeld) as first
physical concept in d-degree step 5→4,
in later steps polarized and appearing as Mass per Volume.
The polarization principle seems to be active
in the gigantic celestial clouds of stuff, so one says, with polarizations
between hotter and colder areas, which contradicts the older views
on terrestrial temperature diffusion.
Newton's binding force was a relation of 180° and only depending
on Distance, a linear entity. The centrifugal force depends on
velocity too, (This holds also for the relation E-M, between electric
and magnetic fields.)
The attraction force between opposite charges
are dependent on the charge value, which got Einstein to put this
force in opposition to the gravitational one, only dependent on
distance. But there is no opposition if we see mass and space
as first complementary poles, in similarity with positive and
One conclusion could be that Newton's gravitation
between different celestial bodies is not a pure attractive one,
or just part of the relation, and that we have to count on an
opposite force at the same time, responsible for the partition
of masses and the distances between them? (Cf. the planets not
attracted into the sun, and the same for the arms of our spiral
5. Can forces act over distances or not?
Newton's gravitational theory seemed to imply that
they could. Gravitation had an immediate effect from far off,
without mediation. Einstein said no. He adopted from Maxwell's
theories about electromagnetism the concept of fields, rather
new at his time, (and saw an opposition between forces and fields).
He meant that the impact of gravitation between
bodies had to propagate as light does, and with the same velocity.
And physicists are still looking for the presumed mediating particle,
But doesn't the concept of "field lines" contradict
this view? Which reality should then be attributed to these "lines"?
And what about his own geodesy of the curved space, the more or
less prescribed pathways as geometrical lines? How is it possible
to deny an immediate effect over distances at the same time as
adopting the concept "fields of forces"!
It seems as if there is a mix of two things in this
general statement, mix of a static and a dynamic relation:
In our model here we have said: it's forces that
create distances, as the acceleration force created Space during
Vector fields, chosen as the concept for the
4-dimensional phase, are not distinguished from forces. Such vector
fields can simplified be seen as potentials with direction, "lines"
of relations - and in a static configuration the relation line
is there, is the immediate mediator.
Compare a railway: the real force is underground,
the need for it, on a more abstract or invisible level. The quantifying
of it in gathering different building material is a later substantiation.
And physicists still lack any god explanation
for these gravitational effects over distances, so one says.
Another thing is if a change occurs in one end of
the relation. This change may have to propagate along the connecting
"line" or field as a kind of wave. Some modern physicists
presume too that gravitons only "can be found" when
big changes occur in celestial masses.
Yet, according to the 5-dimensional model
here, there should be one d-degree of external motion debranched
through -degree step 5 → 4 (that
means polarization and quantifying of a line) even in a 4-dimensional
field, a linear motion:
How to solve these contradictory views?
According to our model such a linear motion should
be an expression for the 5th d-degree and the relation between
mass and the complementary pole, that is the "empty"
space, not directly between two masses, as suggested above.
(This could be one aspect on the fact which
Galilei showed, that heavy and light bodies fall to the ground
with the same acceleration speed - a fact that Einstein had
big difficulty to explain in his book. The same is valid for
the centrifugal force, not depending on the mass.
Another general explanation of Galilei's
experiments, according to our model, could be that vector
fields such as gravitation and an outward acceleration force
as of higher d-degree precedes the creation of masses, and
for this reason are acting independently of such things as
heaviness of these masses.)
So, if we accept that there is a motion (which takes
time), representing a translation of the 5th dimension degree,
in a gravitational vector field, we have still 4 d-degrees as
structural vector elements, more abstract potentials, to be viewed
as a reality preceding the motion and not having to "propagate",
in themselves being "immediate effects" à la
We could have both, an immediate effect over
distances, and something propagating, taking time?
And as suggested above: the attractive "line"
of d-degree 1 could only be a part of the relation.
The linear motion moment assumed in 4th d-degree could perhaps
be connected with the fluctuations in density in the negative
energy of Vacant Space which Dirac (1960) mentions, and "an
infinity" in these density variations which the mathematics
of that time didn't manage to handle. He meant it demanded a radical
change in the physical theories of his time.
Density variations as 1-dimensional L-waves
along "field lines"? Compare the suggestion in our model
that the first physical quantity in d-degree step 5 →4
should be just Density, and that the outer poles defining d-degree
4 should be 0 and 00, zero and infinity.
Something has been said too in later days about
fluctuations in gravitational fields on very small distances,
10-16 m (less than the diameter of protons).
The very small fluctuations that have been detected
in the background radiation of Universe concerns EM-waves,
electromagnetic radiation. This is seen as a rest from Big
Bang and a cause to the unequal distribution of mass in Universe.
But couldn't it alternatively be interpreted as a secondary
result of fluctuations in an underlying or more primary relation
About the velocity of the motional component:
In T-waves, as the electromagnetic waves, the energy has transversal
ways of expression. In gravitational waves, presumed to be longitudinal
L-waves, the energy has not. Couldn't that be a reason for these
L-waves to travel much faster than light? (Oscar Klein said the
propagation of gravitation with the velocity of light was a condition
for Einstein's theory. Right or wrong?)
6. E = - mc2; Einstein and the imaginary
world - and about EPR
It's rather curious that Einstein doesn't mention
Dirac in his book from 1938 and Dirac's second solution to his
own equation: E =mc2, that is
E = - mc2, with the development of Dirac's hole
theory, positrons as "holes" and such things...
It seems as if he didn't like a negative world
or appreciated the "emptiness", in spite of this (relative)
emptiness being a condition for his own moving around.
Nor seems he have liked the imaginary world of which so much indicates
the existence. (Dirac 1958 about positrons: Each negative energy
solution of the equation [E =mc2] is the complex conjugate
to a positive energy solution.)
Einstein introduced √-1
as a factor making time to a space dimension, purely mathematically.
But he dismissed or brushed off every thought
of possible velocities higher than the velocity c
of light, since it should give the Lorentz' transformations
for the special relativity theory imaginary results. It would
give negative lengths.
(It's said that Einstein's presumption that no signals
can propagate faster than light, is a condition for his relativity
theory to be without contradictions.)
But what is a negative length?
It should be a distance in direction inwards the body.
Einstein's dislike of these things has probably connection with
his disregard of the direction "inwards" - and centers
- versus outwards, occupied as he was with outer relations between
Negative lengths as inwards:
Compare negative distances with how 4-dimensional cubes has been
illustrated, as cubic holes inside a substantial positive cube.
This means negative surfaces and volumes too
(We can imagine √ -1
as the side of a negative square defined between the negative
axes in a coordinate system. We can imagine this negative direction
as inwards in relation to more fundamental mass centers.)
There are the many connections between negative values and imaginary
(complex) ones as for Dirac's positrons and for example lg. x
which has a pure imaginary term ip for negative values on x.)
Negative energies, velocities and (surely?) accelerations
have been discovered in microcosm, and as imaginary or complex
realities they must - reasonably - have been essential factors
in the creation of properties as "Mass"
(A simple picture for the principle could perhaps be a crashing
car: its positive velocity being built-in into the car.)
(There are speculations too among some physicists
about backward directed time in connection with quantum phenomena.
(As we could talk about backward directed time built-in into
In biology we can identify a negative curvature
inwards as a main principle of life (see later some extractions
from the booklet Biology).
Inversions is one simple form of the direction
inwards, from the outer side of the unit number one (1) to the
inner side, in direction towards Zero (0). Inwards towards higher
Hence, if we allow us to believe in an "imaginary"
world representing more than a mathematical convention, and connected
with inward direction, - imaginary expressions for not only time
but potentials, surfaces and matter, negative values for acceleration
and velocities - and inverted numbers, we shouldn't be prevented
from imaging velocities higher than c.
Perhaps we had such velocities during an eventual
"inflationary" phase in the beginning of Universe
(?), presumed by some physicists and astronomers. If so, what
about the "gravitational answer" ?
About "pure mathematics": Einstein's formula
E = mc2 includes a factor c squared. And in his general
relativity theory there is a formula for the energy loss through
"gravitational radiation" with a term c5
under the fraction line.
dE/dt = [32 G I2 w6]
/ 5 c5 . Surely only
meant as a mere mathematical term, not intended to be interpreted
as such an enormous velocity, but how if we did ?
In any case, Einstein shut himself out from such
an imaginary world, as it seems. At least in his first theories.
Yet, in spite of his dislike for the imaginary world, Einstein
was one of the contributors to the so-called EPR experiment in
1930th (E for Einstein): an only theoretical experiment (at his
time at least) which concerned quantum mechanics.
Many such experiments have been verified later,
according to Penrose.
If a pair of photons for example separates in different
directions, both with left polarized spin, and direction of the
spin of one of the photons is turned by an apparatus, the spin
direction of the other photon changes mysteriously in the same
This shows on an immediate coupling between
the two photons, which cannot be explained as transfer of information
with the velocity of light. Thus it has been called a "supraluminal
effect" and is not dependent on the distance.
Mutually seen, from a position between them,
the separating photons have a complementary spin direction as
far as I can understand, both before and after turning of the
EPR effects are still not possible to explain with
present quantum theory. (Nor is there any agreement among physicists
so far on how to interpret such things as Heisenberg's uncertainty
principle or the proper sense of Schrödinger's wave function.
Any "potentials" between the two photons
in such examples as mentioned above and other similar experiments
don't the physicists talk about, according to the references.
"Potentials", however abstract, that we have suggested
in our 5-dimensional chain. But if there was such a still undetectable,
connecting "line" as affect between the two photons,
could some kind of perpendicular wall crossing this line change
We could suggest instead that the connection "occurs"
or is there through the common source.
Compare in our model the difference between
the outer connection between complementary poles as representing
a dimension degree, and the inner connection through underlying
higher d-degree as a kind of what is called "superposition"
(should rather be "sub-position"), when a time factor
still could be just a built-in structural element and not yet
realized as a time-creating motion. This with a certain degree
of support in Einstein's own view on motions as structural elements
in illustrations of higher d-degrees.
7. The rotation of the elliptic orbit of Mercury
One of Einstein's famous successes with the general
gravitational theory was to explain this rotation of the elliptic
orbit itself. Not only the planet rotates, so does the orbital
Couldn't we see this in a simple way as an example
or illustration of the views in our model here that geometrical
forms have more of a reality in themselves, and that planes as
2-dimensional structures from the outward point of view could
be interpreted as preceding a linear, 1-dimensional pathway.
A 2-dimensional motion is debranched through
d-degree step 4 →3, when vector
fields inwards/outwards (including gravitation) transforms to
mass and space according to our model. But if the orbit is interpreted
as a structure in itself, it should strictly speaking have a 3-dimensional
motion according to this same model, which should imply a change
in the angle of inclination too?
Some books, referred to above:
Einstein, Albert: Relativity: the special and general theory.
(Swedish edition, Göteborg 1997.)
Einstein, Albert: The evolution of physics
(Swedish edition). 1st edition 1938.Stockholm 1965. (With Infeld,
Einstein, Albert: Field theories, old and new. New York
Klein, Oskar: Einstein's relativity theory in a general applicable
(In Swedish), Stockholm 1933.
Dirac, P.A.M.: The Principles of Quantum Mechanics.
Oxford 1958. 1st edition 1930.
Foster, James: A short course in general relativity. New
(With Nightingale, J.D.)
Renard, Krister: The Foundation of Modern Physics (in Swedish).
Penrose, Roger: Shadows of the Mind. A search for the missing
consciousness. Oxford 1994.
Thompson, D'Arcy: On growth and form (Abridged ed.). Cambridge