## 4+MODEL

4 + Model of the universe, a model based on the geometry of space instead of Lagrangian, Hamiltonian and the principle of least action. It complements them perfectly and gives additional breadth in physics and allows to solve the toughest problems such as the nature of dark energy, lack of antimatter and many others.

**THE SHAPE OF THE UNIVERSE****SOLUTION TO THE PROBLEM OF LACK OF ANTIMATERIA****TIME AND THE FIRST SPATIAL DIMENSION****SPACE EXPANSION & DARK ENERGY****ELEMENTAL PARTICLES****ADDITIONAL DIMENSIONS****MOMENTUM, ENERGY, AND MASS****KINETIC ENERGY AND SPECIAL RELATIVITY****DARK MATTER**

**Note, **The model is being developed intensively so that major changes to the content on this page are possible.

For those who have not read the preface only briefly what this text is about. The general idea is that the universe is basically simple and symmetrical (meaning beautiful). I set a minimum number of rules and made a new model of the universe according to them, such that it agrees with the measurements made in physics and does not necessarily agree with the interpretations of those measurements. The result is astonishing, I got a very complex model but there is no paradox in it, big problems with dark energy and lack of antimatter are systematically solved, they do not appear at all and it is quite clear why, if not longer below is the model so judge for yourself, the model is not yet complete.

4+The model is based on only three basic rules:

Rule 1. Everything is energy, everything that physically exists is just a different form of energy. Its amount is finite and unchangeable and its duration is eternal.

Rule 2. The vector sum of all momentum in all dimensions is equal to zero.

Rule 3. Nature always chooses the most symmetrical solution for any physical phenomenon.

**Rule 1.** Everything is energy. All phenomena that exist in our universe, matter, space, force fields, and everything else are just forms of energy. That mass is one form of energy was shown by Einstein in his work, it was difficult to accept but it turned out to be true, now we need to go a step further and generalize the idea of energy as the only component of the universe, meaning space and matter and absolutely everything that exists in the universe is just one form of energy. The direct consequence of rule one is that the law of conservation of energy applies throughout the universe, meaning the entire universe is a closed system. A very important consequence of the assumption that all energy is that there is no infinitesimal or infinitely large quantity of any phenomenon in the universe (mass, space, force…). That there is no infinitely large quantity stems from the fundamental assumption that total energy is finite and that all phenomena in the universe are made of one part of that energy, so that no phenomenon can have an infinitely large amount. That there is no infinitely small quantity stems from the assumption that everything is energy and it always has its smallest parts - quantum energy. In my model, we have the smallest elements of space, time, and all other phenomena in space.

**Rule 2.** The vector sum of all momentum in all dimensions is equal to zero. Momentum is known in classical physics as the amount of motion, however, it is a much broader term. It appears in all dimensions and the rule that the total vector sum of momentum is equal to zero applies everywhere. Information is the only phenomenon in the universe that is not directly made of energy. It could theoretically exist in its abstract world independent of the physical world made of energy. This abstract world could include other universes or phenomena unknown to us. Looking at the information in our universe we see that the source, carrier, and receiver of information is always made of energy. In this model of the universe, time is information, it is not made of energy. Time is a specific type of information, it springs from events that take place in the material universe.

**Rule 3.** Nature always chooses the most symmetrical solution for any physical phenomenon. It is more of a philosophical nature, there is no obvious reason why it is so but it seems to be generally present. It would be more accurate to say that nature always chooses from all possible solutions the one that requires the least information to be defined.

Following the above rules and especially rule three, that nature always chooses the solution with the highest symmetry, brings us to the shape of the universe.

We humans can detect three spatial dimensions with our senses, it is a common notion that we live in a three-dimensional universe in which time passes. Our senses have deceived us countless times when it comes to the real nature of any physical phenomenon so let’s examine the possibility that space can have any number of dimensions.

The only **dimensionless** object is a material point. If the universe were dimensionless it would have the “shape” of a point but this is definitely not the case.

The only **one-dimensional** object is a line. In a one-dimensional universe, the curvature of a line is not important because it cannot be detected in principle. There is another feature that divides lines into two sets, open and closed lines, open lines have two points that are different from the others, they are the beginning and end of the line. Closed lines do not have any special points, so less information is needed to define these lines. Following rule three I conclude that the universe would have the shape of a closed line if it were one-dimensional.

With **two-dimensional** objects we have an infinite number of possible shapes, the 2D object with the highest symmetry is a circle. This leads to the conclusion that if there were a two-dimensional universe, it would have the shape of a circle. Of course, our universe is not two-dimensional. A circle as a mathematical figure can be represented as an infinite number of circles in each other, but when we look at real physical space that would have the shape of a circle then the number of circles is not infinite because space always has its smallest parts - quanta of space and they have finite size. A circle-shaped space would consist of a finite number of one-dimensional circles. To correctly describe an arbitrary point in that space we need two quantities, the first being the distance of a particular circle from the center and the second being the distance of a point from some reference point per circle. These two sizes are in fact two dimensions of such a space. It is very important to note that these dimensions are not equal, the first dimension has an absolute amount of length and is directed, (it has its beginning and end). The second dimension is closed in itself, moving only along it in the same direction would come to the starting point, the amount of length and direction depends on an arbitrarily selected reference point, the values of length and direction in it are relative to the selected point. Picture below.

By generalizing the circle, it is easy to conclude that the n-dimensional object with the most symmetry is an n-dimensional sphere, it always consists of one (absolute and directed dimension) and n-1 relative and closed dimensions.

The picture below shows a 2D circle and a 3D sphere, it can be seen that the 3D sphere contains one absolute dimension (dimension I) and two relative and closed dimensions (dimension II and dimension III)

The orientation of the first dimension is its fundamental feature and it cannot be changed, it is our arbitrary choice which direction we will declare positive. The logical choice is to declare the direction going from the center to the outside positive, in the following text I will stick to this decision, the direction going from the center to the outside is positive.

If space is **three-dimensional** then following rule 3 it would have to have the shape of a sphere, it would have two of the same spatial dimensions, each closed in on itself and it would have one open, directed dimension going from the center of the sphere to the surface. It is not the shape of our universe because we have three dimensions that we cannot distinguish by anything. So if the universe is three-dimensional then it is not maximally symmetrical. This may not seem like a strong argument against 3D space but it is just one in a series of arguments that tell us that space has multiple dimensions. Another argument is that after a century of research, astrophysics has failed to establish a 3D model of the universe, neither shape nor size. The paradox of the size of the 3D universe stands out, at the beginning, it was extremely small, then a certain (final) time spread at a certain (final) speed and now according to the available measurements it seems to be infinitely large, it just doesn't make sense. And string theory tells us that the universe must have more than three dimensions.

The next logical step would be, let’s assume that our universe has one dimension of space more. It means examining the possibility that our universe is a **four-dimensional** object plus time as a parameter of change in it. Of all the 4D bodies the 4D sphere is the most symmetrical, following rule three if the universe is four-dimensional then it must have the most symmetrical shape and that is the 4D sphere. A 4D sphere has one spatial dimension that is open, has its starting point, and is directed from the center of the sphere towards its surface, which we called positive. It has three classical spatial dimensions that have the property that each is closed in on itself, therefore there is not a single point that would be special, all distances can be measured only relative to an arbitrarily selected point. Since the three classical dimensions of space are enclosed, each universe seems to be infinitely large.

The picture above shows the fact that each "shell" of 4D space is one whole 3D space. That is, for each value of the first dimension we have a whole 3D space.

Hypothetical 4D Universe in which all matter would move in one direction according to the first dimension, from the center to the outside would be exactly the universe as we know it, would have the classic three spatial dimensions in which particles move according to the amount of motion they have in these dimensions. The constant movement of particles directed from the center outwards, according to the first dimension, would be perceived by the observer inside the universe as the passage of time. It would seem to him that he lives in a 3D space in which time flows. Just the way our universe looks to us.

This is a strong argument that the universe is a 4D sphere, but it is still a long way from being able to say that this is a proven fact.

If space has **five or more dimensions** then we should have four or more closed dimensions (classical spatial dimensions) and there are none, neither by instruments nor by our senses do we detect them. According to all evidence, the universe does not have five or more spatial dimensions. The conclusion of this analysis is that space has the shape of a four-dimensional sphere. It has the classic three spatial dimensions and another spatial dimension that differs from the other three.

InIn the picture above we see a 2D cross-section of 4D space, since the three classical spatial dimensions are the same, it is enough to show only one of them. The figure shows an arbitrary zero point of the classical spatial dimension with a dashed line, as well as an arbitrarily selected direction shown by an arrow.

By consistent application of the basic rules, in addition to the shape, the structure of the space can also be determined, according to rule 1, the space must consist of energy. (He can never be just a void) Every form of energy always has its smallest parts, so space must have its smallest parts, hereinafter I will call them the elements of space.

In principle, any arrangement of space elements is possible, as well as the amount of energy that an element contains. According to rule 3, our universe chooses the arrangement that has the most symmetry in it. In the picture above I have given two possible layouts, one the simplest and the other the most symmetrical. The elements of space are greatly magnified to be able to display them, in reality they are objects whose dimension is of the order of Planck length, meaning extremely small.

Layout 1: is seemingly the simplest - all elements of the space contain the same amount of energy (they are the same size) and are therefore evenly distributed throughout the space.

Layout 2: the elements of space with their size and mutual distance follow the shape of a 4D sphere, closer to the center the elements of space are smaller, away from the center they become larger, they contain more energy the farther from the center of the sphere.

If the universe had elements of space arranged according to Schedule 1, then we would solve only some of the big questions in physics but we would get new paradoxes, for example, we would get a universe in which matter enters larger and larger segments of 3D space i.e. the 3D space expands but the average temperature of the matter it contains would not drop. The conclusion is clear, our universe cannot have this arrangement of spatial elements.

If the universe had elements of space arranged according to Schedule 2 (the most symmetrical arrangement), then we would solve almost all major problems that exist in physics today only by analyzing the motion of particles in a 4D space that has the shape of a sphere and the just presented arrangement and size of space elements. only the most important:

- Lack of antimatter in space
- The origin of the arrow of time
- They would explain why entropy increases with the passage of time and why it was so small at the very beginning.
- They would solve the issue of dark energy

I will dedicate a separate text to each of these problems. Now I would just like to emphasize that this degree of agreement between the presented theoretical model and the real physical world leaves no room for a different conclusion from the following. **The space has the shape of a 4D sphere of finite size and has a structure such as is shown in Schedule 2.**

The question now is **what is the real nature of the elements of space**. Following the three basic rules, we came to the conclusion that they are the smallest parts of space and that they are a form of energy, to determine the other properties of spatial elements we must consider the interaction of matter and space. It is known from the general theory of relativity that the presence of any form of matter / energy in a part of space causes the curvature of that part of space. This means that the space and the particle that is on it are not independent, but interact, with the departure of the particle the space returns to its original state. Since we know that space consists of the elements of space, the curvature of space means an increase or decrease in the elements of space on which that matter / energy is located. The classic notion of a particle is that it is a material point that contains some form of energy (one or more of them). The shape and structure of space show us that the elements of space are physically larger when they contain more energy and vice versa. Following the classical notion of a particle, we come to the conclusion that the arrival of a particle on an element of space would cause its increase, it is proportional to the energy of the arriving particle. In the chapter "Gravity" I will show that in the case of an increase in the element of space, a repulsive gravitational force would arise. All previous knowledge tells us that gravity is always an attractive force. This leads us to a very interesting conclusion about the nature of the particle and the element of space in which it is located. The particle has apparent negative energy for the elements of the space in which it is located, with the arrival of the particle on the element of space it loses part of its energy, which leads to it being physically reduced. This phenomenon eventually leads to the curvature of space that is mathematically described in the general theory of relativity.

Rule 1 tells us that the energy that has “gone” from the element of space cannot disappear but that it has only temporarily moved somewhere. This leads to a very important conclusion about the nature of elementary particles, the energy of a particle is in fact dislocated by the energy of space, therefore a particle cannot exist without space at all. An elementary particle is an energy disturbance in the space that travels through it. More about elementary particles in a separate chapter.

Now I would consider the question of where the energy of the spatial element goes when the particle comes to it. In a universe where everything is made of some kind of energy (rule 1) there must be some physical phenomenon into which the energy of the spatial element temporarily went while the particle was on it, since this departure of energy from the spatial element occurs only when the particle is on it. means that this phenomenon must have a direct connection with the particles. If we look exclusively at the element of space then we conclude that the temporarily dislocated amount of energy has gone outside the 4D space, i.e. it is not in any spatial dimension. Since energy cannot be "anywhere", we conclude that there must be an additional (one or more) dimension into which this energy could go, at the same time these dimensions must have a direct connection with elementary particles because the energy in them leaves only those spatial elements where is currently some particle. The fields of elementary forces are the only known physical phenomena that satisfy both of these conditions, they are directly related to particles, that is, without particles, there would be no force fields, they also contain energy. In the 4+ Model, the fields of elemental forces are in fact additional dimensions of the universe. Unlike the 4 spatial dimensions that always possess a certain amount of energy, additional dimensions in empty space have zero energy, you could say they don't even exist, the arrival of a particle in that space also means the departure of energy from 4D space into additional dimensions. More about additional dimensions in a separate chapter.

The elements of space are the smallest parts of space, they are entities, they have no internal structure, so we cannot define any movement (change of position) within the element of space. This means that physical laws involving a change in the position of any particle cease to apply at quantities below the size of the spatial element. These are almost all known laws of physics. It has long been known that the laws of physics do not apply to lengths that are less than Planck's length (1,616 × 10−35 meters). If the elements of space are exactly those lengths then we have an explanation for why we cannot describe events at smaller lengths.

Planck energy is the largest energy that can be contained in a 3D cube of space whose sides are one Planck length long and it is 1,956 × 109 J. It is also the highest energy that an elementary particle can possess. This agrees with the nature of the particle in the 4+ model, the particle does not have its own energy but represents the dislocated energy of space (spatial element), so it is quite clear that a particle cannot have more energy than the element of space it has. This allows us to determine the energy of the space element. Since space is four-dimensional, we can obtain the energy of a 4D spatial element by dividing the energy of a 3D Planck cube by the number of Planck lengths contained in one second (I spatial dimension), which is 3.628x10-36 J

Now that we know a lot of the properties of the elements of space, we can list and analyze them all.

- They contain energy and are energy-dependent, the more energy the larger the element of space and vice versa, the maximum amount of energy they can have is 3,628x10-36 J
- They are physically small, in the case when they have the maximum energy, their length is of the order of 10-35 meters.
- They have at least 4 dimensions, the maximum number is between 11 and 13 dimensions (the nature of some phenomena is not yet completely clear)

The only known physical quantity that satisfies these properties is the String. This would mean that the space consists of a huge number of strings that are arranged next to each other so that they form one large 4D ball, that is, 4D space. The strings retain the structure shown in Figure x closer to the center of the sphere are the strings with less energy and farther from the center are those with higher energy. The strings contain all the energy of the universe. Particles neither bring nor transfer energy to the spatial elements, they only redistribute it differently while they are on that spatial element. That is, the strings temporarily "vibrate" into other dimensions while the particle is on them. Which dimensions it will vibrate into and how much energy it will dislocate depends on the type of incoming particle, each particle has its own energy "signature" and that makes it different from other particles.

This nature of space and particles provides a framework that can unite three major theories: relativity theory, string theory, and quantum loop gravity. This unification can ultimately lead to the theory of everything, that is, to bring physics to the possibility of a mathematical description of the whole universe.

**SOLUTION TO THE PROBLEM OF LACK OF ANTIMATERIA**

So far I have not stated anything about particles in the 4+ model of the universe, for this example, it is important to know only that they move through all dimensions in accordance with the momentum they possess in a given dimension.

The figure above shows a 2D cross-section of a 4D sphere - the universe

The majority of matter is created at the very beginning of time and in the very center of 4D space (4D Spheres). During this creation, a pair of particles-antiparticles is created each time. for particles positively directed, i.e. from the center outwards, due to the obtained momentum in the first dimension, each particle began to move radially from the center outwards, each antiparticle began to move exactly in the opposite direction from the direction of movement of the particle.

Since there is no special division of the 4D sphere, for each particle we can claim that it is a particle and the one that goes opposite to it is an antiparticle. This shows that there is no absolute difference between particles and antiparticles, there is only a relative difference that arises due to the opposite direction of motion. This exactly opposite direction of motion causes both their electric and magnetic fields to be oppositely placed. (Therefore, the positron has the opposite charge from the electron).

Each particle is also an antiparticle to the one that went to the opposite side. Although in fact, both are particles. (this sentence doesn't make much sense until you look at the particles M and L, in the figure above).

The picture above shows the movement of only four particles through 4D space, two particles (M and L) were formed at the very beginning as a pair of particles - antiparticles, but as both moves in the positive direction of the first dimension, it makes them both particles,

The other two particles showed (N and K) "particle" K moves in the negative direction of the first dimension and this makes it an antiparticle, the particle N moves in the positive direction of the first dimension and this makes it a particle. They did not form at the beginning of time but subsequently during the interaction of particles of matter or photons, and then they formed as a pair of particles - antiparticles (due to the preservation of zero momentum in the first dimension). Such events are relatively rare and the antimatter thus formed is quickly annulled with the matter, which is why there is very little antimatter in space.

Better connoisseurs of physics will notice that antimatter particles move in the opposite direction from other particles, so detectors should not detect them, and yet we know that they detect them in experiments, so they would reject the offered solution as incorrect. This 4D model of the universe is a much broader theory and it predicts just such interaction of particles more on this topic in the chapter "ADDITIONAL DIMENSIONS", now only briefly, particles interact through the force field, for interaction between two particles most force fields do not require 4D spatial locality, but only 3D locality.

**The geometry of the universe, which is a 4D sphere, in combination with the law of conservation of zero momentum in all dimensions are the answer to the question why there is significantly more matter in space than antimatter**

**In this example we see that the problem of the lack of antimatter never even existed, it is the product of our misunderstanding of the geometry of the universe. The standard model is correct but our current understanding of the geometry of the universe is not.**

**TIME AND THE FIRST SPATIAL DIMENSION**

It is important to note that of the four spatial dimensions, only the first dimension is directed, this small difference will lead to a completely different movement of particles in it compared to the other three spatial dimensions and ultimately to the fact that we humans do not recognize it as a spatial dimension.

The orientation of the first dimension means that all particles moving on it at the very beginning of time received momentum directed in the same way as the first dimension, it is at that moment the only possible direction, because from the center of the sphere the only direction is towards the surface of the sphere. Since all particles have received momentum in the same direction, there is no possibility to change that direction in later interactions, the movement of all particles continues in the positive direction of the first dimension throughout.

The other three spatial dimensions are not directed, so in them, the momentum of an individual particle can have an arbitrary direction, with the proviso that the total vector sum of the momentum in all dimensions must remain zero. At the beginning of time, the initial momentum in three spatial dimensions was given to particles that do not have a rest mass. After some time and the interaction of all particles and particles with rest mass received a certain amount of momentum in the other three spatial dimensions, this amount is on average significantly less than the initial obtained in the first dimension, so that of the total movement through 4D space, which always takes place at the speed of light, the velocities in the classical three dimensions are significantly less than the speed of light and all the remaining speed is through the first spatial dimension and it is close to the speed of light.

Our entire 3D universe is moving at a speed close to the speed of light through the first spatial dimension. We cannot notice this movement just as we do not notice the movement of the solar system through our galaxy, it is simply beyond the reach of our senses. However, the energy of this motion is very real and measurable, it is the so-called rest energy (which is ironic), given by the famous formula E = mc^{2}, it is the energy that each particle has due to high-speed motion of the 3D universe in the first spatial dimension, more on this topic in the kinetic energy section.

If we were to observe the motion of an absolutely still particle, meaning one that does not move through 3D space at all, the only component of its motion is that through the first dimension, meaning with every second it would make a path of 3 * 10^{8} meters. Since we do not observe this movement, it is easy to make a mistake and conclude that the particle moves through time, that is, that time is the fourth dimension through which the 3D still particle moves.

**Time does not contain energy so it cannot be a dimension. Time is information.** **This information comes from events that take place in space (in its dimensions), the smallest event is when an elementary particle passes from one element of space to an adjacent one. It's a quantum of time. This event is exactly the same regardless of whether the particle has passed into an adjacent element by the first dimension or by one of the three classical spatial dimensions. This means that there is no special "temporal" dimension, there are only four spatial dimensions along which the particles move, time is information about their movement.**

The unit of time is the second, it was determined for historical reasons and as such is accepted today. The very definition of the duration of one second has changed throughout history. The definition of a second in 4D space would be most accurately derived through the motion of a photon through space, we know that this motion is always the same, so the definition of a second would be: for one second the photon passes N = 1,856 *10^{42} spatial elements per spatial dimension through which is moving. This is the number of Planck lengths that a photon crosses in one second.

In 4D space, time is absolute. It comes from the fact that all particles through 4D space always move at the speed of light. The amount of speed of 3 * 10^{8} meters / second is a consequence of our arbitrary determination of units for measuring length and time. It would be natural to define basic units so that the unit of length is equal to one spatial element (Planck length), the unit for time should be Planck time. Then the unit velocity would be c = 1. Although such a system of units would be impractical in everyday use, it would realistically show the processes in which a particle moves through 4D space.

We see that time is defined as a consequence of an event, it is information and through it, we can compare events, once defined unit time becomes an independent parameter with which we can describe events in any dimension or more at the same time.

4D space does not expand, it is created at the beginning of time from the primary energy and as such simply exists. Particles move along it in accordance with their total momentum, which they have in various dimensions. The figure above shows a 2D cross-section of 4D space and the motion of matter along it. Most of the matter was created in the very center of 4D space at the very beginning of time, since then it moves radially from the center outwards, we cannot directly observe that movement, besides that radial movement there is also that component of movement through the other three spatial dimensions. only and can we observe directly.

** **

**The elements of space do not have the same size in the whole universe**, they follow the shape of a 4D sphere - the shape of our universe, they are the smallest in the center and larger in size, their shape and arrangement are shown in the picture above. With the passage of time, the particles always move in the same direction through the first spatial dimension, with such a movement the particles enter the area of increasing spatial elements. The number of spatial elements does not change. **The speed of particle motion depends only on the number of traversed space elements and not on their size. The same applies to the length, that is, to the spatial distance between two particles, it depends only on the number of elements of the space that are between them, it does not depend on their size.**

**The size of a spatial element is directly proportional to the energy it contains.** The reduced Planck constant divided by one second is the energy that each 4D element of space contains in the present time. We use time due to the impossibility to directly measure the distance from the center of the sphere to today's position according to the first spatial dimension. Since matter moves at an average constant speed through the first dimension, we can use time as an indicator of the change in the reduced Planck constant.

This arrangement and size of spatial elements, one could say this structure of space, gives a somewhat strange feature. If we were to take an arbitrary distance L (the distance L is shown by a green line) between two still particles (there is no mutual motion in 3D space), an observer who is part of our universe would see that their mutual distance does not change over time, each measurement would show that the length L is the same, however, if there could be an observer outside our universe he would clearly see that the length L increases with the passage of time, that is, the movement of particles through dimension A. The observer outside our universe is just an interesting objection, his observations have no significance, can only help us create a mental picture of events in 4D space.

This means that as time passes, the particles remain at the same distance on average, so there is no energy added to the gravitational field. The constant gravitational field does not affect the motion of particles, so there is no global slowdown in the movement of matter through any dimension due to the action of gravity. Gravity only on the medium scale of size affects the shape of 4D space. On a global scale, great gravity has no effect on space and the movement of particles along it, this is because the three spatial dimensions are closed, each in itself, they are always the same size so the gravitational effect is reversed. So it is completely irrelevant how much matter the universe has on average, its fate will not depend on it, even if the density is high, there can be no "great compression".

Although the length L remains the same, the movement of particles (matter) through space that has larger and larger spatial elements cannot pass without measurable consequences, the direct consequence is an increase in entropy, more in the chapter "Entropy"

If we look only at 3D space, it is almost absolutely flat. 4 + The model predicts that the amount of energy in the form of space versus that in the form of matter is enormous, their ratio is of the order of 10^{120}. This relationship is known as vacuum catastrophe from quantum field theory (QFD) The source of confusion is that energy when is in the form of space does not curve space. Only energy in the form of particles and the fields of force that particles cause, curves space. Such a large ratio of the energy of space to the energy of matter means that the universe must be extremely flat. Since space is a four-dimensional ratio of the energy of space and the energy of matter that is on average significantly less than the stated amount of 10^{120}, it is of the order of 10^{77}. The amount of 10^{120} refers to the 3D element of space, such an element of space contains 10^{43} 4D elements of space. It is still a huge predominance of the energy of space over the energy of the average amount of matter in space. This means that the space on average must be very flat.

As time passes, the particle constantly enters new 3D sections of 4D space, these 3D spaces are always the same size, there is no expansion or contraction of 3D space (length L does not change) **Since there is no expansion or contraction of 3D space, there is no need to bring into the term "dark energy “Such a phenomenon does not exist, the universe is a closed system and the law of conservation of energy always applies in it.**

The redshift of distant stars is due to an increase in the entropy of the universe. From the time the photon was emitted to the time it was detected, more in the chapter "Entropy"

So far we have seen that 4D space can exist without particles. Such a space would be absolutely peaceful, meaning it would have no events and therefore time could not be defined. A space without particles would only exist, eternal and unchangeable. Unlike space, particles cannot exist as independent objects, they can only exist in space.

Space through which the particles move consists of its smallest parts - the elements of space. The movement of particles along them is a process in which the energy of a particle passes from one element of space to the adjacent one. This process of transition is an elementary event. There can be no less distance than that, and there can be no less time than the time of that event. In order for the transition to take place, it takes some time, once this process is completed, the particle is in a new position, that is, in a new element of space, the element of space is an entity, so there is no particle traveling through it. the movement of the particle is reduced to transitions between the elements of space, more transitions take more time.

**The number of transitions in one second is the true constant of the universe.** It never changes, neither with the passage of time nor with the change of the energy of the spatial elements. It’s the same all over the universe all the time. It is the same on the surface of the planet and in the center of the black hole and in interstellar space.

In the SI system, the unit for time is the second, the time required to move from one spatial element to another is Planck's time, its value is t_p = 5.39 * 10^{-44} s means the number of transitions made by each particle in one second is **Np = 1.855 * 10 ^{43}**

A photon is a specific particle, its total movement through 4D space takes place only through one spatial dimension, movement through the other three dimensions is always equal to zero **s**ince it passes the same number of transitions every second, its speed must be visible as straight and constant.

**The consequence of this movement is that in 4D space all particles always move at the speed of light, this total speed can be vectorized into different amounts in each of the 4 dimensions, more speed in one dimension means less in the others. The total velocity is equal to the vector sum of the velocities in all four dimensions that the particle has. It is always equal to the speed of light.**

All particles that have a rest mass also have momentum in the first dimension, they get it at their formation and keep it while they exist, which means that they always have a part of their movement through the first spatial dimension, therefore their movement through the other three dimensions is always less than the speed of light. Although particles with rest mass move at the speed of light through 4D space, we see only that part that goes through 3D space and it is always less than the speed of light, it is usually significantly smaller, and just such slow movement through 3D space we see for particles with rest mass.

The direction of motion of the particle through the 4D space is parallel to the direction of the total momentum that the particle has. The total momentum of a particle is the vector sum of all momentums in all four spatial dimensions that particle has. On the smallest scale of size, the particle follows the direction of the momentum so that there is a precisely determined probability of transition to a particular adjacent element of space. Since the elements of space are small, of the order of 10 ^ -35 meters, this "wandering" of the particle cannot be noticed at all on an atomic or any larger scale.

So far, I have listed the main properties of particle motion through space. In order to understand and visualize how a particle actually moves through space, we must consider both the energy of the particle and the energy of the spatial element on which it is located and their interaction.

The best image to show the relationship of a particle and space is the relationship of the ocean and the wave on it. An ocean wave cannot exist without the ocean, also the wave does not have its own water but it is only temporarily dislocated ocean water.

**This is exactly the relationship between a particle and space, it is space that contains energy and the particle only temporarily dislocates it.**

The arrival of a particle on a spatial element causes a part of the energy of that spatial element to be temporarily dislocated, that part (amount) is equal to the energy of the particle. As the particle leaves, this dislocated energy returns to the spatial element.

Space contains a huge amount of energy, each spatial element (which is very small, its length is of the order of 10 ^ -35m) contains energy Ep = 1.22 * 10 ^ 28 eV / c ^ 2 This is theoretically the highest value of energy that any a particle can have, the usual energies of a particle are: an electron about 10 ^ 6 eV / c ^ 2, a proton about 10 ^ 9 eV / c ^ 2. Particles can also have additional energy due to motion so that the highest energy of a particle ever recorded is 3.2 * 10 ^ 20 eV / c ^ 2.

The energy of a particle is the dislocated energy of space, meaning that the particle for space has apparent negative energy, it causes a local decrease in the energy of space and thus its local physical reduction and thus curvature. This is contrary to the energy of the particle as seen by classical physics and contrary to our intuition, but it is precisely the negative apparent energy necessary for the gravitational force to be attractive, otherwise, it would be repulsive and the universe would be a radically different place. More on this topic in the GRAVITY section.

** **

The figure above shows the movement of particles through 4D space for one second, for simplicity shows a 2D projection of 4D space, it shows only I and II spatial dimensions, since III and IV are practically equal to II dimensions, we can omit them and that nothing essential to the motion of the particles remains unstated. The motion of each particle begins at the origin of the coordinate system.

From what is shown, it can be seen that all particles move at the speed of light. The velocities of all particles are vectors whose ends lie on a circle of radius equal to the speed of light, the figure above shows only one-quarter of the circle. Particles move through space according to the momentum they possess. In the first spatial dimension, all particles with a rest mass have momentum directed in its positive direction, so that no particle can move in the opposite direction, so it makes no sense to draw the lower half of the velocity circle. Antiparticles move in the opposite direction but we will not discuss them in this chapter. Particles can have momentum in both directions of the second dimension so you should also draw the upper left quarter of the circle, I didn’t do that just for the sake of simplicity, because there’s no significant difference to which side the particles in the other dimension move.

For all particles * (v_{I})^{2} + (v_{II})^{2} = c^{2}* From the above equation it can be seen that the 4D space in my model is Euclidean space, (not Minkowski space). We will see later that all equations from special relativity can also be derived from such a space. (This geometry of space can replace imaginary Minkowski space). More in the chapter "kinetic energy".

The distance traveled by each particle as a function of time is given by the expression **s=ct*** * it is also the vector sum of the paths made by the particle through both dimensions,

**so that for each particle**

*s=s*_{I}+s_{II}

**(s**_{I})^{2}+(s_{II})^{2}**= (ct)**^{2}*if we extend the equation to all four spatial dimensions we get:*

*or in the form*

**(s**_{I})^{2}+(s_{II})^{2}**+(s**_{III})^{2}**+(s**_{IV})^{2}**= (ct)**^{2 }

**(s**_{I})^{2}+(s_{II})^{2}**+(s**_{III})^{2}+(s_{IV})^{2}- (ct)^{2}= 0An absolutely still particle, that is a particle that does not move in 3D space, so its velocity in the second, third, and fourth spatial dimensions is equal to zero. Its total speed through 4D space must be equal to the speed of light which means that its speed through the first dimension is equal to the speed of light.

A slow particle, it generally moves through the first spatial dimension and only occasionally takes a step in the second spatial dimension.

When considering the motion of particles in space, we said that a particle has apparent negative energy for the element of space in which it is located, when a particle reaches an element of space it moves one part of its energy (exactly as much as the energy of the particle) outside 4D space. We didn’t consider then where that shifted energy went. The universe according to the 4+ model is of a fairly simple structure, it is all made of energy and has only 4 spatial dimensions.

The logical conclusion is that there are other dimensions that are not spatial, into which the energy of the particle goes. I call them additional dimensions together.

The question is how many such additional dimensions there are. There are as many as there are different forms of energy. If one form of energy cannot be expressed in any way through the already known, it means that it has its own dimension where its type of energy is manifested.

Another property of all additional dimensions is that their energy is bound to the particles, when the particles would not exist the total energy in all the additional dimensions would be equal to zero. We could say that then no additional dimensions would exist. This makes them different from the four spatial dimensions, they always possess the energy they received by forming at the beginning of time.

We already know most of these dimensions but are not aware of their true nature. The dimensions known so far are:

**Kinetic dimensions**, there are four of them, each is parallel to one spatial dimension with which it shares energy and perpendicular to other spatial dimensions and has no mutual influence with them. The kinetic dimension is the dimension of the momentum that a particle has when it has kinetic energy. In order for two particles, which have no energy other than kinetic, to enter into the interaction, they would have to reach the same element of space in 4D space at the same time. During the exchange of kinetic energy 4D, the locality is preserved. So if they had particles whose kinetic energy is also the only energy, they would act just like particles of dark matter - immeasurably rarely interact with other particles, but their presence would change the space in which they are, which means that they would cause gravity.**The electrical dimension**, it is perpendicular to the first spatial dimension and parallel to the other three spatial dimensions. It is a dimension of electric potential. A very important feature of this dimension is that two particles that are electrically charged through it can exchange energy (interact) if they are close enough to the three classical spatial first dimensions regardless of how far away they are from the first spatial dimension. So 4D locality is violated through it. 3D locality is preserved.

**Weak charge dimension,**

**Three dimensions of color charge**

By the logic of things, these phenomena should be additional dimensions, but they are not: **Magnetic dimension**, all phenomena of magnetism can be explained through the electrical and kinetic dimension**. The gravitational dimension**, it does not exist because gravity is the result of a lack of energy in 4D space, the same energy that is transferred through particles into additional dimensions. The field of gravitational potential is located in the 4D space itself and not in some additional dimension. This is the main reason why gravity is so different from other elemental forces. It is also parallel to the three classical spatial first dimensions perpendicular to the first dimension so that the 4D locality is disturbed through it, but the 3D locality remains preserved.

When a particle comes to one spatial element it causes some of the energy of the space to shift from the shape of the space to the shape of the energy of the particle and go into an additional dimension. If a particle has kinetic energy, when it reaches a spatial element, it makes exactly as much of the momentum of the particle as the energy of the spatial element pass from the spatial dimensions to the kinetic dimension. **The sum of all momentums on all elements of space through which a particle has passed in one second is the total kinetic energy of the particle.**

In 4D space, the total velocity of each particle is * v_{u} = c* so that each particle crosses the path of

*during time*

**l = ct***. For one second*

**t***. The departure of a part of the energy of space into the kinetic dimension is a phenomenon we call momentum, it occurs only on the path taken by the particle, if the particle has no acceleration then the distance traveled and the velocity of the particle lie on the same straight line. In this case we can write that*

**l = c***The kinetic energy is equal to the product of the speed of light and the absolute value of the total momentum of the particle. The total momentum is a vector quantity obtained by the vector sum of all momentums in all four spatial dimensions, the momentum that classical physics knows is only one component of the total momentum.*

**E**_{ku}= cp_{u}If the particle has no other additional form of energy (electromagnetic, gravitational…) then **E = E _{ku}**

Since * E = mc^{2}* is always valid then

*when*

**mc**^{2}= cp_{u}**c**is shortened we get

*or in the form*

**mc = p**_{u}* m = p_{u} / c *since

*is a constant we see that the mass is linearly proportional to the momentum that the particle has.*

**c****The rest mass **is a well-known phenomenon, however, in classical physics, its origin is not very clear.** There is no special mass in 4+ model for which different rules would apply. The mass of a particle is always just a measure (indicator) of how much momentum (and energy) that particle possesses and nothing else.**

A stationary particle by definition has no other form of energy or it is small and is neglected (thermal motion, etc.) Since its mass can be measured very easily, the question arises where is the momentum corresponding to that mass. It is in the first spatial dimension, by a simple calculation, we can see that it is huge and that it causes movement close to the speed of light through the first spatial dimension.

Another important conclusion is that an increase in the kinetic energy of a particle is manifested through an increase in the mass of the particle. So the mass of a particle is an indicator of the energy and momentum that that particle currently has. This is evident from the already known formula * E = mc^{2}* but the rest mass was always treated as a special quantity different from the inertial mass, the relativistic mass was often taken only as an apparent phenomenon.

The novelty brought by the 4 + Model is that there is no difference between the rest mass and the increase in mass due to motion, it is the same phenomenon and follows the same law of increase in mass due to increase in momentum. Any mass is only a consequence of the energy the particle possesses, there are no exceptions, the rest mass is in no way special or different from the inertial or relativistic mass, except for the fact that this motion through the first dimension from which the rest mass comes cannot be directly observed. It is true to claim that all the stated masses are in fact inertial, they are a direct consequence of the motion of the particle through the 4D space.

Let us now see how for one material point with rest mass m0 and velocity v through 3D space, kinetic energy, momentum and mass are defined, classical physics in 3D space and how 4 + Model in 4D space. (pictures below)

U In 3D space, the relationship between momentum and rest mass is given by the equation

From the above, it can be seen that the dependence of momentum and mass is very complex, and no fundamental connection between these two concepts can be discerned.

The dependence of kinetic energy, momentum and mass is given by the expression

*E ^{2} = p^{2}c^{2} + m^{2}c^{4 } *

which also shows a complicated dependence and does not indicate a fundamental connection between momentum mass and particle energy.

In 4D space, the relationship between momentum and rest mass is given by the equation

* p_{u} = mc *except that

*is again the notation for the absolute value of the 4D vector. (picture above right)*

**p**_{u}also valid **E = mc ^{2}** mass and energy are scalars so it is clear that this formula is always valid,

* E = cp_{u}* kinetic energy is equal to the product of the speed of light and the absolute value of the total momentum,

If we write the formula for 3D kinetic energy from classical physics in a different form

*E ^{2} = p^{2}c^{2} + m^{2}c^{4} E^{2} = c^{2} (p^{2} + m^{2}c^{2})*

we see that it accurately describes the relations of sizes in 4D space (picture above right), * p* is the momentum in the three classical spatial dimensions,

*is the momentum in the first spatial dimension and it is always equal to*

**p**_{I}*, The expression in parentheses*

**pI = m**_{0}c*is a vector sum momentum in the first and three other spatial dimensions, so*

**p**^{2}+ m^{2}c^{2}*is the total momentum that the particle has in all four spatial dimensions.*

**(p**_{u})^{2}= p^{2}+ m^{2}c^{2}It follows that * E^{2} = c^{2} *is

*that is*

**p**_{u}^{2}* E = cp_{u}* we have already seen that

*so it follows that*

**p**_{u}= mc

**E = cp**_{u}= mc^{2}From the above, the fundamental connection between mass, kinetic energy and momentum can be seen.

So the equation from classical physics accurately describes the quantities and their relations as they are in the Euclidean 4D space, that is, in the space of the 4+ Model, and that means another confirmation of the correctness of the 4+ Model.

If we were to adopt a natural system of units of measure where * c = 1* then a very interesting fact would be shown

*this means that both*

**E = p**_{u}= m**mass and energy and the absolute value of momentum are the same thing.**Momentum has additional quality, it is a vector and always is collinear with a 4D velocity vector of the observed particle.

If we know only the vector value of the total momentum of a particle, it means that we know its velocity in 3D and 4D space, we know its rest mass, we know the total mass, we know the momentum in the I spatial dimension and we know the momentum in the other three dimensions. In other words, by knowing the 4D momentum of a particle, we know all the quantities that are related to the kinetic energy of that particle.

*In this chapter I have clarified the real nature of the phenomena we already know as: Momentum, Energy and Mass. The simplicity of the nature of these phenomena and the very simple mathematics required to describe them show all the simplicity of the multidimensional model of the universe.*

**KINETIC ENERGY AND SPECIAL RELATIVITY**

In the previous chapter, we saw that every particle that has a rest mass also has a certain momentum in the first kinetic dimension. The ratio of the rest mass to the momentum of a particle in the first kinetic dimension is given by the expression **m=p/c *** or otherwise written,** ***p=mc *** *

Through 4D space, all particles always move at the speed of light. (I have already explained this property in the chapter on elementary particles) We will observe the motion of a particle through the first and second spatial dimensions (one of the three classical spatial dimensions), through the other two classical dimensions of particles there is no motion, I chose this case for simplicity.

The movement of a particle through 4D space is a direct consequence of the momentum that this particle has in additional dimensions. If a particle has momentum in several additional dimensions, then they are vectorized and we get the total momentum. The velocity of the particle is parallel to the vector of the total momentum. If the amounts of momentum change in individual additional dimensions, then both the amount and the angle of inclination of the total momentum change. (picture below) The amount of velocity of a particle does not change (it is always equal to the speed of light) but its angle of motion changes so that it always remains parallel to the total momentum. This change of angle means more or fewer velocities in the II spatial dimension, that is, those velocities that we see directly and call simply - velocity. Unaware that there is another component to worry about, the one through the first spatial dimension.

If we observe a particle moving with velocity * v * through one of the three spatial dimensions. We can calculate the speed of movement through the first spatial dimension because particles through 4D space always move at the speed of light, so it is valid

* c^{2}=v_{I}^{2}+v^{2}* 1.

* v_{I}* - Particle velocity through the first spatial dimension,

*-Particle velocity through one of three spatial dimensions,*

**v***the speed of light*

**c-**Figure 2 shows the particle velocities and the distance traveled in 4D space.

The angle tangent can be determined from a right triangle made up of particle velocities in 4D space

* tan a = v_{I}/v * 2.

When we calculate the angle alpha, we will also be able to calculate the velocities in the first spatial dimension and the velocity in the second spatial dimension (velocity only).

Figure 1 shows the momentums in the first and second kinetic dimensions

The momentum in the first kinetic dimension is given by the expression

* p_{I}=mc* 3.

It follows from the geometry of a right triangle that the momentum is in the II kinetic dimension

* p_{II}=mc/tan a* 4.

The total momentum of the particle through additional dimensions

5.

The particle always moves through the 4D space at the speed of light.

** v_{4D}=c** 6.

**The scalar product of velocity through 4D space and momentum through additional dimensions is Energy.** (this is the definition of kinetic energy)

* E_{u}=v_{4D }p_{u}* (this is true since the velocity vectors and momentum vectors are in the same direction and collinear) 7.

8.

The total energy of a particle comes from two sources, one source is the momentum in the first kinetic dimension which causes the movement of the particle in the first spatial dimension. The first kinetic dimension and the first spatial dimension are parallel. The second source is the momentum in the second kinetic dimension that causes movement through one of the three spatial dimensions (II kinetic and II spatial dimensions are parallel). Figure 3 shows all three energies.

** E_{u}=E_{kI}+E_{kII}** 9.

When the particle has no momentum in the II kinetic dimension, then there is no movement in the observed spatial dimension, the only movement is through the first spatial dimension. The momentum in the first kinetic dimension has the amount given by equation 3. Every particle with rest mass receives it during its formation and it cannot change as long as the particle is in the same shape.

The speed of a particle through 4D space is always equal to the speed of light.

So the energy of motion is caused by the momentum in the first kinetic dimension given by the following expression

** E_{kI}=p_{I *} v_{4D} = mc * c = mc^{2} ** 10.

From Equation 9. It follows that the kinetic energy is equal to the difference between the total energy and the energy due to the momentum in the first kinetic dimension.

11.

If we express the tangent of an angle through the ratio of the velocity through the classical spatial dimension and the total velocity through the 4D space, due to the right triangle they form and can be seen in Figure 2. We get the well-known formula

12.

This is a relativistic form of the formula for kinetic energy.

*Conclusion of this chapter:*

*I got exactly the same formula without using the terms time, and inertial framework. This means that these terms are not necessary to describe the motion of a particle. (They are a necessary tool only if one wants to describe an event that takes place in a multidimensional space in a smaller dimensional space). The 4 + model shows us that events in 4D space are best viewed from the point of view of a global observer, it is at rest in relation to the 4D space itself. In that case, the mathematical description is the simplest and the event itself is easy to understand. In addition, it shows a deep connection between momentum and kinetic energy (7). It gives us a new definition of kinetic energy. It further confirms that the rest mass originates from the kinetic energy of motion through the first spatial dimension. It also further confirms that all particles with a rest mass at the very beginning received a certain momentum in the direction of the first spatial dimension, which means that the universe must have the shape of a 4D sphere. It also means that the solution of the lack of antimatter presented is correct.*

*I did not use any advanced mathematics (integrals, etc.) to get the same results as classical physics, which must use them to come up with a formula for kinetic energy. From the above, it can be seen that the multidimensional approach is correct, (otherwise it would not give such a specific and accurate solution) and the simplicity of physics in several dimensions can be seen.*

If we look at only one of the three spatial dimensions we will see that it is closed in on itself, that is, moving along it in the same direction we would eventually come to a starting point. The whole path would consist of a huge number of elements of space arranged next to each other in a line of the observed dimension.

When an elemental particle reaches an element of space, part of its energy is moved to additional dimensions (in which exactly, depending on the type of particle) the element of space itself is physically reduced, the reduction is proportional to the amount of energy that particle has moved to additional dimensions. The question is what happens to the adjacent elements of space.

One possible explanation is that a rift arises between them because one element has shrunk. This explanation is unlikely because it would bring about the problem of the impossibility of moving other particles in the direction in which there is a cleavage in space, such as has not yet been observed in experiments.

Another much more likely solution is that there is an appropriate amount of pressure between all elements of space in one dimension. Reducing one element of space would cause instantaneous approximation of adjacent elements due to the pressure that exists between them and because space elements are not subject to inertia. In this way, the principled possibility of particle motion in any direction would be preserved. Due to that pressure, the elements of the space would be slightly smaller than their maximum possible size. Since the size of the spatial elements is a quantized size this means that part of the elements will have a maximum size and part will have one or more quanta of energy in additional dimensions. In other words, there will be a constant shaking of all the elements of space, a constant transition of energy into additional dimensions and a return to the shape of space. It is this behavior of empty space that has been described as the existence of virtual particles. These particles are not virtual at all but their cause was unknown. This leads us to the possibility that virtual particles are in fact dark matter. The source of both phenomena is the pressure between the elements of space in each of the three spatial dimensions. The amount of that pressure directly determines the amount of energy that is dislocated from the shape of the space into additional dimensions, and that amount is equal to the total energy of dark matter. So **dark matter is one of the properties of 4D space**.

The reason we cannot detect virtual particles is their short duration and accidental appearance. The coincidence of the appearance of virtual particles is not in question, however the duration is. For virtual particles to be dark matter particles, they must satisfy the condition that their average duration is significantly less than the time required for the average interaction between two particles, otherwise these interactions would constantly occur and their effects would have to be seen in experiments. The requirement for the short duration of virtual particles is not so critical, they can in principle only last a couple of Planck times, and this is definitely not enough to interact with ordinary matter.

If we had a constant electric field and constantly measured its value, these measurements would not show the presence of virtual charged particles because on average an equal number of positively and negatively charged virtual particles would appear so that they would not change the value of the field on average. exist.

If we observed one or more elementary particles for a certain time, we would also not notice any interaction (energy exchange) with virtual particles, because in order for this interaction to take place, a certain time must pass, if the average lifetime of a virtual particle is significantly shorter than the interaction time it will not occur.

The gravitational effect is different, it does not matter to him whether in the observed space we have one particle lasting one second or we have a billion particles where each lasts 1/billion seconds, the gravitational effect is exactly the same. So the existence of virtual particles noticeably affects only the increase in gravity.

It is very important to note that particles of regular matter by their existence in a certain space "modulate" the appearance of virtual particles in the vicinity of that space. Particles of matter cause a decrease in the spatial elements on which they are located, which means a decrease in pressure in that part of space, which results in a decrease in the intensity of the appearance of virtual particles in the vicinity of regular matter. A significant reduction in virtual particles is expected in parts of space with a high density of regular matter. These are primarily the centers of galaxies with supermassive black holes and the surrounding region with a relatively high density of stars and other regular matter. It is possible that this influence of matter on virtual particles extends beyond the ends of galaxies, into intergalactic space, where it collides with influences from other galaxies and thus forms an interference pattern of increasing / decreasing intensity of virtual particles, ie dark matter particles.

For more detailed modeling of the arrangement of virtual particles in space, it is necessary to know the parameters of spatial pressure and its relationship with matter, since none of this is known now, it is impossible to set up a credible model.