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

Who would like to participate here? We are looking for interested people who want to work with us. Binding energy as intersection of spacetime density.

## 1  Introduction

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Dimensional physics (DP) is a theory that unites general relativity (GR) with quantum field theory (QFT). The QFT results, via a common basis in spacetime, from the GR as a correspondence principle. This requires assumptions about the structure of spacetime. There are different spacetimes and each is continuous. The number of space dimensions separates them from each other. The „dimensional transition“ creates the quantisation.

Any form of energy or mass is a spacetime density directly in spacetime. Gravity is a spacetime strain directly in spacetime. A density creates a stretch. Therefore, all „objects and forces“ are changes in spacetime itself. There are no separate objects using spacetime as a „stage“.  Different spacetimes are not only a dynamic stage, they are the only actors. The various manifestations of the elementary particles of the Standard Model, are a combination of low-dimensional spacetime densities. The proposed solution in the DP is thus a geometric approach.

### Motivation

A unification between QFT and GR has been sought for decades. There are various theories with different approaches. A verified solution does not yet exist. One of the best-known approaches is quantum gravity. This word hides a whole bouquet of different approaches. What they all have in common is that they try to quantise gravity and/or spacetime in some form. The solutions are worked out almost entirely in mathematical form.

In the DP, the search direction for the solution path is completely reversed. The GR is set as the basis and the QFT is built up via further assumptions. There must be a clear definition and logic for every object and every relation. Therefore, for every formula there must be a statement as to why it works exactly the way it does. The formula alone is not sufficient. A formula that gives correct results but no one can explain, according to the principle: „Shut up and calculate!“, can be helpful, but is not the goal here. Since GR and QFT are well confirmed, both theories must work again as a result. This requires paradigm shifts in the consideration of physical objects. At the same time, these represent the idea behind the DP:

• Gravity is understood as a stretching of spacetime. Energy and matter as a density of spacetime. A density produces a stretching.
• The statements of GR and Special Relativity Theory (SR) must be regarded as absolutely real effects. These are not just a consideration of an observer.
• There are no separate objects in spacetime. All elementary particles and quantum fields of the Standard Model, as well as gravity, are direct changes in spacetime itself. Different spacetimes are not just a dynamic stage, they are the only actors.
• Spacetime has a structure with transitions into higher- and lower-dimensional spacetimes. The speed of light (SL) is the lower-dimensional boundary. The singularity in a black hole (BL) is the higher-dimensional boundary.
• Connections between spacetimes can only exist via the space dimensions. The time dimension cannot be transferred. This is always firmly bound to the respective spacetime. Each spacetime has its own time dimension.
• D From classical to relativistic physics, time has changed from an absolute to a dynamic time. In DP, the concept of time is weakened again. Time is a distance measure in each separate spacetime to the dimensional spacetime boundary.
• A term already „discarded“ in modern physics is being used anew. Every form of „force“, in the sense of classical mechanics (with gravitation), represents a change in the density of spacetime. This change can occur in two very different ways.
• Exchange of low-dimensional expressions of the spacetime density as exchange particles (QFT)
• Change of the spacetime metric in the same spacetime (GR)
• Since spacetime is continuous, the quantisation of all objects (excluding gravity) is done via a low-dimensional mapping of the spacetime density.
• Spacetime density = state of motion = energy. It is not an object that moves through spacetime. The spacetime density itself is the movement through spacetime.

The DP does not provide a „world formula“. It is, on the basis of a few assumptions and a logical structure, a reason why GRT and QFT work exactly as they are described. Their descriptions are, despite a common basis, very different, because they act differently with the spacetime density in different dimensional spacetimes.

### Predictions

Since QFT arises from GR and both theories work as usual, there is no deviating statement in the DP with the Standard Model. Due to the structure, certain boundary conditions can be set and some additional predictions can be made:

• The standard model is complete. No further elementary particles may be found. The possibilities of low-dimensional geometric mappings are exhausted with the Standard Model. This also applies to dark matter and dark energy.
• There are no magnetic monopoles.
• The Higgs boson has mass as its only property.
• Gravity in our spacetime cannot, from a mathematical point of view, be described by QFT. The search for quantum gravity remains unsuccessful.

### Abbreviations and notation

In the DP, only the spatial dimensions are counted. 3D is our spacetime. The reason for this is that in the DP every possible spacetime necessarily has its own time dimension. These only differ in the number of space dimensions. Therefore, the time dimension does not always have to be counted separately. By „low-dimensional“ we mean all 1D and 2D universes (without the time dimension).

Abbreviations are introduced in the running text. These are listed again in the appendix.

### Let’s start the journey to a theory where everything is spacetime 