a geometrical approach to physics

Part1: The Matrix of space

“No point is more central than this, that empty space is not empty. It is the seat of the most violent physics.” - John Archibald Wheeler

The space

At the beginning of the pondering, space is considered a container. In the empty state it is isotropic, it is empty everywhere. In the 19th century Maxwell gave space a function of a medium, the idea of ​​electro-magnetic space was born. He called it ether. It was also considered as isotropic. Maxwell relativized all movements in space to the ether. The speed of light had an absolute value that is the same everywhere in space. At the end of the 19th century Michelson was able to measure the speed of light at 299,853 ± 60 km / s. Since the measurement was made with an accuracy of ± 60 km / s, the light would have to be significantly slower in the direction of Earth orbit and faster relative to the measuring device towards orbit. Later the measurement accuracy could be increased to ± 10 km / s (the earth speed is approx. 30 km / s). Thus the Maxwell theory of an ether was without a foundation and is based on a paradox. The Dutch mathematician Lorentz solved the problem mathematically with his transformations for space, time and energy. These show only minor differences from the classic values ​​at normal speeds. They only take effect at speeds that were unattainable at the time. The young Einstein wanted to explain this effect explicitly and came to the conclusion that the ether can't have any physical values. This contradicted the Doppler space but also Maxwell's idea. Einstein was in a dilemma. On the one hand, the Einstein space modified the ways of measuring lengths, time and energies; on the other hand, space must not be a medium with friction. He came to the strange conclusion that space only existed as a concept but not physically (without a medium) and can't perform any motion of bodies.

The empty space of Einstein

A physical space without the motion of bodies would be a rigid medium in which only propagation is possible. This medium should have two significant properties: It should be invisible and, despite the apparent emptiness, be able to transmit the greatest energies.

That would be the space, Einstein was looking for

Both properties would be created by space units (space-atoms). These atoms of space contain 4 centers of force in a geometrical constellation, which internally cancel each other out in terms of space, time and energy and add up externally to zero unit. If one regards these centers as neutral space-atoms, then space would be without energy and appear as empty. If one looks at the interior of these space-atoms, then one sees immeasurable energies in a strongly condensed space and a large dilated time. In order to keep in balance and equilibrium of all values, these centers of force are in a certain geometric constellation.

They are octahedral and tetrahedral

terahedron And this is how they are proven: Take a transparent plastic bag and fill it with glass balls. When the spherical centers are connected to each other, you will find the matrix of space geometry. This matrix is able to place any space with 4 colors in a way, that no color has a neighbor of the same color. Since these 4 colors are the symbols of properties, of the energy state and its temporal appearance, such a constellation as a group of four results again in equilibrium.

The philosophical background

As a shortcut: The matrix theory is based on harmony and balance of the primordial phenomena what generate space-time-pulses. These phenomena (axioms) are existing from the beginning, but because of their balance and equilibrium they form an emptiness, an invisible, non-interactive substance of empty space. Only the disturbances of this system create the reality space-time-pulse. In contrast to today's physics, the Matrix-Field-Theory (MFT) does not begin with an absolute chaos of a Big Bang Scenario but with an absolute harmony what forms an apparent void due to the equilibrium of the axioms of space-time-pulse. Empty space is not empty, it is a system of space-time-pulse that in the state of equilibrium, i.e. in perfect balance, has no effect outside of its system. When our universe was born, conditions prevailed that did not allow any asymmetries or disturbances of the system to survive.

Space is created here by a geometric structure, the matrix,
Time through a full cycle of 360 ° from (+) to (-) in every scale of the matrix system and
Pulse declared with the resistance to leave the original state.

This field theory has the advantage that it is a GUT (General Unified Theory) from the start and all further determinations from this point go like the branches from the trunk, while classical science is a mix of experimental results and the search for theoretical affiliations is what often leads to different theories. Classical science thus has many planting sites that then try to unite in one trunk. The recognition of field theory would not overturn physics, but it would fundamentally change the image of the physical world. The exciting thing is that with the geometry of field space, its specific cycles in at least 4 space dimensions and its field tension, the extremely difficult to imagine things such as fermions, bosons, mass, inertia, gravitation etc. can be explained.

The space dimensions

The space dimensions are utilities of our imagination. They become concepts of our intellect and mathematics. Now the question arises, are they real are they physical? To understand this better, an example here is given:

The concept of dimensions starts with dimension zero (D0) and it marks a place. The place but is information, nothing else. The other dimensions therefore only remain information as long as D0 has no physicality. To make the dimensions physical, D0 must be physical. this happends, when it becomes a size in space. Its length is zero as long as it is not measurable. In multiplication, however, it will develop into a physical value. Now D0 becomes D1 in the vector multiplication and this becomes D2 in the same sense etc. Already D1 now has a strength and thickness as D2 will have due to its physicality. D2 is not just a surface, it is like a page of paper with a back (however thin it is). In 2D this is an indication of the exsistance of D3. In short: A dimension becomes a real physical quantity if it has indications of the next higher dimension. If we assume that our D3 space is real, then its physicality is in the 4th dimension.

The 4th dimension must therefore inevitably exist.

The vibration vector in the 4th dimension

The space matrix with its hexagonal, orthogonal and trigonal aspects of its structure is hard to imagine. But how should the oscillation toward the 4th dimension be presented, especially why? Well, in the world of vibrating vectors, the higher dimensions cast their shadows on the lower ones. There are signs of transitions. D0 must have a size, even if this size is below measurability and remains unproved. A D1 line must have a right and a left side in order to transfer to the 2nd dimension. A surface D2 must have a backside to form the 3rd dimension. So D3 must have a direction of oscillation that uses all other oscillation values of the coordinates as a tensor field and also gives you a reality in a new dimension. In short: We are real, even if our components are only vibrations.

The main problem with imagining the 4th dimension of space is that different things can have the same x, y, z values. 4 cubes in 4 colors with the same sizes in the same place x, y, z show us only one cube with one color. In D4 we would see 4 cubes in 4 colors. Unfortunately, the matrix as a geometric structure does not take into accoun our limited imagination. It simply determines there.

Our universe, the proof of 4 spacedimensions

4D univers


Our universe is normally imagined as an expanding sphere. The spherical shape comes from our range of vision, which appears 13.6 billion light years in all x; y; z directions equally. The expansion comes from the Hubble constant, which says that all observable parts of our universe move away from each other depending at their distance. That means approx. 70 km/s per Mpsc (Megaparsec). In other words: 22 km/s per 100,000 LY. So every 100,000 light years the speed of expansion increases. If it increases in 13.6 billion LY every 100,000 LY 22 km/s, then in the end it results in speed of light.

13.6 10^9 / 10^5 * 22 km/s = 13.6 10^4 * 22 km/s = 299 200 km/s

If the BB (Big Bang) or the VB (Very Beginning) moves away from us with V=c, then this means for us, not the VB but we are the ones who have V=c. But this does not correspond to the SR (special relativity) and the GR (general relativity). These say that the radial coordinate of this expansion has zero and infinite values. We would practically only be 2-dimensional. But that is wrong.

The solution offers the inclusion of the 4th spatial dimension in the account. From the prospect of 4th space dimension, our space would be a spherically curved surface (the curved space of Einstein), which propagates as an impulse wave with V=c in 4D hyperspace. All 3 spatial coordinates of our 3D space would remain in normal mode, but the 4D coordinate would then be invisible to us. A secondary effect would be the subatomic particles with V<c.

It should be mentioned that Marco Pereira, MSc in Physics, PhD in Physical-Chemistry, based his extensive theory of a Hypergeometric Universe (HU) on this idea of a universe expanding in hyperspace with V=c. I wrote the first page of my matrix theory in 2016 as webpage. I saw the HU theory as an extensive confirmation. However, it was Billy Lee, free thinker, who drew my attention to the Hubble effect of V=c in relation to the size (13.6 billion LY) of our universe..

As we will see later, hyperspace is absolutely necessary as the basis and carrier of our 3D world. However, its consequences in the context of the creation of our world are not discussed here. Here the existence of hyperspace should be shown as an important part of a matrix theory. It has 4 coordinates, the time is not counted.

 Einstein used time as an equivalent space coordinate to describe his math for a V=c dependent space. This remains in case it comes related to the space we see. In the matrix theory, time is supplemented as a time with (+) and (-) values, because here it is not about the Einstein universe, but about the quantum worlds of the particles. There, time shows itself to be bound to cycles and separated from the universal time. However, a universal cycle of time should to be assumed. This would correspond to the philosophy of perfect harmony.

Euclidean, spherical, relativistic space

space concepts


Of course there are more types of space concepts. They all struggle with the representation on an normal 2-dimensional paper. In principle, all 3 types of the above concepts can be polydimensional. Mathematically speaking, Euclidean space is a concept that corresponds to our normal understanding of space. Other spatial concepts can therefore also be represented as Euclidean. The description of  space also includes distances, areas, volumes and n-dimensional values. However, these are no longer the same for various concepts.

The Euclidean space

This spatial concept is based on an isotropic distribution of its units, which are very small spatial units. They are analog quantities, i.e. they can be divided as required. The distances are calculated by d2=a2+b2+n2 where n stands for the coordinates of further dimensions. In this way, spheres, cones, etc. can be calculated. This type of calculation is sufficient for the vast majority of cases.

The spherical space

Although every sphere, i.e. a circle, a spherical surface, a spherical volume, etc. can be calculated in Euclidean terms, the results in spherical space are different. Its coordinates are all curved with π·r. This alone results in units of different sizes. Due to its curvature of co-ordinates, they become circles, spherical surfaces and curved n-dimensional spaces with unending coordinate lengths that are closed in themselves. The spherical space thus demonstrates in simple ways an infinite space of finite size, as is expected from today's perspective of size of the universe. Here is a formula overview that shows the influence of the spherical space concept in the various dimensions. The designation D1, D2 etc. applies to Euclidean space with 1, 2, etc. dimensions. D1/D2, D2/D3 etc. applies to a measurement in spherical space with 1, 2, etc. dimensions, which in turn is embedded in an additional dimension (Dn+1). A being in the spherical space Dn/Dn+1 does not see the curvature, but only recognizes it indirectly through the result of its measurements.

dimens equations


Here D = dimension, S = string; A = aria; V = volume; W = warp

The logical formula development here would be S1 = diameter; S2 = curved around the circumference; A1 = circular area; A2 = circle curved as a sphere; V1 = sphere volume; V2 is the curved spherical volume; W1 = the spherical 4 dimensional (4D) space; W2 = the curved 4D space.

The calculation of the volume of our universe is about curved space (D3/D4). Although a curvature in  sense of π*r is considered idealized from a physical point of view, the formulas give us a close approximation of the real values, which, as we will see in the following, only occur when determining the measurement to the location inside or outside the space concept.

The relativistic space

While the Euclidean space is isotropic and has the same units, the spherical space has curved coordinates with π·r, the relativistic space consists of unit values ​​dependent on the v=c (speed of light). The units of length are therefore multiplied by the Lorentz factor ɣ. This is the function of v/c, namely ɣ = 1/√1-(v/c)^2. The derivation of the Lorentz factor is described in Wikipedia. For the distance coordinates x; y; z the coordinate value applies and for the time t=t/ɣ. With this factor the coordinates of the Euclidean as well as the spherical space can be modified. It can also be used for higher dimensions (>3). We see here that in the special theory of relativity it is only applicable for a vector (string size) and a time direction, in the general theory of relativity but also for the spatial density. Since the coordinate values ​​dependent on v=c create different unit sizes, entire spatial fields can of course also consist of smaller or larger units, which can then be defined as spatial density. The relativistic space is therefore never isotropic. Here we come to the biggest difference between the old and the new space concept. From a logical point of view, the polydimensional space should always be relativistic and curved with coordinates in (+) and (-) values. The spherical spatial concept shows us that the curved circular surface only results in a sphere with an "above" and "below", so the curvature can have a (+) and (-) value. That should also apply to time as a space coordinate. In the further description we see the application of the space concepts.

The Universe

Among the many spatial concepts, the relativistic and the spherical concept dominate. In the normal distance from our surroundings, however, the Euclidean space applies. All spatial concepts consist of fractals in the smallest scale of which the coordinates become straight, respectively Euclidean.

comoving universe

Picture: Credit Yukterez (Simon Tyran, Wien)

The above picture shows a comoving diagram of the universe from 14 billion LJ (light years) into the past and 80-14 = 66 billion LJ into the future. “Comoving” means relativistic from the point of view of the measuring instruments within the measuring range, which makes sense, since a location outside the universe could bring all sorts of surprises.

The horizontal basis of the diagram shows the distance from the Big Bang to approx. 55 billion LJ in (+) and (-) directions. On the left the time distance in LJ and on the right the time distance as a scale factor a, where a = 0 begins with the Big Bang (Friedmann Lamaitre space concept). The vertical dotted lines mark the coordinate system from the point of view of the observer. This would look curved from outside the universe, but would have parallel lines instead curves diagramms. The horizontal line at approx. 14 billion LJ marks our present time.

Now about the curved lines

The red line means the limits of the event horizon, everything that lies in this area can be observed by us directly or indirectly (in the future).

The blue line means the Hubble area. Everything within the range can be calculated in terms of distance from the Hubble constant.

The brown line means the particle horizon. Everything that lies within this range can be observed today or in the far future. Particles are matter in the sense of galaxies or clusters. The idea behind it is the v=c and the time. Assuming that the universe is expanding, the periphery will expand independently of v=c, whereby relativity would not be violated, since the expansion of space cannot be compared with a speed of space (expansion happens in hyperspace). The situation arises that radiation as an old image of a galaxy moves with v=c from us and is overtaken by the periphery of the space expansion in far future. This situation only arises when the universe is larger than the particle horizon. Beyond the particle horizon lies the true physical future, which can never be reached by instruments. Today's interpretation also includes dark energy.

The beige line means the cone of light, the visible universe. The visible area that can be interpreted with the Hubble constant lies within this line (light orange area) and the Hubble line. Outside this line (yellow) and the Hubble line lies the area of future visibilities that can be interpreted with the Hubble constant.

It is obvious that all colored lines start with infinite size. This is due to the relativistic metric, which makes the distances infinitely large using the Lorentz factor ɣ in the case of an assumed big bang. The time axis as the center line becomes zero. The Big Bang assumption is very likely wrong. The main cause of this idea is that many scientists need a God substitute. Of course, it is also the Hubble constant that logically explains the expansion of space as the Doppler effect. This would be OK, if there were not this nasty discovery of the cosmic microwave background (CMB), which should have arisen evenly around the observation horizon around 380,000 years after the "Big Bang". That is about 0.03% of the 14 billion LJ distance. There you should be able to expect a density focus in the direction of the Big Bang. However, nothing was found.

In the concept of a spherical 4-dimensional hyperspace, a kind of big bang would be possible. The effect in normal 3D space would then be in every point in space. So our universe would develop from itself (in every space point). The weakening of the points in space in time line would produce a proportional increase of distances, which we can measure as expansion. It would be the situation of Copernicus/Ptolomaios. A complex, barely comprehensible view of the world with dark energy etc. would be comprehensible through a new geometrical perspective.

The matrix the fabric of space

The purpose of this space structure is, that an assignment of properties what cancel out each other, results in a space without any external value. As long as these properties cancel each other out as a sum of values in a space unit, these units can keep energies of any size and still appear outside this unit without any physical value. The physical space can carry the highest energies, where the properties of time and energy cancel each other out in this sense that time • energy become the values: (+ +) = red, (+ -) = green, (- +) = yellow and ( - -) = blue and form an equilibrium with 4 colors. The fantastic thing is that the space doesn't cancel itself out. Space becomes a MEDIUM.

MatrixWithin this tetrahedral-octahedral structure the balance of all properties is symmetrical. They exist but cancel out each other. Outside they exist only indirectly, they form a continuum of space-time-pulse. However, the space can no longer be seen as isotropic. It got neutral space atoms as physical carriers of its existence. From now on we have to get used to one thought: our world no longer exists directly, only indirectly. We are the result of a medium. We are the modification of the medium, the disturbance of its equilibrium. Just like its components, our world is not chaotic either. The principles of these order were created when our universe was born. Unimaginable pressures did not allow the inharmonious and the chaotic to survive.

"What we see as material bodies and forces is nothing other than the forms and structures of space and time" - Ermin Schroedinger.
“Everything we see as real is made of things that cannot be seen as real” - Niels Bohr

Here is the geometry of matrix presented. The main problem here is the presentation. How could such a part of space look like? How could it depicted?



The spheres present the status of space with the 4 colors, the values of space-time-pulses. The large spheres represent the larger scale.



By omitting the color information and part of the background, 3 scales of the octahedron are marked by thicker line width. Scale S1, S3; S9. The lining up of the smaller scales shows that they all fit exactly into the larger scale. All points of space in large scales are also points of space in the smallest scales.



Here the octahedra are marked with transparent surfaces.

The tetrahedron

  • size1-unit

    The tetrahedron is the most simplest 3D shape. It fulfills the condition creating a stable construction by the same distances between its 4 corners. To fix the distance, a scale (scale 1) S1 is assumed, which at the moment has no relation to a physical value. Further geometrical considerations refer to it. The 4 colors at the edges form the physical value of this shape. They are intended as space-places, in which there are 4 field centers with 4 properties, which cancel each other out in every respect and result in the value zero on the outside of the system, a condition of empty space.

  • size2-unit

    Since, according to the Planck formula, λ=h•c/E, where λ is the distance between the field centers, the centers here have ½ energy values as S1 (scale 1). S1 as basis of all considerations therefore has the highest energy values. But S2 also shows that its edges are all at the same color. A filled space with distances of S2 cannot hold energies locally as S1 does, they spread with V = c. Here we come to one of the most important properties of "empty space". It turns out that all odd scales cancel each other out to zero and all even scales like S2; S4; S6; S8 etc. result in a scale layer that functions as medium of all forces contained therein. They reproduce or propagate with V = c.

  • size3-unit

    Even in multiple application of tetrahedra, a space filling without gaps, each property (color) finds its balance in the neighboring field.
    The cycle includes 4 states of the space-force continuum but only 2 states of time. This fact seduced the physicists to assign a torsion (spin) or helicity (left / right) to the fermions. The subject will be discussed in more detail later.


    The matrix of EMPTY SPACE therefore shows 2 properties in its innermost structure; one that can hold every imaginable force (S1; S3; S5 etc.) and one that allows the matrix as a medium to spread all energies of our space with V = c (S2; S4; S6 etc.).

    On closer inspection we discover that there is an octahedron inside the tetrahedron S2. But since its corners are formed with the field centers of the tetrahedron, the octahedron is only a space without content. Its size here is S1. An octahedron S2 would be in the intermediate zone of expansion anyway and would therefore only consist of field centers of the same color that are not like S1 or S3; S5; S7 etc. to form a value equilibrium.
    As a spatial form, size S3 has the same properties as S1. Since their rod sizes are 3 times longer than S1, they only interact with 1/3 the energy of S1.

  • S6-Tetrahedron

    As you increase from S1 to S3, the octahedron spaces also increase. Since they also belong to the medium of the matrix, they also contain tetrahedra of size S1. The figure opposite with side length S6 shows that the readable octahedron consists of tetrahedral and octahedral inside.
    From a purely geometrical point of view, each field center is connected 12-fold to its neighboring field centers. As can be seen later in the treatment of octahedra, it is very astonishing that despite the 12 bonds with only 3 neighboring colors (the relevant field center itself has already 1 color) no field center will have a neighbor with the same color. Spaceis filled with colors that always cancel each other out as space values. Later we see that space is not a static construction, it oscillates from compression to decompression, in (+) time to (-) time and forms with the values
    (+ +)=red, (+ -)=green, (- +)=yellow, (- -)=beu, the empty space.



    It is not just an in-between space, it has properties that make it the carrier of our world. It is the seat of matter, while the tetrahedra are the medium.
    Of course, tetrahedron and octahedron as spatial elements form a single structure which together does not leave any empty space. The space is thus completely geometrically defined. There are 2 octahedra + 4 tetrahedra per space unit. These have a volume ratio of 1 to 2 i.e. 1/3 volume tetrahedron and 2/3 volume octahedron.
    However, these values have no direct influence on space.


    octahedron-2A calculation according to Pythagoras (d = √ (x ^ 2 + y ^ 2 + z ^ 2)) would have little sense with this hexagonal spatial structure of the matrix, since a precise calculation here can only have integer values. The space is quantized by the requirement of connected scales. A tetrahedron with colored spaces is shown here. The octahedron in the center was covered with slightly transparent surfaces. The tetrahedra attached to the triangular surfaces represent the spatial properties of a medium. Here the forces of spatial disturbances are passed on with V = c. In this case the resulting tetrahedron would have the size S6. The octahedron is size S3.

    What is special about the octahedron?

    octahedron-3If the surrounding tetrahedra are balanced, the octahedron is empty. If the tetrahedra are unbalanced, then the manko color in the center of the octahedron creates a moment from the 4th missing color in its surroundings. The diagonals are taken over as color from the neighboring octahedra and form a continuous orthogonal space. In this way, large spaces can receive moments and create areas of strength by the manko colors. This orthogonal space is stabilized by the flanking of each octahedron by twice the number of tetrahedra.

    scaled octahedronThe disturbance of larger areas of space on the same scale creates the centers in the octahedron, which create an elastic resistance, resulting in force fields. These manifest themselves as onions around each other in the length ratio of their distances (λ) 1; 3; 9:27; 71 etc. or λ=3^x or 3^(- x). Thus, the octahedra result in a further property of space in addition to the above-mentioned property of an onion-shaped stratification of force-holding areas of uneven scales and force-emitting areas of even scales.



    The true nature of the MATRIX

    The previous explanation of the matrix as a spatial structure gives rise to the feeling that despite its refined geometry and striking compatibility with modern quantum dynamics, it appears to be an arbitrary structure in the areas and scales of physics that are inaccessible to us. In the chapter "Our universe, the proof of the 4th space dimension" a scenario of a world formation is shown, which is based on facts of a century of observation of the universe, the Hubble constant. In 4-dimensional hyperspace, a spherical wave front arises from a center, which propagates into the further hyperspace with V=c. The verbal representation here shows the hyperspace as 3D space, correspondingly our 3D space is presented as a wave front (geometrically a surface). The expansion in 4D space results in the Hubble constant in 3D space, i.e. 22 Km/s per 10*10^4 LJ. This would result in V=c at a distance of 13.6 billion light years. If V=c is seen as the medium speed, then it results in a visible universe of 2 * 13.6 billion light years and if the covered distance in hyperspace is seen as the radius of the entire wave front of the 3D space, then it gives the total size of our universe of

    2 * radius * Pi = 2 * 13.6 * 10 ^ 9 * Pi = rounded 85 billion light years.

    Well, what does this wave front look like from a 3D prospect? What does a curved space with a radius of 13.6 billion light years look like? From a geometrical point of view, the 4D wave front would be filled with 3D space in such a way that its density would produce curved lines of a straight flight, its length of which would again be 85 billion LJ. It is not the curved lines but the appropriately modified metric that would cause this. What would it mean for a super telescope? It could look in any direction in space and see the back of the observer's head after 85 billion LJ. In every direction !!! That would make a lot of head backsides. If now the time and the Hubble constant were included in the calculation, however, then we would never be able to see the size of our universe, it would flee from us faster than V = c. Further considerations are left to the reader.

    The purpose of this consideration is to understand the deep nature of the MATRIX geometry. Every momentum with vector of the 4th dimension would result in a point size in 3D. This would have a local disposition in 3D space. Only from here would this momentum result in local, standing waves in 3D space. Because such momenta oscillate during theire propagation through 4D space (with V=c), the standing waves become standing fields.

    These local spatial points as oscillation and surrounded by their fields take over the geometric spatial pattern of the 4D space as momenta and transfer it 1: 1 into 3D space. Their propagation in 4D structure has an effect in 3D space as a time cycle and thus creates the 4 types of effects in 3D space (++) (+ -) (- +) (-). These effects and the structure of the 4D space are the basic elements of MATRIX.


    die Tiefen der Welt

    At Christmas 2016 I started to put my idea of a space matrix on the web. In 2017 and 2018 the ideas in my head and my 3D CAD platform grew into a zoo of solutions that required a logical order. In July 2018 I started to document these ideas in logical order with Word and pictures. The individual topics actually produced themselves and stunned me with their surprising solutions.

    Gunter Michaelis, Griesbach, den 20.8.2020