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Dr. Henryk Frystacki, May 2021

A new theory and its accompanying model are capable of completely describing the dominant role of dark energy in the construction of our universe and all processes - from the origins to a predicted end and beyond.

The model uses equivalent forces of compression and decompression to describe noticeable and predicted influences of dark energy on spacetime and its baryonic matter.

Compression and decompression in the system with positive and negative energies are generated by relative time dilations and length contractions, preventing four separated parts of dark energy to spontaneously interact.

The description goes beyond the barriers of Planck length and Planck time to be able to accurately display the overall balances of all participating forms of energies. The links to the general theory of relativity and to quantum physics are addressed in a simplified manner and as far as necessary for the basic construction.

A rotational geometric model with dark energy, split into four areas, shows the entire picture. Dark energy oscillations and dark energy waves can be derived from the model as relativistic circular functions.

This model does not require curved manifolds and tensors of the field theory of relativity to display the basic principles: This is only necessary when looking at smaller sections of spacetime for precise calculations of total developments with all kinds of involved energies. Einstein’s relativistic field equations can be extended with this dark energy theory in different ways. These possibilities have been explored. The cosmological constant, originally introduced to keep the size of the dimension of the universe stable, is today used as an impact of an ideal exotic liquid with negative pressure to integrate the influences of space inflating dark energy. This new function of the cosmological constant can be adapted to the dark energy rotation model. Investigations of the relativistic aspects change the views on the perceived space dimensions on a cosmic scale and on the nature of dark energy.

The separation of dark energy into four sectors is derived from an assumed equilibrium of opposing four parts of dark energy with an extreme tension before the Big Bang. The four sectors of dark energy appear with features of spacetime, gravity, electricity and magnetism, after breaking up the equilibrium.

An interaction of dark energy components across the entire system produces baryonic matter, some with features of electric charges and magnetic spins and others being neutral. One part of the dark energy wave, 25% of the total energies minus some contributions to matter production, is phase-shifted by 180 degrees and thus acts as a huge gravity field in addition to the gravity of assumed 5% of produced baryonic matter out of 100% dark energy: an alternative to dark matter has been found.

Dark energy with an equivalent of a mass “m” that is forcibly shifted to an adjacent sector appears with an impulse of p=mc, with speed of light c. Shifted across two energy sector barriers into the opposite sector, this dark energy equivalent of a mass “m” appears as baryonic matter with the energy . Only in this way can the dark energy be converted into positive energies of radiation, matter and impulses.

The model can be mathematically calculated as interconnected “multiverse” with initially 16 dimensions of four 4-dimensional universes. Space and time appear because of shared dimensions and motions in the system. The formal mathematical reduction of dimensions because of the shared ones, leads to the model with remaining 12 dimensions. Depending on the kind of limited observations or symmetry, additional dimensions can be neglected or mathematically eliminated. There is only one universe, but the multiverse aspects help to understand the whole picture.

The theoretical possibility of an elimination of thin space layers is mentioned, caused by a forced equilibrium of dark energy within an empty space without any positive energy. This can be done, using the principles of the rotational model, with appropriate engineering interventions. Theoretically, a speed faster than the speed of light can be achieved in this way, without contradiction to the theory of relativity.

According to the model, the universe ends with another complete blockage of dark energies, once all other energies are transformed back into dark energy. Space and time will disappear in an instant to prepare for a new start. The model shows that all four interacting parts dark energy can reach such an equilibrium because the 'against each other +/- 90 degrees phase-shifted’ parts are blind energies in relation to each other, having no effect from one to the other. A deviation of this ideal phase shift causes interactions between the dark energy sectors, generates baryonic matter and other forms of positive energies and pushes the rotation of the system. The dualism of waves and particles can be explained with the rotational model: all energy processes above Planck thresholds of length and time trigger simultaneously processes below these barriers, causing this dualism. The observation of a particle or a wave is depending on the intervention.

The standard model of physics can describe energy equilibrium schemes with unimaginably large amounts of stored energy:

Two oscillations with the same frequency and the same amplitudes cancel each other completely, if they are shifted against each other by half of their wavelength. This picture can be extended with four identical oscillations that are shifted by a quarter of their wavelength and then superimposed. The two oscillations with a phase shift of 180 degrees will again cancel each other by destructive interference. If a direct interaction of two opposing energy oscillations however is not possible because of a relativistic construction in a model of rotational symmetry, any amount of energy can be stored in such a way without destructive interference.

Example with a mechanical model: We can imagine a cross with four nails at its four equal sized wings. This cross rotates around another nail in the center of the construction. This fifth nail is fixed on a firm base. The opposing wing nails are connected, each pair with a ring rubber that is turned once around the nail in the middle of the construction. With very long wings, very thin ring rubbers and a thin nail in the middle, we can rotate the cross with relatively low energy consumption many times around and the tension in the ring rubbers will grow immensely, if the friction is high enough to guarantee winding up around the central nail and preventing the rotation of the cross in case of its release. The potential energy of the system can grow extremely high, if the ring rubbers are capable to store it.

Once the asymmetry of the rolled-up rubber layer around the central nail gets too strong, the cross will rotate after its release. In case of a theoretically infinitely thin rubber band and an infinitely thin nail, the system will only start to rotate if the nail in the center of the construction is moved across a certain distance to force asymmetry. In case we observe this situation from a position on one of the wings, we will notice a seemingly asymmetry of the entire construction, although there is none. We will notice a tension along our wing, a counter tension from the opposite wing and opposing tensions in both side wings that do not affect us at all as long as there is no critical asymmetry in the system.

We can transfer this situation to a possible construction of the universe with four phase shifted parts of dark energy as storage media in an absolute equilibrium state of totally blocked dark energy. Space and time cannot exist as long as there is absolutely no movement in the system.

Accordingly, the first claim of the model is that space and time will disappear, as soon as the universe reached a “Big Freeze” status: The unimaginably huge size of space until the complete cooling of an empty universe at the absolute zero point of temperature will vanish in an instant, if four phase shifted dark energy components are setting an equilibrium. Baryonic matter and radiation have disappeared and dark energy reached the level of 100%.

Bringing a strong enough asymmetry into this blocked energy system an overlapping of phase-shifted dark energy oscillations will cause extreme vibrations with the assumed production of matter, radiation and the establishment of space and time. The dark energy oscillations begin to move in the model as energy waves. This is the second claim of the model.

The third claim of the model is that it may be possible to actively influence limited thin layers of empty space in a way that a locally limited equilibrium will be forced, resulting in a complete elimination of this layer. This eliminated space is non-existent, meaning it plays no role in the calculations of the theory of relativity.

There are two possible approaches to eliminate space towards a destination. One possibility is an immense increase of relative speed in space with the disadvantage of time dilation and an increasing, for humans even deadly radiation by increasing frequency. Moreover, catastrophic impacts of even small matter accumulations along the travel path can be expected because of the relativistic mass increase. The other possibility is the elimination of all kinds of positive energies, until a forced equilibrium of all negative dark energy has been achieved. In this case, none of the mentioned disadvantages is expected to appear.

Figure 1: Disturbance of the dark energy equilibrium

The unknown zero point of the dark energy equilibrium tension cross is shifted at least to a position lp, tp, because only then time calculations are possible and a universe with three spatial dimensions will become visible. Thus, the universe is born. lp represents a Planck length with no noticeable physical processes below and tp the corresponding time interval of a Planck time. Speed of light radiation processes will appear with speed of light c = lp/tp.

The three axes get physical quantities. t for the time, l for any length or distance in our 3-dimensional space. l1,2,3 serves as volume quantity of 3-dimensional space with three mutually perpendicular axes of a Cartesian coordinate system. l1,2,3 can be exchanged with a spherical volume radius rv, if effects on all three lengths are equal, but then has to be scaled with the spherical volume formula.

The axes of a resulting universe with volume l1,2,3, time t, energy compression co and energy decompression d are defined with a certain angle counterclockwise, in dependence of the sum of all new energy forms that have been generated during the process of the Big Bang and that now counteract the dark energy. In the following figure 2 we will recognize the reason for this necessary rotation of axes.

An interaction with a +/-90 degrees phase-shifted oscillation will be not as violent as interactions of 180 degrees phase-shifted oscillations in the hatched areas with processes of limited destructive interferences.

Dark energy with an equivalent of a mass “m” that is forcibly shifted to an adjacent sector assumingly appears with an impulse of p=mc, with speed of light and tension factor c. Shifted across two sector barriers, this dark energy equivalent of a mass “m” assumingly appears as baryonic matter with the energy . This is how

negative dark energy can be converted into positive energy of radiation and matter.

Figure 2: Relation with Special and General Theory of Relativity

In figure 2, we start any observation in the newly created system with axes l1,2,3 ,t, co and d as reference system. The zero point has been shifted into lp, tp, because a very first Planck length and a very first Planck time became existent and because in this way, we take into account that there are continuous developments below these barriers which we need for our energy balance.

In case we would take the first lp-tp-leap not in negative but in positive directions we completely fail to balance counteracting forces and energies. From our asymmetrical observation point in space l1,2,3 , the influences of the axes co and d remain between the original unidentified zero point and the very first shift point to lp and tp .

Below our Planck’s perception limits neither time nor any length can exist, but a relative compression co and a relative decompression d, beyond precise knowledge according to our standard model of physics. Exactly +/- 90 degrees shifted dark energies do not affect spacetime because of being pure blind energies. Therefore, both appear with decompression. A deviation of this ideal phase-shift will cause interactions with spacetime and simultaneously with its opposite 180 degrees rotated sector.

Any point in the universe can be selected as zero point for observations. Like all two-dimensional forms on a sphere's surface, all three-dimensional creatures in a four-dimensional spacetime will have the impression that they are right in the center. A detailed explanation is given in paragraph 6 of the project summary. Any time measurement can start with zero. At the own inertial system of observation, any change will only be observed after sequential completion of Planck times and, looking at lengths, simultaneously only in distances of Planck lengths, independently of any relative speed against other inertial systems.

Quantum physics that describes movements and probabilities of particles with partial differential equations are not necessary for this level of basic model discussions. We look at macrocosmic developments and sum up all counterreactions below time and space thresholds. Eliminating space, however, will need quantum physics.

Introducing a second Cartesian coordinate system with l’1,2,3, t‘, co‘ and d‘ with a rotation angle reflects the theory of relativity for very simple processes of increasing positive energy. In case an object with a mass and placed on the l1,2,3-axis gains energy for example by increasing relative speed or increasing mass, then we will notice a counterclockwise rotation of the l‘-t‘-system of this object, which corresponds precisely to this change.

The rotation in figure 2 from a starting position P1 to a position P2 represents the results of a calculation with the special theory of relativity for relative length contraction and time dilation in case of a relative speed along a straight line, if we evaluate the projections on the original axes, as shown in the figure.

A spaceship pilot would measure a shorter distance to the destination along l1‘, which corresponds exactly to the projection length on axis l1. A length contraction has been detected. The pilot recognizes in parallel that less time is needed for the trip, given by the projection result on the original t-axis: His or her time line has been stretched as described by the time dilation of the special theory of relativity.

This rotation and the result of relative length contraction and time dilation is valid for any type of positive energy increase, also for the aggregation of masses. As masses fill 3-dimensional space, all three space coordinates have to be taken into consideration for the evaluation of changes. In case of an evenly spherical mass all three spatial coordinates are affected equally. Therefore, l1, l2, und l3 can be combined and simplified as space volume l1,2,3. If mass is spread unevenly and including relative speed and energy impulses in various directions, each space axis has to be calculated independently or split into a sperical part and a metric part.

The formulas of the general theory of relativity describe these situations very precisely. Using the space-time-rotation model, only very simple constellations and effects on spacetime become visible by simple geometry: Coordinates for space location and time move already in this simple rotation model along arcs with spacetime compression and decompression, sperical parts and metric parts, as demonstrated in figure 2.

For complex calculations it is advantegeous to exchange the straight Euclidean metric with curved manifolds of spacetime and tensors of the general theory of relativity, but with extensions of dark energy impacts.

The combined l’,t’, co’, d’-system of all summarized positive energies continues its clockwise rotation from a starting position and current position, until, after an unimaginably long time period, it reaches the Big Freeze position. No form of positive energy is left. Returning into equilibrium, space and time vanish within an unimaginably short time frame across the entire universe. Once more there will be neither time nor space until a new start takes place.

Figure 4: All 4 oscillation sectors have an effect on each other in space volume l1,2,3 and along the timeline t

A complex superposition of oscillations across the entire system, below and above thresholds of appearing length and time, can be sufficiently discussed with a division into four sectors, with astonishingly different functions and effects, if evaluated from an asymmetrical observer position in four-dimensional spacetime.

We divide the system into the sectors ST, E, M and G-H. ST stands for spacetime, E for an area that is capable to produce electrical fields and electrostatic when interacting with ST. This is deducted from the fact that time dilation until a relative standstill of time in relation to the time on timeline t allows static behavior of electric charges. If we rotate an inertial system not counterclockwise + 90 degrees for static behavior but clockwise to the maximum of - 90 degrees, the theoretical relative speed should instead of a positive value, have a negative one. From this point of perspective, with a negative speed of light, the sector ST seems static and frozen. Observed in ST, however, initiated energy fluxes at speed of light should manifest. Only magnetic spins and magnetic fluxes can show these features. Sector M is extremely dynamic and offers an endless potential for technical innovations on the base of quantum physics.

The most complicated part is the sector G-H. G stands for gravitation, H for Higgs field. This 180-degrees phase-shifted sector is the only one with two negative axes in relation to ST and stays permanently below the thresholds of time and length. Its influences are only indirectly observable in ST. Merely at Big Bang and supernovae explosions its oscillations interact with the opposite sector ST, directly.

This is, where it becomes interesting, because counterclockwise rotations of subsystems l‘ - t‘ reflect an increase of positive energy, clockwise rotations a decrease, while it is the opposite way for G-H because of its phase shift of 180 degrees, resulting in two negative axes of the energy cross. The counterclockwise rotation of an energy cross results in decompression towards axis d and the clockwise rotation results in compression towards axis co. This is how the entire sector with all its dark energy has got the feature of gravity, exactly like masses in spacetime ST. Assuming that the dark energy of the sectors E, ST and M drives the actual position of the total l’,t’-energy axis and the entire cross clockwise, sector G-H holds against it. 75% of dark energy minus the contribution to the production of matter are kept in check by nearly 25% of dark energy of the sector G-H, forcing a slowdown of the clockwise rotation towards a Big Freeze. The gravity of all 5% of visible masses is contributing as well. The important fact of these findings is that it is also a part of dark energy that slows down rotation, simply because of its phase shift. Only reaching Big Freeze Status aligns the oscillations, erasing the universe in one fell swoop. Having the effect of gravity, the dark energy of sector G-H will generate halos according to the spreading of masses across entire galaxies. It may, therefore, represent dark matter, being obviously no matter but dark energy with inverted impact on the expansion of the universe.

The calculations of the impacts of a seeming ‘dark matter energy field’ is simple: Let us hypothetically assume a universe without any positive energy, then it will be still curved by a seeming mass influence according to the formulas of the general relativity, because one quarter of the entire dark energy is an opposing energy field, evenly spread across the entire universe. If we add now 5% visible matter, we end up exactly with the situation of our universe. In the calculations, we have to take into account that the dark matter energy field is initially behaving like an evenly distributed mass but then locks in entire galaxies with their uneven distribution of stars and solar systems, due to the construction of the galaxy and according to the formulas of general relativity, extended with this energy field.

Sector G-H, with its inverted energy effects, is then also capable to catalyze atomic nuclei and their subatomic elements. Therefore, it is the perfect candidate for the Higgs field. Sector G-H is awarded with the function of strong interaction in atomic nuclei because of its immense compression. Sector E and sector M are consequently awarded with the function of weak interactions. Under this aspect, atomic nuclei parts are firmly anchored in G-H during production. Electrons with electric features from E and magnetic features form M move freely in ST and are captured by atomic nuclei to achieve electric balance.

The dark energy of ST, expanding ST, behaves like a huge increasing wave of negative energy in relation to all positive energies. The dark energy of G-H, shifted by 180 degrees, can be imagined as a huge decreasing wave of negative energy, trying to stop this expansion.

This constellation is also responsible for the inertia of masses, if they are accelerated in ST. G-H works against this acceleration. In the general theory of relativity an inertia has been postulated as the principle of equivalence. The model makes this equivalence and inertia visible with energy cross rotations.

Figure 4 indicates why gravity cannot be shielded in contrary to electric and magnetic fields and if there could be a solution: The problem seems to be the situation that electric and magnetic fields are generated by adjacent +/-90 degrees phase shifted sectors, gravity, however, by curves of spacetime and thus interactions with the opposite 180 degrees phase-shifted sector G-H. Shielding gravity needs a solution for this different situation.

The dualism of waves and particles could be explained with the model. Let us take the Rutherford-Bohr atomic model, to increase the energy of an electron in the shell of an atom by reaching an orbit with higher relative energy. In this case, the inertial l’,t’-system cross of the electron rotates counterclockwise in figure 3. Releasing this energy by jumping back to the original orbit, turns the l’,t’-system clockwise back to the starting position. The result is the release of an observable electromagnetic wave, caused by interaction from the electron in ST with E and M. The rotating cross of all four axes, however, excites simultaneously also the area G-H via compression co and decompression d to interact with M and E with the very same energy content. This interaction happens below the thresholds of length and time and cannot produce a wave. The energy compression then takes the form of a particle instead, in case of our electromagnetic wave, it will be the generation of a photon with an apparent mass. Both appearances always exist simultaneously.

Now it depends on the experimental intervention, if we recognize either a wave or a particle. We can even change measurement during a running process and get a switching between wave and particle, forwards and backwards. Waves and particles are always existing together and only the observer’s intervention decides if a wave or a particle appears. This is the logical mathematical and physical explanation of the dualism of waves and particles, with support of the dark energy rotation model. Electrons show the same dualism. Electrons can be produced in pairs with positrons with enough electromagnetic energy and forced rotation near an atomic nucleus. As a result, the electromagnetic wave and its counter-reaction photon are separated, producing these two particles of matter and antimatter and simultaneously generating their accompanying waves. The dualism is maintained.

Considering an equal contribution to 5% matter from all four sectors, the relation of Dark Energy : Inverted Dark Energy(dark matter effect) : Baryonic Matter results in 71.25 : 23.75 : 5, meaning the relations of (ST+E+M) : (GH) : Matter. The sum of matter has been estimated with 5%. These relations correspond to the actual measurements of astrophysicists, although we will correct the views on dark energy under project summary because of practical simulation results.

The model can be mathematically calculated from a central observation point as interconnected “multiverse” with 16 dimensions of four 4-dimensional universes: Space and time only appear because of shared dimensions and motions. The formal mathematical reduction of dimensions because of the shared ones, leads to the model with remaining 12 dimensions, and energy cluster simplifications to our 4-dimensional perception spacetime. Taking spacetime ST with four perceived dimensions as reference model for the entire set-up, each sector can be designed with four dimensions, adding up with sixteen. Figure 4 shows the interconnections between ST and E via the t-time axis. Applying the same interconnection for all four sectors, we can cancel four dimensions of the sixteen, ending up with 12 dimensions. Depending on the kind of limited observations, additional dimensions can be neglected or mathematically eliminated, because of a symmetry, less importance, or energy clusters.

The field equations of the general theory of relativity can be extended and adapted in different ways:

The 12-dimensional dark energy construction is calculated as a “multiverse” with four superimposed complete sets of field equations that consider all four components of dark energy. Phase shift perspectives however have to be applied also to all involved positive energy forms. As these field equations already include 10 independent dimensions with 10 differential equations, the overlay and all required phase shift calculations will make the extensions extremely complicated. The field equations of the general relativity alone are only solved for simplified applications.

The cosmological constant, originally introduced to keep the size of the dimension of the universe stable, is today used as an impact of an ideal exotic liquid with negative pressure to integrate the influences of space inflating dark energy. The division into four parts of interacting dark energy could be applied to a new complex definition of the cosmological constant. The result is expected to provide acceptable approximations for the calculation of the stability of galaxies, because the influences inverted dark energy considerably affect major matter distribution clusters across extremely long distances in space. The third possibility is the treatment of inverted dark energy as an evenly distributed mass field. In this case the cosmological constant could be kept in its current form, keeping in mind that it reflects the summarized space inflating influences of dark energies of the sectors ST, E and M.

A short outlook towards experimental confirmations and engineering of a dark energy drive faster than light:

The first step is the experimentally accessible proof that galaxies are stabilized by inverted dark energy. The final confirmation of the model can be realized through a precise length measurement. The elimination of a thin space layer with a forced equilibrium of dark energy should result in the measurement of a shorter distance. In a space laboratory, the measurement would be easier to accomplish as in a laboratory on earth. Dark energy drives using this principle could open the doors to other habitable planets.

Figure 3: Linear v/c scale on t-axis with the linear projection result l’ v/c

Figure 3 shows a simplified calculation principle for relativity, sufficient to estimate the dark energy impacts on the complex field equations of the general theory of relativity.

The linear increase of relative speed v in relation to the speed of light c is superimposed on the original time axis t for a defined time period t1. Reaching the speed of light on a starting axis l1, the axis l1’ has completely rotated to the original time axis t and the time axis t’ has completely rotated to the compression axis co. We know from the theory of relativity that parallel events along an original length l1 will be observed from the starting inertial system as sequential events on l1’ in case of reaching speed of light. In this way the speed of light c has evolved from a speed quantity into a tension quantity.

The linear c-tension scale on the original time axis t therefore causes the linear increase of switching from parallel events to serial events as observation results on the starting inertial system with l1. Calculating the shortages of distance and time with the Pythagoras formula and a linear v/c increase on the time axis with t1 results in the shortage factor , because of .

The corresponding time dilation in this moving inertial system becomes visible in the model: the pilot does not recognize any time dilation in the own inertial system without a possibility to compare clocks. This time dilation is calculated with the reciprocal Lorentz transformation factor .

Any speed v stays in both inertial systems always constant up to the speed of light, which is the reason for time dilation and length contraction.

The relativistic increase of a mass m’, compared with its starting value m0 and according to the precise angle of

a counterclockwise rotation, corresponds to the time dilation, ruled by the Lorentz factor .

We could therefore exchange the volume l1,2,3 with a volume scale for a mass m0. The volume compression of 0.5 means that the mass seemingly has only half of the initial volume to fit in. This is a simplified relativistic view. For a moving observer in the l’,t’-system the volume always stays at it is.

Now we get a relativistic mass increase by counterclockwise rotation of a volume scale axis for m’ instead of l’, applying the Lorentz factor, as with the reciprocal value of the volume contraction over one length contraction. As a principle of equivalence, we can use the accumulation of resting masses in any sperical volume l1,2,3 with an identical increasing rotation angle in comparison with a single point mass in motion, with the corresponding relativistic mass increase. We can also use the apparent masses of photons in the model.

Considering all kinds of positive energies and impulses the field equation of the general theory of relativity has to be used: figure 3 of each individual energy and each process have to be superimposed in complex numerical calculations. The cosmological constant, originally introduced to keep the size of the dimension of the universe stable, is today used as an impact of an ideal exotic liquid with negative pressure to integrate the influences of space inflating dark energy. In detail discussions of calibration errors of spacetime will change this view on dark energy. In addition, the field equations do not include the opposite sector of spacetime. Its influences have to be added, extending the formulas. Dark energy represents about 95% of all energies and has a relatively simple structure compared to all other forms of energy.