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
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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.
Binding energy
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Systems with less energy are more stable. Therefore, no physicist is surprised when several subcomponents combine to form a system and must release energy to reach a stable state. In DP, the reason for the low energy results from the overlap of DRD. Binding energy comes in all colors and shapes. The two examples atomic nucleus and atomic shell are chosen.
Atomic nucleus
In the sun, hydrogen is fused to helium. Binding energy is released during this process. The classical view is that the helium nucleus represents a more stable state than the individual parts and that this is always associated with a lower energy. This does not take into account the full complexity of the process. We are only concerned with the fact that energy must be released. The energy difference is given off in the form of radiation or particles. In which form the energy is given off is not important for the argumentation.
The helium nucleus consists of 2 protons and 2 neutrons as ensemble. These 4 components have less energy/mass after the fusion than the same components individually. The particles have remained the same in all their properties. Only the mass as equivalent of the energy is smaller in the combination. If the strong nuclear force captures the components and forms a helium core, there is actually no reason why energy has to be given off.
When the particles in the core are permanently close together due to fusion, the volume regions of the DRD overlap. This increases the DRD for the nucleus as a whole. From the DP point of view, the whole system has to give up energy to stay at the same energy levels. With this view, there is a reason for the release of energy. The individual neutrons and protons want to retain energy. This higher DRD has to go away. Now, if the nucleus is to be „decayed“, this energy must be put back in, otherwise the individual components such as the neutron and proton will have too little energy.
For the DP no energy is given away to reach a lower and more stable level. Energy is given off to stay at the same level. Therefore, the binding energy increases sharply with the number of nucleons at the beginning and flattens out with more and more nucleons. The overlap cannot increase arbitrarily in relation to the nucleus. Due to the repulsion of the charges, less and less „overlap“ occurs.
For a nucleon number divisible by 4, the geometry of the arrangement seems to have a strong overlap of the volumes. Based on the binding energy, one must be able to obtain conclusions about the geometry of the nucleons. As a further derivation from this approach, it is clear that the volume of an atomic nucleus does not simply increase linearly. Therefore, the volume of an atomic nucleus does not vary as much as one must assume in a „spherical model“ without overlap. In addition, depending on the measurement method, the size of an atomic nucleus does not necessarily give the same results. Depending on how the measurement method interacts with the DRD, different results may be available. This should also be the case for a single proton or neutron. These are also composite. As of iron, another nucleon does not bring a higher DRD to the total volume, but a lower one. The binding energy decreases. The overall overlap decreases due to the new configuration.
In addition, there are so-called „magic numbers“ 2, 8, 20, 28, 50 and 82. This number of nucleons seems to have a very stable bond. According to QFT, when the nucleus is „deformed“, these numbers result in an almost exact sphere, for the entire nucleus. A smooth sphere as a whole has the highest possible overlap of the individual parts.
Atomic shell
When an electron is attracted by the electric field of the proton, the electron is forced into an orbital cloud around the nucleus. The electron thus loses degrees of freedom for motion in space. The beginning and end of the volume for the DRD are now the same (closed geometry). The electron overlaps with itself. For the electron, the DRD and thus the energy has increased. It must give up some of the energy as a photon to keep its energy constant.
For an atom with multiple building blocks, all the individual building blocks overlap. Also the electrons and the nucleons. Thus the structure, the possible energies becomes very fast complex.