On the origin of … in the lattice Universe
We introduce a perfect isotropic lattice, which is purely imaginary, and we will call it the cosmic lattice. The development of its free energy of deformation is expressed per unit volume, which depends linearly on volume expansion and quadratically on volume expansion, shear strain and torsional rotation deformations, and allows us to deduce the Newton’s equation of the lattice.
We are also interested in the propagation of waves in the cosmic lattice. There appears quite surprising phenomena, such as a longitudinal mode coupled to the propagation of transverse waves that are polarized linearly, which disappears for circularly polarized transverse waves. There is also the possibility of propagation of longitudinal waves. But under certain conditions of expansion, the longitudinal propagation mode disappears in favor of localized vibration modes of the expansion.
Among the surprising behavior that may be present in a cosmic lattice is the curvature of wave rays by a volume expansion gradient due to the presence of a strong topological singularity of expansion . This curvature can lead to the formation of « black holes » absorbing all waves passing in its vicinity, or impenetrable « white holes” pushing all the waves away from its vicinity.
Considering a finite imaginary sphere of a cosmic lattice, we can introduce the concept of « cosmological evolution » of the lattice, assuming that one injects a certain amount of kinetic energy inside the lattice. In this case, the lattice has strong temporal variations of its volume expansion, that can be modeled very simplistically assuming that volume expansion remains perfectly homogeneous throughout the lattice during its evolution.
We start by showing that we can separate the field of volume expansion from the other fields in the Newton equation of a cosmic lattice in the case where the concentration of point defects are constant. Then we use these results to obtain the Maxwell’s equations of evolution of a lattice in the case where the volume expansion can be treated as constant.
We apply here the Lorentz transformation to the topological singularities in motion in order to obtain, in the absolute frame of the lattice, the fields of dynamical distortions and velocities associated to screw and edge dislocations, localized rotation charges, twist loops and edge loops moving at relativistic speed. From these fields, their total energy will be calculated. The total energy is the sum of the potential energy stored by the dynamic distortions of the lattice created by the presence of the moving charge and the kinetic energy stored in the lattice by the movement of said charges. The total energy will be shown to satisfy a relativistic dynamics. We will show with the Lorentz transformation that a relativistic term of force is acting on the charges of rotation in movement, term that is perfectly analogous to the Lorentz force in electromagnetism.
In a perfect cosmic lattice satisfying , all microscopical topological singularities like dislocation lines and dislocations/disclination loops satisfy Lorentz transformations based on the transversal wave velocity. As a consequence, a localized cluster of topological singularities which interact with each other via their rotation fields is also submitted globally to the Lorentz transformations.
On this base, we discuss the analogies which exist between our theory of the perfect cosmic lattice and the Special Relativity. We discuss among others the role of «aether» that the lattice plays vis-a-vis a cluster of singularities in movement interacting via their rotation fields. We show that this notion of «aether» gives us a completely new perspective on the theory of Special Relativity, as well as a very elegant explanation to the famous paradox of the twins in Special Relativity.
Here, we study in detail the gravitational interactions of twist disclination loops (TL), which will yield a strong analogy with Newtonian gravitation in the far-field but that will exhibit differences in the near-field. We will also exhibit a dependence of the constant of gravitation on the volume expansion of the lattice.
Next, we focus on the Maxwell formulation of the equations of evolution, which corresponded to the expression of the local laws of physics, such as electromagnetism, as seen by an imaginary Grand Observer (GO). We focus on a hypothetical local observer we call the Homo Sapiens observer (HS) which would be linked to a local framework, and himself composed of clustered singularities of the lattice. This HS observer only knows of local measures with local rods and local clocks constituting his local reference frame. It will be shown that this makes for him the Maxwell equations to become invariant with respect to volume expansion. There then appears a relativistic notion of time for the local HS observers, which will present a strong analogy with the time in the theory of General relativity of Einstein. We will discuss in detail the analogies, and the differences and advantages when compared to General Relativity.
Here, we will look at the very short distance gravitational interaction between a twist disclination loop (TL) and an edge dislocation loop (EL) due to the charge of curvature of the EL and the charge of rotation of the TL and their respective perturbations to the field of expansion.
We show that this interaction between charges of rotation and curvature corresponds to a repulsive force at very short distance that scales in when the loops are separated, but that it is an attractive force between the two loops when they form a dispiration.
This gravitational interaction between a charge of rotation and a charge of curvature presents numerous analogies with the famous ‘weak force’ of particle physics.
In a lattice universe, it is possible to imagine a scenario of cosmological evolution of the topological singularities which form after the big-bang. This scenario explains the formation of galaxies, the phenomenon of dark matter of the astro-physicists, the disappearance of anti-matter from the Universe, the formation of massive black holes in the center of galaxies of matter, the formation of stars and the formation of neutron stars during the gravitational collapse of matter.
Intuitively, we can see that Quantum Mechanics (QM) could be linked to the existence of dynamical solutions of the second partial Newton’s equation of the cosmic lattice, under the form of temporal fluctuations of the field of expansion, associated with the topological singularities of the cosmic lattice when it is without longitudinal waves in the domain . Here, we will show a wave function directly deduced from the second partial derivative equation of Newton for the perturbations of expansion of the lattice which is intimately linked to the moving topological singularities of the lattice, whether they are clusters of singularities or isolated single loops.
We will thus give a rather simple ‘wave interpretation’ of quantum mechanics: the quantum wave function represents the amplitude and phase of gravitational fluctuations coupled to topological singularities. This interpretation implies that the square of the amplitude of the normalized wave function is indeed linked to the probability of presence of the topological singularity which is associated with it!
At the same time, we will recover the Heisenberg incertitude principle, the QM notions of bosons, fermions, and non-discernibility, the Pauli exclusion principle, as well as a physical comprehension of intriguing phenomenas such as entanglement and quantum decoherence.
Here, we will find a solution to the second partial equation of Newton with the torus around a SDL. We will show that there are no static solutions to this equation and that, as a consequence, we will have to search for a dynamic solution for the gravitational perturbations of expansion in the immediate vicinity of the loop. This dynamic solution will turn out to be a quantized movement of rotation of the loop on itself. This solution satisfies the second partial equation of Newton, which becomes in this case the Schrödinger equation as we have seen in the previous chapter!
This movement of rotation of the loop about itself is nothing else than the «spin» of the loop, and we can show that a magnetic moment is associated with it, which corresponds exactly to the magnetic moment of particle physics! Furthermore we will show that, within our theory, this is a real movement of rotation, and that it does not infringe on special relativity, contrary to what the early pioneers of quantum mechanics thought of spin!
We have shown previously that the perfect lattice presents strong analogies with the great theories of modern physics, namely the equations of electro-magnetism, general relativity, special relativity, black holes, cosmology, dark energy and quantum mechanics, and that we can have 3 types of basic topological loop singularities which possess respectively the analogue of an electrical charge, an electric dipole moment or a curvature charge by flexion. It should be noted that the curvature charge is unique to our theory, and explain rather simply several mysterious phenomena, such as the weak coupling force of two topological loops, the dark matter, the galactic black holes, and the disappearance of anti-matter.
Here, we will strive to find and describe the ingredients which could explain, on the basis of topological singularities, the existence of the standard model of particle physics. In other words, we will strive to find mechanisms to generate the fundamental particles such as leptons and quarks, and what could cause three generations of these fundamental particles, and from whence could come the strong force which binds quarks to form baryons and mesons.
This chapter does not pretend to give an elaborate theory or a final, quantitative solution to explain the standard model of particle physics, but rather to show with a few specific arguments that it could be the choice of a microscopic structure of the lattice that could answer the questions of the standard model. Here we will show that there appears a full ‘zoology’ of loops in a well choosen structure of the lattice, and that it resembles the elementary particles of the standard model. We will show the presence of an asymptotic strong force which could bind the topological loops!