Klee Irwin

Klee Irwin
Quantum Gravity Research · Quantum Physics

About

71
Publications
46,041
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340
Citations
Introduction
Quantum Gravity Research consists of a team of dedicated research scientists––physicists, engineers and mathematicians-- developing a first-principles quantum gravity unification theory using E8-derived quasicrystal mathematics. Emergence theory weaves together quantum mechanics, general & special relativity, the standard model and other physics theories into a complete, fundamental picture of a discretized, self-actualizing universe.
Additional affiliations
January 2009 - April 2017
Quantum Gravity Research
Position
  • Managing Director

Publications

Publications (71)
Article
Full-text available
It is shown that the representation theory of some finitely presented groups thanks to their SL2(C) character variety is related to algebraic surfaces. We make use of the Enriques–Kodaira classification of algebraic surfaces and related topological tools to make such surfaces explicit. We study the connection of SL2(C) character varieties to topolo...
Preprint
Full-text available
It is shown that the representation theory of some finitely presented groups thanks to their $SL_2(\mathbb{C})$ character variety is related to algebraic surfaces. We make use of the Enriques-Kodaira classification of algebraic surfaces and the related topological tools to make such surfaces explicit. We study the connection of $SL_2(\mathbb{C})$ c...
Article
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Transcription factors (TFs) are proteins that recognize specific DNA fragments in order to decode the genome and ensure its optimal functioning. TFs work at the local and global scales by specifying cell type, cell growth and death, cell migration, organization and timely tasks. We investigate the structure of DNA-binding motifs with the theory of...
Article
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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...
Article
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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 postulated to be 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...
Article
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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 e9. We investigate Kac–Moody and Borcherds algebras, and we propose a generalization th...
Article
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In our investigation on quantum gravity, we introduce an infinite dimensional complex Lie algebra gu that extends e9. It is defined through a symmetric Cartan matrix of a rank 12 Borcherds algebra. We turn gu into a Lie superalgebra sgu with no superpartners, in order to comply with the Pauli exclusion principle. There is a natural action of the Po...
Preprint
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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...
Article
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Citation: Planat, M.; Aschheim, R.; Amaral, M.M.; Fang, F.; Irwin, K. Graph Coverings for Investigating Non Local Structures in Proteins, Music and Poems. Sci 2021, 3, 39. Abstract: 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 lang...
Article
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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 the projection. However, perfect periodic order is discovered in the perpendicular space when gluing the cut wind...
Article
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In light of the self-simulation hypothesis, a simple form of implementation of the principle of efficient language is discussed in a self-referential geometric quasicrystalline state sum model in three dimensions. Emergence is discussed in the context of geometric state sum models.
Preprint
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It is shown how the secondary structure of proteins, musical forms and verses of poems are approximately ruled by universal laws relying on graph coverings. In this direction, one explores 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 t...
Article
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Every protein consists of a linear sequence over an alphabet of 20 letters/amino acids. The sequence unfolds in the 3-dimensional space through secondary (local foldings), tertiary (bonds) and quaternary (disjoint multiple) structures. The mere existence of the genetic code for the 20 letters of the linear chain could be predicted with the (informa...
Article
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The Kummer surface was constructed in 1864. It corresponds to the desingularization of the quotient of a 4-torus by 16 complex double points. Kummer surface is known to play a role in some models of quantum gravity. Following our recent model of the DNA genetic code based on the irreducible characters of the finite group G5:=(240,105)≅Z5⋊2O (with 2...
Preprint
Full-text available
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 kwown 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) ∼ =...
Preprint
Full-text available
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 $\mathbf{e_9}$. We investigate Kac-Moody and Borcherds algebras, and we propose a gener...
Preprint
Full-text available
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 e9. We investigate Kac-Moody and Borcherds algebras, and we propose a generalization th...
Article
Full-text available
We find that the degeneracies and many peculiarities of the DNA genetic code may be described thanks to two closely related (fivefold symmetric) finite groups. The first group has signature G=Z5⋊H where H=Z2.S4≅2O is isomorphic to the binary octahedral group 2O and S4 is the symmetric group on four letters/bases. The second group has signature G=Z5...
Article
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A popular account of the mixing patterns for the three generations of quarks and leptons is through the characters κ of a finite group G. Here, we introduce a d-dimensional Hilbert space with d = cc(G), the number of conjugacy classes of G. Groups under consideration should follow two rules, (a) the character table contains both two-and three-dimen...
Article
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The authors previously found a model of universal quantum computation by making use of the coset structure of subgroups of a free group G with relations. A valid subgroup H of index d in G leads to a 'magic' state |ψ in d-dimensional Hilbert space that encodes a minimal informationally complete quantum measurement (or MIC), possibly carrying a fini...
Preprint
Full-text available
A popular account of the mixing patterns for the three generations of quarks and leptons is through the characters $\kappa$ of a finite group $G$. Here we introduce a $d$-dimensional Hilbert space with $d=cc(G)$, the number of conjugacy classes of $G$. Groups under consideration should follow two rules, (a) the character table contains both two- an...
Preprint
Full-text available
In this work we explore how the heat kernel, which gives the solution to the diffusion equation and the Brownian motion, would change when we introduce quasiperiodicity in the scenario. We also study the random walk in the Fibonacci sequence. We discuss how these ideas would change the discrete approaches to quantum gravity and the construction of...
Article
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We modify the simulation hypothesis to a self-simulation hypothesis, where the physical universe, as a strange loop, is a mental self-simulation that might exist as one of a broad class of possible code theoretic quantum gravity models of reality obeying the principle of efficient language axiom. This leads to ontological interpretations about quan...
Article
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 i...
Article
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The synthesis of intermetallic material was carried out by means of dehydrogenating annealing of a (TiH 2) 30 Zr 45 Ni 25 sample in vacuum by an electron beam. The properties of the obtained material were studied for establishing the structural phase composition by scanning electron microscopy and X-ray structural analysis. It was found that prolon...
Preprint
Full-text available
The authors previously found a model of universal quantum computation by making use of the coset structure of subgroups of a free group G with relations. A valid subgroup H of index d in G leads to a 'magic' state |ψ in d-dimensional Hilbert space that encodes a minimal informationally complete quantum measurement (or MIC), possibly carrying a fini...
Article
The authors previously found a model of universal quantum computation by making use of the coset structure of subgroups of a free group G with relations. A valid subgroup H of index d in G leads to a ‘magic’ state ∣∣ψ⟩ in d-dimensional Hilbert space that encodes a minimal informationally complete quantum measurement (or MIC), possibly carrying a fi...
Preprint
Full-text available
We modify the simulation hypothesis to a self-simulation hypothesis, where the physical universe, as a strange loop, is a mental self-simulation that might exist as one of a broad class of possible code theoretic quantum gravity models of reality obeying the principle of efficient language axiom. This leads to ontological interpretations about quan...
Article
Full-text available
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 calcu...
Article
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In Part I, we introduce the notion of simplex-integers and show how, in contrast to digital numbers, they are the most powerful numerical symbols that implicitly express the information of an integer and its set theoretic substructure. In Part II, we introduce a geometric analogue to the primality test that when p is prime, it divides \binom{p}{k}=...
Article
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In this paper, we present the construction of several aggregates of tetrahedra. Each construction is obtained by performing rotations on an initial set of tetrahedra that either (1) contains gaps between adjacent tetrahedra, or (2) exhibits an aperiodic nature. Following this rotation, gaps of the former case are “closed” (in the sense that faces o...
Article
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The Boerdijk–Coxeter helix is a helical structure of tetrahedra which possesses no non-trivial translational or rotational symmetries. In this document, we develop a procedure by which this structure is modified to obtain both translational and rotational (upon projection) symmetries along/about its central axis. We show by construction that a heli...
Article
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Let H be a nontrivial subgroup of index d of a free group G and N be the normal closure of H in G. The coset organization in a subgroup H of G provides a group P of permutation gates whose common eigenstates are either stabilizer states of the Pauli group or magic states for universal quantum computing. A subset of magic states consists of states a...
Conference Paper
Full-text available
Aluminum-based quasicrystals form a wide class of icosahedral and decogonal systems, including Al-Fe-TM and Al-Cu-TM (TM are transition metals Ni, Co, Cr). Traditional methods for the synthesis of quasicrystalline materials, such as rapid quenching of liquid melts, the method of mechanical activation fusion, growing from the melt and others, have a...
Poster
Full-text available
The Ti30Zr45Ni25 intermetallic material was synthesized using the hydride cycle technology with dehydrogenation of a portion ofthe (TiH2)30Zr45Ni25 sample by an electron beam in vacuum. Using scanning electron microscopy (SEM / EDX) and X-raydiffraction (XRD) analysis, it was established that under the influence of an electron beam, structural tran...
Poster
Full-text available
Aluminum-based quasicrystals form a wide class of icosahedral and decogonal systems, including Al-Fe-TM and Al-Cu-TM (TM are transition metals Ni, Co, Cr). Traditional methods for the synthesis of quasicrystalline materials, such as rapid quenching of liquid melts, the method of mechanical activation fusion, growing from the melt and others, have a...
Conference Paper
Full-text available
In numerous papers [1,2], the possibility of synthesizing complex intermetallic and quasicrystalline materials based on refractory metals of the zirconium group using hydride technology has been shown. These materials are capable of reversibly absorbing hydrogen in significant quantities above 2 wt.% [3], which allows considering them as materials...
Preprint
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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 geometry bounds the holographic code rate and guarantees quantum error correction for codes grown with any inflation r...
Preprint
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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...
Article
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...
Article
Full-text available
The fundamental group π1(L) of a knot or link L may be used to generate magic states appropriate for performing universal quantum computation and simultaneously for retrieving complete information about the processed quantum states. In this paper, one defines braids whose closure is the L of such a quantum computer model and computes their Seifert...
Preprint
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ABSTRACT: 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.
Article
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A single qubit may be represented on the Bloch sphere or similarly on the 3-sphere S 3 . Our goal is to dress this correspondence by converting the language of universal quantum computing (UQC) to that of 3-manifolds. A magic state and the Pauli group acting on it define a model of UQC as a positive operator-valued measure (POVM) that one recognize...
Preprint
A single qubit may be represented on the Bloch sphere or similarly on the 3-sphere S3. Our goal is to dress this correspondence by converting the language of universal quantum computing (UQC) to that of 3-manifolds. A magic state and the Pauli group acting on it define a model of UQC as a positive operator-valued measure (POVM) that one recognizes...
Article
Full-text available
On a two-dimensional quasicrystal, a Penrose tiling, we simulate for the first time a game of life dynamics governed by non-local rules. Quasicrystals have inherently non-local order since any local patch, the emperor, forces the existence of a large number of tiles at all distances, the empires. Considering the emperor and its local patch as a qua...
Article
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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 projection method within the framework of the dual relationship between the Delaunay and Voronoi cell complexes of the l...
Preprint
Full-text available
It has been shown that non-stabilizer eigenstates of permutation gates are appropriate for allowing d-dimensional universal quantum computing (uqc) based on minimal informationally complete POVMs. The relevant quantum gates may be built from subgroups of finite index of the modular group Γ = P SL(2, Z) [M. Planat, Entropy 20, 16 (2018)] or more gen...
Article
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In geometrically frustrated clusters of polyhedra, gaps between faces can be closed without distorting the polyhedra by the long established method of discrete curvature, which consists of curving the space into a fourth dimension, resulting in a dihedral angle at the joint between polyhedra in 4D. An alternative method—the twist method—has been re...
Conference Paper
Full-text available
The projection method for constructing quasiperiodic tilings from a higher dimensionallattice 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 dualrelationship between the Delaunay and Voronoi cell complexes of the latt...
Article
Full-text available
A logical physical ontology is code theory, wherein reality is neither deterministic nor random. In light of Conway and Kochen’s free will theorem [The free will theorem, Found. Phys. 36(10) (2006) 1441–1473] and strong free will theorem [The strong free will theorem, Not. Am. Math. Soc. 56(2) (2009) 226–232], we discuss the plausibility of a third...
Article
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This paper reviews the empire problem for quasiperiodic tilings and the existing methods for generating the empires of the vertex configurations in quasicrystals, while introducing a new and more efficient method based on the cut-and-project technique. Using Penrose tiling as an example, this method finds the forced tiles with the restrictions in t...
Article
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The goal of this work is to elaborate on new geometric methods of constructing exact and parametric quasiperiodic solutions for anamorphic cosmology models in modified gravity theories, MGTs, and general relativity, GR. There exist previously studied generic off-diagonal and diagonalizable cosmological metrics encoding gravitational and matter fiel...
Conference Paper
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One of the new materials tested in our reactor was a melt spun Nd90Fe10 alloy with a large degree of amorphous or quasicrystalline phase. A fierce exothermic reaction was detected in Nd90Fe10 films upon filling them with hydrogen or deuterium and heating up to ~300 C, which resulted in the melting of the samples and the Cu foil, in which the sample...
Article
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We apply a discrete quantum walk from a quantum particle on a discrete quantum spacetime from loop quantum gravity and show that the related entanglement entropy drives an entropic force. We apply these concepts in a model where walker positions are topologically encoded on a spin network. Then, we discuss the role of the golden ratio in fundamenta...
Article
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We present the emergence of a root system in six dimensions from the tetrahedra of an icosahedral core known as the 20-group (20G) within the framework of Clifford’s geometric algebra. Consequently, we establish a connection between a three-dimensional icosahedral seed, a six-dimensional (6D) Dirichlet quantized host and a higher dimensional lattic...
Article
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The goal of this work on mathematical cosmology and geometric methods in modified gravity theories, MGTs, is to investigate Starobinsky-like inflation 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 soli...
Article
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Quasicrystals are fractal due to their self similar property. In this paper, a new cycloidal fractal signature possessing the cardioid shape in the Mandelbrot set is presented in the Fourier space of a Fibonacci chain with two lengths, L and S, where L/S = φ. The corresponding pointwise dimension is 0.7. Various modifications, such as truncation fr...
Article
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Heterotic supergravity with (1+3)–dimensional domain wall configurations and (warped) internal, six dimensional, almost-Kähler manifolds 6 X are studied. Considering on ten dimensional spacetime, nonholonomic distributions with conventional double fibrations, 2+2+...=2+2+3+3, and associated SU (3) structures on internal space, we generalize for rea...
Article
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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 which approaches the imaginary parts of the zeta zeroes only in the asymptotic (very large N) region. The ordinates...
Article
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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 dynamics of atoms at special sites in QCs, namely, localized anharmonic vibrations (LAVs) and phasons. In the forme...
Article
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Geometric methods for constructing exact solutions of motion equations with first order $\alpha ^{\prime }$ corrections to the heterotic supergravity action implying a non-trivial Yang-Mills sector and six dimensional, 6-d, almost-K\"{a}hler internal spaces are studied. In 10-d spacetimes, general parametrizations for generic off-diagonal metrics,...
Article
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The construction of an icosahedral quasicrystal and a quasicrystalline spin network are obtained by spacing the parallel planes in an icosagrid with the Fibonacci sequence. This quasicrystal can also be thought of as a golden composition of five sets of Fibonacci tetragrids. We found that this quasicrystal embeds the quasicrystals that are golden c...
Article
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A first principles theory of everything has yet to be achieved. An E8 derived code of quantized spacetime could meet the following suggested requirements: (1) First principles explanation of time dilation, inertia, the magnitude of the Planck constant and the speed of light (2) First principles explanation of conservation laws and gauge transform...
Article
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The hard problem of consciousness must be approached through the ontological lens of 20 th 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...
Article
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Inspired by the recent sums of the squares law obtained by [1] we derive the law of the sums of the squares of the areas, volumes and hyper-volumes associated with the faces, cells and hyper-cells of regular polytopes in diverse dimensions by using Clifford algebraic methods [5].
Article
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We present the construction of a dense, quasicrystalline packing of regular tetrahedra with icosahedral symmetry. This quasicrystalline packing was achieved through two independent approaches. The first approach originates in the Elser-Sloane 4D quasicrystal. A 3D slice of the quasicrystal contains a few types of prototiles. An initial structure is...