Cosmology
The figure below illustrates the trigonometric relationship between space-time and field deformations. An object velocity V3 and a contracted field velocity act simultaneously in the particle-field. Geometrically, the particle-field is represented as a blue surface parallel to the dimensional plane D56 and encompasses its three known spatial dimensions. The velocity vector V4 in the wave-field runs parallel to the fourth dimension and corresponds to the vectorial object velocity in the particle-field. It describes the space-time deformation. The velocity vector V5 runs parallel to the fifth dimension and measures the deviation of the field velocity from the maximum velocity c = 299792568 m/s. It describes the field deformation.
The velocity vectors V4 and V5 form the legs of a Pythagorean triangle whose hypotenuse is the maximum velocity c. In the wave-field, both vectors parameterize the relativistic state of an object and represent two opposing reference frames relative to the maximum velocity c. The field angle α characterizes the relativistic state of the object.
V4 = c cos(kt) = c cos(α), V5 = c sin(kt) = c sin(α)
Over a full period T, the prospective trajectory curve forms a hollow sphere in the wave-field. The origin of the inertial system lies at the center. The mass dynamics dM(α) vary with the solid angle and illustrate the four quadrants of the periodic motion. The radial expansion is given by
r(t) = Rmax sin(kuni t)
and describes the expansion behavior of the universe as a quarter period of a sine wave. At maximum expansion (sin = 1), the relativistic energy gain disappears; at minimum contraction, the dynamics reach the Planck length. The same constants and the same trigonometric relationship apply in the microcosm.
Ultimately, the universe draws its circles. Chemistry is possible between the extreme points α = {0°, 90°, 180°, 270°}. The foundation for biological life lies outside these extreme points.
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 accounts for the gravitational potential during the expansion of the universe. The gravitational potential is the space-time potential between the inertial frame and any contracted state in the universe.
F(t) – relativistic gravitational force
ϕglobal(α) – gravitational potential
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
Universal Constants
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.
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 1053 kg.
- Most visible particles are constructed with four of 15 possible mathematical rotational orbits (e.g. protons/neutrons).
MUni = 1,1765 1054 kg ⇒ mass of the universe
rUni = 8,73125 1026 m ≈ 92,35 bill. LY ⇒ maximum volume radius
r(t)current = 29,608 bill. LY ⇒ relativistic state of the field radius
kUni ≈ 3,4336 10-19 1/s ⇒ circular frequency of the universe
T2π ≈ 92,35 bill. years ⇒ period duration of the universe
Texpansion,max.= 23,09 bill. years ⇒ 1/4 one period duration
tcurrent ≈ 7,402 bill. years ⇒ nominal time elapsed since the start of the period
λUni = 1,87861 10-96 m ⇒ wave length of the universe at the point of maximum expansion due to gravitational red shift
UUni ≈ 580,3 bill. LY ⇒ extent of the universe at the point of maximum expansion
Ucurrent = 186,03 bill. LY ⇒ current relativistic size of the universe
Eoverall(t)maxExpansion = 1,06 1071 J ⇒ energy content of the universe at the point of maximum expansion
Eoverall(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
h = 6,626 10-34 Js;
k M = 4,0396 1035 kg/s
the following equation:
h = λx rx m k = 2π rx² m k
Finally, the value for the location sought is a volume radius or wavelength of:
rx = 1,616 10–35 m
(identical to the Planck length)
In order to classify relativistic conditions, Field-Space-Mechanics introduces the field angle α. Relativistic dynamics are sinusoidal. Based on the field radius r, several expansion locations and their events will be mentioned. These are listed below in reverse order at the location of maximum expansion:
α = 90° ⇒ r = 8,73 1026 m (92,35 bill. LY): at the point of maximum expansion
α = 18,7° ⇒ r = 2,8 1026 m (29,608 bill. LY): current extent
α = 1,85 10-40° ⇒ r = 2,82 10-15 m: with this expansion, dark energy begins to interact electrically with a photon field for the first time
α = 1,06 10-60° ⇒ r = 1,616 10-35 m: with this extension, it fits exactly the wavelength for a full period into the volume space
α ≈ 5,7 10-87°…5,7 10-88° ⇒ r ≈ 8,7 10-62 m: with this expansion, the universe completely reverts to the characteristics of a photon,
its wavelength: λ ≈ 1,9 10-7 m = 190 nm
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 λx = 2π rx. 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 are determined based on the energy content using the characteristic constants of the Universal Photon: the space-time constant, the mass-space constant, and the mass-time constant.
Electric potential field
At the location λx = 2π rx, 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 total momentum has a spin-0, which is directed in the opposite direction: 0 = Ppos – Pneg . The space-time deformation, through the global field angle α, forces both impulses to be orthogonal to the dimensional plane D56. The universe forms its electrical voltage potential through the rotation of both partial pulses with spin 1, one above and one below of D56. Electrostatic separation occurs through 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 F4-6, the displacement current generates an electric field effect parallel to the fourth spatial dimension D4. 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, additional partial pulses arise as soon as the volume allows. In this way, the invisible energy (dark energy) is converted into complex matter until the expansion reaches its maximum. The following figure schematically shows the state of our universe’s photon field once all possible quantization processes have been completed. In this process, the photon field has shifted from an orthogonal to a parallel configuration relative to the D56 dimensional plane, thereby generating a specific number of partial impulses. Planck’s constant h applies not only to the universe but also to all generated partial impulses.
Black Holes in the Field-Space Model
Field-Space-Mechanics describes the core of black holes using the wave-field F4-6. The shell lies in the particle-field F1-3. The shell forms the effective event horizon, beyond which no photon can escape once it crosses the boundary.
Shell in the particle-field F1-3
Isotropic: g0i = 0 yields the static 4D solution with the horizon:
rS = 2r Schwarzschild solution
Angular momentum of the shell requires off-diagonal entries in g0i ≠ 0. For rotational distortion effects, the Kerr metric applies with the horizon:
r+ = 1 – √(1 – X²) ≥ r Kerr solution
Χ (Chi) does not originate from the core, but rather from the collapse, merger, and accretion in F1-3. The field radius r equals r+ only when Χ = 1. Without entries in g0i, there is no 4D rotation.
Light from the core does not reach outer space as soon as it falls below the radius of r ≤ r+ or r ≤ rS. The core remains invisible.
Core in the wave-field F4-6
The critical length from k r = c lies at the field radius:
r = GM/c² = rS/2
There, a spin-0 pair with angular momentum is located:
P = P+ + P– = 0
Inside a black hole is a spin-0 structure consisting of two partial photons. Externally, this structure behaves like a neutral object, but is internally polarized. Both partial photons are in a stable, entangled equilibrium.
Angular Velocity and Angular Momentum for the Shell and the Core
When the field radius r is reached, the angular frequency k also enters the visible range. The corresponding shell not only defines the minimum radius for a closed rotation but also determines the maximum angular frequency at which an orbit at this radius is still possible at the maximum velocity c. One period
T = 2π/k = 2πr/c
corresponds exactly to the light’s orbit around the circle with a radius of 2πr. More orbits per unit of time are not possible. U = k/2π is thus the maximum rotational speed of the shell when angular momentum is present.
k = √(G M/r³) –> U = k/2π
Angular momentum of the core for + and – helicity, respectively:
h = M λ c
Maximum angular momentum of the shell:
Lmax_shell = √(G M³ r)
In the Field-Space-Mechanics model, it is possible to compress field bodies to such an extent that the surrounding volume space is just large enough to represent the wavelength of a photon for a single oscillation period. The transformation to black-hole objects must satisfy the formula:
h = λx rx m k = 2π rx² m k
Thus, every black hole begins with a volume radius of:
rx = 1,616 10–35 m
rx = lP = Planck length. This means that the Planck length represents the transitional point between wavelength and field radius, as well as between the macrocosm and the microcosm.
Depending on the mass, the field radius continues to grow and its wavelength continues to decrease.
However, an external event is required to reduce an object’s wavelength to the order of magnitude of its field radius. The collapse of a red giant would be such an event.
The following figure shows a black hole with its axis of rotation. Along its spherical sector, gravity affects the inertial motion of an approaching object differently. At the equator, angular momentum is conserved, creating a balance between the centrifugal force and the gravitational force acting on an object with angular momentum. The rotation must occur in the prograde direction. During a retrograde approach, the angular momenta cancel each other out and the angular momentum conservation breaks down. An object falls into the black hole.
In the radial direction toward the poles, the angular momentum conservation decreases. An object would fall more easily into the black hole.
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. Information is not lost in a black hole; rather, it is released when the black hole dissipates.