Theory of Everything (span 12)

General relativity and quantum mechanics describe seemingly incompatible traits of our universe. Their unification into a theory-of-everything challenged physics for the last century. Here I present GenI (for generic intelligence), a model inspired by artificial intelligence that satisfies both fundamental theories. GenI comprises a random walk process operating on a swarm-like construct and implements the competition among a finite set of ideas. Without any parameter tuning, GenI precisely fulfils the predictions of quantum measurements while its dynamics locally satisfy Einstein’s field equation. The model suggests, that the perceivable universe is evolving according to the collapse of its quantum state rather than a smoothly evolving wave function as widely believed in modern physics. Consequently, gravitation cannot be directly derived from quantum mechanics or vice versa. Both simply describe distinct perspectives onto the previously unknown swarm-like stochastic process operating at the very basis of our universe. (GitHub/BZuS)

The Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000. Currently, six of the problems remain unsolved (Wikipedia).

How close are we to the theory of everything?

Well, we thought we were getting pretty close about a decade ago - but more recent experimental and observational science is making things a LOT harder for the theoreticians:

• The final realization that quantum mechanics and relativity cannot both be correct has created a bit of a problem.
• A theory of “quantum gravity” is needed - and we don’t have it. Even more annoyingly, both quantum mechanics and relativity are very solidly proven to be true.
• Cosmologists found dark matter and then dark energy. They can describe their observed properties - point out that about 96% of everything is dark matter/energy - and then leave particle physicists with a major problem.
• The demands of theoreticians for more data has pushed particle colliders to somewhere close to the limits of our ability to pay for the darned things (although not yet the limits of theoretical feasibility).
• The construction of something significantly bigger than the Large Hadron Collider does not seem likely right now so the data we have may turn out to be the only data we’ll ever have (from particle colliders). Large space telescopes, however, are getting MUCH better and when SpaceX get their StarShip to fly - they’ll be much cheaper and MUCH larger. So getting help from cosmologists MIGHT offer assistance.
• The great hope that String Theory could be the “Theory of Everything” has somewhat tarnished. The last “Superstring revolution” was impressive but it was close to 30 years ago now and we still don’t seem to be adopting it as The Truth.
• String theory predicts that one out of 10⁵ possible realities is the one we live in but fails to mention which one! This is not exactly useful!
• Current string theories seem incompatible with dark energy - which is definitely not good.

There is an additional problem called Background Independence - which is a property that Relativity requires - but which string theory does not seem to reproduce… but this is still a matter of contention. (I confess I do not understand what “Background Independence” actually is… but I Am Not A Theoretical Physicist.) (Quora)

Leptons may be assigned the six flavour quantum numbers: electron number, muon number, tau number, and corresponding numbers for the neutrinos.

• These are conserved in strong and electromagnetic interactions, but violated by weak interactions.
• Therefore, such flavour quantum numbers are not of great use. A separate quantum number for each generation is more useful: electronic lepton number (+1 for electrons and electron neutrinos), muonic lepton number (+1 for muons and muon neutrinos), and tauonic lepton number (+1 for tau leptons and tau neutrinos).
• However, even these numbers are not absolutely conserved, as neutrinos of different generations can mix; that is, a neutrino of one flavour can transform into another flavour.

The strength of such mixings is specified by a matrix called the Pontecorvo–Maki–Nakagawa–Sakata matrix (PMNS matrix). (Wikipedia)

Gell-mann matrices are a complete set of Hermitian noncommuting trace-orthogonal matrices. In addition, they also play an important role in physics where they can be thought to model the eight gluons that mediate the strong force quantum chromodynamics, an analogue of the Pauli matrices well-adapted to applications in the realm of quantum mechanics. (Wolfram)

The action of C⊗O on itself can be seen to generate a 64-complex-dimensional algebra, wherein we are able to identify two sets of generators for SU(3)c.

• Furthermore, we show that these three-generation results can be extended, so as to include all 48 fermionic U(1)em charges.
• The 64-dimensional octonionic chain algebra splits into two sets of SU (3) generators of the form iΛν and −iΛ * ν * , six SU (3) singlets j , six triplets q k , and their complex conjugates.
• These objects are sectioned off above into four quadrants according to their forms: νaν, ν * aν, νaν * and ν * aν * for a in the chain algebra.

Transforming particles into anti-particles, and vice versa, requires only the complex conjugate i → −i in our formalism. (Standard Model from an algebra - pdf)

The pseudoscalar meson nonet. Members of the original meson “octet (8)” are shown in green, the singlet in magenta.

• Although these mesons are now grouped into a nonet (9), the Eightfold Way name derives from the patterns of eight for the mesons and baryons in the original classification scheme.
• The Eightfold Way classification is named after the following fact:
  • If we take three flavors of quarks, then the quarks lie in the fundamental representation, 3 (called the triplet) of flavor SU(3).
  • The antiquarks lie in the complex conjugate representation 3.
• The nine states (nonet) made out of a pair can be decomposed into the trivial representation, 1 (called the singlet), and the adjoint representation, 8 (called the octet).
• The notation for this decomposition is 3⊗3=8⊕1.

Figure below shows the application of this decomposition to the mesons. (Wikipedia)

In order to be four-spinors like the electron and other lepton components, there must be one quark component for every combination of flavour and colour, bringing the total to 24 (3 for charged leptons, 3 for neutrinos, and 2·3·3 = 18 for quarks). Each of these is a four (4) component bispinor, for a total of 96 complex-valued components for the fermion field. (Wikipedia)

The origin of multiple generations of fermions, and the particular count of 3, is an unsolved problem of physics.

• Generations of matter: Why are there three generations of quarks and leptons? Is there a theory that can explain the masses of particular quarks and leptons in particular generations from first principles (a theory of Yukawa couplings)?
• String theory provides a cause for multiple generations, but the particular number depends on the details of the compactification of the D-brane intersections.
• Additionally, E8 grand unified theories in 10 dimensions compactified on certain orbifolds down to 4‑D naturally contain 3 generations of matter.
• This includes many heterotic string theory models.

In standard quantum field theory, under certain assumptions, a single fermion field can give rise to multiple fermion poles with mass ratios of around eπ≈23 and e2π≈535 potentially explaining the large ratios of fermion masses between successive generations and their origin. (Wikipedia)

Why do we see certain types of strongly interacting elementary particles and not others? This question was posed over 50 years ago in the context of the quark model.

• M. Gell-Mann and G. Zweig proposed that the known mesons were qq¯ and baryons qqq, with quarks known at the time u (“up”), d (“down”), and s (“strange”) having charges (2/3,–1/3,–1/3).
• Mesons and baryons would then have integral charges. Mesons such as qqq¯q¯ and baryons such as qqqqq¯ would also have integral charges. Why weren’t they seen?
• They have now been seen, but only with additional heavy quarks and under conditions which tell us a lot about the strong interactions and how they manifest themselves.

The present article describes recent progress in our understanding of such “exotic” mesons and baryons. (Multiquark States - pdf)

These are called hypercomplex numbers, such as, quaternions (4D), octonions (8D), sedenions (16D), pathions (32D), chingons (64D), routons (128D), and voudons (256D). These names were coined by Robert P.C. de Marrais and Tony Smith. It is an alternate naming system providing relief from the difficult Latin names, such as: trigintaduonions (32D), sexagintaquattuornions (64D), centumduodetrigintanions (128D), and ducentiquinquagintasexions (256D). (Wordpress.com)

The set of points in Euclidean 4-space having the same distance R from a fixed point P0 forms a hypersurface known as a 3-sphere where R is substituted by function R(t) with t meaning the cosmological age of the universe. Growing or shrinking R with time means expanding or collapsing universe, depending on the mass density inside (Wikipedia).

Throughout his life, Einstein published hundreds of books and articles. He published more than 300 scientific papers and 150 non-scientific ones. On 5 December 2014, universities and archives announced the release of Einstein’s papers, comprising more than 30,000 unique documents (Wikipedia).

On the other hand, one does not yet have a mathematically complete example of a quantum gauge theory in 4D Space vs Time, nor even a precise definition of quantum gauge theory in four dimensions. Will this change in the 21st century? We hope so! (Clay Institute’s - Yang Mills Official problem description).

Equivalently, they are the linear transformations fixing that hyperboloid of two sheets. If we discard one of the sheets, we obtain the orthochronous (time-preserving) subgroup.

• From the perspective of the centre of the cone, the hyperboloid looks like an open disc. The orthochronous Lorentz transformations precisely correspond to distance-preserving transformations of the hyperbolic plane. These are themselves determined uniquely by a conformal (or anticonformal) transformation of the ‘circle at infinity’.
• Adding an extra dimension, the orthochronous Lorentz group O^{+}(3,1) is isomorphic to the group of distance-preserving transformations of hyperbolic 3-space, which is again isomorphic to the group of (anti-)conformal transformations of the ‘sphere at infinity’, namely our index-2 supergroup of the Möbius group.
• Moreover, this nicely generalises: the group generated by geometric inversions on the n-sphere is abstractly isomorphic to the orthochronous Lorentz group O^{+}(n+1,1).

And when n = 24, we get a very beautiful discrete subgroup, namely the automorphism group of the II(25,1) lattice intimately related to the Leech lattice. (Complex Projective 4-Space)

There are 8 different types of tiny particles, or ‘states’, that we can find in a special kind of space that has 6 dimensions and involves both real and imaginary numbers. These particles include:

• The Higgs field, which doesn’t spin and is represented by 0.
• Fermions, which are particles like electrons, having a spin of plus or minus a half.
• Bosons, like photons, which have a spin of plus or minus 1.
• Anti-fermions, which are like fermions but have a spin of plus or minus two-thirds.
• The graviton, believed to be responsible for gravity, with a spin of 2.

In a diagram at the top left, this 6-dimensional space is shown to be curved. In another diagram at the bottom right, we see two waves that are perpendicular to each other, representing the motion of a particle in a ‘Dirac harmonic oscillator’ – a concept in quantum mechanics. (Physics In History)

Four of the dimensions are the usual four of spacetime. The six (or perhaps seven) extra dimensions are rolled up to be almost unobservable.

• First, let’s see why they exist at all. If N=8 Supersymmetry is correct the universe must be 10 or 11 dimensional.
• Let D be the actual dimensionality of space time. Let d be the apparent dimensionality. (We know d = 4, but let’s think generally.) Then there is a nice relation between D, d and N.
• It follows from the number of spinor dimensions required by the Dirac equation, which is The s mean round down to the nearest whole number. So plugging in d=4 and N=8 (which is the highest value N can have) we get D = 10 or 11. String theory has D=10, M-theory has D=11.
• One dimension is reserved for time, leaving space with 9 or 10 dimensions.

We don’t see 6 (or 7) of these extra dimensions because - we assume - they are rolled up a la Kaluza–Klein theory into a 6 dimensional Calabi–Yau space

In particle physics, SO(10) refers to a grand unified theory (GUT) based on the spin group Spin(10). The shortened name SO(10) is conventional[1] among physicists, and derives from the Lie algebra or less precisely the Lie group of SO(10), which is a special orthogonal group that is double covered by Spin(10).

SO(10) subsumes the Georgi–Glashow and Pati–Salam models, and unifies all fermions in a generation into a single field. This requires 12 new gauge bosons, in addition to the 12 of SU(5) and 9 of SU(4)×SU(2)×SU(2).

• Left: The pattern of weak isospin, W, weaker isospin, W’, strong g3 and g8, and baryon minus lepton, B, charges for particles in the SO(10) model, rotated to show the embedding of the Georgi–Glashow model and Standard Model, with electric charge roughly along the vertical. In addition to Standard Model particles, the theory includes 30 colored X bosons, responsible for proton decay, and two W’ bosons.
• Right: The pattern of charges for particles in the SO(10) model, rotated to show the embedding in E6.
• The matter representations come in three copies (generations) of the 16 representation. The Yukawa coupling is 10H 16f 16f. This includes a right-handed neutrino.

It has been long known that the SO(10) model is free from all perturbative local anomalies, computable by Feynman diagrams. However, it only became clear in 2018 that the SO(10) model is also free from all nonperturbative global anomalies on non-spin manifolds — an important rule for confirming the consistency of SO(10) grand unified theory, with a Spin(10) gauge group and chiral fermions in the 16-dimensional spinor representations, defined on non-spin manifolds. (Wikipedia)

It was based on representations of the noncompact groups SO(3,1) or SL(2,C), so the spin foam faces (and hence the spin network edges) were labelled by positive real numbers as opposed to the half-integer labels of SU(2) spin networks. (Wikipedia)

In four spacetime dimensions, N = 8 supergravity, speculated by Stephen Hawking, is the most symmetric quantum field theory which involves gravity and a finite number of fields.

• It can be found from a dimensional reduction of 11D supergravity by making the size of seven (7) of the dimensions go to zero.

• It has eight (8) supersymmetries, which is the most any gravitational theory can have, since there are eight half-steps between spin 2 and spin −2. (The spin 2 graviton is the particle with the highest spin in this theory.)

• More supersymmetries would mean the particles would have superpartners with spins higher than 2.
• The only theories with spins higher than 2 which are consistent involve an infinite number of particles (such as String Theory and Higher-Spin Theories).
• Stephen Hawking in his Brief History of Time speculated that this theory could be the Theory of Everything.
• However, in later years this was abandoned in favour of string theory.
• The theory contains 1 graviton (spin 2), 8 gravitinos (spin 3/2), 28 vector bosons (spin 1), 56 fermions (spin 1/2), 70 scalar fields (spin 0) where we don’t distinguish particles with negative spin.
• These numbers are simple combinatorial numbers that come from Pascal’s Triangle and also the number of ways of writing n as a sum of 8 nonnegative cubes A173681.
• One reason why the theory was abandoned was that the 28 vector bosons which form an O(8) gauge group is too small to contain the standard model U(1) x SU(2) x SU(3) gauge group, which can only fit within the orthogonal group O(10).

There has been renewed interest in the 21st century, with the possibility that string theory may be finite. (Wikipedia)

There exist scenarios in which there could actually be more than 4D of spacetime. String theories require extra dimensions of spacetime for their mathematical consistency. These are situations where theories in two or three spacetime dimensions are no more useful.

In string theory, spacetime is 26-dimensional, while in superstring theory it is 10-dimensional, and in M-theory it is 11-dimensional.

This classification theorem identifies several infinite families of groups as well as 26 additional groups which do not fit into any family. (Wikipedia)

M Theory and/or Loop Quantum Gravity hold the promise of resolving the conflict between general relativity and quantum mechanics but lack experimental connections to predictability in physics.

• A connection is made to these and other theories vying for the title of a “Theory of Everything” by questioning the value of the traditional Planck unit reference point for the scales at which they operate.
• It also suggests a cosmological model which has acceleration as being fundamental.
• It provides for an intuitive understanding of the Standard Model and its relationship to particle masses and the structure of the atom.

The prediction of particle mass and lifetimes is a good indicator for its validity. (TOE - pdf)

We now place integers sequentially into the lattice with a simple rule: Each time a prime number is encountered, the spin or ‘wall preference’ is switched.

So, from the first cell, exit from 2’s left side. This sets the spin to left and the next cell is 3, a prime, so switches to right. 4 is not prime and continues right. 5 is prime, so switch to left and so on. There are twists and turns until 19 abuts 2. (HexSpin)

We would like to say that our present use of G2 structures (3-forms in 7D) is different from whatone can find in the literature on Kaluza–Klein compactifications of supergravity.

• We show that the resulting 4D theory is (Riemannian) General Relativity (GR) in Plebanski formulation, modulo corrections that are negligible for curvatures smaller than Planckian.
• Possibly the most interesting point of this construction is that the dimensionally reduced theory is GR with a non-zero cosmological constant, and the value of the cosmological constant is directly related to the size of . Realistic values of Λ correspond to of Planck size.

Also, in the supergravity context a 7D manifold with a G2 structure is used for compactifying the 11D supergravity down to 4D. In contrast, we compactify from 7D to 4D. (General relativity from three-forms in seven dimensions - pdf)

In particular, these theories include the compactification of eleven-dimensional supergravity on the seven-sphere S7, which gives rise to a four-dimensional theory with compact non-abelian gauge group SO(8) (11D Supergravity and Hidden Symmetries - pdf)

Straightforward extensions of the Standard Model with massive neutrinos need 7 more parameters (3 masses and 4 PMNS matrix parameters) for a total of 26 parameters. The neutrino parameter values are still uncertain. The 19 certain parameters are summarized here:

• The choice of free parameters is somewhat arbitrary. In the table above, gauge couplings are listed as free parameters, therefore with this choice the Weinberg angle is not a free parameter.
• Instead of fermion masses, dimensionless Yukawa couplings can be chosen as free parameters. For example, the electron mass depends on the Yukawa coupling of the electron to the Higgs field.
• The value of the vacuum energy (or more precisely, the renormalization scale used to calculate this energy) may also be treated as an additional free parameter.
• The renormalization scale may be identified with the Planck scale or fine-tuned to match the observed cosmological constant. However, both options are problematic.

As these theories tend to reproduce the entirety of current phenomena, the question of which theory is the right one, or at least the “best step” towards a Theory of Everything, can only be settled via experiments (Wikipedia)

In QFT this is currently done by manually adding an extra term to the field’s self-interaction, creating the famous Mexican Hat potential well.

• In QFT the scalar field generates four (4) Goldstone bosons.
• One (1) of the 4 turns into the Higgs boson. Unlike popularized, the Higgs itself does not give mass to particles, but represents the symmetry broken scalar field.
• The other three (3) Goldstone bosons are “absorbed” by the three (3) intermediate, electroweak bosons (W+, W-, Z), giving them an extra spin.

This (otherwise) plain and featureless “absorbtion” of the Goldstone modes in the EW field could be a reason why a complex, synergy-creating quality of the scalar field is largely unnoticed in QFT. Obviously this has the potential to become a new research challenge in physics. (TGMResearch)

A lot number of positive color-charges move from the positive charged particle toward the negative charged particles, and negative color-charges move from negative charged particle toward the positive charged particle and they combine in each other.

• According to CPH Theory, gravity is a currency among the objects. Consider the interaction between the earth and the moon: when a graviton reaches the earth, the other one moves toward the moon and pushes the earth toward the moon.
• Because as to maintain equality times - positive and negative color-charges, there is a fixed ratio between the mass and the number of gravitons surrounding.
• Also when a graviton reaches the moon, the other one moves toward the earth and pushes the moon toward the earth.-So earth (In fact everything) is bombarded by gravitons continuously.

Due to the fact that everything is made up of sub quantum energy, the classical concept of acceleration and relativistic Newton’s second law needs to be reviewed. (Gravity in Time space - pdf)

Renormalization is a collection of techniques in quantum field theory, statistical field theory, and the theory of self-similar geometric structures, that are used to treat infinities arising in calculated quantities by altering values of these quantities to compensate for effects of their self-interactions. (Wikipedia)

In this paper we have studied the renormalization of the QCD trace anomaly separately for the quark and gluon parts of the energy momentum tensor.

• While the renormalization of the total anomaly T = Tq + Tg is well understood in the literature [10], our analysis at the quark and gluon level has revealed some interesting new features. The bare and renormalized (Tq,g)α differ by finite operators, and this difference can be systematically computed order by order in αs.
• It is interesting to notice that, at one loop, the renormalized Tq gives the nf part of the beta function. However, this property no longer holds at two-loop, see (5.19).
• Besides, the partition of the total anomaly can be different if one uses other regularization schemes (see, e.g., the ‘gradient flow’ regularization [25]), and it is interesting to study their mutual relations.

We have also found that C¯q,g(µ) does not go to zero as µ → ∞ even in the chiral limit, contrary to what one would naively expect from the one-loop calculation (3.16). (Quark and gluon contributions to the QCD trace anomaly - pdf)

In quantum mechanics, the graviton is a hypothetical elementary particle that mediates the force of gravitation in the framework of quantum field theory. If it exists, the graviton must be massless and must have a spin of 2. This is because the source of gravitation is the stress-energy tensor, a second-rank tensor. This definition of graviton is not able to describe gravitational phenomena, so we need a new definition of graviton. (What is CPH Theory - pdf)

We study the anomalous scale symmetry breaking effects on the proton mass in QCD due to quantum fluctuations at ultraviolet scales.

• We confirm that a novel contribution naturally arises as a part of the proton mass, which we call the quantum anomalous energy (QAE). We discuss the QAE origins in both lattice and dimensional regularizations and demonstrate its role as a scheme-and-scale independent component in the mass decomposition.
• We further argue that QAE role in the proton mass resembles a dynamical Higgs mechanism, in which the anomalous scale symmetry breaking field generates mass scales through its vacuum condensate, as well as its static and dynamical responses to the valence quarks.
• We demonstrate some of our points in two simpler but closely related quantum field theories, namely the 1+1 dimensional non-linear sigma model in which QAE is non-perturbative and scheme-independent, and QED where the anomalous energy effect is perturbative calculable.

Dynamical response of the scalar Hamiltonian HS in the presence of the fermion , generating a contributionto the fermion mass The dotted line represents the dynamical Higgs particles h and the crossed circle denotes the scalar Hamiltonian linear in h. The coupling g between the Higgs field and the fermion is proportional to fermion mass. (Scale symmetry breaking - pdf)

A chiral phenomenon is one that is not identical to its mirror image (see the article on mathematical chirality). The spin of a particle may be used to define a handedness, or helicity, for that particle, which, in the case of a massless particle, is the same as chirality. A symmetry transformation between the two is called parity transformation. Invariance under parity transformation by a Dirac fermion is called chiral symmetry.

• For massless particles – photons, gluons, and (hypothetical) gravitons – chirality is the same as helicity; a given massless particle appears to spin in the same direction along its axis of motion regardless of point of view of the observer.
• For massive particles – such as electrons, quarks, and neutrinos – chirality and helicity must be distinguished: In the case of these particles, it is possible for an observer to change to a reference frame moving faster than the spinning particle, in which case the particle will then appear to move backwards, and its helicity (which may be thought of as “apparent chirality”) will be reversed. That is, helicity is a constant of motion, but it is not Lorentz invariant. Chirality is Lorentz invariant, but is not a constant of motion: a massive left-handed spinor, when propagating, will evolve into a right handed spinor over time, and vice versa.
• A massless particle moves with the speed of light, so no real observer (who must always travel at less than the speed of light) can be in any reference frame where the particle appears to reverse its relative direction of spin, meaning that all real observers see the same helicity. Because of this, the direction of spin of massless particles is not affected by a change of inertial reference frame (a Lorentz boost) in the direction of motion of the particle, and the sign of the projection (helicity) is fixed for all reference frames: The helicity of massless particles is a relativistic invariant (a quantity whose value is the same in all inertial reference frames) which always matches the massless particle’s chirality.

The discovery of neutrino oscillation implies that neutrinos have mass, so the photon is the only confirmed massless particle; gluons are expected to also be massless, although this has not been conclusively tested.[b] Hence, these are the only two particles now known for which helicity could be identical to chirality, and only the photon has been confirmed by measurement. All other observed particles.

The helicity of a particle is positive (“right-handed”) if the direction of its spin is the same as the direction of its motion. It is negative (“left-handed”) if the directions of spin and motion are opposite. So a standard clock, with its spin vector defined by the rotation of its hands, has left-handed helicity if tossed with its face directed forwards.

• Mathematically, helicity is the sign of the projection of the spin vector onto the momentum vector: “left” is negative, “right” is positive.have mass and thus may have different helicities in different reference frames.
• Chiral theories: Particle physicists have only observed or inferred left-chiral fermions and right-chiral antifermions engaging in the charged weak interaction.[1] In the case of the weak interaction, which can in principle engage with both left- and right-chiral fermions, only two left-handed fermions interact. Interactions involving right-handed or opposite-handed fermions have not been shown to occur, implying that the universe has a preference for left-handed chirality. This preferential treatment of one chiral realization over another violates parity, as first noted by Chien Shiung Wu in her famous experiment known as the Wu experiment. This is a striking observation, since parity is a symmetry that holds for all other fundamental interactions.
• Chirality for a Dirac fermion ψ is defined through the operator γ5, which has eigenvalues ±1; the eigenvalue’s sign is equal to the particle’s chirality: +1 for right-handed, −1 for left-handed. Any Dirac field can thus be projected into its left- or right-handed component by acting with the projection operators.
• The coupling of the charged weak interaction to fermions is proportional to the first projection operator, which is responsible for this interaction’s parity symmetry violation.
• A common source of confusion is due to conflating the γ5, chirality operator with the helicity operator. Since the helicity of massive particles is frame-dependent, it might seem that the same particle would interact with the weak force according to one frame of reference, but not another. The resolution to this paradox is that the chirality operator is equivalent to helicity for massless fields only, for which helicity is not frame-dependent. By contrast, for massive particles, chirality is not the same as helicity, or, alternatively, helicity is not Lorentz invariant, so there is no frame dependence of the weak interaction: a particle that couples to the weak force in one frame does so in every frame.
• A theory that is asymmetric with respect to chiralities is called a chiral theory, while a non-chiral (i.e., parity-symmetric) theory is sometimes called a vector theory. Many pieces of the Standard Model of physics are non-chiral, which is traceable to anomaly cancellation in chiral theories. Quantum chromodynamics is an example of a vector theory, since both chiralities of all quarks appear in the theory, and couple to gluons in the same way.
• The electroweak theory, developed in the mid 20th century, is an example of a chiral theory. Originally, it assumed that neutrinos were massless, and assumed the existence of only left-handed neutrinos and right-handed antineutrinos. After the observation of neutrino oscillations, which imply that neutrinos are massive (like all other fermions) the revised theories of the electroweak interaction now include both right- and left-handed neutrinos. However, it is still a chiral theory, as it does not respect parity symmetry.
• The exact nature of the neutrino is still unsettled and so the electroweak theories that have been proposed are somewhat different, but most accommodate the chirality of neutrinos in the same way as was already done for all other fermions.

By Chiral symmetry the Vector gauge theories with massless Dirac fermion fields ψ exhibit chiral symmetry, i.e., rotating the left-handed and the right-handed components independently makes no difference to the theory. We can write this as the action of rotation on the fields:

Massive fermions do not exhibit chiral symmetry, as the mass term in the Lagrangian, mψψ, breaks chiral symmetry explicitly.

• Spontaneous chiral symmetry breaking may also occur in some theories, as it most notably does in quantum chromodynamics.
• The chiral symmetry transformation can be divided into a component that treats the left-handed and the right-handed parts equally, known as vector symmetry, and a component that actually treats them differently, known as axial symmetry.[2] (cf. Current algebra.) A scalar field model encoding chiral symmetry and its breaking is the chiral model.
• The most common application is expressed as equal treatment of clockwise and counter-clockwise rotations from a fixed frame of reference.

The general principle is often referred to by the name chiral symmetry. The rule is absolutely valid in the classical mechanics of Newton and Einstein, but results from quantum mechanical experiments show a difference in the behavior of left-chiral versus right-chiral subatomic particles. (Wikipedia)

Summary of various critical points in the context of superpotential observed in this paper first : Gauge symmetry, supersymmetry, vacuum expectation value of field, superpotential and cosmological constants.

• For SO(3)+ × SO(5)+ case, one can check it by the change of variable of SO(5)+×SO(3)+ case, s → −3s/5 that corresponding potential of SO(3)+×SO(5)+ is obtained while by change of variable, s → −s/7, the potential of SO(1)+ × SO(7)+ can be found from SO(7)+ × SO(1)+ case.
• Although the corresponding superpotential of these two cases may be different from the original ones, the scalar potentials are the same.
• It is natural to ask whether 11-dimensional embedding of various vacua we have considered of non-compact and non-semi-simple gauged supergravity can be obtained.
• In a recent paper [46], the metric on the 7-dimensional internal space and domain wall in 11-dimensions was found. However, they did not provide an ansatz for an 11-dimensional three-form gauge field.-It would be interesting to study the geometric superpotential, 11-dimensional analog of superpotentialwe have obtained.

We expect that the nontrivial r-dependence of vevs makes Einstein-Maxwell equations consistent not only at the critical points but also along the supersymmetric RG flow connecting two critical points. (N = 8 Supergravity: Part I - pdf)

Proceeding, the number line begins to coil upon itself; 20 lands on 2’s cell, 21 on 3’s cell. Prime number 23 sends the number line left to form the fourth (4th) hexagon, purple. As it is not a twin, the clockwise progression (rotation) reverses itself. Twin primes 29 and 31 define the fifth (5th) hexagon, cyan. Finally, 37, again not a twin, reverses the rotation of the system, so 47 can define the yellow hexagon (HexSpin).

There are 14 + 7 × 16 = 126 integral octonions. It was shown that the set of transformations which preserve the octonion algebra of the root system of E7 is the adjoint Chevalley group G2(2). It is possible to decompose these 126 imaginary octonions into eighteen (18) sets of seven (7) imaginary octonionic units that can be transformed to each other by the finite subgroup of matrices. These lead to 18 sets of 7, which we see in figures ​figure-77 and ​figure-88. (M-theory, Black Holes and Cosmology - pdf)

You likely noticed I began with 2 rather than 1 or 0 when I first constructed the hexagon. Why? Because they do not fit inside — they stick off the hexagon like a tail. Perhaps that’s where they belong. However, if one makes a significant and interesting assumption, then 1 and 0 fall in their logical locations – in the 1 and 0 cells, respectively. _(HexSpin)

The electroweak force is believed to have separated into the electromagnetic and weak forces during the quark epoch of the early universe.

• In physical cosmology, the quark epoch was the period in the evolution of the early universe when the fundamental interactions of gravitation, electromagnetism, the strong interaction and the weak interaction had taken their present forms, but the temperature of the universe was still too high to allow quarks to bind together to form hadrons.
• The quark epoch began approximately 10−¹² seconds after the Big Bang, when the preceding electroweak epoch ended as the electroweak interaction separated into the weak interaction and electromagnetism.
• During the quark epoch, the universe was filled with a dense, hot quark–gluon plasma, containing quarks, leptons and their antiparticles.
• Collisions between particles were too energetic to allow quarks to combine into mesons or baryons.

The quark epoch ended when the universe was about 10−⁶ seconds old, when the average energy of particle interactions had fallen below the binding energy of hadrons. The following period, when quarks became confined within hadrons, is known as the hadron epoch. (Wikipedia)

The number 28, aside from being triangular wave of perfect pyramid, is the sum of the first 5 primes and the sum of the first 7 natural numbers.

The intervention of the Golden Ratio can be seen as a way to enter the quantum world, the world of subtle vibrations, in which we observe increasing energy levels as we move to smaller and smaller scales. El Nachie has proposed a way of calculating the fractal dimension of quantum space-time. The resulting value (Figure 7) suggests that the quantum world is composed of an infinite number or scaled copies of our ordinary 4-dimensional space-time.

Setting k=0 one obtains the classical dimensions of heterotic superstring theory, namely 26, 16, 10, 6 and 4, as well as the constant of super-symmetric (αgs=26) and non super-symmetric (αg=42) unification of all fundamental forces. As we have seen in section 2, the above is a Fibonacci-like sequence with a very concise geometrical interpetation related to numbers 5, 11 and φ. (Phi in Particle Physics)

Several aspects of torsion in string-inspired cosmologies are reviewed. In particular, its connection with fundamental, string-model independent, axion fields associated with the massless gravitational multiplet of the string are discussed.

• It is argued in favour of the role of primordial gravitational anomalies coupled to such axions in inducing inflation of a type encountered in the Running-Vacuum-Model (RVM) cosmological framework, without fundamental inflaton fields.
• The gravitational-anomaly terms owe their existence to the Green–Schwarz mechanism for the (extra-dimensional) anomaly cancellation, and may be non-trivial in such theories in the presence of (primordial) gravitational waves at early stages of the four (4) dimensional string universe (after compactification).
• The paper also discusses how the torsion-induced stringy axions can acquire a mass in the post inflationary era, due to non-perturbative effects, thus having the potential to play the role of (a component of) dark matter in such models.

Finally, the current-era phenomenology of this model is briefly described with emphasis placed on the possibility of alleviating tensions observed in the current-era cosmological data. A brief phenomenological comparison with other cosmological models in contorted geometries is also made. (Torsion in String Cosmologies - pdf)

In Fuller’s synergetic geometry, symmetry breaking is modeled as 4 sub-tetra’s, of which 3 form a tetrahelix and the 4th. “gets lost”.

• In the present approach, intermediate (symmetry broken) states are proposed to be latent in the allready extended cube-octahedral matrix, and are actualized or mapped through the trefoil operator. In terms of tetra-logic, it is the invisible, confining icosa-dodeca matrix, acting upon the visible, deconfined cube-octahedral matrix.
• Further, the author proposes a more natural and versatile QFT symmetry breaking mechanism, based on well determined scalar field excitations.
• In QFT, the potential well is based on excitation modes, not on actual excitations, which is a reason why the proposed synergetic action gets obscured.
• A new type of symmetry breaking is proposed, based on a synchronized path integral.

The latter solves into a Goldstone oscillation and a vacuum expectation value (VEV), among other unique properties. The scalar field’s self-interaction is a Golden Ratio scale-invariant group effect, such as geometrically registered by the icosa-dodeca matrix. (TGMResearch)

If right-handed neutrinos exist but do not have a Majorana mass, the neutrinos would instead behave as three (3) Dirac fermions and their antiparticles with masses coming directly from the Higgs interaction, like the other Standard Model fermions.

• The seesaw mechanism is appealing because it would naturally explain why the observed neutrino masses are so small. However, if the neutrinos are Majorana then they violate the conservation of lepton number and even of B − L.
• Neutrinoless double beta decay has not (yet) been observed,[3] but if it does exist, it can be viewed as two ordinary beta decay events whose resultant antineutrinos immediately annihilate each other, and is only possible if neutrinos are their own antiparticles.[4]
• The high-energy analog of the neutrinoless double beta decay process is the production of same-sign charged lepton pairs in hadron colliders;[5] it is being searched for by both the ATLAS and CMS experiments at the Large Hadron Collider.
• In theories based on left–right symmetry, there is a deep connection between these processes.[6] In the currently most-favored explanation of the smallness of neutrino mass, the seesaw mechanism, the neutrino is “naturally” a Majorana fermion.

Majorana fermions cannot possess intrinsic electric or magnetic moments, only toroidal moments.[7][8][9] Such minimal interaction with electromagnetic fields makes them potential candidates for cold dark matter. (Wikipedia)

Beside the operator proof, here we also provide a diagrammatic argument of the above derivation, using the QED in background field in Sec. 5 as an example.

• We show that: taking mass derivatives in one-loop Feynman diagrams Fig. 4 for δEN will exactly produce the one-loop Feynman diagrams for insertion of 4HS.
• The mass derivative has four (4) origins: the explicit mass dependency of the electron propagator, the implicit mass dependency in the energy level EN, the mass dependencies in renormalization constants δm and Z3 − 1, and the implicit mass dependency in the wave function uN.
• The mass derivative of the fermion propagator 1iγ·D−m simply reduces to mψψ¯ operator insertion in the internal electron line as shown in Fig. 7.
• The mass dependency in EN will lead to the wave function renormalization in external legs. The mass dependencies in renormalization constants δm and Z3 −1 will exactly lead to the anomalous energy contribution.

Finally, the mass derivative of the external wave function uN is more complicated, which is shown the remaining diagrams where the mψψ¯ are inserted at external legs. (Scale symmetry breaking - pdf)

The reduction of pure gravity from eleven dimensions down to D = 4 dimensions yields a gravitational theory with seven (7) abelian vector fields Aµn, n = 1,...,7, and 1+27=28 scalar fields, parametrizing the coset space GL(7)/SO(7). The dimensional reduction of the antisymmetric 3-form to D = 4 dimensions gives rise to one 3-form field, seven 2-form fields. (11D Supergravity and Hidden Symmetries - pdf)

The matrix elements of this quark/gluon decomposition of the QCD trace anomaly allow us to derive the QCD constraints on the hadron’s gravitational form factors, in particular, on the twist-four gravitational form factor, Cq,g.

• Using the three-loop quark/gluon trace anomaly formulas, we calculate the forward (zero momentum transfer) value of the twist-four gravitational form factor C¯q,g at the next-to-next-to-leading-order (NNLO) accuracy.
• We present quantitative results for nucleon as well as for pion, leading to a model-independent determination of the forward value of C¯q,g.

We find quite different pattern in the obtained results between the nucleon and the pion. (Twist-four gravitational - pdf)

The Standard Model of particle physics contains only renormalizable operators, but the interactions of general relativity become nonrenormalizable operators if one attempts to construct a field theory of quantum gravity in the most straightforward manner (treating the metric in the Einstein–Hilbert Lagrangian as a perturbation about the Minkowski metric), suggesting that perturbation theory is not satisfactory in application to quantum gravity.

• However, in an effective field theory, “renormalizability” is, strictly speaking, a misnomer. In nonrenormalizable effective field theory, terms in the Lagrangian do multiply to infinity, but have coefficients suppressed by ever-more-extreme inverse powers of the energy cutoff.
• If the cutoff is a real, physical quantity—that is, if the theory is only an effective description of physics up to some maximum energy or minimum distance scale—then these additional terms could represent real physical interactions.
• Assuming that the dimensionless constants in the theory do not get too large, one can group calculations by inverse powers of the cutoff, and extract approximate predictions to finite order in the cutoff that still have a finite number of free parameters. It can even be useful to renormalize these “nonrenormalizable” interactions.
• Nonrenormalizable interactions in effective field theories rapidly become weaker as the energy scale becomes much smaller than the cutoff. The classic example is the Fermi theory of the weak nuclear force, a nonrenormalizable effective theory whose cutoff is comparable to the mass of the W particle.

It may be that any others that may exist at the GUT or Planck scale simply become too weak to detect in the realm we can observe, with one exception: gravity, whose exceedingly weak interaction is magnified by the presence of the enormous masses of stars and planets. (Wikipedia)

Moreover, it is shown that the constraints imposed by the RG invariance of (1.1) allow to determine the power series in αs for ZF as well as ZC in the MS-like schemes, completely from the perturbative expansions of β(g) and γm(g), which are now known to five-loop order [43–48] in the literature.

• Therefore, six renormalization constants ZT,ZL, Zψ, ZQ, ZF and ZC among ten constants arising in (2.3) (2.6) are available to a certain accuracy beyond two-loop order inthe MS-like schemes, and they take the form, (2.8) in the d = 4 − 2 spacetime dimensions with X = T, L, ψ, Q, F, and C; here, aX, bX, cX.…, are the constants given as the power series in αs, and δX,X0 denotes the Kronecker symbol. However, ZM, ZS, ZK and ZB still remain unknown.
• It is shown [8] that these four renormalization constants can be determined to the accuracy same as the renormalization constants (2.8), by invoking that they should also obey the form (2.8) with X = M, S, K, B, and that the r.h.s. of the formulas (2.3), (2.4) are, in total, UV-finite.

Thus, all the renormalization constants in (2.3)–(2.6) are determined up to the three-loop accuracy. (Twist-four gravitational - pdf)

The Gell-Mann matrices, developed by Murray Gell-Mann, are a set of eight linearly independent 3×3 traceless Hermitian matrices used in the study of the strong interaction in particle physics. They span the Lie algebra of the SU(3) group in the defining representation.

Moreover this model represents Quark-Gluon Plasma, with all of the fundamental forces in the early stage after Big Bang. (Youtube)

The four (4) faces of our pyramid additively cascade 32 four-times triangular numbers

• These include Fibo1-3 equivalent 112 (rooted in T7 = 28; 28 x 4 = 112),
• which creates a pyramidion or capstone in our model, and 2112 (rooted in T32 = 528; 528 x 4 = 2112),
• which is the index number of the 1000th prime within our domain,
• and equals the total number of ‘elements’ used to construct the pyramid.

Note that 4 x 32 = 128 is the perimeter of the square base which has an area of 32^2 = 1024 = 2^10). (PrimesDemystified)

Back in 1982, a very nice paper by Kugo and Townsend, Supersymmetry and the Division Algebras, explained some of this, ending up with some comments on the relation of octonions to d=10 super Yang-Mills and d=11 super-gravity.

• Baez and Huerta in 2009 wrote the very clear Division Algebras and Supersymmetry I, which explains how the existence of supersymmetry relies on algebraic identities that follow from the existence of the division algebras. Kugo-Townsend don’t mention string theory at all, and Baez-Huerta refers to superstrings just in passing, only really discussing supersymmetric QFT.
• There’s also Division Algebras and Supersymmetry II by Baez and Huerta from last year, with intriguing speculation about Lie n-algebras and what these might have to do with relations between octonions and 10 and 11 dimensional supergravity. For a nice expository paper about this stuff, see their An Invitation to Higher Gauge Theory.

The headline argument is that octonions are important and interesting because they’re The Strangest Numbers in String Theory, even though they play only a minor role in the subject. (math.columbia.edu)

SU(5) fermions of standard model in 5+10 representations. The sterile neutrino singlet’s 1 representation is omitted. Neutral bosons are omitted, but would occupy diagonal entries in complex superpositions. X and Y bosons as shown are the opposite of the conventional definition

The Lie algebra E6 of the D4-D5-E6-E7-E8 VoDou Physics model can be represented in terms of 3 copies of the 26-dimensional traceless subalgebra J3(O)o of the 27-dimensional Jordan algebra J3(O) by using the fibration E6 / F4 of 78-dimensional E6 over 52-dimensional F4 and the structure of F4 as doubled J3(O)o based on the 26-dimensional representation of F4. (Tony’s Home)

This chapter is intended to provide a brief description of some important issues regarding quark masses, flavor mixing and CP-violation. A comparison between the salient features of quark and lepton flavor mixing structures is also made.

• The SM contains thirteen free flavor parameters in its electroweak sector: three charged-lepton masses,six quark masses, three quark flavor mixing angles and one CP-violating phase.
• Since the three neutrinos must be massive beyond the SM, one has to introduce seven (or nine) extra free parameters to describe their flavor properties: three neutrino masses, three lepton flavor mixing angles and one (or three) CP-violating phase(s), corresponding to their Dirac (or Majorana) nature a
• The 3x3 lepton vs quark mixing matrices appearing in the weak charged-current interactions are referred to, respectively, as the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix Uand the Cabibbo-Kobayashi-Maskawa (CKM) matrix V which all the fermion fields are the mass eigenstates.
• By convention, U and V are defined to be associated with W− and W+, respectively. Note that V is unitary as dictated by the SM itself, but whether U is unitary or not depends on the mechanism responsible for the origin of neutrino masses.
• The charged leptons and quarks with the same electriccharges all have the normal mass hierarchies (namely, me ≪ mµ ≪ mτ, mu ≪ mc ≪ mt and md ≪ ms ≪ m. Yet it remains unclear whether the three neutrinos also have a normal mass ordering (m1 < m2 < m3) or not. Now that m1 < m2 has been fixed from the solar neutrino oscillations, the only likely “abnormal” mass ordering is m3 < m1 < m2
• The neutrino mass ordering is one of the central concerns in flavor physics, and it will be determined in the foreseeable future with the help of either an accelerator-based neutrino oscillation experiment or a reactor-based antineutrino oscillation experiment, or both of them. Up to now the moduli of nine elements of the CKM matrix V have been determined from current experimental data to a good degree of accuracy.

Here our focus is on the five (5) parameters of strong and weak CP violation. In the quark sector, the strong CP-violating phase θ remains unknown, but the weak CP-violating phase δq has been determined to a good degree of accuracy. In the lepton sector, however, none of the CP-violating phases has been measured. (Quark Mass Hierarchy and Flavor Mixing Puzzles - pdf)

Muons are about 200 times heavier than the electron. The larger mass makes them unstable. Muons exist for only about two microseconds—or two-millionths of a second—before they decay. Electrons live forever. The tau; elementary subatomic particle is similar to the electron but 3,477 times heavier. Like the electron and the muon, the tau is an electrically charged member of the lepton family of subatomic particles; the tau is negatively charged, while its antiparticle is positively charged. (ResearchGate)

In principle, there is one further parameter in the Standard Model; the Lagrangian of QCD can contain a phase that would lead to CP violation in the strong interaction.

• Experimentally, this strong CP phase is known to be extremely small, θCP ≃ 0, and is usually taken to be zero.
• The theoretical and experimental pillars of the Standard Model:
  • the twelve (12) fermions (or perhaps more correctly the twelve Yukawa couplings to the Higgs field), mν1, mν2, mν3, me, mµ, mτ, md, ms, mb, mu, mc, and mt ;
  • the three (3) coupling constants describing the strengths of the gauge interactions, α, GF and αS, or equivalently g′, gW and gS;
  • the two (2) Higgs parameters describing the Higgs potential, µ and λ, or equivalently its vacuum expectation value and the mass of the Higgs boson, v and mH; and
  • the eight (8) mixing angles of the PMNS and CKM matrices, which can be parameterised by θ12, θ13, θ23, δ, and λ, A, ρ, η.
  • in principle, there is one (1) further parameter in the Standard Model; the Lagrangian of QCD can contain a phase that would lead to CP violation in the strong interaction. Experimentally, this strong CP phase is known to be extremely small, θCP ≃ 0, and is usually taken to be zero.
• If θCP is counted, then the Standard Model has 12+3+2+8+1=26 free parameters.
• The relatively large number of free parameters is symptomatic of the Standard Model being just that; a model where the parameters are chosen to match the observations, rather than coming from a higher theoretical principle.
• Putting aside θCP, of the 25 SM parameters: 14 are associated with the Higgs field, eight (8) with theflavour sector and only three (3) with the gauge interactions.

Likewise, the coupling constants of the three gauge interactions are of a similar order of magnitude, hinting that they might be different low-energy manifestations of a Grand Unified Theory (GUT) of the forces. (Modern Particle Physics P.500 - pdf)

The Standard Model presently recognizes seventeen distinct particles—twelve fermions and five bosons. As a consequence of flavor and color combinations and antimatter, the fermions and bosons are known to have 48 and 13 variations, respectively.[ (Wikipedia)

The 13 circles of the Metatron’s cube can be seen as a diagonal axis projection of a 3-dimensional cube, as 8 corner spheres and 6 face-centered spheres. Two spheres are projected into the center from a 3-fold symmetry axis. The face-centered points represent an octahedron. Combined these 14 points represent the face-centered cubic lattice cell. (Wikipedia)

We analyze a simple extension of the Standard Model (SM) with a dark sector composed of a scalar and a fermion, both singlets under the SM gauge group but charged under a dark sector symmetry group.

• Sterile neutrinos, which are singlets under both groups, mediate the interactions between the dark sectorand the SM particles, and generate masses for the active neutrinos via the seesawmechanism.
• We explore the parameter space region where the observed Dark Matter relic abundance is determined by the annihilation into sterile neutrinos, both for fermion and scalar Dark Matter particles. The scalar Dark Matter case provides an interesting alternative to the usual Higgs portal scenario.

We also study the constraints from direct Dark Matter searches and the prospects for indirect detectionvia sterile neutrino decays to leptons, which may be able to rule out Dark Matter masses below and around 100 GeV. (Sterile Neutrino portal to Dark Matter II - pdf)

If the angle was 0, the U(1) group would remain unbroken and there would be no mixing with the SU(2) group. This would lead to a single massless boson and 3 remaining massless bosons: Ws and photon. On the other hand, if the angle was 90, the SU(2) group would remain unbroken and there would be no mixing with the U(1) group. This would lead to a single massive boson and 3 remaining massless bosons: Ws and photon. (PhysicsForums)

The standard model involves particle symmetry and the mechanism of its breaking. Modern cosmology is based on inflationary models with baryosynthesis and dark matter/energy, which involves physics beyond the standard model. Studies of the physical basis of modern cosmology combine direct searches for new physics at accelerators with its indirect non-accelerator probes, in which cosmological consequences of particle models play an important role. The cosmological reflection of particle symmetry and the mechanisms of its breaking are the subject of the present review. (MDPI)

When the standard three-neutrino theory is considered, the matrix is 3×3. If only two neutrinos are considered, a 2×2 matrix is used. If one or more sterile neutrinos are added, it is 4×4 or larger. (Wikipedia)

There are four (4) main features of QCD confinement, which appear to parallel the development of the previous section.

• These parallels are best specified with reference to baryons, as follows: Establish any closed surface over a baryon source density P. Then:
• While gluons may flow within the closed surface across various open surfaces, there can be no net flux of gluons in to or out of any closed surface.
• This may possibly be represented by = 0 dG , and the invariance of F → F’ = F under the transformation F → F’= F − dG .
• While quarks may flow within the closed surface across various open surfaces, there can be no net flux of individual quarks in to or out of any closed surface.
• This may possibly be represented by the invariance of P → P’= P under the transformation F → F’= F − dG .
• While there can be no net flux of individual quarks in to or out of any closed surface, there can indeed be a net flux of quark-antiquark pairs in to or out of any closed surface.
• The antiquark cancels the quark, thereby averting a net flux, and in this way, quarks do flow in to or out of the closed surface, but only paired with antiquarks, as mesons.
• This may possibly be represented as 02 ≠ i gG .
• It does not matter how hard or in what manner one “smashes” a baryon, one can still never extract a net flux of quarks or a net flux of gluons, but only a large number of meson jets.
• This may be possibly represented by the fact that in all of the foregoing, the volume and surfaceintegrals apply to any and all closed surfaces.
• One can choose a small closed surface, a large closed surface, a spherical closed surface, an oblong closed surface, and indeed, a closed surface of any shape and size. The choice of closed surface does not matter.
• These mathematical rules for what does and does not flow across any closed surface, in fact, thereby impose very stringent dynamical constraints on the behaviors of these non-Abelian magnetic sources: No matter what flows across various open surfaces, they may never be a net flux of anything across any closedsurface. The only exceptions, which may flow across a closed surface, are physical entities represented by.

Where is the author going with this?

• The magnetic three-form P, and its associated third-rank antisymmetric tensorσµν P , has allthe characteristics of a baryon current density.
• These σµν P , among their other properties, are naturally occurring sources containing exactlythree fermions. These constituent fermions are most-sensibly interpreted as quarks.
• The surface symmetri F → F’ = F under the transformation F → F’= F − dG , tells us that there is no net flow of gluons across any closed surface over the baryon density.
• The volume symmetry
  P → P’= P under F → F’= F − dG , tells us that there is no net flow of quarks across any closed surface over the baryon density.
• The physical entities represented by 2 igG , when examined in further detail, have thecharacteristics of mesons.

It tells us that mesons are the only entities which may flow across any closedsurface of the baryon density. (Lab Notes)

Only more accurate analysis on the involved spectra and on the relative brightness of the two rings, and mainly the discovery of other double rings systems, could be used to finally choose which among these two interpretations is more likely to hold. As to using Klein bottle holes to check the physical existence of other universes, it appears just a matter of time to find a double truncated spiral blurred enough to clearly show a connection with other universes. (Observing another Universe - pdf)

The GUT group E6 contains SO(10), but models based upon it are significantly more complicated. The primary reason for studying E6 models comes from E8 × E8 heterotic string theory. (Wikipedia)

While gravitons are presumed to be massless, they would still carry energy, as does any other quantum particle. Photon energy and gluon energy are also carried by massless particles.

• It is unclear which variables might determine graviton energy, the amount of energy carried by a single graviton.
• Alternatively, if gravitons are massive at all, the analysis of gravitational waves yielded a new upper bound on the mass of gravitons.
• The graviton’s Compton wavelength is at least 1.6×10^16 m, or about 1.6 light-years, corresponding to a graviton mass of no more than 7.7×10−23 eV/c2.[22]
• This relation between wavelength and mass-energy is calculated with the Planck–Einstein relation, the same formula that relates electromagnetic wavelength to photon energy.
• However, if gravitons are the quanta of gravitational waves, then the relation between wavelength and corresponding particle energy is fundamentally different for gravitons than for photons, since the Compton wavelength of the graviton is not equal to the gravitational-wave wavelength.
• Instead, the lower-bound graviton Compton wavelength is about 9×109 times greater than the gravitational wavelength for the GW170104 event, which was ~ 1,700 km. The report[22] did not elaborate on the source of this ratio.

It is possible that gravitons are not the quanta of gravitational waves, or that the two phenomena are related in a different way. (Wikipedia)

As Penrose points out, proton decay is a possibility contemplated in various speculative extensions of the Standard Model, but it has never been observed. Moreover, all electrons must also decay, or lose their charge and/or mass, and no conventional speculations allow for this.

In his Nobel Prize Lecture video, Roger Penrose moderated his previous requirement for no mass, beginning at 26:30 in the video, allowing some mass particles to be present as long as the amounts are insignificant with nearly all of their energy being kinetic, and in a conformal geometry dominated by photons. (Wikipedia)

The Prime Spiral Sieve possesses remarkable structural and numeric symmetries.

• For starters, the intervals between the prime roots (and every subsequent row or rotation of the sieve) are perfectly balanced, with a period 8 difference sequence of: {6, 4, 2, 4, 2, 4, 6, 2}. The entire domain can thus be defined as 1 {+6 +4 +2 +4 +2 +4 +6 +2} {repeat … ∞}.
• As we’ve already suggested, the number 30 figures large in our modulo 30 domain. The Prime Spiral Sieve is Archimedean in that the separation distance between turns equals 30, ad infinitum. The first two rotations increment as follows:
• Interestingly, the sum of the 2nd rotation = 360, the product of the first three primorials, 2 x 6 x 30 = 360, and when you multiply the first five Fibonacci numbers in sequence, you produce 1, 2, 6 and 30? And, speaking of the Fibonacci number sequence, there is symmetry mirroring the above in the relationship between the terminating digits of Fibonacci numbers and their index numbers equating to members of the array populating the Prime Spiral Sieve:
• Remarkably, the sequence of Fibonacci terminating digits indexed to our domain (natural numbers not divisible by 2, 3 or 5), 13,937,179 (see graphic, above), is a prime number and a member of a twin prime pair (with 13,937,177). In case you’re wondering, 13,937,179 is not a reversible prime (as the reversal is a semi-prime: 9,461 x 10,271 = 97,173,931). However, given all the repunits that follow, we take note that both of the reversal’s factors are congruent to 11 (mod 30 & 90). [Note: Repunits are abbreviated Rn, where n designates the number of unit 1’s. Thus 1 is R1 and 11 is R2.]
• Perhaps most remarkable of all, 13,937,179 when added to its reversal 97,173,931 = 111,111,110 (in strict digital root terms, the sum is 11,111,111, or R8) and the entire repeating (and palindromic) Fibo sequence end-to-end (equivalent to two rotations around the sieve) gives you this palindromic equivalency: 1,393,717,997,173,931 ≌ 11,111,111 (mod 111,111,110)… (and interestingly, 11,111,111 * 111,111,110 = 123456776543210).
• Another point of interest: the terminating digits of the first 8 Fibonacci numbers indexed to our domain (13937179) contain two each 1’s, 3’s, 7’s, and 9’s. This is also true of the terminating digits of the first eight members of our domain (17137939).
• Echoing the Fibonacci patterns just described, the terminating digits of the prime roots (17,137,939), when added to their reversal (93,973,171) = 111,111,110. [And note that 111,111,111 * 111,111,110 = 12345678876543210.].
• Yet another related dimension of symmetry: The terminating digits of the prime root angles (24,264,868; see illustration of Prime Spiral Sieve) when added to their reversal (86,846,242) = 111,111,110, not to mention this sequence possesses symmetries that dovetail perfectly with the prime root and Fibo sequences.

And when you combine the terminating digit symmetries described above, capturing three (3) rotations around the sieve in their actual sequences, you produce the ultimate combinatorial symmetry. (PrimesDemystified)

Here is an elegant model to define the elementary particles of the Standard Model in Physics.

• The black spheres are the bosons, the green ones leptons and the rest of the colored ones Murray Gell-Mann’s quarks (red for Generation I, blue for II and orange for III).
• Higgs Boson (aka the God particle) that does not have charge is the vertex between the matter and anti-matter particles.
• The z-boson and its counterpart would lie in the centroids of the tetrahedrons created by folding the triangles to meet up at the Higgs particle.

The next step is to re-gigg the model to account for the collisions and annihilations. Gluons and Photons that don’t have mass are not in the model, but will be the consequences of the interactions. (Hypercomplex-Math)

In physical cosmology, the baryon asymmetry problem, also known as the matter asymmetry problem or the matter–antimatter asymmetry problem,[1][2] is the observed imbalance in baryonic matter (the type of matter experienced in everyday life) and antibaryonic matter in the observable universe.

• Neither the standard model of particle physics nor the theory of general relativity provides a known explanation for why this should be so, and it is a natural assumption that the universe is neutral with all conserved charges.[3]
• The Big Bang should have produced equal amounts of matter and antimatter. Since this does not seem to have been the case, it is likely some physical laws must have acted differently or did not exist for matter and/or antimatter.

Several competing hypotheses exist to explain the imbalance of matter and antimatter that resulted in baryogenesis. However, there is as of yet no consensus theory to explain the phenomenon, which has been described as “one of the great mysteries in physics“. (Wikipedia)

Consider a (purple) world-line String of one World of the MacroSpace of Many-Worlds and its interactions with another (gold) world-line World String, from the point of view of one point of the (purple) World String, seen so close-up that you don’t see in the diagram that the (purple) and (gold) World Strings are both really closed strings when seen at very large scale:

• massless spin-2 Gravitons travel along the (red) MacroSpace light-cones to interact with the intersection points of those (red) light-cones with the (gold) World String;
• scalar Dilatons, with effectively real mass, travel within the (yellow) MacroSpace light-cone time-like interior to interact with the intersection region of the (yellow) light-cone time-like interior region with the (gold) World String; and
• Tachyons, with imaginary mass, travel within the (cyan) MacroSpace light-cone space-like exterior to interact with the intersection points of the (cyan) light-cone space-like exterior region with the (gold) World String.
• Metod Saniga, inphysics/0012033 D4-D5-E6-E7-E8 VoDou Physics Model: It is a well-known fact that on a generic cubic surface, K3, the lines are seen to form three (3) separate groups.
• The first two groups, each comprising six (6)lines, are known as Schlafli’s double-six. The third group consists of fifteen lines. The basics of the algebra can simply be expressed as 27 = 12 + 15.

Note that Gravity may not propagate in the 26 dimensions of the MacroSpace of the Many-Worlds in exactly the same way as it propagates in our 4-dimensional physical SpaceTime. (Tony Smith’s)

Supersymmetry predicts that each of the particles in the Standard Model has a partner with a spin that differs by half of a unit.

• So bosons are accompanied by fermions and vice versa.
• Linked to their differences in spin are differences in their collective properties.
• Fermions are very standoffish; every one must be in a different state.
• On the other hand, bosons are very clannish; they prefer to be in the same state.

Fermions and bosons seem as different as could be, yet supersymmetry brings the two types together.

Each of the 3 Octonionic dimenisons of J3(O)o having the following physical interpretation:

• 4-dimensional physical spacetime plus 4-dimensional internal symmetry space;
• 8 first-generation fermion particles; 8 first-generation fermion anti-particles.

Thus the 26 dimensions stand as the degrees of freedom of the Worlds of the Many-Worlds. (Tony’s Web Book - pdf (800MB Size)).

In the Standard Model, elementary particles are manifestations of three “symmetry groups” — essentially, ways of interchanging subsets of the particles that leave the equations unchanged.

• These three (3) symmetry groups, SU(3), SU(2) and U(1), correspond to the strong, weak and electromagnetic forces, respectively, and they “act” on six types of quarks, two types of leptons, plus their anti-particles, with each type of particle coming in three copies, or “generations,” that are identical except for their masses.
• The fourth fundamental force, gravity, is described separately, and incompatibly, by Einstein’s general theory of relativity, which casts it as curves in the geometry of space-time.

Note that both quarks and leptons exist in three distinct sets. Each set of quark and lepton charge types is called a generation of matter (charges +2/3, -1/3, 0, and -1 as you go down each generation). The generations are organized by increasing mass.

Wave functions of the electron in a hydrogen atom at different energy levels. Quantum mechanics cannot predict the exact location of a particle in space. The brighter areas represent a higher probability of finding the electron (Wikipedia).

1729th decimal digit holds significance in the decimal representation of the transcendental number e. From 1729th digit you can get the first occurrence of all ten digits consecutively and they are 0719425863. (Ramanujan taxicab 1729 - pdf)

Once a black hole has formed, it can continue to grow by absorbing additional matter. Any black hole will continually absorb gas and interstellar dust from its surroundings. This growth process is one possible way through which some supermassive black holes may have been formed (Wikipedia)

Wave–particle duality is the concept in quantum mechanics that quantum entities exhibit particle or wave properties according to the experimental circumstances.[1]: 59  It expresses the inability of the classical concepts such as particle or wave to fully describe the behavior of quantum objects.

During the 19th and early 20th centuries, light was found to behave as a wave, and then later discovered to have a particulate character, whereas electrons were found to act as particles, and then later discovered to have wavelike aspects. The concept of duality arose to name these contradictions. (Wikipedia)

Dark energy is one of the greatest mysteries in science today.

• We know very little about it, other than it is invisible, it fills the whole universe, and it pushes galaxies away from each other. This is making our cosmos expand at an accelerated rate. But what is it?
• One of the simplest explanations is that it is a cosmological constant – a result of the energy of empty space itself – an idea introduced by Albert Einstein.

Many physicists aren’t satisfied with this explanation, though. They want a more fundamental description of its nature. Is it some new type of energy field or exotic fluid? (The Conversation).

Discussing both open and closed bosonic strings, Soo-Jong Rey, in his paper Heterotic M(atrix) Strings and Their Interactions - pdf, says: We would like to conclude with a highly speculative remark on a possible:

• It is well-known that The regularizedone-loop effective action of d-dimensional Yang-Mills theory. For d=26, the gauge kinetic term does not receive radiative correction at all.
• We expect that this non-renormalization remains the same even after dimensional reductions. One may wonder if it is possible to construct for bosonic string as well despite the absence of supersymmetry and BPS states.
• M(atrix) theory description of bosonic strings bosonic Yang-Mills theory in twenty-six dimensions is rather special M(atrix)string theory. The bosonic strings also have D-brane extended solitons, whose tension scales as 1/gB for weak string coupling gB « 1.
• Given the observation that the leading order string effective action of and antisymmetric tensor field may be derived from Einstein’s Gravity in d = 27, let us make an assumption that the 27-th quantum dimension decompactifies as the string coupling gB becomes large. For D0-brane, the dilaton exchange force may be interpreted as the 27-th diagonal component of d = 27 metric.
• Gravi-photon is suppressed by compactifying 27-th direction on an rather than on a circle. Likewise, its mass may be interpreted as 27-th Kaluza-Klein momentum of a massless excitation in d = 27.

In the infinite boost limit, the light-front view of a bosonic string is that infinitely many D0-branes are threaded densely on the bosonic string. (26 Dimensions of Bosonic String Theory - pdf)

Einstein in 1916 proposed the existence of gravitational waves as an outgrowth of his ground-breaking general theory of relativity, which depicted gravity as the distortion of space and time by matter. Until their detection in 2016, scientists had found only indirect evidence of their existence, beginning in the 1970s. The gravitational wave signal was observed in 15 years’ worth of data obtained by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) Physics Frontiers Center (PFC), a collaboration of more than 190 scientists from the United States and Canada. (Reuters)

Month, a measure of time corresponding or nearly corresponding to the length of time required by the Moon to revolve once around the Earth.

• The synodic month, or complete cycle of phases of the Moon as seen from Earth, averages 29.530588 mean solar days in length (i.e., 29 days 12 hours 44 minutes 3 seconds); because of perturbations in the Moon’s orbit, the lengths of all astronomical months vary slightly.
• The sidereal month is the time needed for the Moon to return to the same place against the background of the stars, 27.321661 days (i.e., 27 days 7 hours 43 minutes 12 seconds); the difference between synodic and sidereal lengths is due to the orbital movement of the Earth–Moon system around the Sun.
• The tropical month, 27.321582 days (i.e., 27 days 7 hours 43 minutes 5 seconds), only 7 seconds shorter than the sidereal month, is the time between passages of the Moon through the same celestial longitude.
• The draconic, or nodical, month of 27.212220 days (i.e., 27 days 5 hours 5 minutes 35.8 seconds) is the time between the Moon’s passages through the same node, or intersection of its orbit with the ecliptic, the apparent pathway of the Sun.

As a calendrical period, the month is derived from the lunation—i.e., the time elapsing between successive new moons (or other phases of the moon). A total of 12 lunations amounts to 354 days and is, roughly, a year. (Britannica)

The described Multiverse expansion creates huge parallel Multiverse bubbles with periodic parallel +m matter and periodic –m antimatter clusters, distributed on the bubbles walls.

• Fig. 13a shows parallel Universes/Anti-universe W2n / W2n+1.
• Fig. 13b shows repulsive antigravity between all the nearest matter/antimatter waveguides, e.g. between W-1 (antimatter), W+1 (antimatter) and our matter W0 Galaxies.
• Fig. 13c shows attractive Рravitв betаeen the nearest “dark” waveguides (e.g. between W-2 Dark Matter, W+2 Dark Matter) and our Matter W0 Galaxies.

The visible W-1 (antimatter), W+1 (antimatter) Universes are adjacent to the W0 (our matter)-Universe and have two joint framing membranes M0 and M-1, carrying two joint electrostatic potentials. (Gribov_I_2013 - pdf)

Prof Stephen Hawking’s final research paper suggests that our Universe may be one of many similar (BBC News).

The 26-dimensional traceless subalgebra J3(O)o is arepresentation of the 26-dim Theory of Unoriented Closed Bosonic Strings produces a Bohm Quantum Theory with geometry of E6 / F4. The E6 of the can be represented in terms of:

• 3 copies of the 26-dimensional traceless subalgebra J3(O)o of the 27-dimensional J3(O) by using the of 78-dimensional E6 over 52-dimensional F4 and the structure of based on the 26-dimensional representation of.
• In this view, Lie algebra D4-D5-E6-E7-E8 VoDou Physics model Jordan algebra fibration E6/F4 F4 as doubled J3(O)o F4

In order to reproduce the known spectrum of weakly coupled bosonic string theory, bosonic M theory will have to contain an additional field besides the 27 dimensional gravitational field, namely a three-form potential CFT. (PhiloPhysics - pdf)

In this work we present a matrix generalization of the Euler identity about exponential representation of a complex number. The concept of matrix exponential is used in a fundamental way. We define a notion of matrix imaginary unit which generalizes the usual complex imaginary unit. The Euler-like identity so obtained is compatible with the classical one. Also, we derive some exponential representation for matrix real and imaginary unit, and for the first Pauli matrix

The supposed periodic prolongation of the gravitationally bounded DM hyper-galaxies above and below of our Milky Way galaxy realizes corresponding periodic hyper-galactic Milky Way-stockpile (FiР. 13a, leПt).

This short hвper-interval 10 light minutes of the Milky Way-stockpile contains near 10²⁴ hyper-civilizations inside the 10-seconds 4D-hyperslice. (Gribov_I_2013 - pdf)

The Mathematical Elementary Cell 30 (MEC30) standard unites the mathematical and physical results of 1972 by the mathematician Hugh Montgomery and the physicist Freeman Dyson and thus reproduces energy distribution in systems as a path plan more accurately than a measurement. (Google Patent DE102011101032A9)

Mathematically, this type of system requires 27 letters (1-9, 10–90, 100–900). In practice, the last letter, tav (which has the value 400), is used in combination with itself or other letters from qof (100) onwards to generate numbers from 500 and above. Alternatively, the 22-letter Hebrew numeral set is sometimes extended to 27 by using 5 sofit (final) forms of the Hebrew letters. (Wikipedia)

Since Loop Quantum Grabity (LQG) has been formulated in 4 dimensions (with and without supersymmetry), and M-theory requires supersymmetry and 11 dimensions, a direct comparison between the two has not been possible.

• It is possible to extend mainstream LQG formalism to higher-dimensional supergravity, general relativity with supersymmetry and Kaluza–Klein extra dimensions should experimental evidence establish their existence.
• It would therefore be desirable to have higher-dimensional Supergravity loop quantizations at one’s disposal in order to compare these approaches.
• A series of papers have been published attempting this.[68][69][70][71][72][73][74][75] Most recently, Thiemann (and alumni) have made progress toward calculating black hole entropy for supergravity in higher dimensions.

It will be useful to compare these results to the corresponding super string calculations. (Wikipedia)

F11 (89): The decimal expansion of 89’s reciprocal (1/89) is period-44 (see graphic below) composed of 22 bi-lateral 9 sums = 198, while 89 + 109 = 198, 7920/198 = 40 and 8,363,520/198 = 20 x 2112 (7919’s index number as a member of this domain).

• And, curiously, 198’s inverse (891) + 109 = 1000, while the sum of 89 and 109’s inverses, 98 + 901, = 999.
• Then consider that, while it’s obvious 997 of the first 1000 primes are not divisible by 2, 3, or 5, one might miss the fact that 997 minus its reverasl, 799, = 198 = 89 + 109.
• And for the record we note that 1/109’s decimal expansion is period 108 (making it a ‘long period prime’ in that 1/p has the maximal period of p−1 digits).

This period consists of 2 × 27 or 54 bilateral 9 sums = 486, which (coincidentally?) is the number of primes in the 243 pairs summing to 7920 (more about these, below). (PrimesDemystified)

In physics, a coupling constant or gauge coupling parameter (or, more simply, a coupling), is a number that determines the strength of the force exerted in an interaction.

• Originally, the coupling constant related the force acting between two static bodies to the “charges” of the bodies (i.e. the electric charge for electrostatic and the mass for Newtonian gravity) divided by the distance squared, r².
• The choice of free parameters is somewhat arbitrary. In the table above, gauge couplings are listed as free parameters, therefore with this choice the Weinberg angle is not a free parameter
• The solution to both these problems comes from the Higgs mechanism, which involves scalar fields (the number of which depend on the exact form of Higgs mechanism) which (to give the briefest possible description) are “absorbed” by the massive bosons as degrees of freedom, and which couple to the fermions via Yukawa coupling to create what looks like mass terms.

The next step is to couple the gauge fields to the fermions, allowing for interactions. (Wikipedia)

Eleven-dimensional supergravity is reformulated in a way suggested by compactifications to four dimensions. The new version has local SU(8) invariance. The bosonic quantities that pertain to the spin-0 fields constitute 56- and 133- dimensional representations of E7(+7). Some implications of our results for the S7 compactification are discussed.

Gell-mann matrices are a complete set of Hermitian noncommuting trace-orthogonal matrices. In addition, they also play an important role in physics where they can be thought to model the **eight (8) gluons* that mediate the strong force quantum chromodynamics, an analogue of the Pauli matrices well-adapted to applications in the realm of quantum mechanics. (Wolfram)

Representation theory is a mathematical theory that describes the situation where elements of a group (here, the flavour rotations A in the group SU(3)) are automorphisms of a vector space (here, the set of all possible quantum states that you get from flavour-rotating a proton).

• Therefore, by studying the representation theory of SU(3), we can learn the possibilities for what the vector space is and how it is affected by flavour symmetry.
• Since the flavour rotations A are approximate, not exact, symmetries, each orthogonal state in the vector space corresponds to a different particle species. In the example above, when a proton is transformed by every possible flavour rotation A, it turns out that it moves around an 8 dimensional vector space.
• Those 8 dimensions correspond to the 8 particles in the so-called “baryon octet”.

This corresponds to an 8-dimensional (“octet”) representation of the group SU(3). Since A is an approximate symmetry, all the particles in this octet have similar mass. (Wikipedia)

E8 is at the heart of many bits of physics. One interpretation of why we have such a quirky list of fundamental particles is because they all result from different facets of the symmetries of E8. The enigmatic E8 is the largest and most complicated of the five exceptional Lie groups, and contains four subgroups that are related to the four fundamental forces of nature: the electromagnetic force; the strong force (which binds quarks); the weak force (which controls radioactive decay); and the gravitational force. (Wordpress.com)

Our sidebar is arranged to accommodate The Standard Model presently that recognizes seventeen (17) distinct particles: five (5) bosons and twelve (12) fermions. As a consequence of flavor and color combinations and antimatter, the fermions and bosons are known to have 13 and 48 variations, respectively. Among the 61 elementary particles embraced by the Standard Model number electrons and other leptons, quarks, and the fundamental bosons. (Wikipedia)

In the second opposing term, the position 13 gives a redundant value of the template 7 of 7 × 7 = 49. The opposite prime position 31 as the 11th prime number is now forced as a new axis-symmetrical zero position. (Google Patent DE102011101032A9

The multiverse is a hypothetical group of multiple universes. Together, these universes comprise everything that exists: the entirety of space, time, matter, energy, information, and the physical laws and constants that describe them. The different universes within the multiverse are called “parallel universes”, “other universes”, “alternate universes” (Wikipedia).

Some of the major unsolved problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result. The others are experimental, meaning that there is a difficulty in creating an experiment to test a proposed theory or investigate a phenomenon in greater detail.

Many of these problems apply to LQG, including:

• Can quantum mechanics and general relativity be realized as a fully consistent theory (perhaps as a quantum field theory)?
• Is spacetime fundamentally continuous or discrete?
• Would a consistent theory involve a force mediated by a hypothetical graviton, or be a product of a discrete structure of spacetime itself (as in loop quantum gravity)?
• Are there deviations from the predictions of general relativity at very small or very large scales or in other extreme circumstances that flow from a quantum gravity theory?

The theory of LQG is one possible solution to the problem of quantum gravity, as is string theory. There are substantial differences however. For example, string theory also addresses unification, the understanding of all known forces and particles as manifestations of a single entity, by postulating extra dimensions and so-far unobserved additional particles and symmetries. Contrary to this, LQG is based only on quantum theory and general relativity and its scope is limited to understanding the quantum aspects of the gravitational interaction.

The ‘Grid Square’ Crop Circle is one of the most significant mathematical formations

• Numbers 65 and 325 have reciprocal (1/x) or we can call them wave values that link to certain expressions of electromagnetism. 1/65= .0[153846…] and 1/325= .00[307692…]  are period 6 repeat decimals (digital root 9) that reveal other numbers of significance: 27, 37 & triple digits.
• The math of the ‘Grid Square’ crop circle gives the value of 153846… and when added to another number in the design, close approximations to √5 and Ф can be made.  
• Dividing numbers with digital roots of 3,6,9 by 19.5 also creates these same two number patterns. 19.5 can be seen as 195, a multiple of 65. 19.47° (19.5) is the latitude in which planetary energy is said to upwell. 27 is also connected to the tetrahedron and the tetrahedron is connected to 19.5 degree
• A star tetrahedron nested in a sphere touches at 19.47° north and south latitude. 19.47° has also been noted in the geometry of crop circles and angles connecting them to one another and to sacred sites.
• Dividing integers by 13 (a star prime) creates the same two patterns. 13 is a factor of 65: 1, 65, 5– 3rd prime,13–6th prime.
• VBM polarity pairings are also made every 1st/4th, 2nd/5th, 3rd/6th number. 
• Interestingly, the wave value for 7 (1/7= .142857…) connects perfectly with these two patterns–153846 + 142857 = 296703— the mirror number to 307692. All 3 patterns total 27 and 27 is also a factor of all.

• Because of factor 37, many triple digits are factors: 111, 222, 333, 666, 777, 999

  142+857= 999

  153+846= 999

  307+692= 999

The 37 and 73 are both Star numbers, both have the same shape, but with different Hexagon portions. For a twist we can count them as one extra together and then instead of 36 we get 37. So 37 is the only factor of all 3 patterns. (YouTube)

Like all maximal supergravities, it contains a single supermultiplet, the supergravity supermultiplet containing the graviton, a Majorana gravitino, and a 3-form gauge field often called the C-field.

• It contains two p-brane solutions, a 2-brane and a 5-brane, which are electrically and magnetically charged, respectively, with respect to the C-field.
• This means that 2-brane and 5-brane charge are the violations of the Bianchi identities for the dual C-field and original C-field respectively.The supergravity 2-brane and 5-brane are the long-wavelength limits (see also the historical survey above) of the M2-brane and M5-brane in M-theory. (Wikipedia)

Neutrinos are perhaps the least understood of the known denizens of the subatomic world.

• They have nearly no mass, interact only via the weak nuclear force and gravity, and, perhaps most surprising, the three known species of neutrinos can transform from one variant into another.
• This transformation, called neutrino oscillation, has been demonstrated only relatively recently and has led to speculation that there might be another, even more mysterious, neutrino variant, called the sterile neutrino.
• While the sterile neutrino remains a hypothetical particle, it is an interesting one and searches for it are a key research focus of the world’s neutrino scientist community.
• This means that if right-handed neutrinos exist, they don’t interact with regular matter, only with gravity. Thus, they are “sterile.”

And if they have a significantly larger mass than regular neutrinos, sterile neutrinos would be “cold,” and could be the solution to the dark matter problem. It’s a great idea, but unfortunately, as a new study shows, doesn’t seem to be true. (UniverseToday)

After putting in the proverbial 10,000 hours studying ‘24-beat’ patternization, we’ve come to the conclusion that period-24 is the key to the “Theory of Everything” and that a hypothetical E24 Petrie Projection will one day loom large as E8 is understood to be the leg of a triad, with E16, leading to E24.

• The three being analogous to:
  • Mod 30 → E8 → {3} star polygon …
  • Mod 60 → E16 → {6/2} star polygon …
  • Mod 90 → E24 → {9/3} star polygon …
  • … building geometrically to infinity …
• We’ve dubbed this ‘The Theory of Everything … but the Kitchen Sink.’
• Explore the incredible symmetries that come into focus when the lense aperature, so to speak, of the Prime Spiral Sieve is tripled to modulo 90, synchronizing its modulus with its period-24 digital root, and perhaps you’ll see why we make this bold assertion.

The mathematical balancing and resolution of this domain, which correlates with a hypothetical E24, including structures that determine the distribution of prime numbers, are fundamentally period-24. (PrimesDemystified)