- An author, researcher and entrepreneur, Klee Irwin is the director of Quantum Gravity Research, leading a dedicated t... moreAn author, researcher and entrepreneur, Klee Irwin is the director of Quantum Gravity Research, leading a dedicated team of mathematicians and physicists in developing a first-principles quantum gravity theory to replace the current disparate and conflicting physics theories.edit
In this work, we define quasicrystalline spin networks as a subspace within the standard Hilbert space of loop quantum gravity, effectively constraining the states to coherent states that align with quasicrystal geometry structures. We... more
In this work, we define quasicrystalline spin networks as a subspace within the standard Hilbert space of loop quantum gravity, effectively constraining the states to coherent states that align with quasicrystal geometry structures. We introduce quasicrystalline spin foam amplitudes, a variation of the EPRL spin foam model, in which the internal spin labels are constrained to correspond to the boundary data of quasicrystalline spin networks. Within this framework, the quasicrystalline spin foam amplitudes encode the dynamics of quantum geometries that exhibit aperiodic structures. Additionally, we investigate the coupling of fermions within the quasicrystalline spin foam amplitudes. We present calculations for three-dimensional examples and then explore the 600-cell construction, which is a fundamental component of the four-dimensional Elser-Sloane quasicrystal derived from the E8 root lattice.
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In his study on the geometry of Lie groups, Rosenfeld postulated a strict relation between all real forms of exceptional Lie groups and the isometries of projective and hyperbolic spaces over the (rank-2) tensor product of Hurwitz... more
In his study on the geometry of Lie groups, Rosenfeld postulated a strict relation between all real forms of exceptional Lie groups and the isometries of projective and hyperbolic spaces over the (rank-2) tensor product of Hurwitz algebras taken with appropriate conjugations. Unfortunately, the procedure carried out by Rosenfeld was not rigorous, since many of the theorems he had been using do not actually hold true in the case of algebras that are not alternative nor power-associative. A more rigorous approach to the definition of all the planes presented more than thirty years ago by Rosenfeld in terms of their isometry group, can be considered within the theory of coset manifolds, which we exploit in this work, by making use of all real forms of Magic Squares of order three and two over Hurwitz normed division algebras and their split versions. Within our analysis, we find 7 pseudo-Riemannian symmetric coset manifolds which seemingly cannot have any interpretation within Rosenfeld's framework. We carry out a similar analysis for Rosenfeld lines, obtaining that there are a number of pseudo-Riemannian symmetric cosets which do not have any interpretation à la Rosenfeld.
Transcription factors (TFs) and microRNAs (miRNAs) are co-actors in genome-scale decoding and regulatory networks, often targeting common genes. In this paper, we describe the algebraic geometry of both TFs and miRNAs thanks to group... more
Transcription factors (TFs) and microRNAs (miRNAs) are co-actors in genome-scale decoding and regulatory networks, often targeting common genes. In this paper, we describe the algebraic geometry of both TFs and miRNAs thanks to group theory. In TFs, the generator of the group is a DNA-binding domain while, in miRNAs, the generator is the seed of the sequence. For such a generated (infinite) group π, we compute the SL(2, C) character variety, where SL(2, C) is simultaneously a 'space-time' (a Lorentz group) and a 'quantum' (a spin) group. A noteworthy result of our approach is to recognize that optimal regulation occurs when π looks like a free group F r (r = 1 to 3) in the cardinality sequence of its subgroups, a result obtained in our previous papers. A non free group structure features a potential disease. A second noteworthy result is about the structure of the Groebner basis G of the variety. A surface with simple singularities (like the well known Cayley cubic) within G is a signature of a potential disease even when G looks like a free group F r in its structure of subgroups. Our methods apply to groups with a generating sequence made of two to four distinct DNA/RNA bases in {A, T/U, G, C}. Several human TFs and miRNAs are investigated in detail thanks to our approach.
A comprehensive study of the technical parameters and conditions for the synthesis of ternary alloys in the Ti-Zr-Ni system by the "hydride cycle" method was carried out. The influence on the synthesis process of such parameters as:... more
A comprehensive study of the technical parameters and conditions for the synthesis of ternary alloys in the Ti-Zr-Ni system by the "hydride cycle" method was carried out. The influence on the synthesis process of such parameters as: temperature and annealing time, heating rate, cooling conditions, material composition, dispersion, hydrogen content in the hydrides used, the presence of impurities, mixing and pressing methods, and the degree of pressing of the starting components was determined. The alloys of the following compositions were synthesized and investigated: Ti 40.5 Zr 31.9 Ni 27.6 , Ti 41.5 Zr 41.5 Ni 17 , Ti 40 Zr 40 Ni 20 , Ti 44 Zr 40 Ni 16. The optimal technological parameters and conditions for the synthesis of ternary alloys are determined. It has been established that the key factors in the process of compound formation during hydride dissociation are the dispersion and homogeneity of the initial compacted components. It was found that the synthesis of ternary alloys in the Ti-Zr-Ni system occurs during a short-term exothermic reaction in the "thermal explosion" mode, which begins in the temperature region corresponding to the α↔β polymorphic transformation of zirconium and titanium.
We consider partition functions, in the form of state sums, and associated probabilistic measures for aperiodic substrates described by model sets and their associated tiling spaces. We propose model set tiling spaces as microscopic... more
We consider partition functions, in the form of state sums, and associated probabilistic measures for aperiodic substrates described by model sets and their associated tiling spaces. We propose model set tiling spaces as microscopic models for small scales in the context of quantum gravity. Model sets possess special self-similarity properties that allow us to consider implications on large and observable scales from the underlying (non-ergodic) dynamics. In particular we consider the implication of the underlying aperiodic substrate for the well known problem of time in quantum gravity, and propose a correspondence between small and large scales, the so-called ergodic correspondence, that addresses the emergence of matter properties and spacetime structure. In the process we find a possible bound in the mass spectrum of fundamental particles.
We explore the structural similarities in three different languages, first in the protein language whose primary letters are the amino acids, second in the musical language whose primary letters are the notes, and third in the poetry... more
We explore the structural similarities in three different languages, first in the protein language whose primary letters are the amino acids, second in the musical language whose primary letters are the notes, and third in the poetry language whose primary letters are the alphabet. For proteins, the non local (secondary) letters are the types of foldings in space (α-helices, β-sheets, etc.); for music, one is dealing with clear-cut repetition units called musical forms and for poems the structure consists of grammatical forms (names, verbs, etc.). We show in this paper that the mathematics of such secondary structures relies on finitely presented groups fp on r letters, where r counts the number of types of such secondary non local segments. The number of conjugacy classes of a given index (also the number of graph coverings over a base graph) of a group fp is found to be close to the number of conjugacy classes of the same index in the free group Fr−1 on r−1 generators. In a concrete way, we explore the group structure of a variant of the SARS-Cov-2 spike protein and the group structure of apolipoprotein-H, passing from the primary code with amino acids to the secondary structure organizing the foldings. Then, we look at the musical forms employed in the classical and contemporary periods. Finally, we investigate in much detail the group structure of a small poem in prose by Charles Baudelaire and that of the Bateau Ivre by Arthur Rimbaud.
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Most quasicrystals can be generated by the cut-and-project method from higher dimensional parent lattices. In doing so they lose the periodic order their parent lattice possess, replaced with aperiodic order, due to the irrationality of... more
Most quasicrystals can be generated by the cut-and-project method from higher dimensional parent lattices. In doing so they lose the periodic order their parent lattice possess, replaced with aperiodic order, due to the irrationality of the projection. However, perfect periodic order is discovered in the perpendicular space when gluing the cut window boundaries together to form a curved loop. In the case of a 1D quasicrystal projected from a 2D lattice, the irrationally sloped cut region is bounded by two parallel lines. When it is extrinsically curved into a cylinder, a line defect is found on the cylinder. Resolving this geometrical frustration removes the line defect to preserve helical paths on the cylinder. The degree of frustration is determined by the thickness of the cut window or the selected pitch of the helical paths. The frustration can be resolved by applying a shear strain to the cut-region before curving into a cylinder. This demonstrates that resolving the geometrical frustration of a topological change to a cut window can lead to preserved periodic order.
Considering the predictions from the standard model of particle physics coupled with experimental results from particle accelerators, we discuss a scenario in which from the infinite possibilities in the Lie groups we use to describe... more
Considering the predictions from the standard model of particle physics coupled with experimental results from particle accelerators, we discuss a scenario in which from the infinite possibilities in the Lie groups we use to describe particle physics, nature needs only the lower dimensional representations - an important phenomenology that we argue indicates nature is code theoretic. We show that the quantum deformation of the SU(2) Lie algebra at the fifth root of unity can be used to address the quantum Lorentz group representation theory through its universal covering group and gives the right low dimensional physical realistic spin quantum numbers confirmed by experiments. In this manner we can describe the spacetime symmetry content of relativistic quantum fields in accordance with the well known Wigner classification. Further connections of the fifth root of unity quantization with the mass quantum number associated with the Poincaré Group and the SU(N ) charge. Quantum numbers are discussed as well as their implication for quantum gravity.
The Kummer surface was constructed in 1864. It corresponds to the desingularisation of 1 the quotient of a 4-torus by 16 complex double points. Kummer surface is known to play a role in 2 some models of quantum gravity. Following our... more
The Kummer surface was constructed in 1864. It corresponds to the desingularisation of 1 the quotient of a 4-torus by 16 complex double points. Kummer surface is known to play a role in 2 some models of quantum gravity. Following our recent model of the DNA genetic code based on the 3 irreducible characters of the finite group G 5 := (240, 105) ∼ = Z 5 2O (with 2O the binary octahedral 4 group), we now find that groups G 6 := (288, 69) ∼ = Z 6 2O and G 7 := (336, 118) ∼ = Z 7 2O can be 5 used as models of the symmetries in hexamer and heptamer proteins playing a vital role for some 6 biological functions. Groups G 6 and G 7 are found to involve the Kummer surface in the structure of 7 their character table. An analogy between quantum gravity and DNA/RNA packings is suggested. 8
We introduce a quantum model for the Universe at its early stages, formulating a mechanism for the expansion of space and matter from a quantum initial condition, with particle interactions and creation driven by algebraic extensions of... more
We introduce a quantum model for the Universe at its early stages, formulating a mechanism for the expansion of space and matter from a quantum initial condition, with particle interactions and creation driven by algebraic extensions of the Kac-Moody Lie algebra e 9. We investigate Kac-Moody and Borcherds algebras, and we propose a generalization that meets further requirements that we regard as fundamental in quantum gravity.
In our investigation on quantum gravity, we introduce an infinite dimensional complex Lie algebra g u that extends e 9. It is defined through a symmetric Cartan matrix of a rank 12 Borcherds algebra. We turn g u into a Lie superal-gebra... more
In our investigation on quantum gravity, we introduce an infinite dimensional complex Lie algebra g u that extends e 9. It is defined through a symmetric Cartan matrix of a rank 12 Borcherds algebra. We turn g u into a Lie superal-gebra sg u with no superpartners, in order to comply with the Pauli exclusion principle. There is a natural action of the Poincaré group on sg u , which is an automorphism in the massive sector. We introduce a mechanism for scattering that includes decays as particular resonant scattering. Finally, we complete the model by merging the local sg u into a vertex-type algebra.
In this work, the structural transformation from a crystalline to quasicrystalline symmetry in palladium (Pd) and palladium-hydrogen (Pd-H) atomic clusters upon thermal annealing and hydrogenation has been addressed by means of atomistic... more
In this work, the structural transformation from a crystalline to quasicrystalline symmetry in palladium (Pd) and palladium-hydrogen (Pd-H) atomic clusters upon thermal annealing and hydrogenation has been addressed by means of atomistic simulations. A structural analysis of the clusters was performed during the heating up to the melting point to identify the temperature for the phase transformation. It has been demonstrated that nanometric pure Pd clusters transform from cuboctahedral to icosahedral structures under heating. This transformation is thermally activated process and the activation barrier depends on the cluster size. The activation energy of the cubo-ico symmetry transformation was measured using the variable heating rate method and was found to increase with the cluster size from 0.05 eV for 55 atomic cluster up to 0.66 eV for 147 atomic cluster. Hydrogenation of the nanometric Pd clusters yields to the modification of the transformation barrier in a non-monotonic form. At low H concentration, the transformation barrier decreases, while by increasing H concentration above a certain threshold, the barrier grows again thus making a minimum around a specific hydrogen concentration. This behaviour was rationalized as a competition between two processes, namely: the structure symmetry breaking at low H concentrations and stabilization of cuboctahedral phase of the clusters at high H concentration. The obtained results provide an estimation of the temperature range at which the symmetry transformation should occur under thermal annealing with experimentally achievable heating rates.
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In quasicrystals, any given local patch-called an emperor-forces at all distances the existence of accompanying tiles-called the empire-revealing thus their inherent nonlocality. In this chapter, we review and compare the methods... more
In quasicrystals, any given local patch-called an emperor-forces at all distances the existence of accompanying tiles-called the empire-revealing thus their inherent nonlocality. In this chapter, we review and compare the methods currently used for generating the empires, with a focus on the cut-and-project method, which can be generalized to calculate empires for any quasicrystals that are projections of cubic lattices. Projections of non-cubic lattices are more restrictive and some modifications to the cut-and-project method must be made in order to correctly compute the tilings and their empires. Interactions between empires have been modeled in a game-of-life approach governed by nonlocal rules and will be discussed in 2D and 3D quasicrystals. These nonlocal properties and the consequent dynamical evolution have many applications in quasicrystals research, and we will explore the connections with current material science experimental research.
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Holographic codes grown with perfect tensors on regular hyperbolic tessellations using an inflation rule protect quantum information stored in the bulk from errors on the boundary provided the code rate is less than one. Hyperbolic... more
Holographic codes grown with perfect tensors on regular hyperbolic tessellations using an inflation rule protect quantum information stored in the bulk from errors on the boundary provided the code rate is less than one. Hyperbolic geometry bounds the holographic code rate and guarantees quantum error correction for codes grown with any inflation rule on all regular hyperbolic tessellations in a class whose size grows exponentially with the rank of the perfect tensors for rank five and higher. For the tile completion inflation rule, holographic triangle codes have code rate more than one but all others perform quantum error correction.
We consider quantum transition amplitudes, partition functions and observables for 3D spin foam models within SU (2) quantum group deformation symmetry, where the deformation parameter is a complex fifth root of unity. By considering... more
We consider quantum transition amplitudes, partition functions and observables for 3D spin foam models within SU (2) quantum group deformation symmetry, where the deformation parameter is a complex fifth root of unity. By considering "fermionic" cycles through the foam we couple this SU (2) quantum group with the same deformation of SU (3), so that we have quantum numbers linked with spacetime symmetry and charge gauge symmetry in the computation of observables. The generalization to higher-dimensional Lie groups SU (N), G 2 and E 8 is suggested. On this basis we discuss a unifying framework for quantum gravity. Inside the transition amplitude or partition function for geometries, we have the quantum numbers of particles and fields interacting in the form of a spin foam network − in the framework of state sum models, we have a sum over quantum computations driven by the interplay between aperiodic order and topological order.
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Based on the Cayley-Dickson process, a sequence of multidimensional structured natural numbers (infinions) creates a path from quantum information to quantum gravity. Octonionic structure, exceptional Jordan algebra, and e8 Lie algebra... more
Based on the Cayley-Dickson process, a sequence of multidimensional structured natural numbers (infinions) creates a path from quantum information to quantum gravity. Octonionic structure, exceptional Jordan algebra, and e8 Lie algebra are encoded on a graph with E9 connectivity, decorated by integral matrices. With the magic star, a toy model for a quantum gravity is presented with its naturally emergent quasicrystalline projective compactification.
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Computational assessment of the discrete breathers (also known as intrinsic localised modes) is performed in nickel and palladium hydrides with an even stoichiometry by means of molecular dynamics simulations. The breathers consisting of... more
Computational assessment of the discrete breathers (also known as intrinsic localised modes) is performed in nickel and palladium hydrides with an even stoichiometry by means of molecular dynamics simulations. The breathers consisting of hydrogen and metallic atoms were excited following the experience obtained earlier by modelling the breathers in pure metallic systems. Stable breathers were only found in the nickel hydride system and only for the hydrogen atoms oscillating along 〈1 0 0〉 and 〈1 1 1〉 polarization axes. At this, two types of the stable breathers involving single oscillating hydrogen and a pair of hydrogen atoms beating in antiphase mode were discovered. Analysis of the breather characteristics reveals that its frequency is located in the phonon gap or lying in the optical phonon band of phonon spectrum near the upper boundary. Analysis of the movement of atoms constituting the breather was performed to understand the mechanism that enables the breather stabilization and long-term oscillation without dissipation its energy to the surrounding atoms. It has been demonstrated that, while in palladium hydride, the dissipation of the intrinsic breather energy due to hydrogen-hydrogen attractive interaction occurs, the stable oscillation in the nickel hydride system is ensured by the negligibly weak hydrogen-hydrogen interaction acting within a distance of the breather oscillation amplitude. Thus, our analysis provides an explanation for the existence of the long-living stable breathers in metallic hy-dride systems. Finally, the high energy oscillating states of hydrogen atoms have been observed for the NiH and PdH lattices at finite temperatures which can be interpreted as a fingerprint of the finite-temperature analogues of the discrete breathers.
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Emergence theory is a code-theoretic first-principles based discretized quantum field theoretic approach to quantum gravity and particle physics. This overview covers the primary set of ideas being assembled by Quantum Gravity Research.
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The projection method for constructing quasiperiodic tilings from a higher dimensional lattice provides a useful context for computing a quasicrystal's vertex configurations, frequencies, and empires (forced tiles). We review the... more
The projection method for constructing quasiperiodic tilings from a higher dimensional lattice provides a useful context for computing a quasicrystal's vertex configurations, frequencies, and empires (forced tiles). We review the projection method within the framework of the dual relationship between the Delaunay and Voronoi cell complexes of the lattice being projected. We describe a new method for calculating empires (forced tiles) which also borrows from the dualisation formalism and which generalizes to tilings generated projections of non-cubic lattices. These techniques were used to compute the vertex configurations, frequencies and empires of icosahedral quasicrystals obtained as a projections of the D 6 and Z 6 lattices to R 3 and we present our analyses. We discuss the implications of this new generalization.
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Inspired by the Hilbert-Polya proposal to prove the Riemann Hypothesis we have studied the Schroedinger QM equation involving a highly non-trivial potential, and whose self-adjoint Hamiltonian operator has for its energy spectrum one... more
Inspired by the Hilbert-Polya proposal to prove the Riemann Hypothesis we have studied the Schroedinger QM equation involving a highly non-trivial potential, and whose self-adjoint Hamiltonian operator has for its energy spectrum one which approaches the imaginary parts of the zeta zeroes only in the asymptotic (very large N) region. The ordinates λn are the positive imaginary parts of the nontrivial zeta zeros in the critical line : sn = 1 2 + iλn. The latter results are consistent with the validity of the Bohr-Sommerfeld semi-classical quantization condition. It is shown how one may modify the parameters which define the potential, and fine tune its values, such that the energy spectrum of the (modified) Hamiltonian matches not only the first two zeroes but the other consecutive zeroes. The highly non-trivial functional form of the potential is found via the Bohr-Sommerfeld quantization formula using the full-fledged Riemann-von Mangoldt counting formula (without any truncations) for the number N (E) of zeroes in the critical strip with imaginary part greater than 0 and less than or equal to E.
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The hard problem of consciousness must be approached through the ontological lens of 20th century physics, which tells us that reality is information theoretic [1,2] and quantized at the level of Planck scale spacetime[3]. Through careful... more
The hard problem of consciousness must be approached through the ontological lens of 20th century physics, which tells us that reality is information theoretic [1,2] and quantized at the level of Planck scale spacetime[3]. Through careful deduction, it becomes clear that information cannot exist without consciousness – the awareness of things. And to be aware is to hold the meaning of relationships of objects within consciousness – perceiving abstract objects, while enjoying degrees of freedom within the structuring of those relationships. This defines consciousness as language – (1) a set of objects and (2) an ordering scheme with (3) degrees of freedom used for (4) expressing meaning. And since even information at the Planck scale cannot exist without consciousness, we propose an entity called a " primitive unit of consciousness " , which acts as a mathematical operator in a quantized spacetime language. Quasicrystal mathematics based on E8 geometry [4] seems to be a candidate for the language of reality, possessing several qualities corresponding to recent physical discoveries and various physically realistic unification models.
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Quasicrystals (QCs) are a novel form of matter, which are neither crystalline nor amorphous. Among many surprising properties of QCs is their high catalytic activity. We propose a mechanism explaining this peculiarity based on unusual... more
Quasicrystals (QCs) are a novel form of matter, which are neither crystalline nor amorphous. Among many surprising properties of QCs is their high catalytic activity. We propose a mechanism explaining this peculiarity based on unusual dynamics of atoms at special sites in QCs, namely, localized anharmonic vibrations (LAVs) and phasons. In the former case, one deals with a large amplitude (~ fractions of an angstrom) time-periodic oscillations of a small group of atoms around their stable positions in the lattice, known also as discrete breathers, which can be excited in regular crystals as well as in QCs. On the other hand, phasons are a specific property of QCs, which are represented by very large amplitude (~angstrom) oscillations of atoms between two quasi-stable positions determined by the geometry of a QC. Large amplitude atomic motion in LAVs and phasons results in time-periodic driving of adjacent potential wells occupied by hydrogen ions (protons or deuterons) in case of hydrogenated QCs. This driving may result in the increase of amplitude and energy of zero-point vibrations (ZPV). Based on that, we demonstrate a drastic increase of the D-D or D-H fusion rate with increasing number of modulation periods evaluated in the framework of Schwinger model, which takes into account suppression of the Coulomb barrier due to lattice vibrations. In this context, we present numerical solution of Schrodinger equation for a particle in a non-stationary double well potential, which is driven time-periodically imitating the action of a LAV or phason. We show that the rate of tunneling of the particle through the potential barrier separating the wells is enhanced drastically by the driving, and it increases strongly with increasing amplitude of the driving. These results support the concept of nuclear catalysis in QCs that can take place at special sites provided by their inherent topology. Experimental verification of this hypothesis can lead to new ways of engineering materials containing nuclear active environments based on QC catalytic properties.
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The goal of this work on mathematical cosmology and geometric methods in modifed gravity theories, MGTs, is to investigate Starobinsky-like infation scenarios determined by gravitational and scalar field configurations mimicking... more
The goal of this work on mathematical cosmology and geometric methods in modifed gravity theories, MGTs, is to investigate Starobinsky-like infation scenarios determined by gravitational and scalar field configurations mimicking quasicrystal, QC, like structures.
Such spacetime aperiodic QCs are different from those discovered and studied in solid state physics but described by similar geometric methods. We prove that inhomogeneous and locally anisotropic gravitational and matter field effective QC mixed continuous and
discrete "ether" can be modeled by exact cosmological solutions in MGTs and Einstein gravity. The coeffcients of corresponding generic off-diagonal metrics and generalized connections depend (in general) on all spacetime coordinates via generating and integration
functions and certain smooth and discrete parameters. Imposing additional nonholonomic constraints, prescribing symmetries for generating functions and solving the boundary conditions for integration functions and constants, we can model various nontrivial torsion QC structures or extract cosmological Levi-Civita configurations with diagonal metrics reproducing de Sitter (inflationary) like and other type homogeneous inflation and acceleration phases. Finally, we speculate how various dark energy and dark matter effects
can be modelled by off-diagonal interactions and deformations of a nontrivial QC like gravitational vacuum structure and analogous scalar matter fields.
Such spacetime aperiodic QCs are different from those discovered and studied in solid state physics but described by similar geometric methods. We prove that inhomogeneous and locally anisotropic gravitational and matter field effective QC mixed continuous and
discrete "ether" can be modeled by exact cosmological solutions in MGTs and Einstein gravity. The coeffcients of corresponding generic off-diagonal metrics and generalized connections depend (in general) on all spacetime coordinates via generating and integration
functions and certain smooth and discrete parameters. Imposing additional nonholonomic constraints, prescribing symmetries for generating functions and solving the boundary conditions for integration functions and constants, we can model various nontrivial torsion QC structures or extract cosmological Levi-Civita configurations with diagonal metrics reproducing de Sitter (inflationary) like and other type homogeneous inflation and acceleration phases. Finally, we speculate how various dark energy and dark matter effects
can be modelled by off-diagonal interactions and deformations of a nontrivial QC like gravitational vacuum structure and analogous scalar matter fields.
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We present an icosahedral quasicrystal, a Fibonacci icosagrid, obtained by spacing the parallel planes in an icosagrid with the Fibonacci sequence. This quasicrystal can also be thought as a golden composition of five sets of Fibonacci... more
We present an icosahedral quasicrystal, a Fibonacci icosagrid, obtained by spacing the parallel planes in an icosagrid with the Fibonacci sequence. This quasicrystal can also be thought as a golden composition of five sets of Fibonacci tetragrids. We found that this quasicrystal embeds the quasicrystals that are golden compositions of the three-dimensional tetrahedral cross-sections of the Elser-Sloane quasicrystal, which is a four-dimensional cut-and-project of the E8 lattice. These compound quasicrystals are subsets of the Fibonacci icosagrid, and they can be enriched to form the Fibonacci icosagrid. This creates a mapping between the Fibonacci icosagrid and the E−8 lattice. It is known that the combined structure and dynamics of all gravitational and Standard Model particle fields, including fermions, are part of the E8 Lie algebra. Because of this, the Fibonacci icosagrid is a good candidates, for representing states and interactions between particles and fields in quantum mechanics. We coin the name Quasicrystalline Spin-Network (QSN) for this quasicrystalline structure.