The speed of light is the low-dimensional limit

The singularity in a black hole is the higher-dimensional limit

With r_S\space =\space \frac{2\space *\space l_P^2}{\lambda}, the Schwarzschild radius is directly related to the Compton wavelength

# Dimensional Physics

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Theory unifying general relativity with quantum field theories

Christian Kosmak, Germany Würzburg 2023 Version 4.1 – 05.30.2023 Binding energy as intersection of spacetime density.

## 4 GR with DRD

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In this chapter, all postulates and principles of the GR will be considered with the view of the DP. It will turn out that all postulates and principles of GR can be generated by assumption A-02 (density generates strain). With assumption A-01 (GR correct), this chapter represents a ring closure. One can see that assumption A-01 can actually be formed from assumption A-02 and with the present knowledge is no longer a real assumption.

## Postulate of the Principle of Relativity

The central aspect in DRD is that it is locally undetectable. The DRD adjusts the basis of all geometric objects. All objects are geometric images in spacetime. This means that no change can be detected locally. A metre always remains a metre. The DRD is at the same time the state of motion of the object. No change in geometry can be detected in any state of motion. This means that the state of motion cannot be determined locally on its own. Only in a comparison with another DRD can the state of motion be determined. This results in the principle of relativity for absolutely every DRD of spacetime.

## Principle of contant proper time

From a local point of view, an object does not come closer to the dimensional limit. A metre remains a metre. Therefore, locally the course of time must not change. The result is the constancy of proper time. Only an external observer can detect a change in the course of time.

## Postulate of maximum and constant SL

The SL is the low-dimensional limit in the DP. This is identical for every point in spacetime. Since no approximation to this limit can be determined locally, the SL must always be the same for all objects at every point in time. Since the state of motion is associated with a length contraction, this can only happen up to the length contraction to zero. It follows that there must be a maximum state of motion and that this always has the same value, the constancy of the SL.

## Postulate of the strong equivalence principle

The DRD is locally limited. It begins at zero and ends at zero (vacuum energy). Gravity is directed towards the DRD and has a different value from spacetime to spacetime. Precisely because spacetime is continuous, a difference can always be detected from the beginning to the end of a DRD. Thus gravity continuously changes the DRD. A continuous change in the DRD is a continuous force and is thus an acceleration of the DRD. Gravity and acceleration are identical effects on a DRD. In the case of classical acceleration, this is done by an exchange of DRD and in the case of gravitation by changing the spacetime definition. Both change the DRD. In a gravitational field, this only happens continuously in the direction of mass. In a gravitational field, a DRD feels completely force-free because the change in DRD happens through the spacetime definition. Without an external feedback (for us humans, the ground), this change cannot be detected. This is followed by the postulate of the strong equivalence principle and the freedom from forces of a freely falling object in gravity.

## Relativistic mass increase

The faster a DRD with rest mass becomes, the „heavier“ it must become. The SL must not be reached due to an infinitely high energy. In the DP, the rest mass represents the number of space dimensions with at least one BH that is distributed over these space dimensions. Therefore, with a higher rest mass, it is more difficult to change the DRD (acceleration).

An existing density is increasingly difficult to compress further. Since it becomes increasingly difficult to increase the density for each „portion“ of DRD, the mass must increase for an observer. As a result of the fact that the space dimensions involved become more and more dense, the mass seems to become more and more. The same momentum has a much greater change with a low DRD than with a very high DRD. Since the DRD adds up everything, the ratio of the change in a DRD for the same momentum becomes smaller and smaller.

The increase in energy is absolutely real. For the observer, this means an ever greater mass. Locally, the change is again not recognisable.

## Mass-energy equivalence

In the DP, all objects are a DRD. No matter whether it is a rest mass or an energy. Only the number of spatial dimensions involved is different. Through a interaction between DRDs, a DRD can change the geometry in the low-dimensional expression. Therefore, energy and mass can be transformed into each other. Energy or mass can generally transform into all permitted expressions. The principle of equivalence of energy and mass follows.

## Length contraction and time dilation

Length contraction and time dilation are the actual reasons why the density approach was chosen. These correspond 1:1 to the density in the DRD. These points are not explained again here.

## Hierarchy problem

When comparing the forces, gravity is very small. This is seen as a problem. The DP does not change this either. But there is a reason why gravity as a „force“ is so small compared to the other forces. The other forces are an exchange of DRD as expressions in 2D. Geometric expressions in 2D cannot make a big change in 3D.

It is easier if you see it from the 2D point of view. Changing DRD in 2D is much easier than in 3D. It is easier to change a surface than a volume. Any higher dimensional transition is a big hurdle for changing the DRD. The difference is the DC. Actually, it is not gravity that is so weak, but the expression as 2D DRD has almost no content in 3D. A surface does not impress a volume.

## Black hole BH

Since gravity is generated from the DRD and there cannot be an infinite DRD, it follows that there is no mathematical singularity in an BH. The dilation must not be made to r = 0, otherwise this lies within the DRD and the mass would disappear. The generation of gravity from DRD must be extended for each piece of DRD. Therefore, an BH grows proportionally to the mass.

Since spacetime can theoretically be stretched to infinity, but the DRD can only be compressed to a certain point, this necessarily results in an EH. It is easy to be tempted to equate the EH with the low-dimensional limit and to assume that spacetime ends there. Here a clear no.

The EH is a point at which the change in a DRD due to gravity corresponds to the change in the DRD up to the SL and thus has no particularity locally. For an external observer, a photon must move as a DRD through a stretched spacetime and will thus contain less and less density. From the EH, the SL is no longer sufficient to escape from this stretched spacetime. The photon is locally unaware of the change in the spacetime definition. If the BH is large enough, such as the BH in M87, no force can be detected locally at the EH.

Within an BH, the metric used results in a mathematical and physical change. A simple example is the Schwarzschild metric. The signature of the metric changes from (+1, -1, -1, -1) to (-1, +1, -1, -1). The current thinking on this is that the time component and the radial space component swap character. Time becomes space and vice versa. From the DP’s point of view, this is nonsense. Time remains time and space remains space. What really happens is that the spacetime boundaries in the components change.

• Time component: Outside the BH, there is only a low-dimensional boundary for time. Therefore, the signature is +1. Inside the BH, the low-dimensional boundary is still preserved locally. The event horizon now forms a new additional boundary for time. One would have to slow down to reach it. This is exactly the opposite direction. This additional boundary only exists inside the BH. Outside the BH, the boundary of the event horizon is identical to the lower-dimensional boundary for an observer. Inside the BH, these boundaries are no longer the same. The signature must change.
• Radial space component: Outside the BH, one can move towards or away from the singularity. Inside the BH, the movement in space, even with the SL, is always towards the singularity. The space component loses a possibility of movement. The singularity must change.

From the DP point of view, the information paradox does not exist in BH. All information is connected to spacetime. This does not end in the BH. The information is preserved in the BH. Every piece of information continues to exist in spacetime. The information lies behind the EH, but this is still in spacetime. The information is only no longer accessible to humans. This does not matter for spacetime. There is no problem for spacetime itself.

The GR establishes its failure in a singularity as mandatory. In addition, the GR necessarily creates singularities in the big bang or in an BH. Therefore, the GR is always chalked up to being wrong by itself. From the point of view of the DP, it is exactly the other way round. The GR is a description of 3D spacetime. Thus, it must also describe the limits of spacetime, singularity and SL. The GR defines its own range for validity. If this is left, this 3D description must no longer function. A singularity is a 4D spacetime. The GR does everything right and fails in a singularity. With the spacetime structure from the DP, this behaviour is the only correct one. This again points to a confirmation of the GR.

## Summary on GR

Before dealing with QFT in the next chapter, the most important consequences that force a „rethinking“ are listed again.

• Spacetime is the dynamic stage and the only actor. In DP, in the classical sense, there are no separate objects in spacetime. There are only changes in spacetime itself. This corresponds to the view in QFT. All elementary particles are excitations from various fields. In DP, these excitations are density and expansion. The fields are the different dimensional spacetimes and the intersections of them.

• Density generates strain. The field equation describes the identity of the local density and the global strain in spacetime.

• DRD = energy = state of motion. Every object/energy/mass in the DP is a DRD and thus has a state of motion in spacetime by virtue of its existence. The DRD itself is the state of motion, therefore there is no additional „density function“ moving through spacetime.

• The SL is the lower dimensional limit and a singularity is the higher dimensional limit. All observations and the range of existence of our spacetime must lie between these two limits.

• There are separate lower dimensional spacetimes, each with its own time dimension. If one loses a space dimension through the SL, one necessarily loses the time dimension with it. You cannot gain or lose a space dimension within the same geometric expression. An expression always has a fixed number of spatial dimensions. Therefore, the difference between energy and matter is given. The expression itself must change in an interaction.

• Information occupies spacetime. A piece of information is always bound to the spacetime in which it arose. 