Cosmology

The chapter on cosmology lays the foundations for Field-Space-Mechanics. The geometric structure and the necessity of a 6-dimensional field-space are supported by the thesis that relativistic effects can be represented by trigonometry. This results in a trigonometric relationship between space-time and field deformation for the special and general theories of relativity in Field-Space-Mechanics. The findings provide new insights and more realistic explanations for the expansion behavior of the universe, but also new constants that allow us to conclude that this approach also applies to the microcosm.

The following figure shows the trigonometric relationship between space-time – and field deformation. An object velocity V₃ and a contracted field velocity act simultaneously in the particle-field. The particle-field is geometrically located as a blue area parallel to the dimensional plane D₅₆ and has its three known spatial dimensions. The velocity vector V₄ in the wave-field runs parallel to the fourth dimension and corresponds to each amount of a vector object’s velocity that can be measured in the particle-field. It describes the space-time deformation in the wave-field. The velocity vector V₅ runs parallel to the fifth dimension and, in contrast, represents the extent of the deviation of a field velocity from the maximum velocity c = 299792568 m/s. This velocity thus describes the field deformation. The velocity vectors V₄ and V₅ correspond to two opposing reference systems relative to the maximum velocity and ultimately parameterize the relativistic state of an object in the wave-field. Both vectors form the catheters, while the maximum velocity c represents the hypotenuse in the Pythagorean triangle.

The above illustration shows a snapshot of a space-time deformation using velocity vectors. This corresponds to the special consideration of the theory of relativity for Field-Space-Mechanics. If nominal time t continues to run, this trigonometric representation creates a periodic relationship in which the velocity vectors V₄ and V₅ contract and expand. This dynamic corresponds to the general relativistic consideration.

For the universe, this results in a sinusoidal periodicity for the relativistic amount of its gravitational force relative to the location of the inertial system. The relativistic deviation is described as gravitational potential for its photon field. This relativistic state affects its quantized subspaces. The gravitational force of quanta within the photon field of the universe follows this periodic space-time deformation. If an infinitesimal number of measurement points are recorded for the emitted field deformation relative to the inertial system, a prospective trajectory curve over a period T is created. The expansion dynamics assume a mathematical hollow body shape for the photon field. Another important finding is that the speed of light, which runs parallel to the field velocity V₅, only corresponds to its maximum velocity c when the photon field is no longer slowed down by any additional space-time deformation. Thus, Einstein’s view of the theory of relativity is extended by the gravitational potential of the photon field, which takes into account the entire reference space of the invisible space-time mechanical effects.

The universe ultimately circulates his circles, thereby enabling life on a periodic and temporary basis.

Simulation:

Circular frequency k

The angular frequency is an invariant, non-relativistic reference value and specifies the cycle time, i.e. how often per second a field can be exchanged.

G – gravitational constant

M – mass

R – field radius

Field radius R

A rotating field body within this field radius can no longer escape. A field exchange takes place. This size corresponds to the event horizon of rotating matter.

r(t) – deformed field radius

c – maximum speed

t – nominal time

Sinusoidal periodicity

The sine term takes into account its gravitational potential during the expansion of the universe. The relativistic gravitational force between the universal photon field and any quantized subspace is expressed by the sine periodicity formula.

F(t) – relativistic gravitational force

Field angle α

The field angle α describes trigonometrically the space-time deformed deviation from the inertial system. The special consideration of relativity provides a snapshot, while the general consideration provides a dynamic space-time deformation.

α – field angle

V₅ – field propagation velocity parallel to the fifth dimension

Gravitational force between two objects

This force formula describes the relativistic gravitational force between two objects relative to the dimensional plane D₅₆, which runs parallel to the particle-field.

R – here: distance between the objects

Space-time constant

The product of the field radius and the circular frequency of any object gives the maximum speed c. For the structure of the universe, this means that the volume radius of the universe is proportional to a period duration.

Mass-time constant

Any object mass with its individual circular frequency always results in the mass-time constant.

Mass-space constant

The mass-space constant describes the directly proportional relationship between each event horizon or field radius of matter and its mass.

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Characteristics of the universe according to the model

Selected results are presented below, which provide a numerical example for this universe, assuming the following astronomical values:

Dark energy accounts for 68% of the total mass.
The visible mass is 10⁵³kg.
Most visible particles are constructed with four of 15 possible mathematical rotational orbits (e.g. protons/neutrons).

M_Uni = 1,1765 10⁵⁴ kg ⇒ mass of the universe

R_Uni = 8,73125 10²⁶ m ≈ 92,35 bill. LY ⇒ maximum volume radius

r(t)_current = 29,608 bill. LY ⇒ relativistic state of the field radius

k_Uni≈ 3,4336 10^-19 1/s ⇒ circular frequency of the universe

T_2π ≈ 92,35 bill. years ⇒ period duration of the universe

T_{expansion,max.}= 23,09 bill. years ⇒ 1/4 one period duration

t_current ≈ 7,402 bill. years ⇒ nominal time elapsed since the start of the period

λ_Uni = 1,87861 10^-96 m ⇒ wave length of the universe at the point of maximum expansion due to gravitational red shift

U_Uni ≈ 580,3 bill. LY ⇒ extent of the universe at the point of maximum expansion

U_current = 186,03 bill. LY ⇒ current relativistic size of the universe

E_overall(t)_maxExpansion= 1,06 10⁷¹ J ⇒ energy content of the universe at the point of maximum expansion

E_overall(t)_current = 1,02 10⁷² J ⇒ relativistically decreasing energy content of the universe

Current time dilation factor ≈ 3,12

V₄ = r’(t) = 283966497,5 m/s ⇒ relativistically decreasing field propagation velocity parallel to the fourth dimension

V₅ = 96117356,5 m/s ⇒ relativistically increasing field propagation velocity parallel to the fifth dimension (relativistic speed of light)

The universe is currently expanding faster than the contracted speed of light V₅ with r’(t): 2,95

Birth of the Universe

The universe expands with relativistic characteristics. The following illustration is intended to represent a symbolic diagram between its field radius and its wavelength. The maximum values are known from the field-space model. What does it look like the other way around? Where is the place where the universe came into being? This question seeks to find a place where the universe has just enough volume space available that its wavelength fits exactly once. To do this, both variables must be traced back relativistically until an intersection point is found. In the diagram, this location is marked with λ_x= r_x. Using Planck’s constant h and the universal constants found, the following result is obtained

h = 6,626 10^-34 Js;

k M = 4,0396 10³⁵ kg/s

the following equation:

h = λ_x r_x m k = λ_x² m k = r_x² m k

Finally, the value for the location sought is a volume radius or wavelength of:

r_x= λ_x = 4,05 10^–³⁵ m

It would now be possible to trace the path back to the birth of the universe until the universe transitions into the characteristics of a photon, with the volume radius becoming smaller than its wavelength. This dynamic is illustrated in the diagram on the left at the location λ_x= r_x. Hypothetically, the universe could shrink to a size where it resonates with a higher-level photon. This parent photon is referred to as the universal photon in Field-Space-Mechanics. It would be able to emit part of its energy as a photon. The size of the universe is defined by the characteristic constants from the universal photon with the space-time constant, space-mass constant, and mass-time constant, depending on the energy content.

Electric potential field

At the location λ_x= r_x, a special condition applies whereby the volume space provides a single quantum for the photon field of the universe. This is illustrated in the following figure.

The universe forms its electrical voltage potential through the rotation of both partial pulses with spin 1, one above and one below the dimensional plane D₅₆. The photonic separation would be comparable to two charged capacitor plates. Due to the time-dependent expansion, the variable voltage potential acts like a displacement current with its orthogonally aligned magnetic field. In the wave-field F_4-6, the displacement current generates an electric field effect parallel to the fourth spatial dimension D₄. Electrostatic separation occurs through the dimensional plane D₅₆. With this geometry, a charge is attributed to the charge carriers or it is explained why no charge is present. In the initial stage of the universe, the electric potential (as well as the gravitational potential) is at its maximum and strives toward its minimum until it reaches its maximum expansion.

As a result of the expansion, further partial pulses are created as soon as the volume space allows. In this way, the invisible energy (dark energy) is converted into complex matter until the expansion reaches its maximum. The following figure shows schematically the position of the photon field when all possible quantization processes are complete. The photon field has shifted from the orthogonal to the parallel configuration to the dimensional plane D₅₆, generating a certain number of partial pulses. The partial pulses are a factorized quantity of the photon field and together represent the photon field itself. In this model, Planck’s constant h applies to both the photon field and all quantized particles.

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Black Holes in the Field-Space Model

In the Field-Space-Mechanics model, it is possible to compress objects to such an extent that the surrounding volume space is just large enough to represent the wavelength of a body for a single period. For all objects, the formula

h = λ_x r_x m k = λ_x² m k = r_x² m k

to be fulfilled. Thus, the same geometric condition applies to the space-time deformation of a black hole as to the universe at the beginning of its appearance in the particle-field. The black hole can assume its maximum space-time deformation in the universe with the orthogonal formation to the dimensional plane D₅₆. Hypothetically, the formation would be possible for all objects, including elementary particles. However, an external event is needed to reduce the wavelength of an object to the size of its field radius. The collapse of a red giant would be such an event.

The next illustration shows a black hole with its axis of rotation. Along its spherical sector, gravity has a varying effect on the inertial motion of an approaching object. The gravitational potential is greatest at the equator and decreases to its minimum at the poles.

Black holes can be used to verify the formalisms of Field-Space-Mechanics. The document presents a calculation example for black holes with five times the mass equivalent of the sun. It also describes the end of life of black holes, which results from the relativistic space-time geometry of the universe.