Theory that predicts and explains data about elementary particles, dark matter, early galaxies, and the cosmos

We develop and apply new physics theory. The theory suggests speci c unfound elementary particles. The theory suggests speci c constituents of dark matter. We apply those results. We explain ratios of dark matter amounts to ordinary matter amounts. We suggest details about galaxy formation. We suggest details about in ation. We suggest aspects regarding changes in the rate of expansion of the universe. The theory points to relationships between masses of elementary particles. We show a relationship between the strength of electromagnetism and the strength of gravity. The mathematics basis for matching known and suggesting new elementary particles extends mathematics for harmonic oscillators.


Introduction: context for and summary of results
This unit provides an overview of theory that this essay proposes. This unit discusses context and scope for the proposed theory. This unit discusses relationships between data, proposed theory, and ongoing theory. This unit provides perspective about this essay.

Overview
This unit discusses highlights about proposed theory.
We propose new physics theory. The new theory includes modeling that matches all known elementary particles and suggests new elementary particles. We use the two-word term ongoing theory to denote established theory and some candidate theory that other people suggest. We use the two-word term proposed theory to denote new theory that we suggest.
The following items point to topics that proposed theory addresses. Each item notes aspects that underlie proposed theory or that come from proposed theory.
Extensions to harmonic-oscillator mathematics. Minor changes in assumptions lead to harmonic oscillator states that people might consider to lie below traditional ground states. The resulting math has applications to elementary particle physics.
Mathematics-based modeling pertaining to elementary particles, astrophysics, and cosmology. Extended harmonic-oscillator math provides bases for modeling pertaining to elementary particles, dark matter, dark energy forces, and observations that physicists report. Modeling features solutions to equations featuring isotropic pairs of isotropic quantum harmonic oscillators. Astrophysics (galaxy formation). A combination of dark matter aspects of proposed theory and gravitational aspects of proposed theory leads to galaxy formation scenarios that match observed data.
Fundamental aspects of physics. The work relates a ratio of the masses of two elementary particles to a ratio of the strength of electromagnetism to the strength of gravity. Other formulas interrelate the masses of other elementary particles.

Context for and scope of proposed theory
This unit discusses context for, aspects of, and the scope of proposed theory.
Physics includes issues that have remained unresolved for decades. For one example, describe elementary particles that people have yet to nd. For another example, describe dark matter. For each of those examples, resolution does not necessarily depend on considering models pertaining to translational motion.
Ongoing theory has bases in developing theories of motion without necessarily having descriptions of objects that move. Examples of such theories feature epicycles, elliptical orbits, and the principle of stationary action. Ongoing theory has bases in adding quantization to classical modeling of the motion of objects.
We pursue an approach that catalogs fundamental objects and their properties. The proposed theory approach features, from its beginning, quantized concepts. The approach does not originally address translational motion.
The proposed theory approach and the ongoing theory approach dovetail via symmetries that ongoing theory correlates with kinematics conservation laws. We discuss results that we develop based on elementary particles that proposed theory suggests and on kinematics models that ongoing theory provides.
Proposed theory matches, explains, or predicts phenomena that ongoing theory does not explain or predict. For example, we suggest -with some specicity -descriptions of new elementary particles and of dark matter. [1].) The table matched all the then-known elements and suggested elements that people subsequently discovered.
Physics might benet from new candidates for sets of organizing principles for elementary particles.
Currently, ongoing theory sets of candidate principles (such as principles that correlate with supersymmetry) seem to be unveried or to lack specicity regarding properties of particles.
Proposed theory includes a mathematics-based modeling technique that, in eect, outputs the list of known elementary particles, suggests new elementary particles, and suggests organizing principles for an elementary particle analog to the periodic table for chemical elements. The modeling technique does not require making a choice among ongoing theory kinematics theories.
We think that the set of candidate elementary particles explains some and perhaps most or all of the phenomena that people currently consider when people use known phenomena to point to the possible existence of new elementary particles. Examples of those phenomena include dark matter and baryon asymmetry.
While one mathematics modeling basis outputs the entire set of known and suggested elementary particles, we nd it convenient to divide the set into two subsets. We use the two-word phrase simple particles to point to all of the elementary particles that we do not correlate with the two-word term root forces. We use the two-word term root forces to include bases for phenomena such as electromagnetic elds, gravity, and non-residual aspects of the strong force. We do not separate the notion of boson particles from a broader (than just root forces) concept of forces. For example, sometimes, modeling based on the notion of a strong force provides advantages over modeling based on the notion of gluon particles. This use of the word root reects the notion that some mathematical modeling that has bases in aspects of root forces outputs solutions that correlate with known and suggested simple particles. This use of the word root does not necessarily correlate with notions of root forces being more fundamentalregarding physics or nature -than simple particles.
We think that people can use the set of elementary particles in the context of ongoing theory classical physics and in the context of ongoing theory quantum physics. We think that people can use the set of elementary particles in the contexts of modeling based on each of Newtonian kinematics, special relativity, and general relativity.
People might treat some outputs from the modeling technique as candidates for new simple particles or new root forces. Some or all of the candidates might represent opportunities for research to detect or infer phenomena. The candidates might not conict with veried aspects of ongoing theory.

Rate of expansion of the universe
This unit summarizes -regarding the rate of expansion of the universe -aspects of and relationships between proposed theory, physics data, and ongoing theory.
People suggest the concept of dark energy pressure to explain observed changes in the rate of expansion of the universe. Ongoing theory concepts that people use to try to model aspects of the rate of change include the Hubble parameter (or, Hubble constant), equations of state (or, relationships between density and pressure), and general relativity. People suggest possible incompatibilities between observations and ongoing theory modeling. (See, for example, reference [2], reference [3], reference [4], and communication 71a. However, some people note possible objections to some notions of incompatibility. See, for example, references [5] and [6].) People suggest phenomenological remedies regarding the modeling. (See, for example, reference [7].) People sometimes use the three-word term dark energy forces in discussions that include notions of dark energy pressure.
Each of proposed theory and ongoing theory uses terms such as gravity and gravitation. Proposed theory includes concepts of components of root forces that are related to electromagnetism and gravitation.
For example, regarding electromagnetism, one component correlates with interactions with charge and another component correlates with interactions with nominal magnetic dipole moment. The existence of these components is appropriate because proposed theory accommodates modeling that does not include translational motion. Some objects have non-zero charge and zero nominal magnetic dipole moment.
Some objects have zero charge and non-zero nominal magnetic dipole moment. People correlate the word monopole with the interaction with charge. People correlate the word dipole with the interaction with nominal magnetic dipole moment. Ongoing theory sometimes decomposes aspects of electromagnetism into an electric eld and a magnetic eld. However, ongoing theory notions of photons do not necessarily reect such a decomposition. Similar concepts pertain regarding gravity. Proposed theory uses the sixword term monopole gravity and dark energy forces (or, monopole gravity plus dark energy forces). The monopole gravity component of gravitation correlates well with a Newtonian notion of gravity associated with a non-rotating object that models as existing at a point or as having spherical symmetry. The dark energy force components correlate with -among other phenomena -changes in the rate of expansion of the universe. An example of such other phenomena features aspects correlating with gravity associated with a rotating object. Ongoing theory includes modeling that does not similarly decompose notions of gravity. For example, general relativity does not necessarily separate notions that might correlate with monopole gravity from notions that might correlate with dark energy forces.
Proposed theory regarding spin-two root forces points to a candidate explanation for observed eras in the rate of expansion of the universe. The rst era correlates with a rate that increases with time. The word octupole characterizes the dominant force components for this era. The dominant force components repel objects from each other. The second era correlates with a rate that decreases with time and, if we assume data that references [8], [9], [10], and [11] provide, that ends some billions of years later. The We correlate with the three-word term dark energy forces the spin-two octupole, quadrupole, and dipole components that we just mentioned.
We think that proposed theory provides a candidate means to close gaps between observations and ongoing theory. We think that proposed theory is not incompatible with the ongoing theory notion that the Einstein eld equations can be compatible with repulsion. (Reference [12] discusses the notion that the Einstein eld equations can be compatible with repulsion.)

Dark matter and galaxies
This unit summarizes -regarding dark matter and galaxies -aspects of and relationships between proposed theory, physics data, and ongoing theory.
People suggest various explanations for observations that, starting in the 1880s, suggest that the Milky Way galaxy does not have enough ordinary matter to keep observed stars in their orbits; that, starting in the 1930s, suggest that galaxy clusters do not contain enough ordinary matter to bind observed galaxies into the clusters; and that, starting in the 1930s, suggest that a signicant fraction of observed galaxies do not have enough ordinary matter to keep observed stars in their orbits. While people discuss theories that might not require nature to include dark matter, most observations and theoretical work assume that dark matter exists. (People use the term MOND -or, modied Newtonian dynamics -to describe one set of theories that might obviate needs to assume that nature includes dark matter.) People use terms such as WIMPs (or, weakly interacting massive particles), axions, and primordial black holes to name candidate explanations for dark matter. Some of the candidates are not completely well-specied.
For example, searches for axions span several orders of magnitude of possible axion mass. People suggest that dark matter could have characteristics similar to ordinary matter. (See, for example, reference [13].) assume that nature embraces n isomers of charged simple particles. We assume that each isomer of charged simple particles interacts, via charge and nominal magnetic dipole moment, with its own isomer of so-called PR1ISe-like photons. For n equal to six and n equal to 36, each isomer of charged simple particles does not interact, via charge and nominal magnetic dipole moment, with isomers, other than its own isomer, of PR1ISe-like photons. The PR36ISe case suggests an alternative explanation for dark energy density. From a standpoint of observations, distinguishing between the case of PR6ISe and the case of PR36ISe might prove dicult. For the moment, we de-emphasize the PR36ISe case.
We introduce the word span. We say that the span of each isomer of charged simple particles is one, as in one isomer of charged simple particles. The span of each isomer of PR1ISe-like photons is one, as in one isomer of charged simple particles. For n equal to six, one isomer of the monopole component of gravity interacts with all six isomers of charged simple particles. We say that the span of the monopole component of gravity is six, as in six isomers of charged simple particles. (A span of six does not pertain regarding dark energy forces. For example, the span for each of six isomers of the quadrupole component of dark energy forces is one.) One isomer of charged simple particles correlates with ordinary matter.
The other ve isomers of charged simple particles correlate with dark matter.
PR1ISe does not provide bases for explaining, from fundamental principles, observed ratios of dark matter eects to ordinary matter eects.
PR6ISe provides bases for explaining some observed ratios. For example, regarding densities of the universe, the ve dark matter isomers explain the ve in the ratio ve-plus to one. The WIMP-similar hadron-like particles explain the plus in the ratio ve-plus to one. For example, PR6ISe seems to explain galaxy-related observed ratios of dark matter amounts to ordinary matter amounts.
PR6ISe suggests the following scenario for the formation and early evolution of galaxies.
The scenario features, for each galaxy, the notion of an original clump. Clumping takes place based on the quadrupole component of the gravitational force. The quadrupole component is attractive and has a span of one, as in one isomer of charged simple particles. For each of many galaxies, the initial clump correlates with one isomer of PR6ISe-span-one phenomena. Sometimes, an original clump features, based on the attractive monopole component of root force, more than one isomer of PR6ISe-span-one phenomena. With respect to each isomer in the clump, the repulsive dipole component of gravity drives away from the original clump one isomer of PR6ISe-span-one phenomena. Thus, for essentially all galaxies, the original clump correlates with no more than three isomers of PR6ISe-span-one phenomena.
From a standpoint of observations, three types of one-isomer original clump galaxies exist. Some (perhaps one-sixth of the) one-isomer original clump galaxies feature an ordinary matter original clump. Some (perhaps two-thirds of the) one-isomer original clump galaxies feature a dark matter original clump that does not repel ordinary matter. Some (perhaps one-sixth of the) one-isomer original clump galaxies feature a dark matter original clump that repels ordinary matter. We suggest that some ongoing theory notions of dark matter galaxy correlate with galaxies for which dark matter original clumps repel ordinary matter.
Observations of early galaxies correlate with galaxies for which the original clump contains signicant amounts of ordinary matter. Aside from dark matter galaxies, galaxies for which the original clump features just one isomer of PR6ISe-span-one phenomena might attract and accumulate matter such that eventually (assuming that disturbances, such as collisions with other galaxies, do not occur) the galaxies contain approximately four times as much dark matter that has bases in PR6ISe-span-one phenomena as ordinary matter.
We think that data supports the galaxy formation and evolution scenario. Reference [18] discusses a dark matter galaxy. Reference [19] reports, regarding galaxies about 10 billion years ago, data that seems to support the notion of ordinary matter intensive original clumps. Figure 7 in reference [20] seems to support (especially via data pertaining to redshifts of at least seven) the notion of ordinary matter intensive original clumps. Observations that reference [21] reports might support the notion of approximately four to one ratios. The observation that reference [22] reports might correlate with a three-isomer original clump galaxy.
The galaxy formation and evolution scenario seems to comport with data. For each of many known galaxies, the scenario can comport with the ongoing theory notion of a dark matter halo. For some ordinary matter intense galaxies, the scenario does not comport with some ongoing theory assumptions about roles, in galaxy formation, of dark matter halos.
We think that PR6ISe is not incompatible with inferred galaxy cluster related ratios of dark matter amounts to ordinary matter amounts.
PR6ISe seems to oer an explanation for one piece of data regarding details of the Milky Way galaxy.
(Regarding the piece of data, see discussion, in reference [23], regarding data regarding the stellar stream GD-1.)

Depletion of CMB
This unit summarizes -regarding one observation of depletion of cosmic microwave background radiation -aspects of and relationships between proposed theory, physics data, and ongoing theory.
Results that reference [24] reports about depletion of CMB (or, cosmic microwave background radiation) might dovetail with the existence of isomers of hydrogen atoms. Observations correlate with twice as much depletion as ongoing theory attributes to depletion by ordinary matter hydrogen atoms.
PR6ISe modeling suggests that one isomer of dark matter analogs to hydrogen atoms provide for half of the depletion. Proposed theory might contribute to credibility for assumptions and calculations that led to the prediction for the amount of depletion that correlates with ordinary matter hydrogen atoms.

Other topics
This unit summarizes -regarding various topics -aspects of and relationships between proposed theory, physics data, and ongoing theory.
Regarding proposed theory, people might assume that the following aspects are non-traditional or think that the following aspects are controversial. However, we think that proposed theory shows that these aspects comport with known phenomena, do not contradict known phenomena, do not violate ongoing theory theories for realms in which people have validated the theories, oer ways to strengthen and further understand some ongoing theory, and oer theories that are synergistic with ongoing theory.
Proposed theory points to a formula that possibly links a ratio of the masses of two elementary particles and a ratio of the strengths of two components of root forces. The elementary particles are the tauon and the electron. The force components are electrostatic (or, monopole) repulsion between two electrons and monopole gravitational attraction between (the same) two electrons.
We think that this numeric relationship comports with measurements and points to a possibility for extending physics theory. The formula suggests a tauon mass and a standard deviation for the tauon mass. Based on 2019 data, eight calculated standard deviations t within one experimental standard deviation of the experimental nominal tauon mass.
Proposed theory points to (at least approximate) numerical relationships between the ratios of the masses of the Higgs, Z, and W bosons. These relationships might suggest possibilities for extending physics theories related to the weak mixing angle.
Proposed theory suggests that people might be able to distinguish observationally between the coalescing of two black holes that interact with each other signicantly via the dipole component of dark energy force and the coalescing of two black holes that do not interact with each other signicantly via the dipole component of dark energy force.
Proposed theory suggests resolution regarding the possible mismatch between the elementary particle Standard Model notion that all neutrinos might have zero rest mass and interpretations, of data, that people associate with the notion that at least one neutrino avor (or, generation) has non-zero rest mass. Proposed theory suggests that spin-four components of root forces couple to lepton number (and not to rest mass) and underlie phenomena that people interpret as implying that at least one neutrino has non-zero rest mass. Proposed theory suggests that ongoing theories might interpret those phenomena as correlating with a specic value for a would-be sum of neutrino rest masses. That value is 3α 2 m . The symbol α denotes the ne-structure constant. The symbol m denotes the mass of an electron. That value comports with ongoing theory interpretations of data, as summarized by reference [17]. Proposed theory suggests the possibility that all neutrinos have zero rest mass. While this work may prove controversial, we oer the possibility that it comports with data and resolves an underlying tension regarding ongoing theory. People might consider the notion that interactions mediated by the spin-four components produce an eect that correlates with a notion of an index of refraction -regarding neutrino motion -that is other than one.
Proposed theory suggests details about simple particles and root forces involved during the inationary epoch.
Proposed theory points to a possibility for modeling lepton anomalous magnetic dipole moments via a sum of two terms. Each term correlates with components of root forces. For each of those components, the spin exceeds one. • Outputs information about properties of the elementary particles.
• Outputs types of interactions in which elementary particles participate.
• Dovetails with conservation laws pertaining to motion. • Dovetails with established ongoing theories of motion. • Helps explain data that ongoing theory seems not to explain.
We think that possibilities exist for adding, to the elementary particle Standard Model, new elementary particles that proposed theory suggests. Some of the new elementary particles correlate with symmetries that correlate with current Standard Model elementary particles. Examples include new non-zero-mass spin-one simple bosons, which would correlate with an SU (2) × U (1) symmetry similar to the SU (2) × U (1) symmetry that people correlate with the W and Z bosons. So far, proposed theory does not fully explore the feasibility of adding, to the Standard Model, the particles that proposed theory suggests. For example, we do not explore Lagrangian terms for candidate particles. Also, we do not explore the extent of compatibility between the Standard Model and PR6ISe modeling.

Perspective about this essay
This unit discusses some aspects of this essay.
We try to provide perspective regarding theories and models. Aspects of perspective regarding individual theories and models include correlations with data, limits of applicability, opportunities to make improvements, unresolved aspects, and alternatives. Reference [26] suggests standards regarding such perspective. Aspects of perspective regarding collections of theories or models include synergies between theories and models and include possible discord between theories and models.
We try to structure this essay to facilitate learning. We use an approach that blends known data, ongoing theory, development of new theory, and mathematics. We sometimes show results before we discuss theory that outputs the results. We sometimes use tables to list concepts that are not numeric.

Methods: perspective regarding quantum particle theory
This unit discusses perspective about our development and use of quantum particle theory.
We use the three-word term quantum particle theory to describe a core of our work. The acronym QPT abbreviates the three-word term quantum particle theory. Table 1 suggests goals for QPT. Interactions might change, regarding objects in general, each of internal properties and motion.
Our work contributes to each of the goals that table 1 lists. This essay shows development of QPT via steps that roughly track the goals.
Ongoing theory does not necessarily achieve the rst few goals. Development of ongoing theory has tended to produce theories of motion without necessarily completely knowing the nature of objects that move or without necessarily completely cataloging types of objects that move.
Goals that table 1 lists correlate with potential synergy between proposed theory and ongoing theory.
Together, proposed theory and ongoing theory seem to explain data that ongoing theory seems not to explain. Table 2 notes hunches, concepts and steps that underlie this essay's development of QPT. (Regarding the correlation between spin and number of particles, see table 8c.) The acronym PDE abbreviates the three-word term partial dierential equation. The three-letter term ALG stands for the word algebraic.

Results: elementary particles
This unit lists all known elementary particles and all elementary particles that proposed theory suggests. This unit discusses properties that known elementary particles exhibit and that suggested elementary particles might exhibit. Table 2: Hunches, notions, and steps underlying development of QPT (with the word particles denoting the two-word term elementary particles) Hunches, notions, and steps • A correlation between spin and number of particles points to useful steps forward. • So-called PDE modeling, based on math that dovetails with that correlation, can be useful. • PDE modeling features use of partial dierential equations pertaining to harmonic oscillators.
• PDE modeling correlates allowed spins mathematically with three spatial dimensions.
• PDE modeling uses information about some particles to output aspects of other particles. • So-called ALG modeling features ladder operators pertaining to harmonic oscillators. • ALG modeling uses symmetries pertaining to harmonic oscillators.
• ALG modeling has bases in models that dovetail with the excitement of boson states.
• ALG modeling outputs representations that correlate with particles.
• ALG modeling points to symmetries that correlate with properties of particles.
• ALG modeling points to symmetries that correlate with properties of interactions.
• ALG modeling embraces symmetries correlating with kinematics conservation laws.
• ALG modeling helps bridge between proposed theory and ongoing theory.
• ALG modeling bridging includes aspects correlating with motion.
• ALG modeling includes a feature that we call double-entry bookkeeping.
• PDE modeling also includes aspects of double-entry bookkeeping.

A table of known and suggested elementary particles
This unit shows a table of elementary particles that ongoing theory recognizes or proposed theory suggests.
Proposed theory points to all elementary particles that ongoing theory recognizes and suggests new elementary particles. We use the two-word term simple particle to pertain to each entry in table 3 other than G-family entries and U-family entries. We correlate the two-element term root force with each G-family entry in table 3 and with the U-family entry in table 3. This use of the word root reects the notion that some mathematics-based modeling, which has bases in aspects of root forces, outputs solutions that correlate with known and suggested simple particles. (See discussion related to equation (15). There might not be a need to try to correlate a physics meaning with such use of the word root.) Modeling for each one of the G-family forces points to components for that force. Particle counts in table 3 de-emphasize modeling that would count, for example, a down quark with green color charge as diering from a down quark with red color charge.
We discuss the free simple particles for which m>0 pertains. The 0H particle is the Higgs boson. The three 1C particles are the three charged leptons -the electron, the muon, and the tauon. The two 2W particles are the two weak interaction bosons -the Z boson and the W boson.  (2) (2)) We discuss the free simple particles for which m=0 pertains. The 0I, or so-called aye, particle is a possible zerolike-mass relative of the Higgs boson. Some aspects of ongoing theory suggest a so-called inaton elementary particle. Proposed theory suggests that the aye particle is a candidate for the inaton.
The three 1N particles are the three neutrinos. Some aspects of ongoing theory suggest that at least one neutrino mass must be positive. At least one positive mass might explain neutrino oscillations and some astrophysics data. Some aspects of ongoing theory, such as some aspects of the   We discuss the unfree simple particles for which m>0 pertains. The 0P, or so-called pie, possible particle might correlate with an attractive component of the residual strong force. The 0K, or so-called cake, possible particle might correlate with a repulsive component of the residual strong force. The six 1Q particles are the six quarks. The four 2T, or so-called tweak, possible particles are analogs to the weak interaction bosons. The charge of one non-zero-charge 2T particle is two-thirds the charge of the W boson. The charge of one non-zero-charge 2T particle is one-third the charge of the W boson. The non-zero-charge tweak particles may have played roles in the creation of baryon asymmetry. The non-zero charge tweak particles might correlate with ongoing theory notions of -as yet hypothetical -leptoquarks.
We discuss the unfree simple particles for which m=0 pertains. The six 1R, or so-called arc, possible particles are zero-charge zerolike-mass analogs of the six quarks. Hadron-like particles made from arcs and gluons contain no charged particles and measure as dark matter.
We discuss U-family forces. The eight 2U particles are the eight gluons. In each of ongoing theory and proposed theory, gluons correlate with the strong interaction and bind quarks into hadrons. Proposed theory suggests that gluons bind arcs into hadron-like particles.  This unit discusses aspects that correlate with the development of quantum particle theory.
We extend discussion related to tables 1 and 2.
Mathematics and ongoing theory include partial dierential equations pertaining to isotropic harmonic oscillators. A partial dierential equation correlating with an isotropic multidimensional quantum harmonic oscillator includes an operator that correlates with r −2 and an operator that correlates with r 2 . (See equations (3) and (4).) The symbol r denotes a radial spatial coordinate. The r −2 operator in equation (4) might model aspects correlating with the square of an electrostatic potential. The potential correlates with r −1 . The force correlates with r −2 . The r −2 operator might model aspects correlating with the square of a gravitational potential. The r −2 operator might model aspects correlating with each G-family force ΣG. (See table 22.) The r −2 operator might model aspects correlating with excitations that pertain for each G-family force ΣG and that, thereby, have relevance for each G-family force component ΣGΓ. (See discussion that includes equation (36).) The r 2 operator in equation (3) might model aspects correlating with the square of a strong interaction potential. This strong interaction potential would correlate with excitations related to the 2U subfamily (or, gluons) and with interactions within hadron-like particles. (Ongoing theory includes within the two-word term strong force the notion of a residual strong force. The three-word term residual strong force pertains to interactions between hadronlike particles. Proposed theory suggests correlating the residual strong force with so-called 0P -or, pie -simple bosons and so-called 0K -or, cake -simple bosons.) Ongoing theory includes the concept of asymptotic freedom. The potential correlates with r 1 . The force correlates with r 0 .
PDE modeling might point to results pertaining to other than the G family and the U family. For example, the next two sentences might pertain. Operator aspects that correlate with r 0 might correlate with simple fermions. Operator aspects that correlate with r 0 might correlate with aspects of the weak interaction. (Here, the expression r 0 does not correlate with non-residual aspects of the strong interaction.) We discuss objects and properties.
Each of ongoing theory and proposed theory includes the notion of an object. Models for an object may include notions of internal properties upon which all observers would agree. One such property is charge (or, charge that people would observe in the context of a frame of reference in which the object does not move). Models for objects may include notions of kinematics properties upon which observers might legitimately disagree. One such notion is velocity, relative to observers, of an object. Models can include notions of interactions between objects. An interaction might change -for an object -at least one of some internal properties and some kinematics properties. We discuss the notion of double-entry bookkeeping.
Ongoing theory includes modeling, for photons, that features mathematics correlating with two harmonic oscillators. Ongoing theory correlates modeling for each of two polarization modes with one harmonic oscillator. Each mode can correlate with a spatial dimension that is orthogonal to both the direction of motion of the photon and to the spatial dimension correlating with the other mode.
Proposed theory ALG modeling has bases in a hunch that modeling photons based on four harmonic oscillators has uses. The hunch has bases in the ongoing theory notion of modeling based on four dimensions. Generally, proposed theory associates the one-element term TA-side with modeling that correlates with temporal aspects. The one-element term SA-side correlates with modeling that correlates with spatial aspects. The hunch points to equation (24) and to a concept to which we apply the twoelement term double-entry bookkeeping. The term refers to ALG modeling that maintains a numeric balance between TA-side aspects and SA-side aspects. The balance reects a notion that a sum pertaining to TA-side aspects equals a sum pertaining to SA-side aspects.
|ι Q | = 3 or 0 → |ι Q | = 2 or 1 or 0 ¡ ?, ¡ ? (d) Explanations regarding some symbols Discussion • m>0 → m=0 denotes extending results for m>0 to results for m=0. • The symbol ι Q denotes charge, in units of one-third the negative of the charge of an electron (or, in units of the negative of the charge of a down quark).
• |ι Q | = 3 or 0 → |ι Q | = 2 or 1 or 0 denotes extending results for |ι Q | = 3 or 0 to results for |ι Q | = 2 or 1 or 0. The results correlating with the word from pertain to free particles. The results correlating with the word to pertain to unfree particles.
• The word ongoing denotes aspects of ongoing theory that model the attractive component of the residual strong force via modeling that includes notions of virtual pions.
• The symbol m π denotes the mass (or masses) of pions. • The notation X denotes the notion that this essay generally de-emphasizes the concept X. We posit that there might be an analog -to the periodic table for chemical elements -for elementary particles.
The periodic table reects properties of chemical elements. One relevant property is the types of chemical interactions in which an element participates. One relevant property is the atomic weight. A usual display of the periodic table features an array with columns and rows. Elements listed in a column participate in similar interactions. For a row, the atomic weight of an element is usually greater than the atomic weight for each element to the left of the subject element. Atomic weights in one row exceed atomic weights in rows above the subject row.
We look for patterns regarding the known elementary particles. (See table 3.) Table 8 reects a hunch that the number of elementary particles in a subfamily dovetails with the spin of the elementary particles in the subfamily. Table 8b explains notation that table 8a uses. The spin S correlates with an overall angular momentum for which the expression S(S + 1) 2 pertains. The spin S does not depend on a choice of an axis. Each of the three columns that correlate with the one-word label unfree correlates with a magnitude of charge that diers from the magnitude of charge pertaining to the other two columns labeled unfree. Table 9 lists some quantities that are always integers. The quantities pertain for each elementary particle. The quantities can pertain for objects that contain more than one elementary particle. In terms of measurements, equation (1) pertains. Here, q is the charge of an electron. The symbol ε 0 denotes the vacuum permittivity. We propose the two-element term 3LB number.
3.2.3. PDE aspects of quantum particle theory, plus the existence of simple particles This unit discusses mathematics underlying PDE modeling. This unit develops aspects of quantum particle theory. This unit uses quantum particle theory to match the known simple particles and to predict new simple particles.
Equations (3) and (4) correlate with an isotropic quantum harmonic oscillator. Here, r denotes the radial coordinate and has dimensions of length. The parameter η SA has dimensions of length. The parameter η SA is a non-zero real number. The magnitude |η SA | correlates with a scale length. The positive integer D correlates with a number of dimensions. Each of ξ SA and ξ SA is a constant. The symbol Ψ(r) denotes a function of r and, possibly, of angular coordinates. The symbol ∇ r 2 denotes a Laplacian operator. In some ongoing theory applications, Ω SA is a constant that correlates with aspects correlating with angular coordinates. Our discussion includes the term Ω SA and, otherwise, tends to de-emphasize some angular aspects. We associate the term SA-side with this use of symbols and mathematics. We anticipate that the symbols used correlate with spatial aspects of some physics modeling. We anticipate that TA-side symbols and mathematics pertain for some physics modeling.
The table assumes, without loss of generality, that (ξ SA /2) = 1 and that η SA = 1. More generally, we assume that each of the four terms K _ and each of the two terms V _ includes appropriate appearances of (ξ SA /2) and η SA . The term V +2 correlates with the rightmost term in equation (3). The term V −2 correlates with the rightmost term in equation (4). The four K _ terms correlate with the other term to the right of the equals sign in equation (4). The sum of the two K 0_ terms correlates with the factor D + 2ν SA in equation (7).
Equation (9) correlates with the domains of D and ν SA for which normalization pertains for Ψ(r). For D + 2ν SA = 0, normalization pertains in the limit (η SA ) 2 → 0 + . Regarding mathematics relevant to normalization for D + 2ν SA = 0, the delta function that equation (10) shows pertains. Here, x 2 correlates with r 2 and 4 correlates with (η SA ) 2 . Reference [27] provides equation (10). The dierence in domains, between −∞ < x < ∞ and equation (5), is not material here. (Our use of this type of modeling features normalization. Considering normalization leads to de-emphasizing possible concerns, about variations -as a function of angular coordinates -as r approaches zero, regarding Y (angular coordinates). Considering normalization leads to de-emphasizing possible concerns, regarding singularities as r approaches zero, regarding some Ψ(r).) D + 2ν SA ≥ 0 (9) We use the one-element term volume-like to describe solutions for which D+2ν SA > 0. Here, assuming that we ignore angular coordinates or that a zero value of a factor pertaining to angular coordinates does not pertain, Ψ(r) is non-zero for all r > 0. The term volume-like pertains regarding behavior with respect to coordinates that underlie modeling. We use the one-element term point-like to describe solutions for which D + 2ν SA = 0. Here, Ψ(r) is eectively zero for all r > 0. The term point-like pertains regarding behavior with respect to coordinates that underlie modeling. Some applications feature the numbers of dimensions that equations (11) and (12) show. Equation (11) correlates with a notion of three spatial dimensions. Equation (12) correlates with a notion of one temporal dimension.
We anticipate using equations (13) and (14). Here, each of 2S and 2S T A is a nonnegative integer. (We de-emphasize using the symbol S SA instead of the symbol S.) The case that features equation (13), σ SA = +1, and S = ν SA is a restating of equation (8). The case that features equation (13) and σ SA = −1 correlates with some aspects of proposed theory modeling. (See discussions related to equations (21) and (160).) Similar concepts pertain regarding equation (14) and σ T A .
The following notions pertain.
The symbol S can correlate with ongoing theory notions of spin divided by . The symbol denotes the reduced Planck's constant.
Solutions for which ν SA = −1/2 can correlate with notions of elds for simple fermions.
Solutions for which ν SA = −1 can correlate with notions of elds for simple bosons.
Solutions for which ν SA = −3/2 can correlate with notions of particles for simple fermions.
TA-side PDE solutions are radial with respect to t, the TA-side analog to the SA-side radial coordinate r.
For some solutions, D = D * Along with mathematics correlating with three dimensions and D * SA = 3 and with mathematics correlating with one dimension and D * T A = 1, we anticipate needing mathematics correlating with two dimensions and a case that we denote by D = 2. (Discussion above does not adequately cover the topic of notions of particles for simple bosons. The case of D = 2 is relevant to notions of particles for simple bosons.) Table 12 shows some relationships between some PDE parameters. The symbol XA can denote either SA or TA. Here, we correlate with D the symbols S , ν , Ω , and σ . Each of S , ν , Ω , and σ does not necessarily correlate with uses of S, ν SA , Ω SA , σ SA , S T A , ν T A , Ω T A , or σ T A in models regarding simple particles. For Ω = 0, the table uses the letters NR to denote that the sign of σ is not relevant.
We explore bounds regarding the simple particles that proposed theory suggests.
The order of rows in table 12b correlates with non-decreasing values of Ω SA . A value of spin S correlates with the value of Ω SA . Proposed theory posits that each simple particle correlates with a eld. No larger values of S comport with equation (15). S ≥ 0 and D ≥ 1 (15) 0 ≤ S ≤ 1 (16) Table 12c shows TA-side relationships. Each row correlates with a similar row in table 12b. Here, similarity refers to the information in the columns for which the labels include the two-word term simple particles. For each pair of similar rows, D + 2ν T A = D + 2ν SA pertains. For D + 2ν T A = D + 2ν SA = 0, we require that ξ T A = ξ SA . Equation (17) pertains.

=
For each of simple fermion eld and simple fermion particle, modeling correlates with D + 2ν T A = 0 = D + 2ν SA . The one-element term point-like pertains with respect to TA-side aspects and to SA-side aspects. For the case of S = 0 boson elds, modeling correlates with D + 2ν T A = 1 = D + 2ν SA . The one-element term volume-like pertains with respect to TA-side aspects and to SA-side aspects. For the case of S = 1 boson elds, modeling correlates with D + 2ν T A = −1 = D + 2ν SA . Normalization does not pertain.
Nature includes simple bosons -at least the Z and W bosons -for which S = 1. Table 12b lacks items that would correlate with particles for S = 0 simple bosons or with particles for S = 1 simple bosons. Table 12b notes that solutions for S = 1 boson elds do not normalize.
We explore modeling that uses concepts from each of PDE modeling and ALG modeling. The following notions pertain. The notions provide for PDE solutions -for elds for simple bosons and for particles for simple bosons -that normalize.
Energy times square of time We anticipate applying the following three notions. D XA = 1 correlates with one XA-side one-dimensional harmonic oscillator. Here, XA is one of TA and SA. We label that oscillator as the XA0 oscillator. D XA = 3 correlates with three XA-side onedimensional harmonic oscillators. We label those oscillators as the XA0 oscillator, XA1 oscillator, and XA2 oscillator.
Equation (18) correlates with equations (3) and (4). Here, XA can be either one of TA and SA.
Use of equation (18) allows separation of the terms into clusters. Equation (18) is a sum of D XA terms. Each one of the D XA terms appears in exactly one cluster. For D XA = 1, there is one term (which correlates with the XA0 oscillator) and one cluster (which contains the one term).
For D XA = 3, we use two clusters. One cluster correlates with the XA0 oscillator. One cluster correlates with the XA1-and-XA2 oscillator pair. In the cases of these clusterings (and other possible clusterings), we apply -for each two-oscillator cluster -an analog to equations (3)  Regarding modeling elds for all simple bosons, the following two possibilities pertain.
One can use, for ι S = 0, results that tables 12b and 12c show. One can use, for ι S = 2, the notion of mapping the D = 1 solutions -that tables 12b and 12c show -into the three dimensions that correlate with D = 3. Here, each one of the SA-side solution and the TA-side solution normalizes. Use of D = 3 is not necessarily incompatible with the notion of D = 3 for each of the SA-side and TA-side aspects of the case for which ι S = 0.
One can use the notion that equation (13)  We discuss some aspects of proposed theory modeling. Table 13 notes aspects of PDE mathematics that can pertain for dynamics modeling and ν SA ≥ 0. (For other possible physics applications, for ν SA < 0 and ν SA ≥ 0, see table 11.) In table 13, the associations that the rst row shows provide a basis for the remaining rows. The row that notes ξ SA (η SA ) +2 might point to a series -momentum, angular momentum, and angular momentum times length.
PDE-based modeling might correlate with some aspects of unication of the strong, electromagnetic, and weak interactions. We consider modeling for which 2ν SA is a non-negative integer. Based on the r −2 spatial factor, the V −2 term might correlate with the square of an electrostatic potential. Based on the r 2 spatial factor, the V +2 term might correlate (at least, within hadrons) with the square of a potential correlating with the strong interaction. The sum K 0a + K 0b might correlate with the strength of the weak interaction. (The eective range of the weak interaction is much smaller than the size of a hadron. Perhaps, the spatial characterization r 0 correlates with an approximately even distribution, throughout a hadron, for the possibility of a weak interaction occurring.) Based on the V −2 term, we expect that ξ SA includes a factor 2 .
Electrostatics includes each of interactions that attract objects to each other and interactions that repel objects from each other. One might consider the possibility that, in some modeling, the term proportional to Ω SA /r 2 might seem to allow for repulsion, but not for attraction. (See equations (3) and (4).) However, when equations (17), (19), and (20) pertain, one can swap the Ω SA /r 2 term and the Ω T A /t 2 term in equation (17). The swap leads, in eect, to a new Ω SA /r 2 that has the opposite sign as the old Ω SA /r 2 . The new Ω SA /r 2 would correlate with attraction. For some aspects of modeling, equations (21) and (22) pertain.
A swap, regarding the TA-side (η T A ) −2 t 2 term and the SA-side (η SA ) −2 r 2 term, could lead to modeling that pertains to some aspects of repulsion. ( We note some aspects that this essay de-emphasizes.
This essay de-emphasizes thoroughly discussing the extent to which r, as used regarding QPT modeling pertaining to the existence of simple particles, correlates with coordinates that people might use for spatial aspects of ongoing theory dynamics modeling regarding motion within systems. This essay de-emphasizes thoroughly discussing the extent to which r, as used regarding QPT modeling pertaining to the existence of simple particles, correlates with coordinates that people might use for spatial aspects of ongoing theory kinematics modeling. Similar notions pertain regarding t, as used regarding QPT modeling pertaining to the existence of simple particles. This essay de-emphasizes exploring the extent to which allowing for variation, regarding η SA or η T A , with respect to ongoing theory notions of time or proper time leads to useful models regarding diusion.

A table of free simple particles
This unit shows a table of known free simple particles and proposed free simple particles. Table 14 lists all known free simple particles and all free simple particles that proposed theory suggests.
(Compare with table 8.) QPT work leading to table 12 does not depend on making assumptions regarding m>0 and m=0. QPT assumes that a partial symmetry between m>0 and m=0 pertains. In table 14a, the m=0 column reects that partial symmetry. Regarding ι S = 2S, ongoing theory might suggest a possibility for adding photons. Table 3 might correlate with this notion. However, our development classies 2G as other than a simple particle. Our PDE modeling correlates 2G, in eect, with inputs to modeling that, in eect, outputs table 14a. Equation (23) explains the notation |ι Q |=3. For the case of |ι Q |=3 and m=0, only |ι Q | = 0 pertains. |ι Q |=n denotes |ι Q | = n or 0 (23)

ALG representations for free elementary particles
This unit discusses ALG modeling. This unit discusses ALG representations for free elementary particles. This unit discusses symmetries that correlate with ALG modeling and with some conservation laws. The unit discusses the notion of somewhat conservation of fermion generation.
We discuss aspects of ALG modeling.
Ongoing theory describes photon states via two harmonic oscillators. Ongoing theory features four space-time dimensions. Why not describe photon states via four harmonic oscillators?
Proposed theory describes photon states via four harmonic oscillators. A rst hunch might be that doing so correlates with non-zero longitudinal polarization and a photon rest mass that would be nonzero. However, mathematics allows a way to avoid this perceived possible problem. A second hunch  We consider the left circular polarization mode of a photon. We denote the number of excitations of the mode by n. Here, n is a nonnegative integer. One temporal oscillator pertains. We label that oscillator TA0. The excitation number n T A0 = n pertains. Here, n T A0 = n ≥ 0 pertains. Harmonic oscillator mathematics correlates a value of n + 1/2 with that oscillator. Three spatial oscillators pertain.
Here, n SA0 = −1, n SA1 = n, n SA2 = @ 0 . Oscillator SA0 correlates with longitudinal polarization and has zero amplitude for excitation. (See equation (26).) Oscillator SA1 correlates with left circular polarization. Oscillator SA2 correlates with right circular polarization. The symbol @ _ denotes a value of _ that, within a context, never changes. For left circular polarization, @ 0 pertains for oscillator SA2. The sum n + 1/2 correlates with each of the one TA-side oscillator and the three SA-side oscillators. For the SA-side oscillators, the sum equals (−1 + 1/2) + (n + 1/2) + (0 + 1/2). Table 15 shows excitations for the left circular polarization mode of a photon. For the right circular polarization mode, one exchanges the values of n SA1 and n SA2 . The result is n SA1 = @ 0 , n SA2 = n.
The representation that table 15 shows is invariant with respect to observer. In ongoing theory, each observer would measure both left circular polarization and the same value of n. Observers might disagree with respect to measured values of energy or momentum.
The following concepts and generalizations pertain.
The above discussion correlates with the two-word term ALG modeling. ALG is an abbreviation for the word algebraic. Elsewhere, we discuss PDE modeling. (See discussion related to equation (17).) PDE abbreviates the three-word term partial dierential equation.
For ALG modeling, equation (24) The above discussion extends the domain correlating with equation (25) from n ≥ 0 to n ≥ −1.
Here, a + denotes a harmonic oscillator raising operator. The symbol |_ > correlates with the notion of quantum state. The |n > denotes the notion that the state correlates with n excitations.
One can sum any positive number of values of A ALG . The sum is always zero. We suggest that the expression A ALG = 0 provides a basis for modeling that avoids ongoing theory concerns about unlimited sums of ground state energies.
Some aspects of ALG modeling include notions that people might consider to correlate with the three-word term below ground state. For example, consider the SA-side representation for the ground state of the left circular polarization mode. The proposed theory ground state sum is onehalf. People might think that the ground state sum for a three-dimensional isotropic quantum harmonic oscillator should be three-halves, as in 3 · (0 + 1/2). Regarding equation (6), applications for which ν SA < 0 pertains can exhibit aspects correlating with the term below ground state. Applications for which ν SA ≥ 0 pertains do not exhibit aspects correlating with the term below ground state.
We return to discussion that relates to and extends table 15. Table 17 shows excitations for a photon. For each mode, we posit that the U (1) symmetry that correlates with the permutation (appropriate to the mode) of π n,@0 correlates with the U (1) symmetry that the elementary particle Standard Model associates with photons. One generator correlates with excitation. One generator correlates with de-excitation.
We attempt to represent elementary particles other than photons.   We generalize from work above. We assume that the oscillator pair SA1-and-SA2 correlates with charge or with interactions with charge. We note that ongoing theory interrelates photons and weak interaction bosons. negative charge with SA2 and positive charge with SA1. We do not explore this possibility further. This essay does not explore the possibility of a link between such an assignment regarding charge and the assignment of photon circular polarization modes.) Elsewhere, we discuss a reason, within the bounds of A ALG = 0, for placing κ 0,0 with the TA5-and-TA6 oscillator pair. (See table 38.) We discuss W-family excitations. To describe n excitations of the same state of one of the bosons, we use n T A0 = n = n SA_ , with SA_ correlating with the one boson. An isolated interaction that excites or de-excites the boson conserves the generation of the fermion that participates in the interaction.
For example, an interaction between an electron (or, generation-one charged lepton) and a W +3 boson produces a generation-one neutrino. We say that conservation of generation pertains. We consider some  that table 18 shows to the state characterized by n T A0 = 2, n SA0 = 0, n SA1 = 1, and n SA2 = 1 would violate equation (29). The TA-side raising operations would produce a factor of (1 + 0) 1/2 (1 + 1) 1/2 , which equals 2 1/2 . The SA-side raising operations would produce a factor of (1 + 0) 1/2 (1 + 0) 1/2 , which equals 1.) Equations (29) and (30) imply that one of oscillators TA5 and TA6 participates. There are three generations of quarks. Three is the number of generators of SU (2). We posit that an approximate SU (2) symmetry pertains. (See table 16.) We use the four-word term somewhat conservation of generation (or, the ve-word term somewhat conservation of fermion generation). Ongoing theory seems to correlate this proposed theory notion of non-conservation of generation with the ongoing theory notion of CP violation. (See, for example, reference [28].) We note the possibility that, in appropriate settings, one might be able to detect non-conservation, induced by W-family eects, of lepton generation. (Reference [28] suggests that people may be on the verge of observing evidence of lepton CP violation.) Such a setting might need to be adequately conducive to multiple nearby interactions involving W bosons. Here, the word nearby pertains regarding both ongoing theory notions of temporal aspects and ongoing theory notions of spatial aspects.
We discuss an ongoing theory W-family symmetry. Ongoing theory associates SU (2)×U (1) symmetry with the weak interaction. For proposed theory, we associate U (1) symmetry with excitation and deexcitation regarding each of the three SA-side oscillators. This aspect has parallels to the U (1) symmetry that pertains for photons. We associate SU (2) symmetry with a combination of n W −3 = 0 and n W +3 = 0. For the W-family, the SU (2) and U (1) symmetries combine to form κ 0,0 (or, SU (2) × U (1)).
We extend proposed theory ALG modeling to include the Higgs boson. Table 19 shows excitations for the Higgs (or, 0H) boson. The ground state value n SA0 = 0 correlates with the non-zero mass of the Higgs boson. The lack of an SA1-and-SA2 entry correlates with the Higgs boson having zero charge and not interacting with charge.
A number of SA-side oscillators seems to correlate with each of spin and numbers of particles. For   Table 21 shows representations for 0I, 1C, and 1N simple particles. Each state for which the one-word term boson (or, the result that 2S is an even integer) pertains comports with equation (35). For fermions (or, for particles for which 2S = 1), equation (35) pertains, given two assumptions. One assumption is that we do not count the SA5-and-SA6 oscillator pair, which correlates with SU (2) symmetry, three generators for that group, and three generations of simple particles. One assumption is that each of n SA1 = −1 and n SA2 = −1 disables one oscillator and, in eect, leads to the result N SA = 2. For each of charged leptons and neutrinos, states are either populated or not populated. Each of charged leptons and neutrinos exhibits a TA5-and-TA6 approximate SU (2) symmetry. That symmetry correlates with somewhat conservation of fermion generation. For each of charged leptons and neutrinos, the SA1and-SA2 appearance of a U (1) symmetry may seem surprising. Unlike for elementary bosons, multiple excitations for a single state do not pertain. However, multicomponent objects can include more than one identical (for this discussion) fermion. For example, an atom can contain more than one electron. Table 14 provides a roadmap for developing representations for non-zero spin simple particles for which we do not show representations above. A representation for each unfree non-zero spin simple particle equals the representation for the corresponding free simple particle. For example, a representation for the 1Q 2 j quarks equals the representation for the 1C 3 j charged leptons.

Kinematics conservation laws
This unit shows modeling regarding conservation of energy, momentum, and angular momentum.
We want to discuss the extent to which proposed theory models for ΣG (or, G-family) elds reect encoded information.
We start by exploring modeling related to energy, momentum, and angular momentum.
Ongoing theory discusses models for objects, internal properties (such as spin and charge) of objects, motion-centric properties (such as linear momentum) of objects, and interactions (or, forces) that aect internal properties of objects or motion of objects.
We discuss symmetries that ongoing theory and proposed theory correlate with conservation laws related to motion. Table 23 summarizes symmetries correlating with kinematics conservation laws. Ongoing theory correlates an S1G symmetry with conservation of energy. The one-element term S1G denotes a symmetry correlating with a group for which one generator pertains. Proposed theory considers this S1G symmetry to be a TA-side symmetry. Proposed theory considers that this S1G symmetry correlates with the TA0 oscillator. Ongoing theory correlates an SU (2) symmetry with conservation of linear momentum and an SU (2) symmetry with conservation of angular momentum. Proposed theory considers that each one of these SU (2) symmetries is an SA-side symmetry.
The following concepts pertain.
We extend the notion of free to include free objects other than the free simple particles and free root forces to which table 3 alludes. The notion of free correlates with an object having a well-specied denition and with the object modeling, under some circumstances, as if conservation of energy, momentum, and angular momentum pertain for the object.
Models for the kinematics of free objects need to include the possibility that all three conservation laws pertain. The relevance of all three conservation laws correlates with modeling that correlates with the notion of a distinguishable object and with the notion of a free environment. (Free objects can exist as components of, let us call them, larger objects that are free. For one example, an electron can exist as part of an atom. For another example, a hadron can exist as part of an atomic nucleus that includes more than one hadron. In such contexts, modeling of the kinematics of the electron or hadron does not necessarily need to embrace all three conservation laws. The two-word term conned environment can pertain.) Models regarding the kinematics of unfree objects do not necessarily need to embrace all three kinematics conservation laws. Unfree objects model as existing in the contexts of larger free objects.
The two-word term conned environment pertains.
For an ALG model to embrace conservation of linear momentum and conservation of angular momentum, one, in eect, adds (to a model for an object) four SA-side oscillators and expresses two instances of SU (2) symmetry. Double-entry bookkeeping suggests adding four TA-side oscillators. Proposed theory suggests that, for each of the eight added oscillators, n _ = n T A0 . For at least some modeling, proposed theory suggests combining the four TA-side oscillators with the TA0 oscillator to correlate with an SU (5) symmetry. For such modeling, proposed theory suggests that the TA-side SU (5) symmetry correlates with conservation of energy. (See table 23.) Table 24 shows representations of kinematics conservation laws for free objects. The choice of oscillator pairs XA11-and-XA12 and XA13-and-XA14 correlates with the possibilities for other uses for oscillators XA0-through-XA10. (See discussion related to equation (63).) Here, we know of no correlation between oscillator pair SA11-and-SA12 and spin (for example, a spin of six). Here, we know of no correlation between oscillator pair SA13-and-SA14 and spin (for example, a spin of seven).
Special relativity correlates with boost symmetry, which correlates with an additional SU (2) symmetry. We suggest the possibility for using the oscillator pair SA15-and-SA16 to represent boost symmetry or a lack of boost symmetry. When boost symmetry applies, we suggest maintaining the notion of double-entry bookkeeping but not extending the TA-side symmetry from SU (5) to SU (7). Boost correlates with modeling and not with kinematics conservation laws.
A contrast between tables 20b, 21, and 22 and table 24 pertains. Some information in tables 20b, 21, and 22 correlates with symmetries and conservation laws (or with approximate symmetries and somewhat conservation laws) that pertain regarding quantum excitations. Some information in table 24 correlates with conservation laws that pertain regarding kinematics.
The following modeling can pertain regarding combining two free objects to form one free object.
Each of the two original objects contributes two SA-side SU (2)

G-family forces
This unit discusses aspects regarding G-family forces and regarding components of G-family forces.
This unit shows modeling that links free simple bosons and G-family forces.
We explore modeling that encodes, regarding 2G modes, information about excitations of the overall 2G eld. We consider the left circular polarized mode. Modeling for some excitations correlates with aspects of table 15.
We might also consider an excitation that models -at least conceptually -as combining an excitation of the left circular mode of 4G and the right circular mode of 2G. The combination yields a left circular polarization spin-1 excitation. The combination correlates with 2G.
Equation (36) provides notation that we use for such combinations. The symbol ΣG denotes a subfamily of the G-family of solutions to equation (24). The symbol Γ denotes a set of even integers selected from the set {2, 4, 6, 8}. We use the symbol λ to denote an element of Γ. Each value of λ correlates with the oscillator pair SA(λ − 1)-and-SAλ. (Elsewhere, we discuss aspects correlating with the limit λ ≤ 8. See discussion related to table 26.) For the above example of subtracting spin-1 from spin-2, the notation Γ = 24 pertains and equation (37) pertains. (36)    We posit that the words monopole through octupole correlate, for Newtonian physics modeling, with force laws. Ongoing theory correlates the word monopole with a potential energy that varies as r −1 and with the RSDF of r −2 . Here, r denotes the distance from the center of the one relevant object.

ΣGΓ
RSDF abbreviates the ve-word term radial spatial dependence of force. Here, we de-emphasize angular aspects of forces. (Discussion related to table 28 shows relationships between some solutions that table 25 lists and aspects of ongoing theory. For example, 2G2 correlates with interactions with charge. 2G24 correlates with interactions with nominal magnetic dipole moment.) Table 26 shows representations for the G-family solutions that table 25 lists. The solutions correlate with symmetries pertaining to ground states. For the case of Σ being two, excitations comport with the type of ΣG excitations to which table 17 alludes. For the cases of Σ being four, six, or eight, excitations comport with the type of ΣG excitations to which table 22 alludes. In table 26. the rightmost seven columns comport with double-entry bookkeeping. For example, a TA-side SU (3) symmetry alludes to two additional TA-side oscillators for each of which n T A_ = 0. Those two oscillators plus the TA0 oscillator correlate with κ 0,0,0 (or, with SU (3) symmetry). The symbol A0+ correlates with an oscillator pair for which, for each of the two oscillators, the symbol @ 0 pertains. (Perhaps, see table 16.) The column regarding span pertains regarding aspects of dark matter. (See table 57.) Regarding each Σ > 0 solution that the table shows, the radial behavior of the potential is r n SA0 . The RSDF is r n SA0 −1 .
The TA-side SU (_) symmetries that table 26 shows pertain regarding kinematics and do not pertain regarding excitations. (See discussion regarding table 24.) One might think of these symmetries as correlating with oscillators TA0, TA11, TA12, TA13, and TA14.
Regarding elementary particle physics, we note three notions that might correlate with a limit of λ ≤ 8. Possibly, each one of the three notions is relevant. The limit might correlate with a scaling law. For the Γ of 2468 10 , the one-element phrase hexadecimalpole would pertain. Here, the symbol 10 denotes the number ten. Assuming Newtonian modeling, the RSDF (or, radial spatial dependence of force) would be r −6 . We consider interactions between two similar, neighboring, non-overlapping, somewhat spherically symmetric objects. A ΣG2468 10 force would scale like (υ 3 ρ) 2 /(υr) 6 , in which υ is a non-dimensional scaling factor that correlates with linear size (or, a length), ρ is the relevant object property for the case for which υ = 1, and r is the distance between the centers of the objects. The factor υ 3 provides for scaling for an object that has three spatial dimensions.
The force would be independent of υ. That independence might suggest, from a standpoint of physics, that = 0 pertains. The limit might correlate with a TA-side SU (9) symmetry. Based on thinking that leads to table 26, 10G 10 correlates with a TA-side SU (9) symmetry. Here, the symbol 10 denotes a Γ that contains just the number ten. We posit that remarks regarding equation (34) pertain. Here, we de-emphasize the notion that 16G 16 might be relevant to physics. (See discussion related to table 69.) The solution 16G 16 would correlate with TA-side SU (17) symmetry.
The limit might correlate with the notion of channels. Discussions related to equation (61) and to equation (67) suggest that a λ that exceeds eight is not relevant regarding G-family physics.
Each one of the following two sentences might pertain. Detecting eects of ΣGΓ components for which each of Σ ≥ 10 and λ ≤ 8 pertains would be dicult. Regarding nature, the series 2GΓ, 4GΓ, . . . ends with 8GΓ.
We de-emphasize possibilities that solutions ΣGΓ for which Σ ≥ 10 correlate with G-family physics.
(Discussion regarding equation (49) points to mathematical modeling relevance, to physics that is not G-family physics, of solutions ΣGΓ for which Σ ≥ 10.) Table 27 lists G-family solutions ΣGΓ for which both Σ does not exceed eight and Σ appears in the list Γ. The expressions | − 2 + 4 − 6 + 8| and | − 2 − 4 − 6 + 8| show that two solutions comport with the notion of 4G2468. The expressions | + 2 + 4 − 6 + 8| and | − 2 − 4 + 6 + 8| show that two solutions comport with the notion of 8G2468. We use the symbol Σγ to refer to the set of G-family solutions ΣGΓ for which Σ appears in the list Γ. (See equation (38).) We use the symbol γλ to refer to the set of G-family solutions ΣGΓ for which λ appears in the list Γ and Σ does not appear in the list Γ. (See equation (39).) Proposed theory correlates the two-word term monopole gravity (or, the four-word term monopole component of gravity) with the 4G4 solution. Proposed theory correlates the three-word term dark energy correlate also with -regarding ongoing theory -eects for which people might not use the term dark energy forces.  Statements above regarding 2G and 4G dovetail with concepts that equations (40) and (41) symbolize.
In proposed theory, modeling regarding quantum states and excitations does not necessarily involve modeling pertaining to translational motion. Equation (40)  ΣG ↔ quantum excitations (40) ΣGΓ ↔ a bridge between quantum excitations and kinematics forces (41) We explore the extent to which components of G-family forces interact with simple particles.
For example, 2G68 can interact with an atom but not with an isolated electron. (Table 26

The U family and simple bosons related to U-family forces
This unit shows representations correlating with U-family bosons. This unit correlates some simple bosons with aspects of U-family mathematics but not with U-family forces. Table 29 shows representations for 2U forces and for possible 4U root forces. Each representation comports with equation (35). Each representation includes symmetries that comport with somewhat  We correlate aspects of ΣU solutions with the pie (or, 0P) and cake (or, 0K) bosons.  Table 31 suggests representations for the 0K and 0P bosons. Each one of the cake simple particle and pie simple particle does not interact with simple fermions.
The mass of the pie simple boson might approximate the masses of pions. We do not explore theory that might correlate with the mass of pie simple bosons.  Proposed theory suggests a symmetry regarding ι Q . The symmetry suggests, regarding non-zero-spin simple particles, that each of the cases ι Q = 2 and ι Q = 1 is similar to the case ι Q = 3.
We suggest correlating, with ι 3LB , the two-element term 3LB number. People might want to use the four-element term conservation of 3LB number.   • For free objects, the minimum magnitudes of some non-zero quantities are |q | for charge and three for |ι 3LB |.
• For unfree objects, the minimum magnitudes of some non-zero quantities are |q |/3 for charge and one for |ι 3LB |.
• Each of the quantities charge, ι 3LB , L, and B is additive with respect to components of a multicomponent object.
Proposed theory includes the notion of conservation of ι 3LB .
Each of equations (43), (44), (45), and (46) shows an interaction that would involve the 2T +1 simple particle; transform a matter quark into another simple fermion; and conserve ι 3LB , L, and B. Here, for fermions, the notation 1Φ ι Q ι 3LB ;3L,3B pertains. Here, for bosons, equations show notation of the form 2Φ ι Q ι 3LB ;3L,3B and might suggest that each of L, conservation of L, B, and conservation of B is appropriate. However, discussion related to equation (47) More generally, equation (47) This essay de-emphasizes the possibilities that equation (48) shows.
Regarding equation (47), each of the four possibilities, of which one possibility is 2T +1 −2; , correlates with two possible L-and-B pairs. We assume that charged 2T bosons are ambiguous with respect to each of L and B. Generally, interactions conserve ι 3LB , do not necessarily conserve L, and do not necessarily conserve B. Non-conservation of L and B correlates with involvement -in the interactions -of 2T ± bosons. One might deploy the ve-word phrase somewhat conservation of lepton number and the ve-word phrase somewhat conservation of baryon number. Table 33 notes concepts regarding values, for objects, of ι 3LB , L, and B. Here, we consider that a proton or other hadron with no more than three quarks can correlate with the notion of free. The following notion also pertains. For a hadron-like particle that includes no more than three quarks and arcs, the restrictions to integer charge and integer baryon number preclude the presence of both quarks and arcs. Table 34 shows changes, to representations, to reect conservation of lepton number minus baryon number. Non-zero charge T-family bosons provide the only way to change either the lepton number or the baryon number of a fermion.

Conservation of charge
This unit shows modeling that correlates with conservation of charge. Table 35 shows changes, to representations, to reect conservation of charge. All interactions conserve charge.

Simple bosons that are related to G-family solutions
This unit correlates some simple bosons with zero-spin solutions that correlate with G-family mathematics but not with G-family force components.
Proposed theory suggests that 2T 0 and 2T 0 correlate with the rst two solutions that equation (49) shows. The last two solutions that the equation shows would correlate, in some order, with 2T 2 and 2T 1 .
We use these results to estimate masses for 2T simple bosons. (See discussion related to equation (104).)

ALG modeling regarding rest energy and freeable energy
This unit suggests ALG modeling pertaining to rest energy and freeable energy.
Some modeling points to quantities that come in integer units and that add. Examples of additive quantities include charge and lepton number minus baryon number. Related integer forms are, respectively, ι Q and ι 3LB . For each of ι Q and ι 3LB , modeling correlates with U (1) symmetry.
Possibly, people can develop useful similar modeling regarding other quantities.
For example, modeling pertaining to a combination of the 4G property of rest energy and the 6G property of freeable internal energy might correlate with aspects of equation (50). Here, SU (4) might pertain regarding oscillators SA3 through SA6. For some modeling, work above correlates SU (2) with the SA3-and-SA4 oscillator pair. Perhaps, the other SU (2) correlates with the SA5-and-SA6 oscillator pair. Perhaps, for some modeling, the U (1) correlates with an additive quantity.
The term −f SA correlates with the SA5-and-SA6 oscillator pair and one SU (2) symmetry. The term f SA is the square of a freeable energy. For f SA > 0, f SA might, for example, correlate with models for transitions of quarks from higher-mass generations to quarks of lower-mass generations. For f SA > 0, f SA might correlate with models for beta decay via the weak interaction. The relevant U (1) symmetry correlates with a conservation law. (See equation (50).) For example, lowering the square of rest energy (mc 2 ) 2 correlates with lowering the square of relevant freeable energy f SA . The relevant U (1) symmetry correlates with a value that can add across similar systems.
In equation (51), the term +(P J SA c) 2 might correlate with an energy that correlates with observed angular momentum. The terms +(P c) 2 and +(P J SA c) 2 might correlate with oscillators SA11 through SA14 and with a combination of conservation of angular momentum and conservation of momentum.
In equation (51), the expression −f T A + (P J T A c) 2 correlates with the TA-side SU (4) symmetry. The TA-side SU (4) symmetry correlates with the proposed theory notion of an SU (5) symmetry that correlates with conservation of energy. The TA-side SU (4) symmetry also correlates with the ongoing theory notion of an S1G symmetry that correlates with conservation of energy. (See table 37.) Presumably, f T A ≥ 0 pertains.
For each of a binary star system and a hydrogen atom, +(P J T A c) 2 correlates with an ability to transit to a state of lower rest mass. The term −(P J SA c) 2 correlates with an ability to transit to a state of higher rest mass. Table 38: Concepts relevant to some simple particles for which Σ = 1 or Σ = 2 (with χ −1,0 denoting -for n SA0 -a choice of minus one or zero; with the fourth column providing information correlating with the relevant symmetry; and with the three-element item SCons of generation abbreviating the four-word term somewhat conservation of generation) XA_ SA-side Symmetry Regarding equation (53), the term −(P J SA c) 2 might correlate with the term -in equation (4) -that is proportional to Ω SA /r 2 . In equation (3), the sign of the relevant term would be positive, just like the sign of the term that is proportional to r 2 . The Ω SA /r 2 term might correlate with a notion of, in eect, an ability to store freeable energy. The term +(P J T A c) 2 might correlate with the term -in the TA-side analog to equation (4) -that is proportional to Ω T A /t 2 .
3.3.6. Relationships regarding three charges and three generations for some simple particles This unit discusses relationships, pertaining to some simple particles, regarding numbers of charges, numbers of generations, and relevant symmetries.  (52) and (53). Table 38 does not discuss the Higgs, aye, pie, and cake simple bosons.

Modeling regarding refraction and similar phenomena
This unit discusses proposed theory modeling regarding the refraction of light. This unit discusses modeling regarding the existence of neutrino oscillations. This unit points to modeling regarding gluons.
We explore modeling regarding contexts in which a zerolike rest mass elementary particle interacts Mathematically, there are four cases to consider. The case of free and n T A0 = 0 pertains for Gfamily forces. The case of free and n T A0 = −1 pertains for (at least) neutrinos. The case of unfree and n T A0 = −1 pertains for gluons. The case of unfree and n T A0 = 0 is not necessarily physics-relevant. (Proposed theory does not predict the existence of unfree simple particles for which n T A0 = n SA0 .) Each of equations (54) and (55) oers, based on using the range −1 < n SA0 < 0, a possible basis for modeling regarding the zerolike rest mass elementary particle. (We contrast −1 < n SA0 < 0 with n SA0 < −1. Uses of the expression n SA0 < −1 pertain for applications related to components of Gfamily forces, for some modeling regarding gluons, and not necessarily for other purposes. Regarding the applications related to components of G-family forces, see Here, double-entry bookkeeping pertains to models for which at least one of the TA-side set of harmonic oscillators and the SA-side set of harmonic oscillators is not necessarily isotropic. For each of the three physics-relevant cases, each of equations (54) and (55) For the case of free and n T A0 = −1, for each relevant SA-side oscillator, n SA_ = −1. One cannot satisfy double-entry bookkeeping by adding to A ALG SA . Satisfying double-entry bookkeeping correlates with adding something positive to at least one of the two TA-side oscillators that correlate with SU (2) somewhat conservation of generation symmetry or to at least one of the TA-side oscillators that correlate with conservation of energy symmetry. This case correlates with neutrino oscillations.
For the case of unfree and n T A0 = −1, discussion is not as straightforward as is discussion for the other two physics-relevant cases. Discussion related to table 39 and table 40 pertains regarding gluons.
(See discussion related to equation (56).) Each of the three relevant cases might point to opportunities to develop new modeling. People might try to express kinematics conservation laws in terms of combinations, across modeling for each of a few interacting particles, via harmonic oscillator math. People might try to develop parallels to ongoing theory equations that, for example, sum momenta. We choose not to pursue -in this essay -such possible opportunities.

Gluon interactions
This unit discusses aspects regarding modeling gluons and modeling U-family interactions.
The 2U solutions correlate with gluons. Here, we provide details correlating with ALG modeling and with the κ −1,−1,−1 interaction centric symmetry that correlates with the relevant ongoing theory SU (3) symmetry.
We denote the three relevant oscillators by the symbols SA0, SAo, and SAe. (See table 29a.) Here, o denotes a positive odd integer and e denotes the positive even integer that is one greater than o. Table 39 shows details regarding 2U solutions. The expression κ −1,−1,−1 correlates with A ALG T A = −3/2. Each one of the six SA-side π 0,−1,−2 permutations pertains. Each permutation correlates with A ALG T A = −3/2. Table 39 suggests notation for gluon-related solutions. The set of three permutations for which 0, −1, and −2 appear in cyclic order correlates with interactions with one of unfree matter simple fermions and unfree antimatter simple fermions. The set of the other three permutations correlates with the other choice between unfree antimatter simple fermions and unfree matter simple fermions.
Regarding unfree matter simple fermions, each of oscillators SAe, SAo, and SA0 correlates with a color charge. Relative to an ongoing theory standard representation for gluons, one of SAe and SAo correlates with the color red, the other of SAe and SAo correlates with the color blue, and SA0 correlates with the color green.
Ongoing theory correlates gluons with zero mass and with phenomena that proposed theory correlates with 2U solutions. We consider 2U phenomena regarding dynamics inside hadron-like particles. In such a frame of reference, proposed theory modeling based on equations (56) and (57) pertains. (Perhaps, compare with discussion, pertaining to refraction, regarding equations (54) and (55).) Here, the notation a ← b correlates with the three-element phrase a becomes b (or, with the notion that b replaces a). Here, the symbol → denotes, in the mathematical sense of a limit, the two-word phrase goes to.
A gluon correlates with a weighted sum of two or three erase-and-paint pairs. For each pair, the erase part correlates with, in eect, an ability to erase, from the unfree simple fermion that absorbs the gluon, a color. The paint part correlates with, in eect, an ability to paint, on to the unfree simple fermion that absorbs the gluon, a color. The value n SA_ = 0 denotes an ability for a gluon to erase or paint the color charge correlating with the SA_ oscillator. Equation (60)  Each of equation (61) and equation (62) Proposed theory suggests that each channel can correlate with a unique blank (or, κ 0,−1 ) SA-side oscillator pair in the range from SA3-and-SA4 through SA9-and-SA10. (Perhaps note table 17 and table   22.) For this purpose, isotropic weighting pertains regarding oscillator pairs.
We discuss possible aspects of modeling for an interaction that de-excites a G-family boson. The following notions pertain.
The incoming state de-excites by transferring one unit of excitation to one of the channels. For that channel, equation (63) pertains.
The new SA-side SU (2) symmetry adds an extra kinematics-conservation-like symmetry that cannot last. (See table 23.) The interaction includes converting the κ 0,0 symmetry to something, pertaining  (63) and an SA-side application of equation (63).
We think that the notion does not adversely impact results to which we allude.) The We explore relationships between masses of the 2W (or, W and Z), 0H, and 0I bosons. Table 41 shows, in the column for which the label includes the word experimental, rest energies for the known non-zero-mass simple bosons. (See reference [17].) Notation such as 2W1 and 0H0 extends the notion of Γ -as pertaining to oscillators relevant in ALG models for G-family solutions -to notions of Γ for ALG models relevant to elementary particle families other than the G family. The most accurately known of the three masses is the mass of the Z boson. The column for which the label includes the word calculated shows results based on equation (64) and on assuming that nine correlates with the square of the mass of the Z boson. Equation (65) shows the size of one unit. The related mass is ≈ 30.396GeV/c 2 . In We discuss approximate ratios for the squares of masses of the Higgs, Z, and W bosons. Based on the ratios (of squares of masses) that equation (64) shows, the possibly least accurately suggested mass is that of the W boson. Equation (64) 12e.) The following correlations might pertain regarding relative squares of masses. (See table 36 and table   12e To the extent that m W does not exactly comport with equation (64) We explore concepts regarding 0G∅.
One might assume that the 0I solution correlates with S = j λ∈Γ = 0. (See table 36.) The result S = 0 correlates with a relative square of mass of one. (See table 12e.) The mass would approximately equal 30.4GeV/c 2 . We know of no observations that would support the existence of such a particle. We note that, for each of the W, Z, and Higgs bosons, the 0GΓ solution has n T A0 = 0. (See table 26.) For the 0G∅ solution, n T A0 = −1.
For each Σ ≥ 2 ΣGΓ solution that nature embraces, the mass is zero. We suggest that each solution correlates with σ = +1 and S = 1. Per table 12e, the relative mass correlates with D + 2ν = 0.
We suggest that the 0G∅ solution correlates with σ = +1 and S = 1. The notion of zero mass pertains.

A prediction for the tauon mass
This unit suggests a relationship, which ongoing theory seems not to discuss, between the ratio of the tauon mass to the electron mass and a ratio of a strength of electromagnetism and the strength of gravity. This unit discusses the notion that adequately increasing the experimental accuracy of either one of the tauon mass and the gravitational constant leads to a prediction regarding the other quantity.
This unit discusses aspects, related to G-family physics, that the ratio of force strengths suggests. This unit discusses the concept of channels.
Equation (68) possibly pertains. Here, m denotes mass, τ denotes tauon, denotes electron, q denotes charge, ε 0 denotes the vacuum permittivity, and G N denotes the gravitational constant. Equation (68) predicts a tauon mass with a standard deviation of less than one eighth of the standard deviation correlating with the experimental result. (For relevant data, see reference [29].) Equation (71) shows an approximate value of β that we calculated, using data that reference [29] shows, via equation (67).) β ≈ 3477.1891 ± 0.0226 (71) The factor of 4/3 in equation (67) correlates with notions that 2G2 correlates with four so-called channels and 4G4 correlates with three channels. For a 2G2 interaction between two electrons, the strength for each channel is ((q ) 2 /(4πε 0 ))/4 and four channels pertain. For a 4G4 interaction between two electrons, the strength for each channel is G N (m ) 2 /3 and three channels pertain. Equation (72) characterizes a per channel ratio that pertains for interactions between two electrons.
The following notes pertain.
To the extent that equation (68) correlates with nature, a more accurate experimental determination of G N or m τ could predict a more accurate (than experimental results) value for, respectively, m τ or G N .
Equation (68) links the ratio of two simple particle masses to a ratio of the strengths of two G-family force components.
Equation (68) For this discussion, we assume that we can work within aspects of proposed theory that de-emphasize translational motion. Below, the symbol 1f correlates with a non-zero-charge non-zero-mass simple fermion that pertains throughout the discussion. We conne our attention to 1f1b→1f1b interactions such that the exiting simple fermion is the same as the entering simple fermion. Each symbol 1b denotes a boson. The outgoing boson is not necessarily the same as the incoming boson. The simple fermion correlates (as do all simple fermions) with S = 1/2 (or, Σ = 1). Regarding modeling, we assume that no translational motion pertains. Hence, no kinematic angular momentum pertains. We assume that conservation of angular momentum pertains. Below, in a symbol of the form 1f1b(Σ = _), the expression Σ = _ pertains for the boson.
The expression that equation (75)  The expression 1f1b(Σ = 2)→1f1b(Σ = 0) can pertain for each of the following cases -1b(Σ = 2) correlates with 2G, 1b(Σ = 2) correlates with 2W, and 1b(Σ = 2) correlates (for a case in which unfree pertains for the 1f particle) with 2U. This notion might correlate with ongoing theory notions that correlate with relationships between the strengths of the electromagnetic, weak, and strong interactions.  : Possible relevance -regarding some interaction strengths -of the ne-structure constant (with the symbol O denoting the two-word term ongoing theory; with the symbol P denoting the two-word term proposed theory; and with the symbol * denoting the expression (

The masses of quarks and charged leptons
This unit shows a formula that links the masses of the six quarks and three charged leptons.
We discuss a formula that approximately ts the masses of the six quarks and three charged leptons.
Based on equations (64) and (77) and based on modeling for the G-family, proposed theory might entangle concepts related to mass and concepts related to charge more deeply than does ongoing theory.
Equations (88) and (89) explore the possibility for a relationship -perhaps similar to equation (67) -regarding the ratio m µ /m or the ratio m τ /m µ . Equation (90) shows the result that we compute based on data from reference [17]. Equation (91) shows the result that we compute based on data from reference [29]. The main dierence between the two sets of data lies in values of the gravitational constant, G N . (The two references present the same value for the tauon mass. However, for each result, we use a tauon mass that is based on equation (67).) We do not explore possible signicance for the notion that 1 + x ≈ 10/9.
x ≈ 0.110033 (90) x ≈ 0.110031 (See reference [17]. Reference [30] provides the lowest of the upper limits that reference [17] lists.) The integer j correlates with generation. Equation (92)   We explore three sets of assumptions regarding choices of modeling.
First, we assume the ongoing theory notion that neutrino oscillations correlate with interactions that we correlate with the 4G subfamily.  We perform a check regarding reasonableness of proposed theory regarding interactions that couple to lepton number. We consider our interpretation of aspects of ongoing theory. We consider gravitational interactions between two electrons. Equation (94)

Neutrino masses
This unit discusses the notion that all neutrinos might have zero mass, even though people interpret neutrino oscillations and other observed phenomena as suggesting that at least one avor of neutrino correlates with non-zero mass. We discuss aspects related to neutrino oscillations.

Anomalous magnetic dipole moments
This unit discusses a proposed theory approach to explaining anomalous magnetic dipole moments.
We explore an approach to estimating a τ . The 4G26 solution might correlate with the ongoing theory result of α/(2π). The 6G24 solution might correlate with contributions of the order α 2 .
We assume that, for a charged lepton cl, equation (101) Table 48 shows approximate possible values for a 6G24,1 and a 6G24,t , based on tting data that equations (97) and (98) show and using various candidates for t cl . We de-emphasize the notion that 8G26 might also contribute to an actual value. Table 49 provides, based on table 48 and equation (101), some possible suggestions for a τ − (α/(2π)). Based on the notion that contributions to a scale as α (Σ−2)/2 and on results that table 48 shows, it might seem unlikely that a 6G24,1 correlates with 8G26. However, it is possible that the strength of interactions correlating with 4G26 diers from the ongoing theory result that correlates with α/(2π) and that a 6G24,1 correlates with such a dierence.
Given remarks just above, we explore another approach to estimating a τ .
We assume that the strength of each of 4G26 and 8G26 does not change with generation. We assume that, in eect, equation (102) pertains. We assume that, in eect, equation (103)  Generally, modeling based on ongoing theory is -as of now -better for calculating energies than is modeling based on proposed theory. Sometimes, such as for this example regarding anomalous magnetic dipole moments, proposed theory points to possible modeling that seems to be simpler than ongoing theory modeling.

Possible masses of tweak (or, 2T) simple particles
This unit discusses possible masses for tweak simple particles.   Table 50 lists possible roles for the aye particle and for the 0I solution.
We discuss items that table 50a shows.
Discussion related to equation (130) pertains regarding just after ination.
Some aspects of ongoing theory propose interactions that would produce unspecied particles that people might not have detected. For example, people propose an interaction K 0 L → π 0 +X for which there is an intermediate state of two simple fermions that interact via a W boson and produce the so-designated • Helps explain scaling by factors of α correlating with adding vertices or with increasing spin • Simplies some aspects of modeling (and does not necessarily correlate with nature) X particle. (See reference [34].) Here, the symbol K 0 L correlates with the K-long meson. The symbol π 0 denotes a zero-charge pion. To the extent that this interaction actually occurs, proposed theory suggests the possibility that the X particle is an aye simple boson.
Ongoing theory proposes concepts such as interactions with a so-called quantum vacuum. Proposed theory can dovetail with modeling that features a quantum vacuum and can dovetail with modeling that does not embrace a notion of quantum vacuum. Interactions with 0I bosons might produce eects similar to eects that ongoing theory correlates with the notion of interactions with a quantum vacuum.
Discussion related to equation (137) pertains regarding non-zero density of dark energy.
Equation (106) We discuss items that table 50b shows.
Discussion related to the relative strengths of some components of G-family forces points to terms proportional to α (Σ−2)/2 . (See discussion related to equation (75) and discussion related to equation (93).) Possibly, modeling based on the 0I solution correlates with aspects regarding spins and interactions. (See discussion related to equation (76).) Table 21a shows a representation for the ground state of the 0I solution. The next two sentences provide possible interpretations. People might interpret the SA-side of the representation as implying that, in nature, the aye particle would not excite. (See table 21a.) People might interpret the SAside representation as correlating with ve channels and, therefore, with the notion that excitement can pertain. (Regarding channels, see discussion regarding equation (67) and discussion regarding equation (61).) Proposed theory suggests that the second possibility pertains.

Lack of magnetic monopoles and a possible lack of some electric dipole moments
This unit suggests modeling that would comport with the notion that nature does not include an elementary particle magnetic monopole. This unit suggests modeling that would comport with the notion that nature does not include a non-zero electric dipole moment for any elementary particle. The 2G2 solution correlates with electromagnetic (not magnetic) monopole moments.

Other aspects regarding elementary particles
This unit discusses three related formulas that produce lengths. This unit discusses some proposed theory symmetries and some aspects of ongoing theory CPT-related symmetries. This unit suggests insight, that proposed theory might provide, regarding the strong CP problem and regarding axions.

A series of formulas for lengths, including the Planck length
This unit discusses three related formulas that produce lengths.
We suggest a series of formulas for lengths. Equation (109)

CPT-related symmetries
This unit discusses some proposed theory symmetries and some aspects of ongoing theory CPT-related symmetries. abbreviates the three-word phrase spatial side parity (or, SA-side parity).
Ongoing theory includes notions of C (or, charge-reversal) transformation and approximate symmetry, P (or, parity-reversal) transformation and approximate symmetry, and T (or, time-reversal) transformation and approximate symmetry. In ongoing theory, invariance under CPT transformation pertains. A signicant dierence between SSP symmetry and P symmetry might pertain and might correlate with gluons and with color charge.
People might want to consider implications of the possibility that conservation of each of TSP, ASP, and SSP pertains more exactly than does conservation of (respectively) T, C, and P. This possibility might explain aspects of the strong CP problem. (Regarding CP violations, see, for example, reference [35].)  To the extent that nature exhibits the relevant ongoing theory suggestion for non-zero CP violation, proposed theory suggests that some of the following statements might pertain. Table 52  This unit discusses dark matter models that might explain observed ratios of dark matter aspects such as density to ordinary matter aspects such as density. This unit discusses a model that might explain eras regarding the rate of expansion of the universe. This unit discusses models that might explain aspects regarding galaxy formation. This unit discusses other astrophysics phenomena and other cosmology phenomena. This unit lists topics, regarding aspects of the cosmology timeline, for which proposed theory suggests insights. Table 53: Aspects of nature -that ongoing theory discusses or suggests -for which proposed theory seems to provide insight that might augment insight that ongoing theory suggests Aspect • Eras during which the rate of expansion of the universe increases or decreases.
• Ratios of dark matter amounts or eects to ordinary matter amounts or eects.
• Details regarding the inationary epoch.
• Details regarding just after the inationary epoch.
• Details regarding mechanisms leading to baryon asymmetry.
• Details regarding fundamental components of dark matter.
• A possible additional source of acoustic oscillations that inuenced the formation of laments.
• Details regarding some aspects of galaxy formation.
• Details regarding dark matter objects that would be smaller than galaxies. This unit discusses aspects of nature -correlating with the terms dark matter, dark energy, astrophysics, and cosmology -for which proposed theory might provide more details or better-dened explanations than does ongoing theory. Table 53 lists some topics for which proposed theory seems to provide insight that might augment insight that ongoing theory suggests.
We discuss immediately below some, but not all, of the items that table 53 lists.
Ongoing theory suggests notions regarding three known eras in the rate of expansion of the universe.
One era features an accelerating (or, increasing) rate and correlates with the so-called inationary epoch.
A later multibillion-year era features a decelerating (or, decreasing but still positive) rate. The current multibillion-year era features an accelerating rate. Proposed theory suggests an explanation that has bases in components of 4G forces. The explanation does not necessarily depend on ongoing theory notions of dark energy pressure or on ongoing theory modeling based on general relativity. The proposed theory explanation might be generally compatible with ongoing theory models. The proposed theory explanation points to some subtleties that ongoing theory modeling might miss. Ongoing theory suggests that the early universe includes a so-called inationary epoch. Ongoing theory proposes a role, during that epoch, for a so-called inaton particle. Proposed theory suggests that the aye (or, 0I) simple particle correlates with the notion of an inaton. Proposed theory suggests that octupole components of 4G forces provided for rapid expansion.
Ongoing theory suggests that the achievement of baryon asymmetry occurred after the formation of the universe. Ongoing theory proposes mechanisms that might have catalyzed baryon asymmetry.
Ongoing theory does not necessarily point to the tweak simple bosons that proposed theory suggests exist. Proposed theory suggests that tweak bosons catalyzed the achievement of baryon asymmetry.
Ongoing theory provides various hypotheses regarding descriptions for dark matter and regarding the possibilities for substantial objects that might be signicantly smaller than galaxies and contain mostly dark matter. Proposed theory suggests specic descriptions for fundamental components of dark matter.
Proposed theory suggests some specics regarding some objects that would be signicantly smaller than galaxies and would contain mostly dark matter.

Summary of methods: models that have bases in isomers of charge
This unit posits that most dark matter correlates with isomers of the charged simple particles. This unit shows models that have bases in one, six, and 36 isomers of charged simple particles. This unit compares features of ongoing theory, PR1ISe modeling, PR6ISe modeling, and PR36ISe modeling.
We introduce the symbols that equations (115) and (116) show. The symbol 1Q⊗2U denotes a particle that includes just quarks and gluons. The word hadron pertains for the particle. The one-element term hadron-like pertains for the particle. Examples of such particles include protons, neutrons, and pions. The symbol 1R⊗2U denotes a particle that includes just arcs and gluons. The one-element term hadron-like pertains for the particle. The particle does not include quarks.
1Q ⊗ 2U A 1R⊗2U hadron-like particle contains no charged simple particles. The 1R⊗2U hadron-like particles do not interact with 2γ. The 1R⊗2U hadron-like particles measure as being dark matter.
Work above does not explain observed ratios of dark matter eects to ordinary matter eects. Some of the ratios correlate with amounts that correlate with gravitational eects. People correlate those eects with the term mass. One of the ratios might correlate with depletion of CMB (or, cosmic microwave background radiation). Ongoing theory seems not to explain these ratios.
Work above correlates with so-called PR1ISe modeling.
The rst-known one of the ratios comes from interpretations of measurements of CMB. People infer that the universe includes somewhat more than ve times as much dark matter as ordinary matter. People use, regarding the amount for each of dark matter and ordinary matter, the four-word term density of the universe. As far as we know, inferred ratios of density of the universe of dark matter to density of the universe of ordinary matter do not vary much for times that are at least somewhat more than 380 thousand years after the Big Bang. (Communication 71e indicates a ve-plus to one inferred ratio regarding 380 thousand years after the Big Bang.) We explore the notion that a ve to one ratio reects something fundamental in nature. We posit that the universe embraces six isomers of charged simple particles. One isomer of the monopole component of gravity (or, 4G4) interacts with all of the six isomers of charged simple particles. We say that one isomer of 4G4 spans six isomers of charged simple particles. Each isomer of charged simple particles correlates with its own isomer of at least two components of 2G forces. Each isomer of charged particles correlates with its own isomer of 2G2. Each isomer of charged particles correlates with its own isomer of 2G24.
The span for each of 2G2 and 2G24 is one.
We use the two-element term PR6ISe modeling to refer to models that embrace the notion that the universe embraces exactly six isomers of charged simple particles. The two letters PR abbreviate the two-word term physics relevant. The three letters ISe abbreviate the four-word term isomers of the electron.
PR6ISe modeling can explain the ve-plus to one ratio of dark matter density of the universe to ordinary matter density of the universe.   We preview features of each of PR1ISe, PR6ISe and PR36ISe modeling.

Spans for simple particles, components of root forces, and some objects
This unit discusses the notion that nature embraces more than one isomer for each of some simple particles, some components of root forces, and some hadron-like particles.
We consider the context of PR6ISe modeling.
We start from the span of six that we posit for 4G4. We consider TA-side symmetries for G-family  (3), SU (5), and SU (7) divides evenly the integer 48, which is the number of generators of SU (7). Regarding 4G4, we posit that the expression 6 = g 7 /g 3 is relevant. (Regarding notation, see equation (34).) We generalize. We assert that, for each G-family solution for which a TA-side symmetry of SU (j) pertains, equation (117) provides the span.
We assume that we can generalize from the assumption that the span of 2G2 is one. For each G-family solution with no TA-side symmetry, the span is one. The W boson has non-zero charge. We assume that the span of the W boson is one. A span of one comports with information that tables 26 and 36 show.
The following sentences pertain. A span of six pertains for the Z boson. A span of one pertains for the Higgs boson.
We discuss spans for simple particles and other objects that we do not correlate directly with G-family solutions.
Each charged simple fermion has a span of one. We assume that the span for 2U parallels the span for the Z boson. The span for 2U is six. We assume that the spans for 0K and 0P parallel the span for 2U. The span for 1Q⊗2U is one, based on the non-zero charges of 1Q particles. We assume that a span of six pertains for each zero-charge simple fermion. We assume that the span of 1R⊗2U is six.
Equation (118) shows notation for denoting the span, s, for a simple particle or a component of a root force.

Σ(s)Φ or Σ(s)ΦΓ
(118) Ongoing theory does not consider the notion of a span of more than one. Equation (119) characterizes an ongoing theory photon. The notation ⊕ · · · alludes to the remaining components, such as 2G68.
For each of each simple particle, each hadron-like particle, and each component of G-family forces, the one-word term span denotes the number of isomers of a set of, at least, non-zero-charge simple particles with which an isomer of the particle or force component interacts. The set includes all non-zero-charge simple particles and the ongoing theory photon 2(1)G. We consider all three of PR1ISe modeling, PR6ISe modeling, and PR36ISe modeling.    We discuss concepts regarding the 2(2)G68 solution.
The 2(2)G68 solution does not belong to the set of 2γ solutions and does not belong to the set of γ2 solutions. The 2(2)G68 solution does not correlate with interactions with individual simple fermions. Table 46 correlates λ = 8 with leptons and baryons. Table 38 correlates λ = 6 with changes of internal states for multicomponent objects. We posit that 2(2)G68 correlates with some electromagnetic (or, Σ = 2) interactions with atoms and other objects. Each of 2(1)G2 and 2(1)G24 correlates with some electromagnetic (or, Σ = 2) interactions with atoms and other objects that include both baryons and leptons.
Unlike for the cases of electromagnetic interactions that correlate with 2(1)G2 and 2(1)G24, 2G produced by ordinary matter objects interacts with dark matter objects (for the case in which PR6ISe pertains to nature) or doubly dark matter objects (for the case in which PR36ISe pertains to nature) via 2(2)G68. Unlike for the cases of electromagnetic interactions that correlate with 2(1)G2 and 2(1)G24, 2G produced by some dark matter objects (for the case in which PR06ISe pertains to nature) or by some doubly dark matter objects (for the case in which PR36ISe pertains to nature) interacts with ordinary matter via 2(2)G68.
We discuss ratios that PR6ISe or PR36ISe might predict or explain. Table 58 lists some approximate ratios of dark matter eects to ordinary matter eects that PR6ISe modeling might explain. Proposed theory designed PR6ISe modeling to explain the ve-plus to one ratios that people observe regarding densities of the universe. Here, the ve correlates with dark matter isomers and the plus correlates with hadron-like particles that do not interact with 2γ force components.
Galaxy clusters seem to be suciently large to comport with similar ratios. Discussion just above regarding 2(2)G68 correlates with the one to one ratio. (See, also, discussion related to equation (128).) Ratios of zero to one and four to one comport with roles of dark energy forces in scenarios regarding galaxy formation. (See discussion related to   • For 0I, we assume that the span is one of one or six. (d) Notes regarding the case PR36ISe Notes • For each ΣΦ with Φ = G or I and with a PR6ISe span of six or two, we assume that 2G pertains.
• For each 4GΓ with a PR6ISe span of six or two, we assume that 4G pertains.
• For 0I, we assume that the span is one of one, six, or 36. 0 Amount of stu in some early galaxies 4 Amount of stu in some early galaxies 0 Amount of stu in some later galaxies 4 Amount of stu in some later galaxies

Densities of the universe
This unit discusses various densities of the universe. This unit explores numerical relationships that interpretations of data suggest.
Ongoing theory discusses ve partial densities of the universe. The symbol Ω ν denotes neutrino density of the universe. The symbol Ω c denotes dark matter (or, cold dark matter) density of the universe. The symbol Ω b denotes ordinary matter (or, baryonic matter) density of the universe. The symbol Ω γ denotes photon density of the universe. The symbol Ω Λ denotes dark energy density of the universe. Each of the ve densities correlates with data. Equation (121) pertains regarding the total density of the universe, Ω.
Proposed theory suggests equation (122). The symbol Ω 1R2U denotes 1R⊗2U density of the universe. The symbol Ω ib denotes dark matter baryonic density of the universe. (The letter i symbolizes the word isomer.) The symbol Ω iγ denotes dark matter photon density of the universe.
We interpret data regarding recent states of CMB (or, cosmic microwave background radiation) as correlating with equation (123). The symbol Ω 1R2U correlates with the plus in the ratio ve-plus to one. The relationship Ω b Ω γ pertains regarding data. (Reference [17] provides data regarding Ω b Ω γ .) Equation (127) estimates Ω 1R2U for the current state of the universe. (Reference [17] provides the data that equations (124), (125), and (126) show.) Reasons exist for not taking the results that equation (127) shows to be exact. For example, we note the size of the standard deviation in equation (125).

Dark matter ratios inferred from data regarding cosmic microwave background radiation
This unit discusses dark matter ratios that people infer from data about cosmic microwave background radiation.
We know of up to two types of CMB (or, cosmic microwave background radiation) observations that might measure ratios of dark matter eects to ordinary matter eects.
One type of observation measures ratios of dark matter density of the universe to ordinary matter density of the universe. (See discussion that leads to table 55  The other type of observation might also measure ratios of dark matter eects to ordinary matter eects related to CMB. People measure absorption of CMB via hyperne interactions with hydrogen-like atoms. (See reference [24].) The amount of absorption is twice or somewhat more than twice the amount that people expected. At least one person speculates that the amount above expectations correlates with eects of dark matter. (See reference [36].) Proposed theory suggests the following explanation. Solution 2(2)G68 has a span of two. 2(2)G68 interactions are 2(2)GΓ interactions. Equation (128)  2G68 4.6. The rate of expansion of the universe This unit discusses dark energy forces and suggests an explanation for eras regarding the rate of expansion of the universe.
Two thought experiments set the stage for discussing aspects regarding the rate of expansion of the universe.
We consider one thought experiment. We consider two similar neighboring clumps of stu. We assume that the clumps are moving away from each other. We assume that the clumps will continue to move away from each other. We assume that, initially, interactions correlating with RSDF r −(n+1) dominate regarding interactions between the two clumps. We assume that the two clumps interact via interactions correlating with RSDF r −n . We assume that no other forces have adequate relevance. We assume that the distance between the objects increases adequately. Eventually, the RSDF r −n force dominates the RSDF r −(n+1) force.
We consider a similar thought experiment. We consider two similar neighboring clumps. We assume that these clumps are less interactive (for example, less massive) than the two clumps in the rst thought experiment. Generally, dominance of the RSDF r −n force over the RSDF r −(n+1) force occurs sooner for the two clumps in the second thought experiment than it does for the two clumps in the rst thought experiment. Table 59 summarizes, regarding the rate of expansion of the universe, eras and 4G force components.
In this context, the eras pertain to the largest objects that people can directly infer. Early acceleration pertains for some time after the Big Bang. Then, deceleration pertains for some billions of years. (Regarding observations that correlate with the eras that correlate with deceleration and recent acceleration, see references [8], [9], [10], and [11].) Acceleration pertains for the most recent few billion years.  Proposed theory suggests that the ongoing theory notion of dark energy forces (or, dark energy pressure) correlates with the components, other than 4(6)G4, of 4γ.
A better characterization than the six-word term rate of expansion of the universe might feature a notion of the rates of moving apart of observed very large astrophysical objects.

Phenomena during and just after ination
This unit discusses phenomena that might correlate with times during and just after the inationary epoch.
Ongoing theory suggests that an inationary epoch might have occurred. Ongoing theory suggests that the epoch ended around 10 −33 seconds to 10 −32 seconds after the Big Bang. We are not certain as to the extent that data conrms the occurrence of an inationary epoch.
Ongoing theory includes models that people claim would support notions of ination. The models point to states of the universe, at and somewhat after the inationary epoch, that would provide bases for evolution that would be consistent with observations about later phenomena and would be consistent with aspects of ongoing theory. (Reference [37] summarizes aspects related to ination, points to references regarding ongoing theory, and discusses some ongoing theory work.) Reference [12] suggests the possibility that a repulsive aspect of gravity drove phenomena correlating with the inationary epoch. The reference suggests that the composition of the universe was nearly uniform spatially. The reference suggests the importance of a so-called inaton eld. 0I + 4(1)G2468x → 0I + 4(1)G2468y (129) References [12] and [37] suggest that inaton particles dominated (what proposed theory would characterize as) the non-root-force composition of the universe for some time after the inationary epoch.
Inatons produced a cascade of interactions that led to a preponderance of protons, neutrons, and electrons. Clumping of the resulting hydrogen atoms led to the formation of stars.
Proposed theory suggests the possibility that, for some time just after the inationary epoch, the 0I + 0I → 2G + 2G (130) Discussion above de-emphasizes the question of the extent to which, for clumps or objects that involve multiple simple particles, 4γ octupole repulsion might dominate 4γ quadruple attraction for at least some time after the end of the inationary epoch.
Discussion above de-emphasizes the notions of isomers and spans. Discussion above de-emphasizes the notion of phenomena that might have preceded the inationary epoch.
We discuss isomers and spans.
Our work considers three PRnISe cases -n is one, n is six, and n is 36. Table 57 suggests that the span for each of the quadrupole component of 4γ and the two octupole components of 4γ is one. For each one of the PR6ISe case and the PR36ISe case, the span of 0I might be one or might be more than one. For each one of the PR6ISe case and the PR36ISe case, the proposed theory possibility that the span of 0I is one might point to the notion that each of the n isomers originally develops similarly to and originally somewhat essentially independently from the other (n minus one) isomers. More substantial coupling between isomers might start with the production of simple particles that have spans that exceed one. Coupling might also involve, for example, contributions correlating with the 4G48 component of 4γ, the 4G4 component of 4γ, and the 2G248 component of 2G. For each one of the PR6ISe case and the PR36ISe case, the proposed theory possibility that the span of 0I is more than one would point to yet more robust coupling -early on -between isomers.

Baryon asymmetry
This unit discusses proposed theory explanations for baryon asymmetry.
To the extent that the early universe featured essentially the same number of antimatter quarks as matter quarks, something happened to create baryon asymmetry. The two-word term baryon asymmetry correlates with the present lack, compared to matter quarks, of antimatter quarks.
Aspects of ongoing theory consider that early in the universe baryon symmetry pertained. Ongoing theory posits mechanisms that might have led to asymmetry. Some conjectured mechanisms would suggest asymmetries between matter simple fermions and antimatter simple fermions. One set of such simple fermions might feature the neutrinos. (See reference [38].) Proposed theory suggests scenarios that might have led to baryon asymmetry.
In one scenario, equations (131) A threshold energy might be in or above the range of 208 GeV to 221 GeV. (See equation (104).) A corresponding temperature is about 2 × 10 15 degrees Kelvin. As far as we know, this result is not inconsistent with established ongoing theory.

Galaxy clusters, ratios of dark matter amounts to ordinary matter amounts, and laments
This unit discusses, for galaxy clusters, observed ratios of dark matter amounts to ordinary matter amounts. This unit notes possible implications, regarding laments, of dark matter baryon acoustic oscillations.
Regarding some galaxy clusters, people report inferred ratios of dark matter amounts to ordinary matter amounts.
References [39] and [40] report ratios of ve-plus to one. The observations have bases in gravitational lensing. Reference [41] reports, for so-called massive galaxy clusters, a ratio of roughly 5.7 to one.
(Perhaps note reference [42].) The observations have bases in X-ray emissions.
Proposed theory is not incompatible with these galaxy cluster centric ratios.
Reference [43] suggests a formula that correlates -across 64 galaxy clusters -dark matter mass, hot gas baryonic mass (or, essentially, ordinary matter mass), and two radii from the centers of each galaxy cluster. The reference suggests that the formula supports the notion of a correlation between dark matter and baryons. Proposed theory might suggest a correlation, based on proposed similarities between most dark matter and ordinary matter. We are uncertain as to the extent to which people might consider that the formula supports this aspect of proposed theory.
Proposed theory is compatible with the ongoing theory notion that ordinary matter centric baryon acoustic oscillations contributed to the formation of laments.
Regarding models for which n (as in PRnISe) exceeds one, each of the ve dark matter isomers has its own baryon-like particles and its own 2(1)G physics. Proposed theory suggests, for models for which n (as in PRnISe) exceeds one, that dark matter baryon-like acoustic oscillations occurred in the early universe. Proposed theory suggests that dark matter baryon-like acoustic oscillations contributed (along with ordinary matter baryon acoustic oscillations) to the formation of laments.

Evolution of dark matter isomers, plus an explanation for aspects of the Bullet Cluster
This unit discusses the notion that various ones of the one ordinary matter isomer and the ve dark matter isomers evolve dierently from some of the other isomers. This unit explains aspects of observations regarding the Bullet Cluster.
We consider either PR6ISe modeling or PR36ISe modeling. For each case, there are ve dark matter isomers and one ordinary matter isomer.
Possibly, the evolution of each one of the six isomers paralleled the evolution of each of the other ve isomers.
Such parallel evolution might lead to diculties regarding explaining observations regarding the socalled Bullet Cluster.
People use the two-word term Bullet Cluster to refer, specically, to one of two galaxy clusters that collided and, generally, to the pair of galaxy clusters. The clusters are now moving away from each other.
Ongoing physics makes the following interpretations based on observations. For each of the two clusters, dark matter continues to move along trajectories generally consistent with just gravitational interactions.
For each of the two clusters, stars move along trajectories generally consistent with just gravitational interactions. For each of the two clusters, gas somewhat generally moves along with the cluster, but generally lags behind the other two components (dark matter and stars). Regarding such gas, people use the acronym IGM and the two-word term intergalactic medium. Ongoing theory suggests that the IGM component of each original cluster interacted electromagnetically with the IGM component of the other original cluster. Electromagnetic interactions led to slowing the motion of the gas.
If each of the six dark matter isomers evolved similarly, there might be problems regarding explaining aspects of the Bullet Cluster. One might expect that, in each galaxy cluster, more (than the observed amount of ) dark matter would lag. The lag would occur because of one-isomer 2G-mediated interactions within each of the ve dark matter isomers. Possibly, for each dark matter isomer, there would not be enough star-related stu to explain the amount of dark matter that is not lagging. Possibly, there would not be enough 1R⊗2U dark matter to signicantly help regarding explaining the amount of dark matter that is not lagging.
We discuss the notion that four isomers evolved somewhat similarly to each other, the other two isomers evolved similarly to each other, and the somewhat similar four isomers evolved dierently from the similar two isomers.
Thus, M = 3 pertains. We imagine that there is a particle for which M = 18. For interactions between two such particles, the strength per channel for the 2G2 component of electromagnetism equals We explore mathematics that correlates each of the six relevant isomers with a range of M . In equation (135), the integer n numbers the isomers. isomer n ↔ 3n ≤ M ≤ 3n + 3, for 0 ≤ n ≤ 5 (135) Table 60 shows interpretations regarding modeling for the six isomers. (Compare with table 43.) Here, for n ≥ 1, the M = 3n generation relevant to isomer n equals the M = 3(n − 1) + 3 generation relevant to isomer n − 1. Within an isomer, an overall result correlates with the same cyclic ordering, for generations, that table 43 shows. Table 61 shows, for each value of n, relationships between baryon generation and lepton generation. Table 61 extends table 60 and includes baryons. For each n, the order for baryons is generation one, generation two, and then generation three.
We discuss the time, in the evolution of the universe, before and around which each of the six isomers forms its own isomer of protons and other hadrons. Without loss of generality, we correlate ordinary matter with n = 0. Isomer three proceeds on a path that parallels the evolution of ordinary matter.
We discuss isomers one and four. For each of isomers one and four, there are more tauon analogs than there are tauons for isomer zero. Possibly, before isomers form hadron-like particles, the evolution of each of isomers one and four diverges from paralleling the evolution for isomer zero. This essay de-emphasizes that possibility. This essay discusses the possibility that the analogs to tauons catalyze nuclear fusion reactions at rates that exceed rates for ordinary matter.
We discuss isomers two and ve. For each of isomers two and ve, there are more muon analogs than there are muons for isomer zero. For each of isomers two and ve, there are more tauon analogs than there are tauons for isomer zero. Possibly, before isomers form hadron-like particles, the evolution of each of isomers two and ve diverges from paralleling the evolution for isomer zero. This essay de-emphasizes that possibility. This essay discusses the possibility that the analogs to muons and the analogs to tauons catalyze nuclear fusion reactions at rates that exceed rates for ordinary matter.
Regarding isomers one, two, four, and ve, we are uncertain as to how far fusion proceeds and as to the extent of then near-term consequences. At a minimum, the four isomers that exhibit enhanced fusion produce abundances of heavy analogs to atomic nuclei. We de-emphasize discussing the extent to which analogs to white dwarf stars, analogs to neutron stars, or black holes might form.
Presumably, each one of the four isomers that exhibit enhanced fusion somewhat rapidly features mainly just non-zero mass objects and a somewhat analog to CMB (or, ordinary matter centric cosmic microwave background radiation). From that time forward, the dominant eects are cooling and 4G interactions.
We return to discussion of the Bullet Cluster.
Based on discussion related to tables 60 and 61, proposed theory suggests that, for each of the two galaxy clusters, at least 80 percent of the incoming isomeric dark matter would pass through the collision with just gravitational interactions having signicance. The 80 percent correlates with values of n of one, two, four, and ve. Proposed theory suggests that essentially all of the incoming 1R⊗2U dark matter would also pass through the collision with just gravitational interactions having signicance.
We think that these proposed theory notions can comport with various possible ndings about IGM after a collision such as the Bullet Cluster collision. The ndings might point to variations regarding the fractions of IGM that, in eect, stay with outgoing clusters and the fractions of IGM that, in eect, detach from outgoing clusters.
We discuss possible aspects regarding an outgoing cluster.
Suppose that, before a collision, ordinary matter IGM comprised much of the ordinary matter in the cluster. Suppose that, because of the collision, the cluster has a signicant net loss of ordinary matter IGM. After the collision, the cluster could have a (perhaps somewhat arbitrarily) large ratio of amount of dark matter to amount of ordinary matter.
We discuss possible aspects regarding detached IGM.
To the extent that IGM detaches from galaxy clusters after the clusters collide, the detached IGM might form one or more objects. Some such objects might have roughly equal amounts of dark matter and ordinary matter. The dark matter would correlate with a value of three for n.

Galaxies, including formation and including ratios of dark matter to ordinary matter
This unit suggests scenarios for the formation and evolution of galaxies. This unit discusses, for galaxies, observed ratios of dark matter amounts to ordinary matter amounts.
We discuss galaxy formation and evolution scenarios and aspects pertaining to the amounts of ordinary matter and dark matter in galaxies. We assume that nature comports with at least one of PR6ISe modeling and PR36ISe modeling. (Neither ongoing theory nor PR1ISe modeling includes the notion of dark matter isomers. We think that it would be, at best, dicult to explain -based on for example 1R⊗2U dark matter -ratios, that observations suggest, of dark matter amounts to ordinary matter amounts.) For now, we de-emphasize some phenomena such as 1R⊗2U hadron-like particles and collisions between galaxies.
We anticipate that such galaxy formation and evolution scenarios will explain galaxy centric data that tables 53 and 58 show.
Models for galaxy formation and evolution might take into account the following factors -one-isomer repulsion (which correlates with the 4G2468a and 4G2468b solutions), one-isomer attraction (which correlates with 4G246), two-isomer repulsion (which correlates with 4G48), six-isomer attraction (which correlates with 4G4), laments (which correlate with eects of early universe baryon acoustic oscillations), statistical variations in densities of stu, and collisions between galaxies. Modeling might feature a notion of a multicomponent uid with varying concentrations of gas-like or dust-like components and of objects (such as stars, black holes, galaxies, and galaxy clusters) for which formation correlates signicantly with six-isomer (or 4G4) attraction.
We focus on early-stage formation and evolution. For purposes of this discussion, we assume that we can de-emphasize collisions. We suggest the two-word term untouched galaxy for a galaxy that does not collide, before and during the time relevant to observations, with other galaxies. We emphasize formation scenarios and evolution scenarios for untouched galaxies. (Communication 71c and communication 71b discuss data that pertains regarding a time range of about one billion years after the Big Bang to about 1.5 billion years after the Big Bang. Observations suggest that, out of a sample of more than 100 galaxies or galaxy-like rotating disks of material, about 15 percent of the objects might have been untouched.) We assume that dierences regarding the early evolutions of various isomers do not lead, for the present discussion, to adequately signicant dierences -regarding galaxy formation and 4G interactions -between isomers. (Perhaps, see discussion regarding table 60.) We organize this discussion based on the isomer or isomers that originally clump based on, respectively, 4G246 attraction or 4G246 and 4G4 attraction. Each one of some galaxies correlates with an original clump that correlates with just one isomer. Multi-isomer original clumps are possible. Because of 4G48 repulsion, an upper limit on the number of isomers that an original clump features might be three.
We discuss a scenario for the formation and evolution of a galaxy for which the original clump contains essentially just one isomer. Regarding this isomer, we use the word featured. We assume that PR6ISe modeling pertains. We assume that stu that will become the galaxy is always in somewhat proximity with itself. We assume that no collisions between would-be galaxies or between galaxies occur.
Early on, stu correlating with each one of the six isomers expands, essentially independently from the stu correlating with other isomers, based on repulsion correlating with 4(1)G2468a and 4(1)G2468b.
Then, each isomer starts to clump, essentially independently from the other isomers, based on attraction correlating with 4(1)G246.
With respect to clumps correlating with any one isomer, 4(2)G48 repels one other isomer and repels some stu correlating with the rst-mentioned (or, featured) isomer.
A galaxy forms based on a clump that contains mostly the featured isomer.
The galaxy attracts and accrues, via 4(6)G4 attraction, stu correlating with the four isomers that the featured isomer does not repel. The galaxy can contain small amounts of stu correlating with the isomer that the featured isomer repels.
We explore the extent to which the galaxy formation scenario comports with observations.
Observations of stars and galaxies tend to have bases in ordinary matter isomer 2G phenomena (or, readily observable electromagnetism). (The previous sentence de-emphasizes some observationsregarding collisions between black holes or neutron stars -that have bases in 4G phenomena.) People report ratios of amounts of dark matter to amounts of ordinary matter.
We discuss observations correlating with early in the era of galaxy formation.
Reference [19] reports zero-plus to one ratios. The observations have bases in the velocities of stars within galaxies and correlate with the three-word term galaxy rotation curves. Proposed theory suggests the above galaxy evolution scenario comports with this data. Presumably, other galaxies have one-isomer clumps that do not feature the ordinary matter isomer. Early on, those galaxies would not emit much 2G radiation that people could detect. People would not see such galaxies.
Reference [20] provides data about early stage galaxies. (See, for example, gure 7 in reference [20]. The gure provides two graphs. Key concepts include redshift, stellar mass, peak halo mass, and a stellar -peak halo mass ratio.) Data correlating with redshifts of at least seven suggests that some galaxies accrue, over time, dark matter, with the original fractions of dark matter being small. Use of reference [44] suggests that redshifts of at least seven pertain to times ending about 770 million years after the Big Bang. We suggest that our galaxy evolution scenario comports with this data.
We discuss observations correlating with later times.
Reference [21] discusses some MED09 spiral -or, disk -galaxies. A redshift of approximately z = 1.57 pertains. (See reference [45].) The redshift correlates with a time of 4.12 billion years after the Big Bang.
(We used reference [44] to calculate the time.) Reference [21] reports ratios of amount of dark matter to amount of ordinary matter of approximately four to one. The observations have bases in gravitational lensing.
To the extent that such an MED09 galaxy models as being nearly untouched, proposed theory oers the following possibility. The galaxy began based on a one isomer clump. The clump might have featured the ordinary matter isomer. The clump might have featured a dark matter isomer that does not repel ordinary matter. Over time, the galaxy accrued stu correlating with the isomers that the original clump did not repel. Accrual led to a ratio of approximately four to one.
To the extent that such an MED09 galaxy models as not being untouched, proposed theory oers the following possibility. One type of collision merges colliding galaxies. One type of collision features galaxies that separate after exchanging material. For either type of collision, incoming galaxies having  [46].) The observations have bases in light emitted by visible stars. This case correlates with the three-word term dark matter galaxy. Proposed theory suggests that this galaxy might have formed based on a core that included the isomer that repels the ordinary matter isomer. Table 62 suggests a method for cataloging not-signicantly-collided galaxies that formed during the rst few billion years after the Big Bang. We use the one-element term not-signicantly-collided to include possible collisions during the formation of original clumps and to exclude subsequent collisions. We use the one-element term spiral-like to include spiral dark matter galaxies. We use the two-element term possibly spiral-like to include the possibility that multi-isomer original clumps might produce other than spiral-like galaxies. some, and few pertains regarding the galaxies that pertain for the relevant row in the table. Regarding the rightmost column, the following notions pertain. The word early might correlate with redshifts that exceed roughly seven (and, possibly, with some smaller redshifts). The word later might correlate with redshifts that do not exceed roughly seven (or, a number less than seven). We embrace an ongoing theory use of the three-word term dark matter galaxy.
The following notions pertain regarding other data of which we know. Here, the ratios are ratios of dark matter amounts to ordinary matter amounts.
Reference [47] discusses six baryon-dominated ultra-diuse galaxies that seem to lack dark matter, at least to the radius studied by gas kinematics via observations of light with a wavelength of 21 centimeters. These observations seem not to be incompatible with a scenario correlating with an original clump that features the ordinary matter isomer.
Reference [48] discusses 19 dwarf galaxies that lack having much dark matter, from their centers to beyond radii for which ongoing theory suggests that dark matter should dominate. These observations measure r-band light that the galaxies emitted. These observations seem not to be incompatible with a scenario correlating with an original clump that features the ordinary matter isomer.
The galaxy NGC1052-DF2 might correlate with a ratio of much less than one to one. (See reference [49].) The observation has bases in the velocities of stars -or, galaxy rotation curves. This observation seems not to be incompatible with the scenario correlating with an original clump that features ordinary matter. A dierent observation suggests results that dier from the previous observation.
Reference [50] suggests, for NGC1052-DF2, that at least 75 percent of the stu within the half mass radius is dark matter. To the extent this suggestion comports with nature, phenomena related to NGC1052-DF2 might correlate with results that reference [21] discusses regarding some MED09 galaxies. (See discussion above regarding MED09 galaxies.) Proposed theory seems to be not incompatible with either ratio. Proposed theory might not, based on known data, be able to refute either ratio.
The galaxy NGC1052-DF4 might correlate with a ratio of much less than one to one. (See reference [51].) The observation has bases in the velocities of stars -or, galaxy rotation curves. This observation seems not to be incompatible with the scenario correlating with an original clump that features ordinary matter.
The compact elliptical galaxy Markarian 1216 has an unexpectedly large amount of dark matter in its core and may have stopped accumulating each of ordinary matter and dark matter approximately 4 billion years after the Big Bang. (See reference [22].) Observations feature the X-ray brightness and temperature of hot gas. This galaxy might correlate with the case correlating with the threeelement term 3IS including OM and with an original clump that features three isomers. One isomer would be the ordinary matter isomer. Around the time that the galaxy stopped accruing material, there was -near the galaxy -essentially nothing left for the galaxy to attract via 4(6)G4.
The galaxy XMM-2599 stopped producing visible stars by approximately 1.8 billion years after the Big Bang. (See reference [52].) People speculate regarding a so-called quenching mechanism.
Proposed theory might suggest that phenomena similar to phenomena that might pertain regarding Markarian 1216 might pertain regarding XMM-2599.
People report other data. We are uncertain as to the extents to which proposed theory provides insight that ongoing theory does not provide.
One example features a rotating disk galaxy, for which observations pertain to the state of the galaxy about 1.5 billion years after the Big Bang. (See reference [53].) People deduce that the galaxy originally featured dark matter and that the galaxy attracted ordinary matter. In terms that table 62 uses, this galaxy might correlate with 1IS: DMn or with 2IS: DMn, DMn .
One example features so-called massive early-type strong gravitation lens galaxies. (See reference [54].) Results suggest, for matter within one so-called eective radius, a minimum ratio of dark matter to dark matter plus ordinary matter of about 0.38. Assuming, for example, that measurements correlating with material within larger radii would yield larger ratios, these observational results might support the notion that the galaxies accumulated dark matter over time.
One example pertains to early stages of galaxies that are not visible at visible light wavelengths.
(See reference [55].) Observations feature sub-millimeter wavelength light. We might assume that proposed theory galaxy formation scenarios comport with such galaxies. We are not certain about the extent to which proposed theory might provide insight regarding subtleties, such as regarding star formation rates, correlating with this example.
We are uncertain as to the extent to which proposed theory might provide insight regarding possible inconsistencies -regarding numbers of observed early stage galaxies and numbers of later stage galaxies -that correlate with various observations and theories. (For a discussion of some possible inconsistencies, see reference [56].) We are uncertain as to the extent to which proposed theory might provide insight regarding the existence of two types -born and tidal -of ultra-diuse galaxies. (See reference [57].) Observations that we discuss above indicate that some galaxies do not exhibit dark matter halos. Proposed theory that we discuss above comports with the notion that some galaxies do not exhibit dark matter halos.
We discuss other eects, within galaxies, that might correlate with dark matter.
People study globular cluster systems within ultra-diuse galaxies. Regarding 85 globular cluster systems in ultra-diuse galaxies in the Coma cluster of galaxies, reference [58] suggests that 65 percent of the ultra-diuse galaxies are more massive than people might expect based on ongoing theory relationships, for so-called normal galaxies, between stellar mass and halo mass. We are uncertain as to the extent to which proposed theory might explain this result. For example, proposed theory might suggest that phenomena related to isomers might play a role. (See, for example, table 62.) Higher-mass galaxies might tend to feature more dark matter isomers (or tend to feature more material that correlates with such isomers) than do lower-mass galaxies.

Aspects regarding some components of galaxies -stars and black holes
This unit discusses some aspects regarding ordinary matter, dark matter, stars, and black holes. For one example, data regarding the stellar stream GD-1 suggests eects of an object of 10 6 to 10 8 solar masses. (See reference [23].) Researchers tried to identify and did not identify an ordinary matter object that might have caused the eects. The object might be a clump of dark matter. (See reference [62].) Proposed theory oers the possibility that the object is an originally dark matter centric clump of stu.
For other examples, people report inhomogeneities regarding Milky Way dark matter. (See references [62] and [63].) Researchers note that simulations suggest that such dark matter may have velocities similar to velocities of nearby ordinary matter stars. We suggest that these notions are not incompatible with proposed theory notions of the existence of dark matter stars that would be similar to ordinary matter stars.

High-mass neutron stars
This unit suggests proposed theory that might explain some aspects regarding high-mass neutron stars.
The following results have bases in observations. An approximate minimal mass for a neutron star might be 1.1M . (See reference [64].) The symbol M denotes the mass of the sun. An approximate maximum mass for a neutron star might be 2.2M . (See references [65] and [66].) Some ongoing theory models suggest a maximum neutron star mass of about 1.5M . (See reference [66].) Observations correlate with most known neutron star pairs having masses in the range that equation We discuss possibilities for observing dark matter eects without creating dark matter.
People attempt to directly detect dark matter. (See, for example, reference [70].) Some eorts look for WIMPs. We are uncertain as to the extent to which these eorts might be able to detect 1R⊗2U hadron-like particles. Some eorts look for axions. We are uncertain as to the extent to which these eorts might attribute axion sightings to eects that correlate with the dierence that equation (138) shows.
Proposed theory suggests new possibilities for directly detecting dark matter or doubly dark matter.
To the extent that PR6ISe pertains to nature and PR36ISe does not pertain to nature, the following discussion pertains to detecting dark matter. To the extent that PR36ISe pertains to nature, the following discussion pertains to detecting doubly dark matter. The basis for one possibility is the dierence between 2(6)G248 and 2(1)G248. Here, a detector might feature a rotating magnetic dipole moment, with the axis of rotation not matching (and perhaps being orthogonal to) the axis correlating with the magnetic dipole. Independent of that possible means for detection, people might try to infer 2(6)G248 phenomena correlating with dark matter magnetic elds (or -for the PR36ISe case -2(6)G248 phenomena correlating with doubly dark matter magnetic elds). A basis for another possibility is the dierence between 2(2)G68 and 2(1)G68. Proposed theory suggests that 2G68 correlates with, at least, some atomic transitions.
We discuss three possibilities for making and detecting dark matter.
Equations (139) .) Eects that ongoing physics correlates with the two-word term Pauli exclusion might imply that the probability for the original three quarks to be adequately close to each other is low.
We speculate about means for detecting such a conversion of a neutron into a three-arc hadron-like particle. We assume that the neutron resides in an atomic nucleus in a target material. Given the relevant energies, we assume that the three-arc particle exits the target. We speculate that people would not detect the three-arc particle. With one target and enough conversions that do not produce escapes of atomic nuclei, people might detect a change in the isotopic composition of the target. Possibly, an easiest detection would correlate with eects other than those we just mentioned. Such eects might correlate with byproducts of the interaction. Equations Compared with trying to detect the conversion of a neutron into dark matter, the possibility for converting a proton oers advantages and disadvantages. One advantage might be the possibility for detecting the weak interaction that the W +3 boson would catalyze. Another advantage might correlate with an ability to use colliding beams instead of an approach that might feature one beam and a xed target. One disadvantage might be the need to use higher energy for the incoming particles.
Equations (145) and (146) show interactions that convert a positron and an electron into the fermion components for a 1R⊗2U hadron-like particle that would have some similarity to a neutral pion. A threshold energy could be about 81 GeV. Detecting the 1R⊗2U particle might prove dicult. To the extent that the preferred decay of the particle features a matter neutrino and an antimatter neutrino, detecting decay products might prove dicult.
4.17. Constancy of the density of the universe ratio regarding dark matter and ordinary matter This unit discusses the notion that relative densities of the universe pertaining to dark matter and ordinary matter likely have not changed much for billions of years.
Proposed theory points to types of stu that measures as dark matter. Regarding each of PR1ISe modeling, PR6ISe modeling, and PR36ISe modeling, one type of stu is 1R⊗2U hadron-like particles.
Regarding PR6ISe modeling and PR36ISe modeling, dark matter also includes ve dark matter isomers, each of which is similar to ordinary matter 1Q⊗2U plus ordinary matter 2(1)G.
Elsewhere, we discuss possible threshold energies pertaining to reactions that might produce 1R⊗2U hadron-like particles. (See, for example, discussion regarding equations (145) and (146).) The relative densities of the universe of 1R⊗2U hadron-like particles and ordinary matter 1Q⊗2U hadron particles might be essentially constant after the universe cools to a temperature correlating with an energy of 81 to ordinary matter 1Q⊗2U.
The actual ratio of dark matter density of the universe to ordinary matter density of the universe might not much change after the cooling to the temperature correlating with the energy 81 GeV. That energy correlates with a temperature of about 10 15 degrees Kelvin. That temperature correlates with a time that is less than 10 −4 seconds after the Big Bang. (Reference [71] notes that a temperature of 10 13 degrees Kelvin correlates with a time of 10 −4 seconds after the Big Bang.) Measured ratios of dark matter density of the universe to ordinary matter density of the universe would not much change regarding times for which equation (147)  We note aspects that discussion elsewhere in this essay de-emphasizes.
Early in the evolution of the universe, quarks, arcs, and gluons formed hadron-like seas. The seas might have undergone phase changes, with the last changes featuring at least one transition from seas to hadron-like particles. Proposed theory is not incompatible with an ongoing theory notion of possible large-scale atness for the universe.

Discussion: theories and models for motion
This unit discusses aspects of kinematics modeling and aspects of dynamics modeling. This unit suggests limits on the applicability of general relativity. This unit catalogs interaction vertices, for interactions that involve simple particles and root forces, that correlate with a possible proposed theory parallel to some aspects of ongoing theory quantum eld theory. This unit suggests possibilities for developing dynamics modeling based on proposed theory. This unit discusses possible dynamics modeling for hadron-like particles, nuclear physics, and quantum transitions.

Perspective regarding quantum modeling and kinematics modeling
This unit discusses relationships between quantum modeling and kinematics modeling.
Proposed theory might seem to include a problem regarding possible dissonance between modeling pertaining to quantum interactions and modeling pertaining to kinematics. We think that resolution lies in the notion that motion of a simple particle or of a photon can occur without the simple particle or photon undergoing a quantum transition. Proposed theory modeling regarding quantum transitions and ongoing theory modeling regarding motion have some independence from each other. Discussion regarding equations (40) and (41) provides an example regarding phenomena related to ΣG (or, the G-family).

Perspective regarding models that feature gravitation
This unit discusses models for non-quantum interactions between objects and gravity. This unit suggests limits regarding the applicability of modeling based on general relativity. This unit suggests possible opportunities for research regarding modeling various aspects of large-scale physics.

Models for interactions with gravity
This unit discusses models for non-quantum interactions between objects and gravity.
Equation (150) shows Newtonian modeling regarding gravity. Each m _ denotes the mass of an object. The symbol − → r denotes a vector pointing from object one to object two. The symbol r denotes the distance between the two objects and the length of the vector. The symbol − → F denotes the force that object one exerts on object two. The symbol − → a denotes the acceleration that pertains regarding the motion of object two.
The factor m 2 appears in each of the leftmost and rightmost parts of equation (150 We consider the motion of a free simple boson or of a quantum that correlates with a G-family force. While general relativity comports with various phenomena, people discuss possible problems regarding the applicability of general relativity to large-scale physics. (See, for example, reference [72].) Also, people express other concerns regarding modeling pertaining to large-scale physics. For example, reference [7] alludes to possible concerns correlating with the Hubble constant (or, a Hubble parameter).
Proposed theory oers possible insight and resolution regarding such concerns.  Concepts such as those we just mentioned might point to opportunities for observational and theoretical research regarding each of the following topics and regarding relationships between the following topics -the domain of applicability of general relativity; equations relating pressures to densities; the notion and applicability of the concept of a Hubble parameter; notions regarding geodesic motion; and the spans and the strengths of forces correlating with the 4G48, 4G246, 4G2468a, and 4G2468b solutions.
We de-emphasize in this essay possible problems with trying to, in eect, extend modeling, based on general relativity, to very early times after the Big Bang.

Modeling that proposed theory suggests regarding dynamics
This unit contrasts possible dynamics modeling, based on proposed theory, with ongoing theory dynamics modeling.
Discussion above in this essay features proposed theory suggestions regarding elementary particles and dark matter, plus ongoing theory notions regarding motion. We generally assume that the QPT particle set and ongoing theory models for motion dovetail adequately well with each other.
Aspects -discussed above in this essay -of proposed theory verge on suggesting modeling regarding motion. Equation (52) provides an example.  • As or more successful regarding describing allowed states.
• As or less successful regarding estimating -based on limited use of observed data -energies for allowed states.
• Easier or simpler -when applicable -to use.
• Based on more rigorous use of mathematics.

Interaction vertices that involve simple particles and root forces
This unit catalogs interaction vertices, for interactions that involve simple particles and root forces, that correlate with a possible proposed theory parallel to some aspects of ongoing theory quantum eld theory.
We explore notions correlating with the second row in table 11.
This work generalizes from work above that, nominally, pertains for free simple particles. Equations (11) and (12) For proposed theory modeling of interactions that involve simple particles and root forces in free environments, the PDE notion of the mathematical limit expression (η SA ) 2 → 0 pertains. (See discussion related to equation (10).) Here, (η T A ) 2 → 0 pertains. We say that the vertex models as being point-like with respect to coordinates. Here, point-like refers to the temporal coordinate and refers to either a radial spatial coordinate or three spatial coordinates.
An example of modeling of interactions that involve simple particles in so-called conned environments might feature modeling regarding interactions with a quark that exists within a proton.
For proposed theory modeling of interactions that involve simple particles and root forces in conned environments, the PDE notion of (η SA ) 2 > 0 can pertain. (See discussion related to equation (160).) The expression that equation (157) shows might correlate with the size of the multicomponent object that correlates with the term conned environment. We say that the vertex models as being volume-like with respect to coordinates. Here, volume-like refers to, at least, either a radial spatial coordinate or three spatial coordinates. Volume-like correlates also with a non-point-like domain for the temporal coordinate.

Dynamics models for some objects
This unit discusses possibilities for developing, based on mathematics that quantum particle physics uses, models for some multicomponent objects and for temporal aspects of quantum transitions.
We explore notions correlating with the third and fourth rows in

Dynamics models for hadron-like particles
This unit discusses an approach, compatible with proposed theory, for modeling aspects, in hadrons, correlating with quarks and gluons. This unit illustrates the notion that modeling for components of a multicomponent object does not necessarily need to correlate, for each component, with conservation of angular momentum and conservation of linear momentum. This unit calls attention to possible dierences between modeling for the dynamics of hadron-like particles that contain no more than three quarks and modeling for the dynamics of hadron-like particles that contain more than three quarks.
We discuss the notion that each hadron-like particle that includes no more than three quarks (or, 1Q particles) and arcs (or, 1R particles) does not include both quarks and arcs. Discussion related to table 33 suggests that a hadron-like particle has a charge for which the magnitude is either zero or a non-zero integer multiple of |q | and has a baryon number that is either zero or a non-zero integer multiple of one. For a hadron-like particle that includes no more than three quarks and arcs, the restrictions to integer charge and integer baryon number preclude the simultaneous presence of more than zero quarks and more than zero arcs. A tetraquark might contain a matter-and-antimatter pair of quarks and a matter-and-antimatter pair of arcs.
We discuss modeling for dynamics in hadrons that contain no more than three quarks.
Ongoing theory QCD (or, quantum chromodynamics) modeling correlates with symmetries, for each of quarks and gluons, that correlate with special relativity.
We explore the notion that proposed theory suggests possibilities for modeling that correlates one subset of those symmetries with motion for quarks and another subset of those symmetries with motion for gluons.
Modeling for a free hadron requires two TA-side SU (5) symmetries and four SA-side SU (2) symmetries. (See discussion regarding equation (24).) Proposed theory suggests that each one of bosons (within the hadron) and simple fermions (within the hadron) can contribute one TA-side one SU (5) symmetry and two SA-side SU (2) symmetries. Such modeling would not use -for each of bosons and simple fermions -one TA-side SU (5) symmetry and two SA-side SU (2) symmetries. Dynamics modeling -for each of bosons and simple fermions -can correlate with just the previously unused one TA-side SU (5) symmetry and two SA-side SU (2) symmetries. Here, the bosons are gluons and the simple fermions are quarks. Table 67 pertains.
This proposed theory dynamics modeling correlates with the notion that neither one of quarks and gluons behaves like a free simple particle. Proposed theory suggests that a hadron-like particle must include at least two (non-virtual) unfree fermions. (The notion of virtual correlates with ongoing theory. Proposed theory dovetails with modeling that includes the notion of virtual fermions and with modeling that does not include the notion of virtual fermions.) We discuss notions that might correlate with modeling that might output masses for hadrons.
References [76] and [77] suggest opportunities to improve understanding regarding modeling that might explain the masses of hadrons such as protons. Proposed theory suggests concepts that might help regarding such opportunities. One concept correlates with avoiding relying on modeling that correlates with special relativity. (See discussion nearby above.) One concept correlates with equations (3) and (4) and with D = 3. Here, the term that is proportional to r 2 might correlate with the square of a potential. For a two-quark hadron, the potential associated with one quark aects the other quark. For a three-quark hadron, the potential associated with two quarks aects the third quark.
We discuss modeling for dynamics in hadrons that contain more than three quarks.
Reference [78] suggests that some of the dynamics within at least some pentaquarks correlates with the dynamics for a system composed of a meson-like particle and a baryon-like particle. The meson-like particle features a matter quark and an antimatter quark. The baryon-like particle features three matter quarks. Aspects that proposed theory correlates with the pie simple particle and with the cake simple particle might play roles in such dynamics.
Modeling might consider that, if hexaquarks exist, some hexaquarks have parallels to atomic nuclei.

Dynamics models for nuclear physics
This unit suggests possibilities for developing proposed theory models for atomic nuclei.
We discuss nuclear physics.
Ongoing theory bases some aspects of modeling on notions of a Pauli exclusion force and on notions of a Yukawa potential. Ongoing theory correlates these eects with notions of a residual strong force. exp(−tr/(|η T A | · |η SA |)) → exp(−r/|η SA |) People might develop models, for atomic nuclei, based on potentials that correlate with spatial aspects of equations (160) and (161).
Some ongoing theory modeling for atomic nuclei correlates with potentials similar to harmonic oscillator potentials. People might develop models based on notions of a possible 4U subfamily.
We are uncertain as to the extent to which such models for atomic nuclei would improve on ongoing theory techniques.

Dynamics models for quantum transitions
This unit discusses the possibility that aspects of proposed theory pertain to temporal aspects of quantum transitions.
People may have observed quantum transitions that take non-zero time. (See reference [80].) Proposed theory suggests that people can model such aspects of transitions via volume-like vertices.
Modeling that features volume-like vertices might parallel temporal aspects of equation (160). (See discussions regarding equations (21) and (160).) 6. Discussion: theories and models for objects This unit discusses relationships between various theories and models that pertain regarding objects.
This unit discusses possible synergies between proposed theory and the elementary particle Standard Model. This unit notes that proposed theory is not necessarily compatible with supersymmetry. This unit notes that aspects of proposed theory might help people explore the relevance of string theory to elementary particle physics. This unit suggests modeling that would comport with the notion that nature does not include a non-zero neutron electric dipole moment. This unit explores concepts related to the masses of hadron-like particles that include arc simple fermions. This unit discusses phenomena that might correlate with times before the inationary epoch. This unit shows a possible link between dynamics modeling that we suggest and a notion of entropy.

The elementary particle Standard Model
This unit discusses possible synergies between proposed theory and the elementary particle Standard Model.
People might try to add to the Standard Model some of the symmetries that proposed theory suggests.
Examples include conservation of charge, somewhat conservation of fermion generation, and somewhat conservation of lepton number.
We discuss adding to the Standard Model some of the simple particles and root forces that proposed theory suggests.
To the extent that satisfying symmetries such as SU (3) × SU (2) × U (1) boson symmetries suces, people might be able to add, to the Standard Model, simple particles and root forces that proposed theory suggests.
Proposed theory might provide a basis for extending the Standard Model to include concepts related to mass and to forces that correlate with bosons that have spins of at least two.
People might explore synergies between Standard Model approaches and proposed theory approaches to various topics. One such topic is anomalous magnetic dipole moments.
We do not speculate regarding the extent to which people might nd synergies between Lagrangian aspects of the Standard Model, models such as discussion related to refraction suggests, and kinematics conservation laws. (Regarding refraction, see discussion related to equation (55).)

Supersymmetry
This unit notes that proposed theory is not necessarily compatible with supersymmetry.  Tables 3 and 56 seem, in themselves, to be incompatible with supersymmetry. People might explore the notion of layering supersymmetry over results that tables 3 and 56 show. However, given aspects of proposed theory, supersymmetry might not be necessary to explain known phenomena.

String theory
This unit notes that aspects of proposed theory might help people explore the relevance of string theory to elementary particle physics.  We discuss rest energies for 1R⊗2U hadron-like particles.
The rest energy of a proton does not dier much from the rest energy of a neutron. For hadrons composed of generation-one quarks, the masses of hadrons do not vary much based on the masses of the quarks or on the charges of the quarks. The rest energies of 1R⊗2U hadron-like particles that contain exactly three arcs might approximate the rest energy of the proton, which is about 938 MeV. (Reference [17] provides data regarding hadron masses.) The rest energies of 1R⊗2U hadron-like particles that contain exactly two arcs might approximate the rest energy of the zero-charge pion, which is about 135 MeV.
We explore another concept for estimating masses for 1R⊗2U hadron-like particles. The concept has bases in the relative densities of the universe of 1Q⊗2U hadrons and 1R⊗2U hadron-like particles.
Nature might have created concurrently, essentially, the current populations of 1Q⊗2U hadrons and 1R⊗2U hadron-like particles. We assume that each of 1Q⊗2U hadrons and 1R⊗2U hadron-like particles consists mainly of three-fermion particles. We explore three cases, in which, respectively, the span, s, of 1R⊗2U hadron-like particles to density of ordinary matter. The symbol m _ denotes the rest mass of a typical hadron-like particle. The leftmost use of the ratio m 1R⊗2U /m 1Q⊗2U correlates with rest energy (or rest mass) per particle. The rightmost use of the ratio m 1R⊗2U /m 1Q⊗2U occurs as the input to a calculation of an exponential and correlates with a hypothesis regarding the relative number of particles that nature created.
The respective values of Ω ib /(s · Ω b ) are ∼ 0.33, ∼ 0.054, and ∼ 0.0090. For each value of s, two mathematical solutions exist. The respective solutions, expressed in terms of m_c 2 and in units of GeV are ∼ 0.6 and ∼ 1.5, ∼ 0.06 and ∼ 4.4, and ∼ 0.009 and ∼ 6.6. Table 68 summarizes some possible rest energies for 1R⊗2U hadron-like particles.

Speculation regarding phenomena before ination
This unit discusses phenomena that might correlate with times before the inationary epoch.
We speculate about phenomena that might have preceded the inationary epoch.
Proposed theory correlates an SU (5) symmetry with conservation of energy. The number of generators of SU (5) is 24. Equation (167) might pertain. Here, g U (1) denotes the number of generators for U (1) and equals two. The number 24 equals six times two times two. One factor of two might correlate with the possibility for two values of handedness for leptons. One factor of two might correlate with the possibility for two values for handedness for baryons. The factor of six might correlate with the relevance of six isomers regarding color charge. Specically, the factor of six might correlate with a π r,b,g symmetry correlating with red, blue, and green color charges and with oscillators SA0, SAo, and SAe. (See table   40.) Here, six equals three times two. There are three possibilities regarding the color associated with SA0. For each of the three possibilities, there are two possibilities for the color associated with SAo.
To the extent that such aspects correlating with the SU (5) symmetry comport with nature, one might consider models that suggest 24 somewhat similar entities. People might apply the two-word term our universe to one of the 24 somewhat similar entities.
We note, but do not pursue further, the possibility that theory might correlate, with the Big Bang, a transition that involves, in eect, a decoupling of the possible 24 somewhat similar entities.

Entropy
This unit shows a possible link between dynamics modeling that we suggest and a notion of entropy.
We consider cases of multicomponent objects that involve k + 1 peer component objects. Here, k is a nonnegative integer.
We consider the case of k = 1. The multicomponent object includes two peer component objects.
Compared with dynamics symmetries for the multicomponent object, the two peer components collectively contribute one too many instance of each of conservation of energy symmetry, conservation of angular momentum symmetry, and conservation of momentum symmetry. Modeling can re-assign the extra three symmetries to a combination of the two peer components and a eld -such as a gravitational eld -that correlates with interactions between the peer components.
We consider the case of k > 1. Here, we de-emphasize the possibility of non-peer subdivision. An example of non-peer subdivision involves the sun, earth, and moon. For this example of non-peer subdivision, one might use two steps, each correlating with k = 1. The rst step considers each of the sun and the earth plus moon to be objects. The second step considers the earth plus moon to be a multicomponent object consisting of the earth and the moon. Without adequately signicant additions to modeling, this example might correlate with modeling for which -regarding ocean tides -eects of lunar gravity pertain and eects of solar gravity do not pertain.
For k > 1, ongoing theory modeling becomes more complex than ongoing theory modeling for twobody (or, k = 1) systems. Many applications might pertain -for example, to astrophysical systems, to ideal gasses, and so forth. For some applications, keeping the number of elds at one might correlate with a notion of entropy and, at least within that notion, with the ongoing theory expression for entropy that equation (168) shows. Here, people might want to consider at least one of the two cases j = k + 1 and j = k. Here, people might want to consider each of a notion of entropy for physical systems and a notion that might correlate, regarding mathematics-based modeling, with a term correlating with the word entropy.

Numbers of dimensions
This unit speculates regarding some aspects of the topic of numbers of dimensions.
Proposed theory suggests that, at least in some sense, a number -three -of spatial dimensions correlates with D * SA = 3 and a number -one -of temporal dimensions correlates with D * T A = 1. (See equations (11) and (12).) Proposed theory includes modeling that features other than three spatial dimensions. (See, for example, the SA-side aspects of representations that table 22 shows or the column labeled D in table 12b.) Ongoing theory includes modeling that features other than three spatial dimensions.
Some proposed theory uses of notions of D * SA = 3 and D * T A = 1 include modeling that correlates with ν SA < 0 and that outputs a list of known and possible elementary particles. (See table 11.) As far as we know, ongoing theory does not include parallels to such proposed theory modeling. Ongoing theory aspects that correlate with three spatial dimensions and one temporal dimension tend to correlate with proposed theory aspects for which ν SA ≥ 0 pertains. (See table 11.) Equations (11) and (12) might provide a characterization that can be useful, for much physics modeling, of the notions of three spatial dimensions and one temporal dimension.

Arrow of time
This unit notes that proposed theory may provide perspective regarding the topic of arrow of time.
Equation (21) and discussion related to equation (18) suggest a notion of a Ψ(t, r) that correlates with the TA0-and-SA0 oscillator pair. (See equation (6).) We suggest that equation (169) might pertain. The domains t > 0 and r > 0 pertain for Ψ(t, r). Without loss of generality, we posit that η T A > 0 pertains regarding after an interaction, η T A > 0 does not pertain regarding before an interaction, η T A < 0 pertains regarding before an interaction, and η T A < 0 does not pertain regarding after an interaction. We posit that η SA > 0 pertains regarding elementary particles that exit an interaction, η SA > 0 does not pertain regarding elementary particles that enter an interaction, η SA < 0 pertains regarding elementary particles that enter an interaction, and η SA < 0 does not pertain regarding elementary particles that exit an interaction. Of the four possibilities η T A > 0 and η SA > 0, η T A < 0 and η SA < 0, η T A > 0 and η SA < 0, and η T A < 0 and η SA > 0, mathematically, Ψ normalizes for only the rst two possibilities. To the extent that this modeling correlates with the topic of arrow of time, the lack of dual normalization regarding each of the case of incoming and the case of outgoing might provide insight. Ψ(t, r) ∝ exp(−tr/(η T A η SA )) The proposed theory notion that aspects of modeling of conservation of energy correlate with an SU (5) symmetry (and not necessarily with an ongoing theory notion of S1G symmetry) might provide insight regarding the topic of arrow of time. Proposed theory tends to correlate SU (_) symmetries with origins (with respect to coordinates) and with radial coordinates. 7.3. The Higgs mechanism, entanglement, and tachyon-like behavior This unit provides possible proposed theory perspective regarding the ongoing theory notions of a Higgs mechanism, entanglement, and tachyon-like behavior.
At least to the extent that one models the universe as being a conned environment, the following statements might pertain.
The aye (or, 0I) boson correlates with the Higgs mechanism or Higgs eld.
Theory does not completely disentangle any object from a notion of the universe minus that object.
These notions correlate with a large-scale notion of tachyon-like behavior.

Notions that might link physics constants and modeling
This unit speculates regarding relationships between some minimal non-zero values that people observe and some aspects of proposed theory. This unit notes that proposed theory might point to opportunities to further explore relationships between charge and mass. This unit suggests a possible opportunity to explore relationships between handedness, chirality, helicity, lepton number or baryon number, rotation, and spin. Table 69 shows speculation about possible conations regarding two notions. One notion is the Σ in G-family mathematical solutions ΣGΓ. One notion is quantities (or, properties) with which some Σγ components of G-family forces interact. Each quantity (or, property) might pertain for each of some Table 69: Possible conations regarding G-family solutions and properties with which G-family forces interact (with (_) denoting a suggested smallest non-zero property magnitude, _, regarding modeling free objects; and with ((_)) denoting a dierent type of non-zero physics constant) We are uncertain regarding the usefulness of further pursuing notions that we discuss immediately above. • Hone some measurements regarding some known particles.
• Verify or rule out the notion that gravity does not produce the main contributions to neutrino oscillations.
• Verify or rule out the relationship that we suggest regarding the tauon mass and the gravitational constant.
• Verify, hone, or refute relationships, that we suggest, between particle properties and other constants.
• Verify or rule out the description of dark matter that we propose.
• Determine properties of dark matter.
• Hone, extend, or rule out aspects that we suggest regarding galaxies.
• Add details -or rule out aspects that we suggest -regarding the cosmological timeline.
• Determine ranges of usefulness regarding -and test synergies between -various theories and models.
• Predict and try to verify other phenomena that might correlate with proposed theory.
8. Discussion: possible opportunities for experimental or observational research This unit suggests themes for experiments and observations that people might want to conduct. Table 70 suggest themes for experiments and observations that people might want to conduct. This essay de-emphasizes the topic of when techniques and technology will suce to enable specic experiments or observations. We de-emphasize the topic of when -for each of various predictions we or other people make based on proposed theory -falsiability becomes feasible.

Concluding remarks
This unit discusses possible opportunities based on proposed theory.
Proposed theory might provide impetus for people to tackle broad agendas that our work suggests.
Proposed theory might provide means to fulll aspects of such agendas. Proposed theory might fulll aspects of such agendas.
Opportunities might exist to develop more sophisticated theory and modeling than the theory and modeling that we present. Such a new level of work might provide more insight than we provide.
Proposed theory might suggest -directly or indirectly -opportunities for observational research, experimental research, development of precision measuring techniques and data analysis techniques, numerical simulations, and theoretical research regarding elementary particle physics, nuclear physics, atomic physics, astrophysics, and cosmology.
Proposed theory might suggest applied mathematics techniques that have uses other than uses that we make.

Acknowledgments
The following people pointed to topics or aspects that we considered for inclusion in the scope of the   Table 71 lists communications for which the following two sentences pertain. This essay cites the communication. We did not necessarily nd information sucient to qualify the communication for inclusion in the bibliography.