Dimensional Physics
Everything consists of space-time.
Everything consists of space-time.
This is about the development of our universe. It is all based on the GR. We will have to broaden our view of the universe to include higher- and lower-dimensional spacetimes. We define that the term “universe” always includes all these spacetimes. A spacetime is just a particular spacetime configuration. The universe is a collective term for everything.
For cosmology, we will connect the spacetimes across the dimensional boundary to form a universe. This means that our universe is defined not by one spacetime, but by recursive spacetimes. Each of these spacetimes is a potential field in itself.
We can specify what the Big Bang really was, but we cannot determine its true origin. We can specify an object for dark matter, but this is not a new elementary particle. Dark energy is no longer needed.
Here, too, there is a fundamental question that is not asked often enough for me. Why is our space-time expanding? Is it space-time or just space as described in the textbooks? The field equations of GR show that a static universe does not work. GR does not really allow for a static universe. Yes, but mathematics do not force an object to do anything. There must be a reason built into this mathematical model.
In addition, we will learn about further “deformations” of spacetime in this chapter. The picture is not yet complete. These deformations are not possible in all spacetimes. This depends on the number of spatial dimensions. We need all these ingredients to build a clean and coherent picture for GR and the universe itself.
We have an approach with space-time density and space-time boundaries. Therefore, every n-dimensional space-time volume has an infinite number of lower-dimensional space-times and at least one higher-dimensional space-time. We look at how these affect each other across the different numbers of space dimensions. This will be important again later for Part 3 QFT. From this approach, it will also become clear that QFT and cosmology go hand in hand. Much more than in the standard model. We make it easy for ourselves again and start from zero.
This is very easy for us. We had already discussed this at the boundaries of space-time. That was the discussion with the mathematical abstraction of a point. There can be no space-time without a space dimension. We are done with that. Space-time without a space dimension will no longer be discussed.
If we have one space dimension, then we always have one time dimension in addition. Thus, one space-time. In DP, there can only be one time dimension in a space-time configuration, since this is the distance measure to the space-time boundary.
The problem with only one space dimension arises from the GR. This cannot be mapped in a space-time with only one space dimension. The task is to determine the deformation of the space and time components in relation to each other. With only one spatial dimension, no space-time curvature can be determined. General relativity only starts with two spatial dimensions. Even if we could have a density and a curvature in only one spatial dimension from a purely logical point of view, there is no low-dimensional space-time to go with it. There can be no mass-energy equivalents, since there can be no low-dimensional QFT. However, these are the sources of spacetime curvature. Conclusion: In a spacetime with only one spatial dimension, there can be no mapping of spacetime density or spacetime curvature.
Does that mean 1D is out? No, not quite. For us, 1D is usable and must be used. Contrary to GR, we can work with extrinsic characteristics. This does not work in 1D. We get a higher spacetime density in 2D if 1D has an extrinsic characteristic there. In 2D, there is more 1D spacetime.
Figure 32 shows more 1D spacetime in a 2D spacetime over a wave.
We will need this again in Part 3 for the description of neutrinos. In cosmology, it is important for us to note that a 1D spacetime cannot have a mapping of a spacetime density and thus of a spacetime curvature. There can be no development within spacetime in 1D. No cosmology is possible within 1D.
In 2D, we are “almost happy”, but only almost. We can fully map the GR in a 2D spacetime, with one crucial limitation. In scientific terms, the degree of freedom that allows spacetime curvature to propagate through space is missing. In layman’s terms, everything is fixed. In 2D, there is no possibility for space-time curvature and thus also for space-time density to change.
We often imagine 2D as our 3D space-time “squeezed” onto a surface. This idea is completely wrong. No planet, no sun, no galaxy or life can form there. Something is either statically present or not. There are only two possibilities for a mapping:
Nothing more is possible. The reason for this is simple. We don’t have a low-dimensional QFT available in 2D. To map elementary particles, a QFT must be available. In 1D, we only have the possibility of an extrinsic mapping of a space-time density in 2D. This gives us neutrinos. We have reached the end of the line. We can only map neutrinos as elementary particles in 2D. Further mappings of a space-time density may only exist without a low-dimensional QFT. We already had that with the limits of space-time. Only a black hole is a spacetime density without a low-dimensional mapping. Cosmology is the development of spacetime. A black hole in 2D cannot have any development because everything is static.
2D is therefore out for cosmology. In particular, a 2D spacetime is very different from our 3D spacetime. The fact that 2D is completely static will benefit us again later in QFT.
We have finally arrived at our space-time. We will see that a 3D space-time is something very special. We have two “vital” features for us from 3D
With these small considerations, it should already be clear that life as we can define or understand it only and exclusively exists in 3D space-time. Since the rest of the chapter is almost exclusively about our 3D space-time, we can end this description here.
We must not stop at 3D. We have black holes in our space-time. These are the transition to a higher-dimensional space-time. This makes it certain that our 3D space-time is embedded in at least one 4D space-time. That’s the good news and the bad news. Good, because this provides an explanation for the Big Bang. We describe the big bang in the next section. Bad, because we open Pandora’s box with it. We get two big problems.
We have determined at the boundaries of spacetime that every n-dimensional spacetime volume must have an infinite number of (n-1)-dimensional spacetimes. If there is at least one 4D spacetime, then there are also an infinite number of 3D spacetimes. If we look for an explanation for experimental findings from the cosmos, we get a new, huge solution space. The 3D spacetimes could influence each other. If we are looking for a “culprit” for dark matter or dark energy, something can certainly be built from an infinite number of 3D spacetimes.
We do it here like the GR. There, for reasons of parsimony, no higher- or lower-dimensional spacetime was explicitly assumed and everything was placed in the 3D spacetime. We will stick to this principle for the possible solutions. The first attempt at an explanation should always come from our spacetime. Only if there is no other way will we resort to the infinite number of other 3D spacetimes or the 4D spacetime.
If there is a space-time with 4 space dimensions, then we just have to increase our mathematics by one space dimension and then we can calculate everything again in 4D. This probably works well with the GR. It all gets a bit more complicated, but it is possible in principle.
With QFT from 4D, the fun stops. QFT from our space-time is already very complicated. This is just about manageable for two reasons. If you can say that at all.
A QFT in 4D has 3D as a lower-dimensional substructure. In 3D, there is an evolution of the images in space-time. Nothing remains fixed. The possibilities of the images are only extrinsic characteristics and black holes in our 2D QFT. In 3D, there is everything that can be seen in our universe. The QFT in 4D must be unbelievably complicated. In addition, black holes form in our space-time. These are again a connection in 4D. This is the reason for the physical and mathematical worst case.
This is so far removed from anything I can imagine that I keep my hands off it. This makes 4D an absolutely unsatisfactory solution. However, we will move at least one approach to a region because we cannot examine it. This is not really a solution, but only a “postponement”. However, the DP urgently requires this approach.
Of course, we cannot stop at 4D either. Mathematically, recursion can go on forever. How many spatial dimensions would there be then? I don’t know.
But we can make an estimate. If we want to have a QFT mapping from an n-dimensional spacetime to an (n-1)-dimensional spacetime, then the spacetime density in the n-dimensional spacetime must not be a black hole. It follows that the total spacetime density of our 3D spacetime in 4D is not sufficient for a black hole (further argumentation in the next section on the big bang). We must be a quantum of space-time in 4D and not a collection of quanta. Our space-time started as a single space-time density.
In our space-time, the Planck mass is the criterion for a black hole. The simplest 2D representation of a black hole is an electron (Planck mass in 2D). The difference between 3D and 2D is already about 10^{22}. The universe has a total mass of about 10^{57} kg. The Planck mass in our space-time is only 10^{-8} kg. The difference from 3D to 4D must therefore be at least about 10^{65}. This value increases extremely quickly with each spatial dimension in a spacetime. If there is no longer enough spacetime density in a spacetime to map the Planck mass, the recursion breaks off. I don’t think we’ll get out of the single-digit range of spatial dimensions.
We have gathered enough to almost be able to resolve the big bang. We can’t quite do it because we have to “shift” into the realm of unsatisfactory solutions. We will need 4D here. We want to describe a big bang in a 3D space-time. We will see that a big bang has a lot to do with QFT.
The big bang from the textbook has three fundamental problems.
There is no answer to any of these questions in the textbook. The development of the universe is simply (much too simply here) traced back to the Planck time and Planck length. Spacetime, energy in spacetime, fields, fluctuations, coupling of fields with spacetime, etc. must then simply be present. We do not want to start our universe that way.
Let’s try everything we have so far:
In fact, we also have to start with 3 space dimensions for the big bang. However, we are dealing with only 3 space dimensions in the DP just like in textbook physics. We cannot clarify the 3 questions again. For this, 3D space-time is simply not enough. The textbook covers a variety of fields. We have to switch to something else. Unfortunately, there is only one option left. The unsatisfactory 4D solution. Let’s try to solve the 3 questions.
As always, the DP points us in the right direction, since there are almost no options. To get a space-time density in n-dimensional space-time, there must simply be a space-time density in (n+1)-dimensional space-time. Since the space-time density represents the space-time itself, this “low-dimensional mapping” is a real generation of the space-time.
This makes it clear:
The big bang is a mapping of a 4D space-time density as a local QFT onto a 3D possibility
I know that’s not very spectacular for a big bang. But within DP, this is the only possibility we have.
When we look at our body, we could see ourselves as almost divine beings. Every single elementary particle of our body, and there are a hell of a lot of them, has an infinite number of images in lower-dimensional spacetimes. We are made up of an infinite number of 2D and 1D spacetimes with black holes. Just wow! Now comes the damper. From the point of view of a 4D spacetime, we are what? The best description is probably “nothing”. Our universe as a whole is just an arbitrary space-time density in this sense. Whether there are also elementary particles etc. in this realm, I have no idea. As I said, I stop right there. The QFT in 4D must be solved by smarter people. Only a black hole in our space-time creates an effect in 4D again. Everything else is not relevant for 4D.
What we can do is exclude an important mapping. We cannot be a black hole in 4D. Otherwise, there would be no low-dimensional mapping for this space-time density. Since our universe exists, this is out of the question. The same argument also applies to the recurring idea that our universe is a 3D black hole and we are at the center of the black hole. Even then, the space-time density should not have a low-dimensional image. However, I am quite sure that we are subject to QFT in my environment.
Sorry that the big bang is so simple. We can now state exactly what the big bang is in our space-time. But we have not solved the basic problem. It was simply moved from 3D to 4D. Then where does the spacetime density in 4D come from? I have no idea. I can’t even say whether we are just a possibility in 4D or whether we count as something real in a measurement there. I admit, this solution is very unsatisfactory. But it’s the only one we have.
For the “starting condition” of the Big Bang, the textbook assumes the Planck length and Planck time. But why? Presumably, it is assumed that there is no smaller length or time in our universe. If the size of the universe is calculated back, you have to stop here at the latest. Are the Planck length and Planck time really good assumptions for the starting condition of the universe? Not for the DP. There are two reasons for this:
Like the GR, we assume continuous space-time. There must be no smallest values for time or length. Otherwise, we would not have a continuum. Where does this lower limit come from?
In DP, the Planck length or Planck time has no relevance on its own. These are the values that we use for c, d and h. However, these values always occur in a combination. This combination of values is crucial. Thus, these are not the smallest units of space or time.
Where the DP and the textbook approach are identical, the Planck length and Planck time are the smallest barrier for an interaction. If you want to have a limited interaction in these areas, then so much energy is needed that the value of d is exceeded and it goes into a black hole. Both theories agree that there must be no interaction whatsoever in this area.
For now, let’s disregard the origin of space-time and fields from the textbook approach in the big bang. We want to let the big bang arise from a fluctuation, symmetry break or similar, as desired, but this is not possible at the Planck scale. At this level, space and time are not defined. How should an interaction take place in space and time?
I understand that we need a lower limit and that we have drawn one for lack of a better one. Sorry, that just doesn’t make sense. Can we specify something better in the DP?
We cannot calculate the starting size exactly. However, we can make an estimate again. Our approach for the calculation is d, the dimensional constant. We are sure that our universe did not start as a black hole. Then the space-time density must not have been too large. This allows us to specify a minimum size for the distribution of energy during the Big Bang, which must not be exceeded. We make the calculation a little easier and not 100% exact, since it is only an estimate. We take the reciprocal value of d, then it is a little more obvious.
\cfrac{E_P}{l_P}\space >\space \cfrac{E_V}{l_{searched}}\space \implies\space l_{searched}\space >\space E_V\space *\space dWe assume that the reciprocal value of d must always be greater than the right-hand side. If the fraction on the right-hand side is greater than or equal to the left-hand side, a black hole should be formed. Then insert everything:
Energy in vacuum approx. : 7.67\space *\space 10^{-10} joule/m^3
d: 8.26\space *\space 10^{-45}
l_{searched}\space >\space 6.338\space *\space 10^{-54}
Oops! That’s smaller than the Planck length. We also simply applied the energy from a volume to a length. We have to do the size estimation per space dimension. Our entire spacetime starts small.
l_{searched}\space >\space \sqrt[3]{6,338\space *\space 10^{-54}}\space \implies\space l_{searched}\space >\space 1,85\space *\space 10^{-18} Meter
This is still very small as a lower limit. A proton is about 1000 times larger. However, the starting point is at least 17 orders of magnitude away from the Planck length.
For me, this is one of the most important topics in cosmology. This is also a reason for assuming the DP with the space-time density and the space-time boundaries. How can the fluctuation or the symmetry break of a field of the QFT influence space-time?
Space-time (or just space) expands. What about the fields? Do they cause space-time to expand? If so, then there must be a coupling. If not, then these fields must not expand with space-time? Were they already present at the infinite before? Then the big bang only affects space-time and not QFT fields? If field fluctuations in space-time should trigger something, then there must be a coupling.
We can ask questions ad infinitum, but it always comes back to the fact that the fields of QFT must couple to spacetime. Otherwise, these fields would simply not trigger anything. I have never seen a description of this. It’s a huge gap in QFT, but it’s not being worked on.
In the DP, we have an easy time of it. All fields of QFT are low-dimensional spacetime configurations. Low-dimensional spacetimes arise only with the mapping of the spacetime density from the higher-dimensional spacetime. These fields were not there before the Big Bang. Therefore, it cannot have been a fluctuation for us.
From the boundaries of space-time, it follows that geometric concepts such as size, length, etc. do not exist between 2D and 3D. Whether 3D space-time expands is completely irrelevant to a 2D space-time. The coupling we know are the particles of the standard model. This is the only possible mapping of the space-time density across the boundary. An electron shortly after the Big Bang, shortly before the speed of light or on its way into the center of a black hole is always an identical electron. The electron does not care what drives space-time. It must only be the mapping of a space-time density.
In DP, the QFT mapping for the big bang is not relevant for our 3D space-time in the first step. However, the big bang is a 4D QFT mapping in 3D. This is how space-time is actually created. Our entire universe is probably a 4D elementary particle.
The dimensional transition via space-time density is the only coupling of the different space-times to each other
Let us now turn to the fundamental question of cosmology. Why is the universe expanding and what is actually expanding?
Don’t give me: “The Friedmann equations from the GTR determine that there is a scale factor for space (not space-time). Therefore the universe must expand.” No, no and no again. Mathematics describes nature. Mathematics is not a “force” of nature that can produce an effect. If such a statement is made on the basis of a description, then there must be a physical reason for it. This is built into the mathematical model.
What is the reason? The answer in textbook physics is very simple: it is not known. Unfortunately, this answer is given too rarely. The mathematics of general relativity is always used to argue. Dark energy is only there for later exponential growth. For the first few billion years, let’s say, it played no role in the expansion. We need an immediate expansion with and after inflation. Yes, exactly, we still need inflation so that the observations fit together. Then dark matter and dark energy are added, etc.
The observation of the expansion and the scale factor from the Friedmann equations fit together so nicely that the whole of cosmology has been built on them. We already have the Big Bang, so the rest could be identical. We will show that the descriptions, from a certain point of view, are almost identical. However, we will use completely different foundations in the DP.
For this reason, we will make a change in the structure of the text. Until now, we had first or simultaneously built up the classical view from the textbook together with the DP. Then the comparison is easier. This no longer works here. We will first build the cosmology from the DP’s point of view. Later we will compare it with the classical view. The approaches are too different. Thus, the basis of the cosmology, from the point of view of the DP, will seem a bit strange to professionals in cosmology. Example: In the DP, space-time changes and not just space. We will see that this is also the case with the Friedmann equations. It is just very well hidden. For the full picture of cosmology, Chapter 6 must therefore be worked through completely in the given order. The reference to textbook physics comes only at the end.
Let us ask again: Why is space-time expanding? This question can be answered very easily in DP. Simply because of the existence of space-time.
From the chosen approach, it follows that space-time can never be a static structure in itself. We do not need to look for the why. It is the other way around: without a space-time expansion or compression, the approach of the DP makes no sense.
If a spacetime point is a state of motion, then it is not yet clear how or whether the spacetime components must deform. So far, we have two deformations for the spacetime density and one for the spacetime curvature:
Let’s look at the options available to see if we can use them for the expansion.
A scalar space-time density sounds very good. This is exactly what we are looking for in terms of expansion. However, we have a problem here. This scalar space-time density for a mass-energy equivalent is defined by the fact that the energy is higher than in the surrounding area. This means that the time and space components become shorter to an identical extent. The length definition becomes smaller. We need an increase, which is the observation. This makes it clear that it is not that wrong. Only the direction is wrong. This means that expansion could be the opposite. An increase in the definition of time and length.
But the next question arises immediately. If a spacetime density must necessarily expand in a scalar manner, why does a mass-energy equivalent not do the same? In principle, there is no difference between an elementary particle and the complete space-time in the big bang, as a space-time density. But the elementary particle does not expand. We are very sure about that. What is the difference? Fortunately, there is a killjoy and an exception. In this section, we will only deal with the killjoy.
The killjoy is QFT. Every space-time density from 3D has a low-dimensional mapping. This mapping, across the dimensional boundary, knows no geometric information such as “size”. The mapping in QFT is, seen in 3D, actually something like a point size. The 3D space-time is now no longer independent. It can no longer change the space-time components as long as the QFT has a fixed mapping. We absolutely need an interaction so that the mappings of space-time can be distributed differently in QFT. Without it, everything remains fixed. Space-time as a whole has no mapping in QFT in 2D. At most, there is the particle zoo from the standard model. With that, space-time must “decay” and expand.
This is like the previous one, only the space-time density is mapped onto a specific spatial dimension (direction). The big difference is that the momentum is a mapping in 3D. This is explicitly not protected by the mapping in QFT. We see this behavior, for example, in neutrinos. These particles are stable and were produced in large quantities in the early phase of the universe. The neutrinos as such are still measurable today. The momentum of these neutrinos has decreased due to the expansion.
Here is another remark about motion. The momentum is explicitly a vectorial spacetime density. Only this can be perceived as motion in spacetime itself. In order to perceive a particle, we first need the scalar spacetime density. The motion of the particle is then the vectorial spacetime density. Therefore, the expansion must be a scalar spacetime density. Nothing moves in spacetime.
The vectorial space-time density is the same as the scalar space-time density for expansion in the opposite case. The opposite case of an impulse is a negative impulse. Should expansion then be a braking? A loss of energy for space-time? You see, it remains exciting. The resolution will come in this chapter.
In the case of space-time curvature, the length definition increases and the time definition decreases. The greater length looks good at first. Why not gravity? The changes in the components of gravity are out of the question for two reasons.
Space-time curvature is not a reaction of space-time on itself. For space-time curvature, we absolutely need different space-time densities. This is what gravity reacts to. If you will, space-time curvature is a passive reaction. An imbalance must first be created, for example by QFT. In the direct mapping from 4D to 3D, there is no reason to assume that space-time was not perfectly homogeneous. 4D would not recognize any fluctuation in 3D. Right at the Big Bang, the space-time curvature in our space-time should have been zero. Therefore, no expansion results from gravity.
We can exclude the second reason on the basis of observations. Gravity is always directed towards a center and decreases with distance. According to observations, we need an expansion that is almost identical everywhere in the universe. This cannot be done with any interaction whose effect depends on a range.
How would we have come to a similar result if we had looked at the possible changes in the space-time components in an overview? There are only time and space components. These can only increase and decrease. The number of possible combinations is small. We expand the first overview of the deformations:
deformation
deformation
space-time curvature/gravitation
space-time density
antigravity
expansion
Figure 33 shows the possible deformations of space-time.
We have the known deformations. But there may also be a counterpart to each of these. In physics, the counterpart is often called “anti”. Therefore, we call the counterpart to gravity: antigravity and the counterpart to spacetime density: expansion. Please do not call it anti-spacetime density.
We do not allow a certain type of combination. If there is a change in a spatial component, then also in the time component and vice versa. We do not allow the possibility of a change in the spatial component without a change in the time component or vice versa. Changing the definition of length is always a step towards or away from the space-time boundary. Since time is the measure of distance to the space-time boundary, within the DP a change in space and time always works together. If we have learned anything from the SRT and the ART, it is that space-time is to be regarded as a single substance. The components change together with the same strength or not at all. An expansion that only includes space but not time is not possible for us. This is where we once again oppose the current doctrine of expansion. The resolution comes later and is surprisingly simple.
What we can easily see in this diagram is that gravity is not the counterpart of expansion. This is often explained incorrectly. Gravity only ensures the continuum in space-time. Gravity does not care about expansion or shrinking. It only reacts to the fluctuations of the density of space-time. But it does not explicitly change the density of space-time.
This makes it clear what increases with expansion. The length and time definition becomes larger. Even with expansion, there is no squeezing or pulling. At each point in space-time, the length and time definition is increased. This leads to the larger distances. We cannot recognize the change in the time definition, since this does not add up over a distance. We do that at the end when comparing with textbook physics.
But wait a minute. If this happens identically everywhere in the universe, I wouldn’t be able to detect this increase at all. Almost right. But the elementary particles that everything is made of don’t go along with this. QFT doesn’t allow it. Thus, space-time always gets larger in relation to an object. In addition, we measure this from within a gravitational field. Although gravity is not the counterpart, it does put resistance to the expansion. The expansion wants to have a larger time definition, gravity a smaller one. Space-time with gravity increases the resistance to expansion.
We now have all the pieces together to describe the course of the expansion. In doing so, we will find that a form of matter must explicitly form, dark matter. This only forms when space-time behaves in a certain way, when there is inflation. Since dark matter is created, inflation in the DP looks different than in textbook physics.
We already had that. A space-time density from 4D is mapped into our space-time. This is how our space-time is created. The space-time density is completely homogeneous. The figure is below the dimensional constant, otherwise a black hole would form. We have already made an estimate for the size. Nevertheless, space-time starts with an extremely high space-time density. Then space-time expansion sets in. The QFT actually takes some time. Thus the expansion starts before the QFT.
At the beginning of the expansion, inflation is mandatory in the DP. There is no additional field, there is no fluctuation, there is no symmetry breaking, there is no… (think of any name, it has probably existed before). Nevertheless, there is an exponential growth of the length definition. The solution is very simple. Let’s look at the graphic.
Figure 34 shows the Lorentz factor. This determines length contraction and time dilation as an exponential function. The horizontal axis is the speed and the vertical axis is the Lorentz factor.
Wikipedia: Von Klamann – Eigenes Werk, Gemeinfrei, https://commons.wikimedia.org/w/index.php?curid=6755675
This is the illustration of length contraction and time dilation (Lorentz factor) from the SR. That’s exactly what it’s about. We just have to reverse the direction. We need a time and length relaxation. The big bang is the starting point. That’s the red circle. Somewhere very far up. Whether a 3D spacetime starts with an inflationary phase depends only on the amount of spacetime density that is mapped by 4D.
We also don’t need another “vacuum condition” for inflation to stop again. This all happens automatically here. The entire process of inflation is already included in GR. Inflation itself is a different process here than in textbook physics. Contrary to textbook physics, we don’t need inflation to solve certain problems. Flatness of space-time, horizon problem, etc. We don’t have these problems at all with the starting condition of homogeneous space-time density. But inflation is still there and cannot be avoided in a 3D space-time with so much space-time density..
During inflation, something happens that I mistakenly saw in an old version of the DP within a black hole. Black holes are created. Not just any black holes, but the smallest possible black holes. But one step at a time.
Space-time expands. This means that there is a change in energy for space-time. Space-time “thins out”. According to our logic, this is less energy. Nothing changes for space-time itself. One meter remains one meter, because the definition changes. It follows that locally there is no change in energy for space-time. You simply have to distribute the energy over a larger volume. The content is diluted, the total amount does not change. This means that energy conservation follows from DP for the whole space-time with expansion. The space-time density only changes.
An elementary particle will not be able to withstand the extreme dilution in the inflation phase due to QFT. Then the energy of the particle will increase exponentially. This is the same as with gravity. No interaction from the outside, but still a change. In the case of gravitation, this is due to the opposing deformation of space and time. Thus, without a change in the conditions of energy. Here, however, space and time increase uniformly. The elementary particle gains energy because the valency of the space-time density of the elementary particle changes in relation to its environment. We have called this a potential field. Here, it is directly related to energy.
Space-time is a potential field for energy
This means that every elementary particle in the inflation phase that does not decay quickly enough receives an exponential increase in energy. But this is only possible up to the dimensional constant. Then a black hole forms, with the exact Planck mass. This gives us the smallest possible black hole that can form in our space-time. Once the exponential growth of the length definition is over, this can no longer happen.
If space-time is a field of potential, black holes must necessarily form from the first elementary particles in combination with inflation.
These smallest black holes have a very special property. The cross section is close to zero. With a little calculation, you quickly come to the conclusion that a black hole with the Planck mass has a Schwarzschild radius of 2 Planck lengths. That’s damn small. It is so small that absolutely no particle from the standard model fits into the black hole in one piece. If such a black hole wants to eat, it has to get an elementary particle in as a quantum (in one piece).
These are black hole corpses. They can’t do anything with matter. So these black holes remain what they are from the moment they are created. These black holes thus have the following properties:
This means that these black holes in the DP are dark matter. Again, no new elementary particles or fields. The formation of dark matter is necessarily foreseen in the process.
The dark matter no longer have a QFT representation as black holes. However, these are not enlarged by the expansion. Gravity is a resistance to expansion. This resistance is not very high at a Planck mass. However, dark matter also occupies a very small region of space. There, the effect of expansion is very small.
This tiny cross-section only plays a role between black holes. In the early universe, there is a higher probability that dark matter will clump together. Two black holes merge into one black hole with twice the mass. This gives us the possibility in the DP that there are black hole seeds very early on. It should therefore come as no surprise if a JWST finds more and larger black holes than the standard model allows. We don’t have to wait for star formation and collapse.
As can be seen from the diagram, inflation does not stop abruptly; it decays. Not linearly slowly, but still quickly. However, this has the effect that the elementary particles at this time have a greater momentum than assumed by the standard model. The rarefaction of spacetime to the spacetime density of a particle can also show up in momentum. For a black hole, it is no longer sufficient, but for a larger momentum it is. However, momentum is the “antagonist” of gravity. In exactly the other direction, it follows that momentum from an interaction in an early universe is no longer of much value. It follows that when calculating how clumped the universe is due to gravity, there are two errors here:
This means that you cannot simply calculate it back linearly. This is much more complicated.
The long straight line after the kink is the most boring part of the development. Don’t forget to read the diagram from right to left. Here everything goes as described in the textbook. The approximately 14 billion years of space-time lie almost completely on this straight line. Inflation and the kink have an enormous effect, but in terms of time they are the smallest part. From the straight line on, the expansion rate can be considered almost constant.
According to the theory, the expansion should decrease more and more from the past towards the future. However, observations show the opposite. The culprit is quickly found here. If it is not spacetime itself, then it is the QFT. In textbook physics, the vacuum is identified as the driver of expansion through quantum fluctuations. In our approach, QFT does exactly the opposite. It prevents a spacetime density from expanding. In our approach, the vacuum is also a spacetime density and therefore has energy. This must also be mapped in QFT. This is how the quantum fluctuation in the vacuum arises. No negative energy has to be borrowed for pair formation. Spacetime corresponds to energy. Thus, energy is always present.
But the energy is thinning out. Less energy, in connection with the QFT, means less “braking power” against expansion. At the time when the background radiation was formed, the QFT was still able to slow down the expansion of space quite well. Therefore, the expansion rate was lower there. This means that the expansion rate is higher today. On the straight line, the braking effect of QFT is more important than in the early phases. This is the reason for the different observations of the expansion rate.
What we don’t have is dark energy. This is not needed in DP.
The expansion is measured mainly by the redshift of photons. This should not be possible with our logic. The QFT prevents an expansion of the space-time density. I have called QFT a killjoy. I also mentioned that there is an exception. The exception is the photon. If it weren’t for this exception, we wouldn’t be able to observe an expanding universe.
The photon has no rest mass and therefore explicitly cannot have a QFT picture as a black hole. A photon is an extrinsic expression of a 2D space-time in 3D. There is no expression in 2D itself. If we stick to the wave picture of the photon, then the wavelength is given in 3D and not in 2D. This results in the higher space-time density in 3D and cannot be captured by QFT.
Therefore, the redshift, as an increase in wavelength, is directly the space-time expansion. This redshift is not an effect of objects moving apart. This is the expansion itself.
We urgently need to look at the mathematics of GR here. So far, we have used the field equation in this form:
G_{\mu\nu}\space =\space k\space *\space T_{\mu\nu}
The Einstein tensor indicates the curvature of space and the energy-momentum tensor indicates the source. The energy-momentum tensor is the collection of all the different mass-energy equivalents. However, a part is missing from the collection of mass-energy equivalents. More precisely, the largest part of the energy in the universe. The spacetime itself, the vacuum. In a vacuum, the energy-momentum tensor is zero.
But that does not correspond to our idea. Every point in spacetime is an energy greater than zero. So we have to include an equally distributed variable in the equation for the vacuum. The mathematically simplest thing is a constant for the metric. In fact, this is one of the few changes in the field equation that does not destroy the structure behind the field equation.
We have to take the field equation with the cosmological constant. The formula then looks like this:
G_{\mu\nu}\space =\space k\space *\space T_{\mu\nu}\space -\space \Lambda g_{\mu\nu}
I write the cosmological constant on the side of the energy-momentum tensor, since this is an energy contribution. The cosmological constant is simply a scale factor on the space-time metric. This fits with our explanation. Space-time experiences a relaxation of length and time to the same extent. This is simply a constant number. The sign must be different from that of the energy-momentum tensor. This part of the energy produces a “negative” energy contribution. A larger spacetime density is a plus and a smaller one is then a minus.
There are many more aspects to cosmology than are listed in this chapter. However, we have to limit ourselves somewhere. As a final part on cosmology and also part 2, we want to compare the view of DP and textbook physics.
Here we will only compare the view from the Friedmann equations for DP. Anything else would mean a very long text. We will see that there are actually only very slight differences. We have to get to the bottom of the question and assumption behind the Friedmann equation. Then we get something similar to the SRT. Although the space-time density does not appear compatible with the SRT, we get the same results.
The first step to the Friedmann equations is the assumption that the universe is homogeneous and isotropic. Observation of our immediate surroundings, e.g. the home galaxy, indicates the opposite. Therefore, in the assumption that this is valid for large scales in the universe. This is not the case. According to the energy-momentum tensor, the mass distribution is completely homogeneous, without any grain. This leads us to two points.
These two points have several implications.
Homogeneous and isotropic enters the signature as 100% homogeneous and isotropic. This means that there are no distinguishable mass-energy equivalents in this approach. The universe is regarded as a single large mass-energy equivalent. A “granularity” no matter how fine or coarse is not intended. Thus, the mass density c^2\rho in the 00 element of the energy-momentum tensor is a real continuum. This is a very good description of an energy density. Full agreement.
Since the energy density in the 00 element cannot show any fluctuation, there can be no gravity from the point of view of DP. In textbook physics, the reaction to the energy density is also seen as gravity. But then a repulsive one. We do not classify this as gravity, but as expansion. The deformations of the space-time components are different. Except for the naming, however, there is also agreement.
The big sticking point is the pressure on the 11, 22 and 33 elements. Let me ask a simple question about this. Where should this pressure come from? The textbook has a simple answer: thermodynamics. There are particles in the universe that interact and that creates pressure. In principle, it is assumed that the energy density of a mass distribution corresponds to that of dust. The individual particles then participate in the thermodynamics. The mass distribution behaves like a liquid. There is always pressure in it. The entire assumption for the pressure is based on the fact that mass is present in point-like particles. We don’t know it any other way. These particles have an impulse and thus they generate a pressure. A pressure on what? Mass with impulse generates a pressure on space-time? Then we have the discussion with the coupling to space-time on our backs again. If we assume individual particles, then this should also be included in the energy density. But that is a pure continuum. The pressure does not match the energy distribution.
The whole thing means that two assumptions are included in the energy-momentum tensor. A homogeneous and isotropic distribution of the energy density and a pressure of the particles on themselves. The granularity for the pressure is not included in the energy density. The pressure lies on the 11, 22 and 33 elements. This is not a pressure like an impulse in a certain direction. I would see this as a self-fulfilling prophecy. We put in a “scalar” pressure and get a “scalar” reaction of space-time to it.
In DP, this pressure arises due to length and time relaxation. This is a “negative” energy for the energy distribution. The signs of energy density and pressure must be different. According to the deformations of the space-time components, these are each the counterpart of the other. The cosmological constant is the behavior of the metric. The pressure is the corresponding energy value for it.
We can thus conclude that the DP enables the assumptions for the Friedmann equations better and more simply than textbook physics can.
There is still a major difference to be discussed here. From the Friedmann equations, one obtains a scale factor for space and not for space-time. In the DP, however, we always assume a change in space-time. Space as an independent object no longer exists there. What is the difference here? Simple answer: there is no difference.
In the Friedmann equation, the time component also changes. This is best seen when the energy-momentum tensor with the signature is inserted into the equation. We obtain a term in the Einstein tensor for the 00 or better tt component of the energy-momentum tensor. It looks like this:
\cfrac{\dot{R^2}}{R^2}\space +\space \cfrac{k}{R^2}\space =\space \cfrac{8\space *\space \pi\space *\space G}{3}\rho
The time component has an active effect. The problem with this is that we cannot recognize the effect on time at all with the given question and assumption of a homogeneous and isotropic universe. The following picture::
Figure 35 shows the development of a distance over time
We are at point A and measure a distance to point Z. The rest of the alphabet lies as points in the distance. At time t = 0 we have a fixed distance R between A and Z. We make a new measurement at t = 10. As a function R (10), since the distance must depend on the time.
Each letter on the route has now increased by x. This applies equally to each letter, since we are assuming a continuum. If we now want to determine the distance, the change is added up over the distance. The further away the letter is, the greater the distance has become. We see this in the expansion of the universe.
Due to the continuum, time also accelerates for each letter along the way. Time relaxation is a faster passage of time. This means that the passage of time is identical in each letter. There is no difference in the passage of time from one letter to the next. The crucial point, however, is that we want to query the new distance at point A for R(10). The change has already been incorporated into the time parameter 10. These are no longer the identical 10 seconds as at t = 0. We just can’t determine that. The time definition has changed. 10 time units are 10 time units for each letter on the route.
The change in distance adds up in time. The change in time is already included in the question and does not add up. Of course, space-time is always adjusted in the Friedmann equation as well. We just can’t determine it.
That was a lot of work so far. The basic idea behind DP and how it can be applied in physics should now be clear. Certainly not all questions about DP or the interaction with SR and GR have been answered. If you still have questions, please use the contact form on the page..
But we still have a big piece missing, Part 3 the QFT. This part is currently February 2025 not yet completed in a new version. I’m working on it. Since QFT is quite a bit more complicated than GR, it will take some time. I don’t want to provide the QFT from an old version because some things have changed that are no longer correct in the old version. If you want to be informed when it is available, enter the text “Abo” in the contact form. Then you will receive an email when I have finished a new part. This will probably take 4-5 updates
Until then, have fun with the DP and your own thoughts on it, which I hope you will share with me.
Christian Kosmak, Würzburg February of 2025
www.dimensionale-physik.de