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Elementary Particles, Objects, and the Cosmos
Toward One Model Thomas J. Buckholtz
ii
Elementary Particles, Objects, and the Cosmos Toward One Model Edition 1
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Contents
Preface 1
2
vii
Perspective - before and during this work
1
1.1
1
Context and scope
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1
Physics and models
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1.2
Aspects of recent models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1.3
Scope of our work
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.2
Observations, models, and inferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.3
Meta-model MM2 and models MS2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.4
Mathematical bases for models
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
1.5
Notes - storyline, writing, vocabulary, and research . . . . . . . . . . . . . . . . . . . . . .
5
Known and possible elementary particles 2.1
2.2
7
Perspective - elementary particles and math solutions
. . . . . . . . . . . . . . . . . . . .
Summary - elementary particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
2.1.2
Summary - possibly relevant mathematical solutions . . . . . . . . . . . . . . . . .
11
2.1.3
Interactions, vertices, and elementary particles
. . . . . . . . . . . . . . . . . . . .
12
. . . . . . . . . . . . . . . . . . . . . . . . . .
14
Solutions, particles, and particle properties 2.2.1
Perspective - ALG solutions and PDE solutions . . . . . . . . . . . . . . . . . . . .
14
2.2.2
ALG solutions
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
2.2.3
Photons and 2G2& . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
2.2.4
ALG ground-state solutions for which
2.2.5
PDE solutions
N [E] ≤ 3
and
N [P ] ≤ 3
. . . . . . . . . . .
14
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
2.2.6
Correlations between MM2 solutions and elementary particles . . . . . . . . . . . .
14
2.2.7
Solutions that might correlate with non-zero-mass elementary bosons . . . . . . . .
14
2.2.8
Solutions that might correlate with elementary fermions . . . . . . . . . . . . . . .
15
2.2.9
Neutrinos - Dirac fermions or Majorana fermions?
. . . . . . . . . . . . . . . . . .
15
2.2.10 Solutions that might correlate with G-family elementary bosons . . . . . . . . . . .
15
2.2.11 Solutions that might correlate with Y-family elementary bosons . . . . . . . . . . .
15
2.2.12 Models correlating with gluons
15
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.13 Properties of non-zero-mass elementary particles
3
7
2.1.1
. . . . . . . . . . . . . . . . . . .
15
Symmetries, patterns, and elementary-particle properties
17
3.1
17
Perspective - models, patterns, and symmetries . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1
Summary - models, patterns, and particle properties . . . . . . . . . . . . . . . . .
3.1.2
Summary -
σ+
symmetries and
σ−
17
symmetries . . . . . . . . . . . . . . . . . . . .
19
3.2
CPT-related symmetries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
3.3
Free-ranging motion and the Poincare group . . . . . . . . . . . . . . . . . . . . . . . . . .
21
3.4
SU (3) × SU (2) × U (1)
21
symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
iv
CONTENTS
3.5
G-family symmetries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
3.6
G-family forces and properties of objects . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
3.7
Interaction vertices - size and proximity
3.8
Symmetries related to
3.9
Masses of non-zero-mass elementary fermions
SU (17)
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
. . . . . . . . . . . . . . . . . . . . . . . . .
21
. . . . . . . . . . . . . . . . . . . . . . . .
22
3.10 Properties of non-zero-mass elementary bosons
4
Ordinary matter, dark matter, and dark energy
23
4.1
Perspective - dark matter and dark energy . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
4.1.1
Uses of the terms dark energy and dark matter . . . . . . . . . . . . . . . . . . . .
23
4.1.2
Data regarding ordinary matter, dark matter, and dark-energy stu
4.1.3
Bases for ENS48, ENS06, ENS02, and ENS01 models
4.1.4
Elementary particles and
4.2
5
symmetry
23 25
. . . . . . . . . . . . . . . . . . . . . .
26
Ordinary matter, dark matter, and dark-energy stu . . . . . . . . . . . . . . . . . . . . .
27
4.2.1
ENS48 models for ordinary matter, dark matter, and dark-energy stu . . . . . . .
27
4.2.2
ENS06 models for ordinary matter, dark matter, and dark-energy stu . . . . . . .
29
4.2.3
ENS02 models for ordinary matter, dark matter, and dark-energy stu . . . . . . .
29
4.2.4
ENS01 models for ordinary matter, dark matter, and dark-energy stu . . . . . . .
29
Cosmology timeline and some astrophysics phenomena 5.1
6
SU (7)
. . . . . . . .
. . . . . . . . . . . . . . . .
Perspective - cosmology and forces
31
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
5.1.1
Summary - cosmology timeline and phenomena . . . . . . . . . . . . . . . . . . . .
31
5.1.2
Dominant forces within and between two neighboring clumps
32
. . . . . . . . . . . .
5.2
The moment of the big bang and shortly thereafter . . . . . . . . . . . . . . . . . . . . . .
33
5.3
Expansion - from the big bang until now . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
5.4
Baryon asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
5.5
Clumping - ordinary matter and dark matter
33
. . . . . . . . . . . . . . . . . . . . . . . . .
Systems, subsystems, and models 6.1
Perspective - systems and subsystems
35 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
6.1.1
Summary - results regarding subsystems . . . . . . . . . . . . . . . . . . . . . . . .
35
6.1.2
Summary - approach regarding modeling subsystems . . . . . . . . . . . . . . . . .
37
6.2
ALG symmetries pertaining within composite particles . . . . . . . . . . . . . . . . . . . .
39
6.3
σ−
39
6.4
Some equations correlating two somewhat-coupled objects . . . . . . . . . . . . . . . . . .
39
6.5
Fused systems and ssionable systems
39
6.6
6.7
models and
σ+
models
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5.1
Fused systems
6.5.2
Pair creation and entangled states
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
39
6.5.3
Particle decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
PDE modeling for aspects within objects . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
6.6.1
States of a system that includes elementary particles and/or other objects . . . . .
39
6.6.2
Objects similar to the hydrogen atom
40
6.6.3
Nuclear physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
6.6.4
Neutron stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
6.6.5
Possible generalizations to include more astrophysics and the entire G-family
. . .
40
. . . . . . . . . . . . . . . . . . . . . . . .
40
. . . . . . . . . . . . . . . . . . . . . . . . .
Phenomena people model via general relativity 6.7.1
Models correlating with
6.7.2
Models correlating with
σSR+ symmetries σGR+ symmetries
. . . . . . . . . . . . . . . . . . . . . .
40
. . . . . . . . . . . . . . . . . . . . . .
40
v
CONTENTS
7
Other phenomena, physics constants, and foundation topics 7.1
7.2
7.3
7.4
7.5
7.6
8
41
. . . . . . . . . . . . . . . . . . . . .
41
7.1.1
Summary - foundation topics, physics constants, and phenomena . . . . . . . . . .
41
7.1.2
Notes - physics-foundation topics and physics constants
42
Physics-foundation topics
. . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
7.2.1
Arrow of time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
7.2.2
Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
7.2.3
Numbers of dimensions
7.2.4
Minimum quantities
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
Physics constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
mass(tauon)
7.3.1
A correlation between
7.3.2
The ne-structure constant
and
GN
. . . . . . . . . . . . . . . . . . . . . .
43 43
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
Elementary-particle phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
7.4.1
Neutrino oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
7.4.2
G-family lasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
7.4.3
Detecting or producing dark matter
. . . . . . . . . . . . . . . . . . . . . . . . . .
44
Cosmology and astrophysics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
7.5.1
CMB cooling
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
7.5.2
Objects containing ordinary matter and dark matter . . . . . . . . . . . . . . . . .
44
7.5.3
Quasar formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
7.5.4
The galaxy rotation problem
44
7.5.5
The spacecraft yby anomaly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Somewhat free-ranging
σ−
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Models and modeling 8.1
9
Perspective - phenomena, constants, and foundation
44 44
45
Perspective - MM2MS2, traditional, and future models . . . . . . . . . . . . . . . . . . . . 8.1.1
Summary - MM2MS2 and traditional models
8.1.2
Notes - current and future models
45
. . . . . . . . . . . . . . . . . . . . .
45
. . . . . . . . . . . . . . . . . . . . . . . . . . .
45
8.2
Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
46
8.3
MM2MS2 models and traditional physics models
. . . . . . . . . . . . . . . . . . . . . . .
46
8.4
General relativity and MM2MS2
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
46
8.5
The Standard Model and MM2MS2
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Perspective - during and after this work 9.1
9.2
Opportunities - physics and modeling
46
47
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
47
9.1.1
Phenomena that people might try to detect, measure, or infer . . . . . . . . . . . .
47
9.1.2
Theory that people might enhance or develop . . . . . . . . . . . . . . . . . . . . .
Opportunities - general
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49 51
Bibliography
53
Index
55
vi
CONTENTS
Preface
Physics seems to have hit impasses. Decades old observations beget terminology but not explanations. Terminology may be ambiguous. For example, dark energy correlates with at least two possibly unrelated sets of observations. And, dark matter correlates with at least two possibly unrelated sets of observations. Inferences about observations feature attempts to invent, use, or extend theories and models that, individually, may not adequately pertain to observations and that, collectively, may not adequately integrate to provide bases for explaining observations.
Predictions, such as for new elementary particles, seem
vague. And, apparently, people are not observing such particles. In summary, experiments, observations, theories, and models explore many possibilities but seem to lead to too few answers. Perhaps it is time to tackle an unsolved problem, via a new approach. We try to develop a basis for cataloging known and predicting other elementary particles.
The
approach involves math that, while not very deep, seems to have been historically de-emphasized, to provide a basis for cataloging and predicting elementary particles, and to provide a basis for integrating historically useful physics theories and models. Aspects, models, and theories that we correlate include elementary particles and their properties, the elementary-particle Standard Model, the cosmology timeline, special relativity, quantum mechanics, and general relativity. We provide a basis for models that may pertain to and integrate aspects of physics that people correlate with topics including elementary-particle physics, nuclear physics, atomic physics, dark matter, dark energy, astrophysics, and cosmology. We show how to develop models.
We develop models.
We
discuss how to apply the models to such topics. We apply models to aspects of various of those topics. We try to explain known phenomena. We try to predict other phenomena. We hope that this work provides, at least, precedent and impetus for people to try to tackle such a broad agenda. And, this work may provide a means to tackle such an agenda and may provide progress toward ful lling that agenda.
- Thomas J. Buckholtz Portola Valley, California USA January 2017
vii
viii
DEDICATION
To Helen Buckholtz
In memory of Joel and Sylvia J. Buckholtz
With appreciation to each of many people who contributed to my being able to attempt this work
Chapter 1 Perspective - before and during this work
This unit discusses context for our work, the scope of our work, and some aspects of this presentation of our work.
1.1 Context and scope This unit discusses context for our work and the scope of our work.
1.1.1 Physics and models This unit discusses relationships between nature and models of nature. Physics discusses aspects of nature. Physics includes models of aspects of nature. People derive, from models, practical value and emotional value. Models evolve. People test the practical scope of a model. People hone the model. People develop related models. People extend the practical scope of models.
1.1.2 Aspects of recent models This unit discusses relationships between current and needed physics models. Table 1.1 shows names or themes for some models. Physics includes the rst ve models. As of 2016, physics may lack an adequately useful model that outputs information about elementary particles and their properties.
Name or theme
Status (as of 2016)
Special relativity Quantum mechanics General relativity
Established and possibly evolving
Elementary-particle Standard Model Cosmology timeline Elementary particles and their properties
Needed
Table 1.1: Some physics models
1
2
CHAPTER 1.
PERSPECTIVE - BEFORE AND DURING THIS WORK
Each of the rst ve models has roots in people's eorts to model and understand speci c phenomena. Overlaps between the ve models exist. For example, people integrate aspects of special relativity and aspects of quantum mechanics. People use such an integration to explain phenomena that people discuss based on Newtonian mechanics and/or classical electrodynamics. People recognize that each one of some of the rst ve models likely is incomplete.
For example,
people know of phenomena for which people think that elementary particles yet to be described or added to the Standard Model may play integral roles. Perhaps dark matter includes elementary particles that people have yet to describe, detect, or infer. People recognize that each one of some of the rst ve models does not necessarily integrate well with other ones of the rst ve models. For example, people try to integrate quantum mechanics and general relativity. People might recognize the possibility that people do not know the extents to which to try to explain some phenomena based on possibilities for improving individual models, integrating models, and/or developing other models. A likely example features phenomena people correlate with the term rate of expansion of the universe. Regarding the elementary-particle Standard Model, as of 2016, people seem not to have a list of candidates for new elementary particles, other than perhaps a graviton. Before 2016, people used aspects of the evolving Standard Model to predict particles such as the Higgs boson. As of 2016, people may not have extrapolated from the Standard Model to yet new elementary particles. People might consider the concept that the 2016 Standard Model includes, as an input to the model, a list of known elementary particles. We think traditional physics lacks a model for elementary particles and their properties.
Perhaps,
people can use such a model to provide inputs, including a list of possible particles, to work evolving the elementary-particle Standard Model. Perhaps people can learn, from such a model for elementary particles, concepts for integrating aspects of all six models.
1.1.3 Scope of our work This unit summarizes the scope of our work. We provide a basis for models that may pertain to and integrate aspects of physics that people correlate with topics including elementary-particle physics, nuclear physics, atomic physics, dark matter, dark energy, astrophysics, and cosmology. We show how to develop models. We develop models. We discuss how to apply the models to such topics. We apply models to aspects of various of those topics. We try to explain known phenomena. We try to predict other phenomena. We develop a basis to develop models that correlate with elementary particles. Using that basis, we develop models that correlate with all known and some possible elementary particles. By extending that basis, we possibly provide means to do the following activities. We attempt to do aspects of the following activities. 1. Predict elementary particles. 2. Provide steps toward understanding contexts for, understanding the scopes of, adding aspects to, and extending the scopes of models that table 1.1 lists. 3. Provide steps toward integrating, across models, aspects of models that table 1.1 lists.
TBD This unit lists opportunities people might want to pursue.
(Also, this unit typi es other similarly
titled units below. In each such similar unit below, there is no introductory paragraph.) 1. To what extent does work herein provide bases for useful predictions?
1.2.
OBSERVATIONS, MODELS, AND INFERENCES
3
2. To what extent does work herein provide bases for useful explanations? 3. To what extent might work herein impact modeling based on traditional models or based on future models?
(Impact might include helping extend models, unify models, understand the ranges of
applicability of models, and so forth.)
1.2 Observations, models, and inferences This unit discusses concepts pertaining to observations, models, and inferences. Some aspects of discussions of nature feature observers and observations. Observations can include results from experiments. Some aspects of discussions of nature feature modelers and models. Models can include theories. Some aspects of discussion of nature feature inference-makers and inferences. Inferences can include results of using models to extrapolate from known observations to possible observations. Extrapolation can include interpolation. When discussing nature, people use language. Language can include words and mathematical expressions. Interpretation of language can include literal interpretation and emotional interpretation. We think that attention to overlaps and distinctions between observations, models, and inferences is useful.
TBD 1. Throughout physics and physics-related models, to what extent do the following correlate (at least pairwise) with each other? (a) Aspects of nature being modeled. (b) Techniques for measuring aspects of nature. (c) Environments in which measurements take place. (d) Models (and symmetries correlating with models) people try to apply. (e) Mathematics bases for models.
1.3 Meta-model MM2 and models MS2 This unit discusses aspects of models that our work includes. We discuss models based on solutions to equations involving isotropic pairs of isotropic quantum harmonic oscillators. We correlate a subset of the solutions with the set of elementary particles that correlates with the Standard Model as of the year 2016. We discuss possibilities that other solutions correlate with elementary particles not discovered as of 2016. The acronym MM2 stands for meta-model two. Use of the acronym correlates with the possibility that people may nd and use other such meta-models, including meta-models based on mathematics other than math underlying MM2, that correlate with known and possible elementary particles. Use of the acronym also correlates with the existence of MM1, a meta-model that reference [1] discusses. MM2 and MM1 have aspects in common. We correlate possible elementary particles and/or yet other solutions with other physics phenomena. Some of the phenomena correlate with the topics of elementary-particle physics, astrophysics, or cosmology. Some of the phenomena correlate with other topics. The acronym MS2 stands for model set two. Use of the acronym correlates with the possibility that people may nd utility in some of the models based on MS2. Use of the acronym correlates with the
4
CHAPTER 1.
Aspect A goal (regarding understanding)
PERSPECTIVE - BEFORE AND DURING THIS WORK
Traditional approach
MM2MS2
Elementary-particle
List of elementary particles and properties
interactions and kinematics
List of elementary
Input to the approach
Output from the approach
particles Math basis
Lagrangian
Hamiltonian
Individual HO
Isotropic pairs of isotropic quantum HO
Energy for quantum states
Quantum states that correlate with nature
(energy)1 , (mass)1 , (angular momentum)1 integer ν ≥ 0
(energy)2 , (mass)2 , (angular momentum)2 integer 2ν < 0
HO (harmonic oscillators) Solutions Units (correlating with HO) Radial HO solutions
rν e−r
2
/(2η 2 )
∗ DQE =1
Use of number of time-like dimensions
D∗ = 3
Use of number of space-like dimensions Spin,
integer 2S ≥ 0 S(S + D∗ − 2) = S(S + 1) 0 ≤ S(S + D∗ − 2) = σΩ Ω = S(S + D∗ − 2) Ω = ν(ν + D − 2), D ≥ 1 σ = +1 P P σ = ±1 A (AQE − AQP ) QP P P P = (1/2)~ω = {(1 − 1) × (1/2)(~ω)2 } = 0 →∞ =0
S
Total spin (in units of
~2 )
Ω σ Sum over boson ground-states
Table 1.2: Features of models and mathematics - MM2MS2 compared to traditional approaches
possibility that people may nd and use other such models. Use of the acronym also correlates with the existence of MS1, models that reference [1] discusses. MS2 and MS1 have aspects in common. To denote the combination of MM2 and MS2, we use the acronym MM2MS2.
1.4 Mathematical bases for models This unit contrasts some mathematics we use with some mathematics people use in traditional physics modeling. Table 1.2 summarizes some dierences between models and mathematics we use and models and mathematics people use for some traditional approaches to describing nature. Here, the subscript with energy-like aspects and/or time-like aspects. The subscript pects and/or space-like aspects.
Regarding the symbol
momentum-like and/or space-like. The symbol parameter. Each of
r
and
η
r
D∗
QP
QE correlates
correlates with momentum-like as-
that does not have a subscript, we imply
denotes a radial coordinate. The symbol
η
denotes a
has dimensions of length.
TBD 1. What other applications might people make of mathematical bases we use to develop MM2MS2?
1.5.
5
NOTES - STORYLINE, WRITING, VOCABULARY, AND RESEARCH
1.5 Notes - storyline, writing, vocabulary, and research This unit suggests perspective about this expression of our work and about aspects of our work.
Storyline
This unit discusses aspects of the storyline we develop.
We try to provide information in an order correlating with a storyline that the reader can follow, that fosters understanding, and that the reader can use to discuss our work with other people. In so doing, we intertwine data, interpretations of data, models, development of models, and mathematics underlying models. Sometimes, we provide forward references to information.
Writing
This unit discusses aspects of writing we present.
We use a practice of embedding (in sentences) parenthetical elements (such as the two parenthetical elements this sentence exhibits). Sometimes, such a parenthetical element provides details.
In such cases, the reader may be able
to read the sentence either as written or without reading (some of ) the parenthetical elements.
We
think this dual-read structure includes useful information and facilitates people's understanding, without necessitating our including (possibly cumbersome) explanatory statements. Sometimes, a parenthetic element provides alternative wording or de nes a term or phrase. Generally, we start such an element with the word or and we follow the word or with a comma.
Vocabulary
This unit discusses concepts related to terminology.
Possibly, we use a term, such as a word or phrase or symbol, when discussing more than one of observations, our models, and other models. Possibly, people do or should interpret a term dierently in each of two or more contexts. For example, consider the terms elementary particle and mode. elementary particle can correlate with W boson or with one of the W term W boson to correlate with a concept of both of the W
+
one of the W W
−
−
and W
+
and W
−
In traditional physics, the term
+
and W
−
bosons. People use the
bosons or with a concept of either
bosons. People do not use the term mode to correlate with just one of W
+
and
. In traditional physics, the term elementary particle can correlate with photon. People use the term
photon mode to correlate with a concept of one of a left-circularly polarized photon and a right-circularly polarized photon. People do not use the term elementary particle to correlate with just one photon mode. We try to oer some clarity by emphasizing terminology centric to observations and to models. In doing so, we sometimes introduce a term such as a word or symbol. We may suggest relationships between the term we introduce and vocabulary people use in traditional models. Sometimes, we relate two statements or concepts, say St1 and St2. We might say that St1 correlates with St2. We might say that St1 links with St2. We might say that St1 dovetails with St2. Such wording does not necessarily imply that St1 equals St2. Such wording does not necessarily imply that St1 implies, causes, or includes as a subset St2. Such wording does not necessarily imply that St2 implies, causes, or includes as a subset St1. Sometimes, we start a sentence with the words people might say that.
We use this wording to
indicate, for example, that interpretations of the sentence might vary based on interpretations of words in the sentence, interpretations of data about nature, models that people use, and so forth. Regarding the elementary-particle Standard Model, we use terms such as Standard Model and 2016 Standard Model. Regarding the cosmology standard model, we use terms such as cosmology timeline. Regarding terms such as elementary particle, eld, photon, and graviton, the following statements pertain. 1. People might make various uses of each of the terms eld and elementary particle. 2. People might say that our work oers the possibility of considering that two MM2 elds combine to correlate with a eld for photons.
(See equation 2.1 and table 2.3.)
People might say that
6
CHAPTER 1.
PERSPECTIVE - BEFORE AND DURING THIS WORK
2G2& intermediates interactions based on the charges of interacting objects. People might say that 2G24& intermediates interactions based on the spins of objects.
People might say that 2G24&
intermediates interactions based on the nominal magnetic dipole moments of objects. 3. People might say that our work oers the possibility of considering that those two elds (and/or a eld for photons) contribute to a more encompassing eld that correlates with quantum electrodynamics (or, QED) phenomena people observe in atoms. (See tables 2.3 and 6.2.) 4. People might say that our work correlates with the existence of choices regarding use of the term graviton. One choice includes just 4G4&. (See table 2.3.) Another choice includes all of the 4G items that table 2.3 lists.
People might say that 4G4& intermediates interactions based on the
masses (or on the energies and momenta) of interacting objects. People might say that the other 4G items intermediate interactions based on spin-like properties of interacting objects.
Research
This unit suggests aspects related to interpreting our work.
People might say that some of our work regarding elementary particles correlates with the phrase pattern matching, with the phrase theory of what, and/or with the phrase models of what. People might say that the pattern matching features mathematical bases that are relatively simple compared to some mathematical bases people traditionally use regarding the physics of elementary particles. People might say that, in some cases, known data does not su ce for making rm choices from lists of choices our work produces. People might say that such lists feature tractable numbers of discrete, somewhat well-de ned choices. People might say that existences of such choices provide improvements compared to traditional theories for which choices may be less well de ned and may feature continuous ranges of numbers. Absent direct evidence that the possible elementary particles that we discuss exist, we explore possible existence of the particles by showing how their existence might provide explanations for known phenomena people correlate with the topics nuclear physics, atomic physics, dark matter, dark energy, astrophysics, and cosmology. People might say that some of our work regarding topics other than elementary particles correlates with the phrase theory of how and/or with the phrase models of how. People might say that some of our work provides models for how to integrate models pertaining to elementary-particle phenomena and models pertaining to cosmology.
People might say that our work
provides new choices for modeling phenomena for which traditional models provide useful results. People might say that, to the extent our work correlates with and does not misinterpret known data, the scope of the work points to possible usefulness for the work and extensions to the work. Here, the variety of aspects of nature we address correlates with the phrase scope of the work. People might say that, to the extent the work does not correlate with or does misinterpret known data, such discrepancies do not necessarily invalidate some portions of the work and/or some applications of the work. People might say that, to the extent such discrepancies exist, people might be able to remove discrepancies by improving aspects of the work and/or by reinterpreting data.
TBD 1. Develop and propagate vocabulary that helps people avoid negative aspects of ambiguities. 2. Resolve (to an appropriate extent) ambiguities that correlate with sentences that start with the phrase people might say that.
Chapter 2 Known and possible elementary particles
This unit catalogs known elementary particles and predicts elementary particles.
2.1 Perspective - elementary particles and math solutions This unit discusses known and predicted elementary particles, discusses mathematics solutions that correlate with elementary particles, and notes aspects about modeling interactions between elementary particles.
2.1.1 Summary - elementary particles This unit discusses elementary particles correlating with mathematical solutions correlating with MM2. Table 2.1 shows a set of subfamilies of elementary particles that may be su cient to correlate with
σ correlates with mathematics we use in MM2MS2. (See tables σ = −1 happens to correlate with elementary particles either that
currently known physics. The symbol 1.2 and 2.2.) The mathematics value
people have observed only in bound states (that is, only within composite particles) or that possibly can exist (in conditions that people can today observe or create) only in bound states. value
σ = +1
The mathematics
happens to correlate with elementary particles either that people have called free-ranging
or that people might call free-ranging. The term free-ranging correlates with the applicability, regarding kinematics, of Poincare group symmetries (or, symmetries that people correlate with special relativity).
m2 provides mass (m = 0).
In table 2.1, the column labeled mass (m
6= 0)
or zero rest
information regarding whether particles have non-zero rest (MM2MS2 models consider that an object interacts with
gravity via the object's energy and momentum.
Thus, models correlate with gravity interacting with
neutrinos, even though {in MM2} neutrinos have zero mass. People might say that, for a photon {or for any other object}, energy and momentum may correlate with aggregate properties that include a cloud of virtual particles that correlate with the photon {or other object}.) The column labeled F shows names of families of elementary particles. In table 2.5, we discuss motivations for family names. The column labeled
S
lists spins. Here, the values correlate with the
S
in the total spin
S(S + 1)~2 .
The
column labeled sF shows names of subfamilies. We use the notation nF to denote a subfamily. Here, n denotes the non-negative integer
2S .
The symbol F correlates with the name of a family. The next two
columns show aspects of the extent to which we think people know of particles within each subfamily. We use the word some as an abbreviation for the phrase some but not all. The leftmost of those two columns summarizes the extent to which people have (we think) identi ed phenomena that people would (we think) correlate (based on traditional physics) with relevant particles. The rightmost of those two 7
8
CHAPTER 2.
m2
σ
+1
sF
Eects correlated
Names given
with ... particles
to ... particles
Known particles
6= 0 6= 0
H
0
0H
all
all
Higgs boson
C
1/2
1C
all
all
Charged leptons
0
N
1/2
1N
all
all
Neutrinos
3/2
3N
no
no
6= 0
W
1
2W
all
all
Z and W bosons
1
2G
possibly all
some
Photon
2
4G
some
some
3
6G
no
no
4
8G
no
no
Q
1/2
1Q
all
all
R
1/2
1R
no
no
Y
1
2Y
all
all
0
0O
no
no
1
2O
no
no
0
−1
S
F
KNOWN AND POSSIBLE ELEMENTARY PARTICLES
G
6= 0 0 0 6= 0
O
Quarks Gluons
Table 2.1: A possibly complete set of elementary-particle subfamilies Category
Math usage
σ = ...
yes
σ±
no
Use
Models ...
Relevant models ...
σ = −1 σ = +1 σ− σ+
correlate with some elementary particles
σ− σ−, σ+ σ− σ+
correlate with some elementary particles model bound states model free-ranging states Table 2.2: Uses of the symbol
σ
columns indicates the extent to which people assigned (as of 2016) names that correlate with particles. (People might say that traditional use of the word photon does not pertain to some of the particles we correlate with the 2G subfamily. People might say that the term graviton might correlate with one 4G particle {that people have yet to nd} or with the combination of all 4G particles {of which people have found none}.) The column labeled known particles mentions (at least by names of sets of particles) all known elementary particles. Table 2.2 summarizes aspects regarding uses we make of the symbol
σ+ and σ−.
σ.
The table notes the symbols
People might say that we correlate each of these symbols with concepts related to kinematics
(including possibilities for ssion or other decays). People might say that we correlate
σ+ with models for
which people might say the phrase free-ranging subsystem pertains. People might say that we correlate
σ−
with models for which people might say the phrase bound subsystem pertains. For example, a
σ−
model might pertain for objects (such as quarks) bound in a subsystem (such as a composite particle). People might model composite particles (such as pions and protons) as either free-ranging (or, as bound (or,
σ−)
and some types of
components (for example, of atomic nuclei). Table 3.1 lists some types of
σ−
σ+
σ+)
or
models
models.
Table 2.3 shows G-family elementary particles that may correlate with nature. the term spatial dependence of force.
SDF abbreviates
The SDF column shows (in the sense of Newtonian physics) a
characteristic of the force (that the particle intermediates). (We assume that a more rigorous treatment can deal with relativistic concepts such as concepts correlating with the not in nite speed of light.) Here,
r
denotes the distance between (the appropriate centers of ) two interacting entities. People might say
that, for SDF of
r−3 ,
the interaction has dipole-like characteristics. (The only G-family particles that
intermediate monopole interactions are 2G2&, 4G4&, 6G6&, and 8G8&.) Table
??
pertains regarding
correlations between interaction strengths and properties (such as charge and spin) of objects. Table
??
2.1.
σ
9
PERSPECTIVE - ELEMENTARY PARTICLES AND MATH SOLUTIONS
m2
F
S
sF
Particle
SDF
2G2&
r−2
2G24& 1
2G46&
2G
2G68& 2G248& 2G468& 4G4&
+1
=0
G
4G26& 2
4G48&
4G
4G246& 4G268& 4G2468&
3
6G
4
8G
r−3
6G6& 6G28& 8G8&
r−4 r−2 r−3 r−4 r−5 r−2 r−3 r−2
Table 2.3: G-family elementary particles
correlates eras regarding the rate of expansion of the universe with eects of interactions mediated by G-family particles. Table 6.2 correlates 2G particles with eects people observe regarding atoms. People might say that equation 2.1 (pertains regarding {at least, elds} and) correlates aspects of traditional models with aspects of MM2MS2. The 2G24& component couples to (for example) spins of elementary particles.
photon ↔ 2G2& + 2G24&
(2.1)
People might say that the pervasiveness of unbounded-range (especially, G-family) forces correlates with inherent inaccuracies in
σ+
models. Nevertheless, people might use the symbol
σ+
to characterize
natural (or experimental) environments pertaining to aspects of nature. Table 2.4 discusses numbers of particles and numbers of modes. Notation of the form {n1 ,n2 } correlates with the concept that
n1
pertains for one of the two relevant columns and
n2
pertains for the other
of the two relevant columns. The table shows, in the column labeled matter/antimatter particles, the number of particles people would consider not to be either matter or antimatter. People might say that each of these particles is its own antiparticle. Examples include the Higgs boson and the Z boson. Discussion related to equation
??
explores the topic of whether to model neutrinos as being Dirac fermions
(or, as correlating with the case of zero matter/antimatter particles and three matter particles) or as being Majorana fermions (or, as correlating with the case of three matter/antimatter particles and zero matter particles). The table shows, in the column labeled matter particles, the number of particles people would consider to be matter particles. People would consider that, for each matter particle, there is an antimatter particle. For each G-family particle, two modes exist. One mode is left-circularly polarized. The other mode is right-circularly polarized. People might say that the following statements pertain to yet-to-be-found elementary particles correlating with MM2. 1. 3N particles might contribute to a form of dark matter and/or might contribute to inferred densities of the universe. 2. 2G particles (other than 2G2& and 2G24& {See equation 2.1.}) correlate with known eects such as ne-structure splitting. (See table 6.2.)
10
CHAPTER 2.
σ
m2
F
6= 0 6= 0
+1
−1
Matter/antimatter
Matter
particles
particles 0
0
0H
Higgs boson
1
1/2
1C
Charged leptons
0
1/2
1N
Neutrinos
6= 0
W
3
3N
1
2W
Z and W bosons
1
1
2G
Photon
6
2
4G
6
3
6G
2
4
8G
1
Q
1/2
1Q
R
1/2
1R
Y
1
2Y
0
0O
1
0
1
2O
1
1
O
Modes per particle
{0, 3}
3/2
G
6= 0
Known particles
C N
6= 0 0 0
sF
H
0
0
S
KNOWN AND POSSIBLE ELEMENTARY PARTICLES
{0, 15}
Quarks
1
0
2
6 6
Gluons
8
Table 2.4: Numbers of particles and modes
(a) Possibly, MM2MS2 provides bases for models that can be alternatives to QED (or, quantum electrodynamics) models. 3. 4G particles correlate with known gravitational eects and possibly with eects yet to be identi ed. 4. 6G particles correlate with eects yet to be identi ed. 5. 8G particles correlate with eects yet to be identi ed. 6. 1R particles might contribute to forms of dark-energy stu and and/or contribute to inferred densities of the universe. Possibly, 1R particles correlate with modeling (of interactions between elementary particles) in which each interaction vertex involves one or more fermions and involves excitation or de-excitation of one boson state. (For example, 1R particles would, in eect, intermediate interactions for which traditional models consider that one gluon produces two gluons.) 7. 0O particles might be components (along with 1Q particles and/or 1R particles) of yet-to-be-found composite particles. 8. 2O particles might have been key to the creation of baryon asymmetry.
2O particles might be
components (along with 1Q particles and/or 1R particles) of yet-to-be-found composite particles.
TBD 1. To what extent do the known and possible elementary particles to which tables 2.1, 2.3, and 2.4 allude and possibilities for multiple instances of some of these particles (See table 4.3.) su ce to explain known phenomena and inferred aspects (including dark matter and dark energy) of nature? 2. To the extent the known and possible elementary particles to which tables 2.1, 2.3, and 2.4 allude and possibilities for multiple instances of some of these particles (See table 4.3.) do not su ce to explain known phenomena, which of the solutions (that do not correlate with items tables 2.1, 2.3, and 2.4 list) that table 2.5 (or an extension to table 2.5) shows might correlate with elementary particles?
2.1.
σ
+1
−1
11
PERSPECTIVE - ELEMENTARY PARTICLES AND MATH SOLUTIONS
m2 6= 0 6= 0 0 6= 0 0 6= 0 6= 0 0 0 0 6= 0
S
Known
F
Motivation for the name
0
Higgs boson
H
Higgs boson
1/2
Charged leptons
C
Charged leptons
1/2, 3/2
Neutrinos
N
Neutrinos
1
Z and W bosons
W
Weak-interaction bosons
1, 2, 3, 4
Photon
G
Gamma ray
1/2, 3/2, ...
Quarks
Q
Quarks
3/2, 5/2, ...
I
1/2, 3/2, ...
R
3/2, 5/2, ...
D
1, 2, ...
Gluons
0, 1, 2, ...
Y
The shape of the letter
O
O, as in leptoquarks
Table 2.5: Families of possibly relevant solutions
3. To what extent would 3N particles correlate (except possibly regarding having spin-3/2 and not having spin-1/2) with phenomena people might correlate with the term sterile neutrino? 4. To what extent does use of what extent can people use
σ+ models correlate with signi cant errors σ− models to reduce the signi cance of such
regarding modeling?
To
errors?
5. To what extent might models consider that, for each G-family elementary particle, each mode correlates with the term anti mode with respect to the other mode? 6. To the extent the known and possible elementary particles to which tables 2.1, 2.3, and 2.4 allude and possibilities for multiple instances of some of these particles (See table 4.3.) su ce to explain known phenomena, what insight might people gain regarding the topic (and possible non-existence) of magnetic monopoles? 7. To the extent the known and possible elementary particles to which tables 2.1, 2.3, and 2.4 allude and possibilities for multiple instances of some of these particles (See table 4.3.) su ce to explain known phenomena, what insight might people gain regarding the topic of supersymmetry?
2.1.2 Summary - possibly relevant mathematical solutions This unit lists families and subfamilies of mathematical solutions correlating with a math basis we use. Table 2.5 lists families of mathematical solutions that might correlate with known elementary particles and possible elementary particles. (This list alludes to solutions correlating with a superset of the solutions needed to correlate with tables 2.1, 2.3, and 2.4.) For each family of solutions correlating with known particles, we use a term associated with known such particles to motivate the choice of name. (For the Gfamily the hypothetical graviton also pertains.) The family letter I correlates with the word invisible. The family letter R is the letter alphabetically next after Q. Possibly, D-family particles would not interact much with each of electromagnetism and gravity. The letter Y correlates with the shape of one type of interaction vertex (including incoming and ongoing particles) people correlate with gluons.
The word
leptoquarks denotes a type of elementary particle that people hypothesize. We are not certain the extent to which 2O particles would correlate with people's use of the term leptoquark. MM2MS2 correlates possible elementary particles with G-family solutions for which
S = 3 and S = 4.
MM1MS1 shows and de-emphasizes such solutions. (Reference [1]) MM2MS2 de-emphasizes solutions, other than 3N solutions and G-family solutions, for which Table
S ≥ 3/2.
?? illustrates (for a subset of mathematical solutions) the concept that we de-emphasize (regard-
ing possible physics-relevance) some mathematical solutions (for which table 2.5 does not have entries).
12
CHAPTER 2.
Type
Incoming fermions
0F−B2F 1F±B1F 2F+B0F
KNOWN AND POSSIBLE ELEMENTARY PARTICLES
One boson eld ... by one unit
Outgoing fermions
0
de-excites
2
1
excites or de-excites
1
2
excites
0
Table 2.6: MM2MS2 interaction vertices
People might say that, below, we discuss solutions (that may not be physics-relevant) so as to illustrate mathematics and/or patterns that seem to pertain regarding physics-relevant solutions. In units below, we to the following. 1. Discuss mathematics correlating with the phrase solutions to equations involving isotropic pairs of isotropic quantum harmonic oscillators. 2. Correlate a member of a subset of MM2 solutions with each known (as of 2016) elementary particle. Each of these solutions correlates with an item in table 2.5. 3. Correlate members of another subset of MM2 solutions with possible elementary particles. Each of these solutions correlates with an item in table 2.5. 4. De-emphasize (but do not completely dismiss) another subset of solutions. Each of these solutions correlates with an item in table 2.5. 5. Dismiss (as being not physics-relevant) other solutions.
TBD 1. To the extent the known and possible elementary particles that would correlate with table 2.5 do not su ce to explain known phenomena, what extensions to table 2.5 might correlate with elementary particles?
2.1.3 Interactions, vertices, and elementary particles This unit discusses some aspects regarding modeling interactions in which elementary particles partake. In traditional physics, interactions play key roles. People measure properties of elementary particles (or of objects or of subsystems) based on interactions in which the elementary particles (or other objects or subsystems) participate. In physics, models for interactions play key roles. Traditional quantum physics features concepts people correlate with the term interaction vertex. People might say that MM2MS2 models contain aspects analogous to aspects of interaction vertices in traditional physics models. (See table 2.6.) For example, regarding MM2MS2 models for each of some vertices, people might consider that an elementary fermion enters the vertex, the creation or destruction of an elementary boson correlates with the vertex, and an elementary fermion leaves the vertex.
For
such a vertex, we use the symbol 1F±B1F. Each of three pairs of characters in 1F±B1F correlates with one of the three aspects (of a model for the vertex), which are respectively one fermion enters, creation or destruction of a boson occurs, and one fermion exits. We use the symbol 0F−B2F to correlate with another type of vertex. People might say that, for these vertices, a boson enters, destruction of the boson occurs, and two fermions (perhaps, a matter-particle-and-antimatter-particle pair) leave. Destruction of a matter-fermion-and-antimatter-fermion pair correlates with the symbol 2F+B0F. People might say that MM2MS2 models correlate with the following statements. 1. For each elementary particle, MM2 includes a point-like construct and a non-point-like construct. (See discussion correlating with table
??.)
2.1.
13
PERSPECTIVE - ELEMENTARY PARTICLES AND MATH SOLUTIONS
2. At an interaction vertex, models correlate with the following. (a) For one boson non-point-like construct, the interaction destroys the incoming non-point-like construct and creates an outgoing non-point-like construct with an excitation number that diers from the incoming-construct excitation number by either plus one (if people would consider that the interaction creates the boson) or minus one (if people would consider that the interaction destroys the boson). (b) Exactly one of 1F±B1F, 0F−B2F, and 2F+B0F pertains. (c) For a 1F±B1F vertex, the interaction destroys the non-point-like construct correlating with the incoming fermion and creates the non-point-like construct correlating with the outgoing fermion. i. Depending on circumstances, the outgoing fermion may dier from the incoming fermion with respect to observer-invariant properties such as rest mass, charge, or color charge. ii. Depending on circumstances, the outgoing fermion may dier (from the perspective of any one observer) from the incoming fermion with respect to observer-dependent properties such as energy, momentum, or spin state. iii. Each of the four non-point-like constructs (of which two correlate with the term boson and two correlate with the term fermion) correlates with a point-like construct. A. One point-like construct correlates with properties of the boson state that the interaction (at least, in eect) destroys. B. One point-like construct correlates with properties of the boson state that the interaction (at least, in eect) creates. C. One point-like construct correlates with properties of the fermion state that the interaction (at least, in eect) destroys. D. One point-like construct correlates with properties of the fermion state that the interaction (at least, in eect) creates. (d) For a 0F−B2F vertex or a 2F+B0F vertex, similar concepts pertain.
Models consider (in
eect) before and after states for the relevant boson. Models consider (in eect) before and after states for each of the two relevant fermions. 3. People might say that, for an occurrence (in nature) of an elementary particle, MM2MS2 models correlate with (and require) a vertex that creates the elementary particle and a vertex that destroys the elementary particle. We discuss (here) those concepts because (below) the following statements pertain. 1. Work related to elementary fermions directly exhibits aspects of the concepts. 2. Work related to gluons directly exhibits aspects of the concepts. 3. People may tend to overlook relevance of aspects of the concepts. (a) Regarding an interaction that de-excites (by one unit) an elementary boson, people may deemphasize the aspect that an outgoing non-point-like boson solution pertains. (b) Regarding an interaction that excites (by one unit) an elementary boson, people may deemphasize the aspect that an incoming non-point-like boson solution pertains. (c) Regarding work related to elementary bosons other than gluons, people may de-emphasize the relevance of modeling two vertices (not just one vertex) and, therefore, may de-emphasize the relevance of considering that (in some sense) two (possibly similar or seemingly equal) solutions correlate with one occurrence of one elementary particle.
14
CHAPTER 2.
KNOWN AND POSSIBLE ELEMENTARY PARTICLES
TBD 1. To what extent does nature exhibit aspects for which limiting MM2MS2 to three types (1F±B1F, 0F−B2F, and 2F+B0F) of interaction vertices correlates with inadequate modeling? 2. To what extent does nature exhibit aspects for which 1F±B1F interaction vertices would need to correlate with a non-zero dierence (between the incoming and outgoing fermions) in (the observer-
S(S + 1)~2 )?
invariant quantity) total spin (or,
(Regarding
S,
see, for example, table 2.1.)
2.2 Solutions, particles, and particle properties This unit catalogs known and predicted elementary particles and describes some properties of elementary particles.
2.2.1 Perspective - ALG solutions and PDE solutions This unit introduces concepts and terminology related to mathematics we use.
1
2.2.2 ALG solutions This unit discusses ALG mathematics solutions.
2
2.2.3 Photons and 2G2& This unit compares aspects of traditional-physics models for photons and aspects of our models that
3
correlate with some aspects of photons.
2.2.4 ALG ground-state solutions for which N [E] ≤ 3 and N [P ] ≤ 3 This unit lists some ALG math solutions and correlates some such solutions with elementary particles.
4
2.2.5 PDE solutions 5
This unit discusses PDE mathematics.
2.2.6 Correlations between MM2 solutions and elementary particles This unit discusses correlations between mathematics solutions and elementary particles.
6
2.2.7 Solutions that might correlate with non-zero-mass elementary bosons This unit discusses correlations between math solutions and non-zero-mass elementary bosons.
1 This 2 This 3 This 4 This 5 This 6 This 7 This
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2.2.
15
SOLUTIONS, PARTICLES, AND PARTICLE PROPERTIES
2.2.8 Solutions that might correlate with elementary fermions This unit discusses correlations between math solutions and elementary fermions.
8
2.2.9 Neutrinos - Dirac fermions or Majorana fermions? This unit discusses possibilities for modeling neutrinos as being Dirac fermions or as being Majorana
9
fermions.
2.2.10 Solutions that might correlate with G-family elementary bosons This unit discusses math solutions that correlate with zero-mass free-ranging elementary bosons.
10
2.2.11 Solutions that might correlate with Y-family elementary bosons This unit discusses math solutions that correlate with zero-mass non-free-ranging elementary bosons.
2.2.12 Models correlating with gluons This unit discusses aspects of models for vertices for some interactions involving gluons.
2.2.13 Properties of non-zero-mass elementary particles This unit summarizes some properties of non-zero-mass elementary particles.
8 This 9 This 10 This 11 This 12 This 13 This
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13
12
11
16
CHAPTER 2.
KNOWN AND POSSIBLE ELEMENTARY PARTICLES
Chapter 3 Symmetries, patterns, and elementary-particle properties
This unit discusses symmetries and patterns correlating with aspects of elementary-particle physics, provides formulas that correlate with masses of known elementary particles, shows a basis for the weak mixing angle, and predicts properties for yet-to-be-found elementary particles.
3.1 Perspective - models, patterns, and symmetries This unit summarizes results and concepts regarding symmetries, patterns, and elementary-particle properties.
3.1.1 Summary - models, patterns, and particle properties This unit summarizes results regarding models, symmetries, patterns, and elementary-particle properties. MM2MS2 provides a possibly new basis for modeling much physics. People might say that, regarding models, people should explore similarities and dierences between patterns (in nature) that new and traditional models re ect. Similarly, people might explore similarities and dierences regarding extrapolations that produce patterns that people correlate with predictions. Regarding models related to elementary-particle physics, each of MM2MS2 and traditional models uses concepts of symmetries to express some patterns. People might say that our work shows the following. 1. MM2MS2 models dovetail with traditional models regarding aspects of the following concepts. (a) CPT-related symmetries. i. We show a possibly new concept correlating C symmetry (or, charge conjugation symmetry), P symmetry (or, parity transformation symmetry), T symmetry (or, time reversal symmetry), and CPT symmetry. (b) Poincare-group symmetries (and concepts people correlate with terms such as special relativity and free-ranging). i. Regarding
σ+
models, we use Poincare group symmetries for aspects of kinematics. We
assume, from traditional models, correlations between Poincare group symmetry and, for example, conservation of energy, momentum, and angular momentum. Thereby, aspects of MM2MS2 include conservation of energy, conservation of momentum, conservation of angular momentum, and
E 2 = (mc2 )2 + P 2 c2 17
(or, equation
??).
18
CHAPTER 3.
SYMMETRIES, PATTERNS, AND ELEMENTARY-PARTICLE PROPERTIES
ii. Regarding
σ− models, we discuss modeling for which Poincare group symmetries need not
apply. For example, for composite particles, Poincare group symmetries need not pertain for quarks and gluons.
(Poincare group symmetries pertain to, for example, a proton
{that is not part of, for example, a multi-nucleon atomic nucleus}. Aspects of traditional models use aspects of Poincare group symmetries for modeling the internals of a proton. MM2MS2 possibly provides an alternative set of symmetries.) (c) The 2016 Standard Model notion of
SU (3) × SU (2) × U (1)
symmetry.
i. People might say that our models correlate with such a symmetry. ii. People might say that our bases for this symmetry dier from bases correlating with the 2016 Standard Model.
In MM2MS2, the
U (1)
component correlates with models
correlating with the weak interaction (or, W-family particles). In traditional models, the
U (1)
component correlates with models correlating with the electromagnetic interaction.
2. MM2MS2 points to the following concepts. (Traditional models may not point to some of these concepts. Traditional models may point to some of these concepts, but with results that dier from MM2MS2 results.) (a) Symmetries correlating with models regarding the G-family, that may correlate with aspects of modeling that people might correlate with the topic of intrinsic curvature regarding space-time coordinates that models use. (b) Properties of elementary particles (and of objects) correlating with forces that traditional physics does not include. i. For example, one such property might correlate with 6G6&, which people might characterize as the spin-3 member of the series 2G2& (or, photon except for the photon's coupling to spin), 4G4& (or, {possibly} graviton), 6G6&, and 8G8&. (c) A possible correlation between masses of weak-interaction bosons and the range of the weak interaction. (d) A series of (formulas for) lengths that might correlate with a pattern. i. The (formulas for) lengths correlate respectively with radii of black holes, the Planck length, and the range of the weak interaction. (e) A mathematical symmetry that might correlate with nature's including more than one ensemble (or, more than one copy of {at least} 2016 Standard Model elementary particles). i. This symmetry correlates with relevance, regarding aspects of kinematics, of the Poincare group. ii. Each ensemble would also include a copy of each of some of the {non 2016 Standard Model} elementary particles we predict. (f ) A formula correlating with patterns regarding masses of quarks and charged leptons. (g) A formula correlating with the masses of the known non-zero mass elementary bosons (or, the H, W, and Z bosons). i. People might say that this work provides insight regarding the weak mixing angle (or, Weinberg angle). (h) Patterns that might correlate with charges and masses for O-family bosons. i. People might say that this work correlates with, for each O-family boson, predicting the spin and charge of the particle and pointing to a set of possible rest masses. Depending on the particle, the set of possible rest masses includes 3, 10, or 20 numbers. (i) Possible insight into threshold energies that high-energy experiments to try to detect O-family bosons might need to surpass.
3.1.
σ± σ+
19
PERSPECTIVE - MODELS, PATTERNS, AND SYMMETRIES
Symbol
Discussion
Generic
Math
σSR+
σ(1, 0, 3)+
Modeling term or use
Application
Free-ranging motion;
Special-relativistic
Poincare group symmetries
kinematics;
σ = +1
σ+
models for
fermions and bosons (for example)
σGR+
σ(1, 0, 2)+
σCP −
σ(j, 0, l)−
Possibly, general-relativistic kinematics
σ− σGY −
-
σHA−
-
σ−
Composite-particle internal
models for
σ = −1
symmetries
fermions and bosons
Bound states (based on G-
Possibly, atomic nuclei;
and Y-family forces)
possibly, neutron stars
Bound states (based on
Hydrogen atom (for example)
G-family forces) Table 3.1:
σ+
symmetries and
σ−
symmetries
i. Possibly, production of one O-family boson requires production of at least a pair of Ofamily bosons or a triplet of O-family bosons. If, for example, production requires producing at least a pair, the input energy needed to produce an O-family particle likely exceeds at least twice the rest energy of the particle.
3.1.2 Summary - σ+ symmetries and σ− symmetries This unit summarizes some concepts regarding symmetries correlating with free-ranging states and regarding symmetries correlating with bound-state physics. Table 3.1 lists sets of models we consider.
We discuss immediately below aspects correlating with
σ(j, k, l)±, j denotes a number of 1-generator symmetries, k denotes a number of 2-generator symmetries, l denotes a number of 3-generator symmetries, and ± correlates with the ± in the symbol σ±. For some cases, we do not suggest math-related symbols.
each generic symbol. For symbols of the form
1. The following statements pertain regarding
σSR+.
(a) The term SR abbreviates the term special-relativistic. (b) People correlate with special-relativistic models Poincare group symmetries. These symmetries include one 1-generator symmetry and three 3-generator symmetries. 3-generator symmetry with the group
People correlate each
SU (2).
(c) People correlate conservation of energy with the 1-generator symmetry. People correlate conservation of momentum with one 3-generator symmetry.
People correlate conservation of
angular momentum with another 3-generator symmetry. People correlate boost (or, symmetries correlating with the concept in special relativity of boost) with the third 3-generator symmetry. 2. The following statements pertain regarding
σGR+.
(a) The term GR abbreviates the term general-relativistic. (b) We posit correlating with models based on general relativity one 1-generator symmetry and two 3-generator symmetries. We correlate each 3-generator symmetry with the group (c) We correlate conservation of energy with the 1-generator symmetry. vation of momentum with one 3-generator symmetry. momentum with the other 3-generator symmetry.
SU (2).
We correlate conser-
We correlate conservation of angular
20
CHAPTER 3.
SYMMETRIES, PATTERNS, AND ELEMENTARY-PARTICLE PROPERTIES
(d) We generally de-emphasize the notion that other (similar) symmetries might pertain. 3. The following statements pertain regarding
σCP −.
(a) The term CP abbreviates the term composite particle. (b) We posit that modeling based on
σ(j, 0, l)−
models provides an alternative (to QCD {or
quantum chromodynamics}) means for modeling internals of composite particles. (c) For MM2MS2 models,
0≤j≤1
and
0 ≤ l ≤ 3.
4. The following statements pertain regarding
σGY −.
(a) The term GY correlates with concept that, in atomic nuclei, G- and Y-family bosons intermediate relevant forces. (b) We posit that modeling based on MM2MS2 techniques provides an alternative (to shell-model techniques) means and/or an augmentation to traditional (or, shell-model) means for modeling internals of atomic nuclei (and/or internals of neutron stars). (c) For (at least some) applications, equation 3.1 pertains. 5. The following statements pertain regarding
σHA−.
(a) The term HA correlates with the term hydrogen atom. (b) We posit that modeling based on MM2MS2 techniques provides an alternative (to QED {or quantum electrodynamics}) means for modeling internals of atoms and other (similar {for example, positronium} or more complex {such as molecules}) objects. (c) For (at least some) applications, equation 3.2 pertains.
(ξ 0 /2)η 2 (ξ 0 /2)η 2
is a positive number and
(ξ 0 /2)η −2
is a positive number and the limit
is a positive number
(ξ 0 /2)η −2 → 0+
pertains
(3.1)
(3.2)
People might say that the following statements pertain. 1. We emphasize (compared to discussion of modeling correlating with based on
σSR+
(and, in particular,
σ(1, 0, 3)+
and
σ(1, 0, 3) + c
σGR+) discussion of modeling
{See table
??.}).
2. We (in eect) explore the notion that, though people obtain useful results from models based on general relativity, MM2MS2 might provide alternative means for modeling phenomena that people model via general relativity.
TBD 1. To what extent does or might
σ(1, 0, 2)+ correlate with modeling based on general relativity?
And,
to what extent might other symmetries pertain? 2. To what extent might people nd useful the use of models based on
σCP −
concepts?
3. To what extent might people nd useful the use of models based on
σGY −
concepts?
4. To what extent might people nd useful the use of models based on
σHA−
concepts?
5. To what extent might people reduce (by honing bases for work we show regarding MS2) use (to develop MS2 or something similar to MS2) of inputs (for example, regarding kinematics) from traditional models?
3.2.
21
CPT-RELATED SYMMETRIES
3.2 CPT-related symmetries 1
This unit discusses a way in which our work correlates with CPT symmetry.
3.3 Free-ranging motion and the Poincare group This unit correlates Poincare-group (or, special relativity) symmetries with a possibly physics-relevant,
2
so-called instance symmetry.
3.4
SU (3) × SU (2) × U (1)
symmetry
This unit correlates our work with Standard Model
SU (3) × SU (2) × U (1)
3
symmetry.
3.5 G-family symmetries This unit discusses symmetries correlating with free-ranging zero-mass elementary bosons and discusses
4
the spatial dependence of forces correlating with free-ranging zero-mass elementary bosons.
3.6 G-family forces and properties of objects This unit discusses particle properties correlating with interactions mediated by G-family elementary
5
bosons.
3.7 Interaction vertices - size and proximity This unit discusses a correlation, for weak interaction bosons and other non-zero-mass elementary bosons,
6
between range and particle mass.
3.8 Symmetries related to SU (17) This unit correlates
SU (17)
7
symmetries with aspects of G-family physics and symmetries.
3.9 Masses of non-zero-mass elementary fermions 8
This unit shows a formula that ts the masses of the three charged leptons and six quarks.
1 This 2 This 3 This 4 This 5 This 6 This 7 This 8 This
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22
CHAPTER 3.
SYMMETRIES, PATTERNS, AND ELEMENTARY-PARTICLE PROPERTIES
3.10 Properties of non-zero-mass elementary bosons This unit shows a formula that ts the masses of known non-zero-mass elementary bosons, correlates with the weak mixing angle, and predicts a nite number of possible masses for each of the non-zero-mass yet-to-be-found elementary bosons our work predicts.
9 This
9
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Chapter 4 Ordinary matter, dark matter, and dark energy
This unit provides a nite number of choices for de nitions and explanations regarding dark matter and dark energy.
4.1 Perspective - dark matter and dark energy This unit introduces and summarizes choices for de nitions and explanations regarding dark matter and dark energy.
4.1.1 Uses of the terms dark energy and dark matter This unit discusses possible ambiguities regarding uses of the term dark energy and regarding uses of the term dark matter. People might say that people make two possibly not well correlated uses of the term dark energy. One use correlates with inferences based on data about CMB (or, cosmic microwave background) radiation. People infer that more than two-thirds of the (current) density of universe consists of something people call dark energy. We correlate, with such inferences, the term dark-energy stu. Another use correlates with inferences based on data about light people correlate with sources in distant large objects. People, infer that the objects move away from people (and from each other) with increasing velocity. People use terms such as dark-energy pressure to correlate with the acceleration. We correlate, with such inferences, the term dark-energy forces (or, dark-energy pressure). People might say that people may make eventually incompatible uses of the term dark matter. One current use correlates with inferences based on data about CMB radiation. People infer that a signi cant fraction of the density of universe consists of something people call dark matter. Another use correlates with inferences people make about galaxies and gravitation. People say that, within observed galaxies, signi cant fractions of the matter are dark matter. We think that uses may change for each of the concepts of dark matter, dark-energy stu, and darkenergy forces. Such change (possibly including abandonment of terms and/or introduction of new terms) might correlate with further understanding of relevant aspects of nature.
4.1.2 Data regarding ordinary matter, dark matter, and dark-energy stu This unit summarizes some data regarding densities of ordinary matter, dark matter, and dark-energy stu. 23
24
CHAPTER 4.
ORDINARY MATTER, DARK MATTER, AND DARK ENERGY
The following terms pertain regarding measurements pertaining to ordinary matter, dark matter, and dark-energy stu. 1. For stu correlating with ordinary-matter density of the universe, we use the term OMS, which is an acronym for the phrase ordinary-matter stu. (a) People report inferences (from data) of various contributions to the ordinary-matter density of the universe. Reported contributions include ones correlating with each of the terms baryon, CMB radiation, and neutrino. We know of no discussion of possible contributions correlating with (for example) the 3N subfamily. 2. For stu correlating with dark-matter density of the universe, we use the term DMS, which is an acronym for the phrase dark-matter stu. 3. For stu correlating with dark-energy-stu density of the universe, we use the term DES, which is an acronym for the phrase dark-energy-stu stu (or dark-energy stu). Data regarding inferred ratios of densities (Ω ) of the universe correlate with the following. (These uses of the symbol
Ω
to not correlate with uses related to spins {of elementary particles} of the symbol
Ω.)
Regarding the recent state of the universe, we use data from reference [3]. 1. Regarding inferences pertaining to (a) A number of
∼ 5.2
Ω(DM S)/Ω(OM S),
the following statements pertain.
pertains to the recent state of the universe.
(b) People might say that inferences correlate with notions that numbers similar to 5 may pertain since times relatively (with respect to the current age of the universe {or, approximately
13.8 × 109
years}) soon after the time at which atoms rst formed (or, about
3.8 × 105
years
after the big bang). 2. Regarding inferences pertaining to
Ω(DES)/(Ω(DM S) + Ω(OM S))
the following statements per-
tain. (a) A number of
∼ 2.2
pertains to the recent state of the universe.
(b) Numbers have grown from
∼0
(pertaining to the early universe) to the present number.
TBD 1. Determine correlations (and/or lack of correlations) among the following. (a) Data (possibly correlating with dark matter, dark energy, and dark-energy stu) and inferences (about dark matter, dark energy, and dark-energy stu) from data. (b) Concepts we propose for OMS, DMS, and DES. (c) Concepts (such as WIMPs {or, weakly interacting massive particles}, axions, and primordial black holes) that people propose for DMS. (d) Densities of the universe correlating with G-family bosons other than OMS photons. 2. Hone de nitions of the terms ordinary matter, dark matter, dark-energy forces, dark-energy pressure, and dark-energy stu.
4.1.
25
PERSPECTIVE - DARK MATTER AND DARK ENERGY
MM2MS2 OME phenomenon
Possible interpretation
3N particles
dark matter
Composite particles that feature 2O particles
dark matter
(and at least one of 1Q and 1R particles) A sea comprised of 1R and 2Y particles
dark-energy stu
Composite particles that include 1R and 2Y particles
dark-energy stu
G-family particles, other than photons and contributors to gravitation
dark-energy forces
Table 4.1: Ordinary-matter ensemble phenomena that people might correlate with other than ordinary matter
4.1.3 Bases for ENS48, ENS06, ENS02, and ENS01 models This unit introduces bases for models that possibly pertain regarding dark matter and regarding darkenergy stu. We provide four sets of
σ(1, 0, 3)+
models regarding dark matter and dark-energy stu. The models
dier based on interpretation of the QE-like mathematical SU(7) symmetry we correlate with MS2 models that include Poincare group symmetries. The number of generators correlating with SU(7) is 48. The term ensemble correlates, roughly, with a copy of (a somewhat extended) set of (mainly 2016 Standard Model) elementary particles. An ensemble does not include G-family particles other than 2G2&, 2G24&, 4G246&, and 4G2468&. 1. ENS48 models correlate with the possibility that the universe includes all 48 ensembles.
(Here,
equation 4.1 pertains.) 2. ENS06 models correlate with the possibility that the universe includes exactly 6 ensembles. (Here, equation 4.2 pertains.) 3. ENS02 models correlate with the possibility that the universe includes exactly 2 ensembles. (Here, equation 4.3 pertains.) 4. ENS01 models correlate with the possibility that the universe includes exactly 1 ensemble. (Here, equation 4.4 pertains.)
48 = (generators{SU (7)})/1
(4.1)
6 = (generators{SU (7)})/(generators{SU (3)})
(4.2)
2 = (generators{SU (7)})/(generators{SU (5)})
(4.3)
1 = (generators{SU (7)})/(generators{SU (7)})
(4.4)
Regarding the ensemble that includes the known set of 2016 Standard Model elementary particles, we use the term ordinary-matter ensemble and the acronym OME. Table 4.1 lists MM2MS2 phenomena that might correlate with both the ordinary-matter ensemble and phenomena that people might correlate with at least one of the terms dark matter, dark-energy stu, and dark-energy forces. Table 4.2 pertains. The following statements may pertain.
(We make traditional use of the term photons.
Equation
2.1 pertains. Table 4.3 provides information about spans. People might say that, regarding elementary fermions, table 4.2 correlates with the choice of 48 instances {See table 4.3.}) 1. Inferences pertaining to dark matter may, in eect, include eects of the following aspects of the ordinary-matter ensemble.
26
CHAPTER 4.
ORDINARY MATTER, DARK MATTER, AND DARK ENERGY
Portion (of a type of stu or of a type of particles) that correlates with Models
the ordinary-matter ensemble dark matter
dark-energy stu
ENS01
all
ENS06
small or none
∼ one-half ∼ one-sixth
ENS48
small or none
small or none
ENS02
G-family particles, other than photons
∼
two- fths
varies (based on span) varies (based on span)
varies (based on span)
Table 4.2: Correlations between ENS.. models and aspects of the ordinary-matter ensemble
(a) Phenomena that table 4.1 correlates with the term dark matter. (b) Primordial black holes (and possibly other hypothesized {but perhaps not all that well de ned} types of dark matter). 2. Inferences pertaining to dark-energy stu may, in eect, include eects of the following aspects of the ordinary-matter ensemble. (a) Phenomena that table 4.1 correlates with the term dark-energy stu. 3. While people include in the density of ordinary matter a density for photons, perhaps people would be uncertain as to how to model concepts that would correlate with densities for other G-family particles. People might say that the following pertain. 1. Regarding approximately ve-to-one ratios of density of dark matter to density of ordinary matter, ... (a) ENS06 and ENS48 models explain the ratios. (b) ENS01 and ENS02 models do not necessarily explain such ratios. 2. Regarding approximately two-plus-to-one ratios of density of dark-energy stu to other (or, darkmatter plus ordinary-matter) stu, ... (a) ENS48 models are not incompatible with and may explain the ratios. (b) ENS01, ENS02, and ENS06 models do not necessarily explain such ratios.
TBD 1. Make inferences (from data, some of which may not {as of 2016} be available) su cient to validate and/or rule out aspects of ENS01, ENS02, ENS06, and ENS48 models. 2. Determine the extent to which use (at least one of ) ENS01, ENS02, ENS06, and ENS48 models.
4.1.4 Elementary particles and SU (7) symmetry This unit discusses some symmetries that correlate with models regarding dark matter and dark-energy stu and discusses some results that correlate with models regarding dark matter and dark-energy stu. Each row in table
SU (7)
??
exhibits QE-like symmetry that includes a mathematical
correlates with 48 generators.
SU (7)
symmetry.
For ENS48 models, MS2 posits that the 48 generators correlate
with the possibility that each row for which no more QE-like symmetry than
SU (7)
pertains correlates
with 48 possible instances (in nature) of the elementary particles that correlate with the row.
4.2.
27
ORDINARY MATTER, DARK MATTER, AND DARK-ENERGY STUFF
For elementary bosons, table 4.3 reinterprets symmetries from table
??
and from table
??.
In the
SU (2) symmetries, the table shows the number of QE-like symmetries for particles for which σ = +1 and shows the number of QP-like symmetries for particles for which σ = −1. In each (boson) case, there exists one more oscillator for which the ground-state value correlates with the SU (2)
column labeled relevant
symmetries.
(For QE-like symmetries, oscillator E0 pertains.
pertains.) Regarding each each case for which
SU (n)
that table 4.3 lists,
n
For QP-like symmetries, oscillator P0
is the total number of relevant oscillators. For
σ = +1 and the number of SU (2) symmetries is non-zero, the instances column shows
the number of generators for the relevant group. For elementary bosons, in the span per instance column, the table shows the number
48/instances.
The word span correlates with the scope of the force correlating
with an instance of a boson. For G-family forces, the table shows SDF (or, spatial dependence of force). Regarding 4O and 4Y, we list mathematical results, even though MM2 may correlate with nature not exhibiting elementary particles correlating with 4O solutions or with 4Y solutions. For each elementary fermion for which
σ = +1,
possibly concepts similar to concepts relevant to 2G2& pertain.
For each
of 1C, 1N, and 3N, the number of instances would be 48. Possibly, the relevant symmetry for each of
SU (3) and the number of instances is 8. For that case, the relevant symmetry couples SU (2) symmetry with a QP-like SU (2) symmetry that correlates with 3 generations. For each elementary fermion for which σ = −1, possibly no relevant symmetry pertains and the number of instances is 48. Possibly, the relevant symmetry for 1Q and 1R is SU (3) and the number of instances is 8. For that case, the relevant symmetry couples an SU (2) symmetry (that, if thought of as being QE-like {or QP-like}, balances a QP-like {or QE-like)} SU (2) symmetry that correlates with 3 generations) with 1C and 1N is
a QE-like
one of the oscillators E2 or E1 (or P1 or P2). We extend such thinking to the 3N, 3Q, 3I, 3R, and 3D subfamilies, even though nature might not exhibit elementary particles correlating with the 3Q, 3I, 3R, and 3D subfamilies.
Even though MM2MS2 does not correlate fermions with forces, we list span per
instance. Below, we assume that, for each elementary fermion, the number of instances (that would correlate with work that table 4.3 shows) is 48. Below, we discuss possibilities that, for particles for which table 4.3 shows (or {for fermions} we assume) 48 instances, the number of physics-relevant instances is 48, 6, 2, or 1. We correlate with these possibilities, receptively, the terms ENS48, ENS06, ENS02, and ENS01.
TBD 1. For an elementary fermion, to what extent does nature exhibit phenomena that might correlate with number of instances for the fermion? 2. For an elementary fermion, to what extent do ENS48, ENS06, and ENS02 models vary signi cantly based on an assumed (or derived) number of instances for the fermion?
4.2 Ordinary matter, dark matter, and dark-energy stu This unit discusses four models, of which one model may best correlate with dark matter and dark-energy stu.
4.2.1 ENS48 models for ordinary matter, dark matter, and dark-energy stu This unit discusses models that feature, in essence, 48 instances of each Standard Model elementary
1
particle.
1 This
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28
CHAPTER 4.
Particle
ORDINARY MATTER, DARK MATTER, AND DARK ENERGY
Relevant
or
SU (2)
subfamilies
symmetries
2G2&
Symmetry
Instances
Span per instance
SDF
0
-
48
1
r−2 r−2 r−3 r−2 r−3 r−3 r−4 r−2 r−3 r−3 r−3 r−4 r−4 r−4 r−5
4G4&
1
SU (3)
8
6
2G24&
0
-
48
1
24
2
8
6
8
6
6G6&
2
4G26&
1
2G46&
1
SU (5) SU (3) SU (3)
4G246&
0
-
48
1
8G8&
3
1
48
6G28&
2
24
2
4G48&
2
24
2
2G68&
2
24
2
2G248&
1
8
6
4G268&
1
8
6
2G468&
1
SU (7) SU (5) SU (5) SU (5) SU (3) SU (3) SU (3)
8
6
4G2468&
0
-
48
1
0H
0
-
48
1
0O
0
-
48
1
2W, 2O, 2Y
1
8
6
4O, 4Y
2
1C, 1N
0 or 1
-
1Q, 1R
0 or 1
-
3N
0 or 2
-
3Q, 3I, 3R, 3D
0 or 2
-
SU (3) SU (5) or SU (3) or SU (3) or SU (5) or SU (5)
24
2
48 or 8
(1 or 6)
48 or 8
(1 or 6)
48 or 24
(1 or 2)
48 or 24
(1 or 2)
Table 4.3: Instances and spans for solutions
4.2.
ORDINARY MATTER, DARK MATTER, AND DARK-ENERGY STUFF
29
4.2.2 ENS06 models for ordinary matter, dark matter, and dark-energy stu This unit discusses models that feature, in essence, six instances of each Standard Model elementary
2
particle.
4.2.3 ENS02 models for ordinary matter, dark matter, and dark-energy stu This unit discusses models that feature, in essence, two instances of each Standard Model elementary
3
particle.
4.2.4 ENS01 models for ordinary matter, dark matter, and dark-energy stu 4
This unit discusses models that feature just one instance of each Standard Model elementary particle.
2 This 3 This 4 This
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30
CHAPTER 4.
ORDINARY MATTER, DARK MATTER, AND DARK ENERGY
Chapter 5 Cosmology timeline and some astrophysics phenomena
This unit adds de nition to some traditional aspects of the cosmology timeline and proposes adding elements to the cosmology timeline. We discuss possibilities regarding the cosmology timeline and regarding uses of models. We assume ENS48 models pertain. We think that people can adjust aspects of the work to accommodate ENS06 models, ENS02 models, and/or ENS01 models.
TBD 1. Modify work (in this unit) to correlate with ENS06 models, ENS02 models, and/or ENS01 models.
5.1 Perspective - cosmology and forces This unit summarizes contributions we suggest regarding the cosmology timeline and discusses aspects regarding dominance of forces that govern, for example, the so-called rate of expansion of the universe.
5.1.1 Summary - cosmology timeline and phenomena This unit summarizes contributions we suggest regarding the cosmology timeline. People exhibit cosmology timelines. Generally, the timelines include events and eras. Generally, the earliest item is an event that people call the big bang. People might say that MM2MS2 adds to the timeline and/or provides insight regarding eras on the timeline regarding the following items. 1. The instant of and an era after the big bang. (a) At the instant of the big bang, conservation of energy does not pertain for the universe. Possibly, energy populates states for at least some G-family bosons. i. People might say that, at the instant of the big bang, the relevant
σ(1, 0, 3)+
1-generator
symmetry does not pertain. ii. People might say that such G-family bosons might include 2G2&, 2G24&, 4G246&, and 4G2468&. 31
32
CHAPTER 5.
COSMOLOGY TIMELINE AND SOME ASTROPHYSICS PHENOMENA
(b) Then, conservation of energy pertains, the physics-relevant number of ensembles populate roughly equally, and (possibly) pair production based on G-family bosons populates fermion states such that, within each (physics-relevant) ensemble, matter fermions and antimatter fermions balance. 2. Expansion of the universe, from the big bang until now. (a) Forces mediated by G-family bosons provide mechanisms driving expansion and provide for changes in the inferred (and so-called) rate of expansion of the universe. 3. A possible in ationary epoch. (a) To the extent nature exhibits a so-called in ationary epoch, perhaps a quark (or 1Q) plasma (and/or a 1R-plasma) transits (during this epoch) from including signi cant in uence by Ofamily bosons to having most in uence by gluons (or, Y-family bosons). 4. A possible evolution from (what people might call) baryon balance to baryon asymmetry. Here, balance or asymmetry refers to relative numbers of matter particles and antimatter particles. (a) In the ordinary-matter ensemble, interactions mediated by charged 2O-subfamily bosons convert antimatter quarks into matter quarks. Concurrently, interactions mediated by W bosons convert antimatter charged leptons into neutrinos and convert neutrinos into matter charged leptons. To the extent neutrinos behave as Dirac neutrinos, the number (per unit of volume) of background antimatter neutrinos exceeds the number (per unit volume) of background matter neutrinos. 5. Clumping (and anti-clumping) regarding ordinary matter and dark matter. (a) Around the time that atoms rst form, forces mediated by G-family bosons lead to speci c types of clumping and anti-clumping within (each of ) and between (both of ) ordinary matter and dark matter.
TBD 1. Beyond items traditional cosmology timelines include and/or items we discuss, what other events or eras might a cosmology timeline feature? 2. To what extent do data correlate with a possible (traditional cosmology) in ationary epoch (or, era for which people use terms such as cosmic in ation, cosmological in ation, or in ation and to which people ascribe a possible time range starting at about lasting until a time between
−33
10
seconds and
−32
10
10−36
seconds after the big bang and
seconds after the big bang)?
3. To the extent data point to (or models suggest) an in ationary epoch, to what extent might a phase transition from 1Q+2O to 1Q+2Y correlate with that epoch? (Here, the symbol 1Q+2O denotes a sea of quarks and {signi cantly among O-family and Y-family bosons} 2O-subfamily bosons. Here, the symbol 1Q+2Y denotes a sea of quarks and {predominately among O-family and Y-family bosons} 2Y-subfamily bosons.) Or, to what extent might such a phase transition be from 1Q+2O to 1R+2O, or from 1Q+2O to 1R+2Y, or from 1R+2O to 1R+2Y?
5.1.2 Dominant forces within and between two neighboring clumps This unit discusses an evolution regarding forces that dominate within and between neighboring clumps of stu. We do a thought experiment.
5.2.
33
THE MOMENT OF THE BIG BANG AND SHORTLY THEREAFTER
We consider two similar, neighboring clumps of stu. for example, a solar system.)
(Each clump, in today's universe could be,
For the moment, we consider that the two clumps correlate with the
same ensemble. As the universe evolves (People might use the term expands.), dierent forces dominate regarding each of the clumps and regarding interactions between the clumps. For the moment, we assume that the clumps formed early enough so that the dominant forces were, for some time, forces for which SDF of
r−5
pertains.
As the universe evolves, forces correlating with SDF of
Then, forces with SDF of
r
−3
become dominant. Then, forces with SDF of
r
−2
r−4
become dominant.
become dominant. For a
period in which a particular SDF (roughly) dominates, we use the term era. (See table
??.)
Some notes pertain. 1. Smaller objects progress through eras faster than do larger objects. Pairs of neighboring smaller objects progress through eras faster than do neighboring pairs of larger objects. 2. The above analysis emphasizes G-family forces.
Composite particles and atomic nuclei correlate
with an era in which electromagnetism and the strong force dominate. For electromagnetism, SDF of
r−2
(usually) dominants.
potential correlates with
r
1
For the strong force, the square of potential correlates with
, and SDF correlates with
r
0
in which SDF of
r
pertains.
the
.
3. Some known large objects have yet to transit from an era in which SDF of
−2
r2 ,
r−3
pertains to an era
(Within such objects, adequately smaller objects have made the
transition.) 4. The possibility that the universe includes more than one ensemble does not signi cantly aect general results of this thought experiment. 5. People might say that concepts such as that the material in a solar system may not have been a clump earlier in the history of the universe to do not signi cantly impact the usefulness of the concept of such eras.
5.2 The moment of the big bang and shortly thereafter This unit discusses models pertaining to the instant of the big bang and to times somewhat thereafter.
1
5.3 Expansion - from the big bang until now 2
This unit discusses a model correlating with changes in the so-called rate of expansion of the universe.
5.4 Baryon asymmetry This unit discusses a model for the creation of baryon asymmetry.
3
5.5 Clumping - ordinary matter and dark matter This unit discusses models correlating with clumping and anti-clumping within and between ordinary
4
matter and dark matter.
1 This 2 This 3 This 4 This
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34
CHAPTER 5.
COSMOLOGY TIMELINE AND SOME ASTROPHYSICS PHENOMENA
Chapter 6 Systems, subsystems, and models
This unit explores topics regarding modeling bound-state and other multi-object systems and may provide insight into, for example, the physics of composite particles and the physics of atoms. People might say that some work in this unit is speculative and/or not adequately complete.
6.1 Perspective - systems and subsystems This unit summarizes work regarding multi-object systems, composite particles, and atoms.
6.1.1 Summary - results regarding subsystems This unit summarizes results regarding multi-object systems, composite particles, and atoms. Much physics correlates with the notion that an observer system observes an observed system.
A
model for an observed system may correlate with concepts of subsystems. Much modeling correlates with modeling interactions between subsystems. We explore possibilities for using techniques correlating with MM2MS2 to model subsystems.
We
explore concepts including the following. 1. People may be able to use an alternative (to Poincare group symmetries) set of symmetries to model interactions between components of composite particles. (a) Table 6.1 shows such symmetries. (b) We discuss how such symmetries might combine to form Poincare group symmetries for a composite particle (that exists in circumstances that correlate with 2. People might use an equation of the form
f2 + E 2 = (mc2 )2 + P 2 c2
σ+
models).
to model some aspects of nature.
(a)
f2 < 0
correlates with a system that can decay.
(b)
f2 > 0
correlates with a system that features bound states of subsystems or objects.
3. By considering a system with two slightly interacting subsystems and the equation
2 2
P c
E 2 = (mc2 )2 +
, people may be able to do the following.
(a) Derive the Dirac equation (which pertains to elementary fermions). (b) Gain insight regarding the notion that masses of quarks and charged leptons can be linked by a formula that (roughly) features linear relationships between logarithms of masses. 4. By considering systems for which
f2 > 0, people might gain insight regarding entangled subsystems. 35
36
CHAPTER 6.
sF
Symmetry
0O
σ(1, 0, 3)− σ(0, 0, 1)− σ(1, 0, 2)− σ(0, 0, 2)− σ(1, 0, 1)−
1Q, 1R 2Y, 2O 3Q, 3I, 3R, 3D 4Y, 4O
Table 6.1:
σ(j, 0, l)−
5. By considering systems for which
SYSTEMS, SUBSYSTEMS, AND MODELS
symmetries for solutions for which
σ = −1
f2 < 0, people might gain insight regarding eects of environments
on rates of decay. 6. We show that people might be able to use
ξΨ(r) = (ξ 0 /2)(−η 2 ∇2 + η −2 r2 )Ψ(r)
(or, equation
??)
to model systems (at least, systems like the hydrogen atom) for which interactions mediated by G-family bosons provide essentially all the force-centric kinematic eects.
(Applications of the
equation may also accommodate the strong interaction. Such applications do not explicitly address the weak interaction.) 7. For the hydrogen atom (and for similar objects that feature one positively charged object and one negatively charged lepton), we correlate (approximately) each of various eects (such as nestructure splitting) with G-family bosons. (a) Table 6.2 summarizes some results. (b) People might say that, possibly, the following statements pertain. i. Hyper ne splitting correlates with 2G468&. ii. The Lamb shift correlates with 2G248&. (c) People might say that, depending on details regarding such correlations, our work possibly predicts eects beyond ne-structure splitting, the Lamb shift, and hyper ne splitting. 8. For nuclear physics, we note possibilities that people can extend our work to reproduce or add to results from (for example) the shell model. 9. For neutron stars, we note possibilities that people can extend our work to reproduce or add to known modeling results. 10. People may be able to correlate astrophysics phenomena and/or atomic-physics phenomena with (almost) each G-family boson. (a) Table 6.3 shows results. (b) People might say that some results in table 6.3 are speculative. 11. Regarding phenomena people model based on general relativity, we note possibilities that people can extend our work to model such results based on MM2MM2 bases and intrinsically at space-time coordinates (or
σ(1, 0, 3)+
symmetries).
12. We show results from models that correlate with MM2MS2 techniques and (or, symmetries that people might correlate with general relativity).
σ(1, 0, 2)+
symmetries
6.1.
37
PERSPECTIVE - SYSTEMS AND SUBSYSTEMS
Observations
S
SDF
2G2&
1
r−2
2G24&
1
G-family
Related quantities
Related terminology
boson (Main) energy levels Spin-spin coupling
Rydberg constant (RH or dipole moment
r−3 2G46&
1
2G68&
1
?
?
Lamb shift
?
?
?
Hyper ne splitting
?
?
?
Other (?)
?
?
?
?
4G26&
2
?
6G28&
3
?
4G48&
2
?
2G248&
1
?
2G468&
1
?
4G246&
2
?
4G268&
2
?
Other
Fine-structure splitting
R∞ )
g≈2
(Nominal) magnetic
Anomalous magnetic dipole moment
a = (g − 2)/2 ≈ α/(2π) ≈ a − α/(2π)
r−3
r−4
Table 6.2: Possible correlations between hydrogen-atom observations and G-family particles
TBD 1. For what ranges of nature and models of nature do the following statements pertain? (a) Models pertaining to
σ− behavior within subsystems correlate with symmetries that correlate
with removal of the 1-generator symmetry and one 3-generator symmetry from Poincare group symmetry. (b) Symmetries that correlate with removal of the 1-generator symmetry and one 3-generator symmetry from Poincare group symmetry correlate (locally, within a subsystem) with conservation of momentum and with conservation of angular momentum, but not necessarily (locally within the subsystem) conservation of energy. (that includes the subsystem) for which
σ+
Conservation of energy pertains to a system
pertains.
6.1.2 Summary - approach regarding modeling subsystems This unit summarizes aspects of our approach regarding modeling multi-object systems, composite particles, and atoms. The following statements pertain. 1. We explore topics in the following order. (a) Models that correlate with the notion of atness or near atness. i. Topics correlate with the symbols
σSR+, σCP −, σGY −,
and
σHA−.
(See table 3.1.)
(b) Models that do not necessarily correlate with the notion of atness or near atness. i. Topics correlate with the symbol
σGR+.
(See table 3.1.)
2. We try to extend MM2MS2 techniques (which generally pertain to elementary particles) to model systems involving two or more objects.
38
CHAPTER 6.
Observations or conjectures
G-family
S
SDF
boson
SYSTEMS, SUBSYSTEMS, AND MODELS
Related terminology
Related quantities
or concepts
Atomic physics: (Main) energy levels Spin-spin coupling
2G2& 2G24&
1
r−2
1
2G46&
1
2G68&
1
?
?
Lamb shift
2G248&
1
Hyper ne splitting
2G468&
1
4G4&
2
r
−3
Monopole aspects of
Charge (and charge
electromagnetism
current)
(Nominal) magnetic
g≈2
dipole moment Anomalous magnetic
Fine-structure splitting
dipole moment
a = (g − 2)/2 ≈ α/(2π) ≈ a − α/(2π)
r−4
Astrophysics: (Classical physics)
r−2
gravitation
Monopole aspects of
Rest energy (or
gravitation
energy and momentum)
Hypothetical scalar
6G6&
3
corrections to gravity
8G8&
4
(Large-object recent)
4G26&
2
accelerating expansion
6G28&
3
(of the universe)
4G48&
2
r−2 r−3
Hypothetical dipole aspects of gravitation
Eects would scale with rest energy Eects would not scale with rest energy
(Large-object previous)
4G246&
2
decelerating expansion (of the universe)
4G268&
r
−4
2
Hypothetical
Eects would scale
quadrupole aspects
with rest energy
of gravitation
Eects would not scale with rest energy
Big bang; (initial)
4G2468&
2
r−5
Hypothetical
Eects would scale
accelerating expansion
octupole aspects of
with spin (and not
(of the universe)
gravitation
with rest energy)
Table 6.3: Possible (including speculative) correlations between phenomena and G-family particles
6.2.
39
ALG SYMMETRIES PERTAINING WITHIN COMPOSITE PARTICLES
6.2 ALG symmetries pertaining within composite particles This unit discusses possibilities for applying some techniques pertaining to modeling elementary particles
1
to modeling composite particles and other multi-object systems.
6.3
σ−
models and σ+ models
This unit discusses possibilities that adding a term to the equation
E 2 = (mc2 )2 + P 2 c2
might correlate
with useful models regarding bound states and/or regarding decay such as radioactive decay.
2
6.4 Some equations correlating two somewhat-coupled objects This unit discusses applying the equation
3 coupled objects.
E 2 = (mc2 )2 + P 2 c2
to a system that consists of two somewhat-
6.5 Fused systems and ssionable systems This unit discusses some concepts regarding multi-object systems.
6.5.1 Fused systems This unit discusses a spectrum of bound-state systems.
4
6.5.2 Pair creation and entangled states 5
This unit discusses models for matter/antimatter particle-pair creation and for entangled states.
6.5.3 Particle decay This unit discusses a possible basis for models pertaining to decay such a radioactive decay.
6
6.6 PDE modeling for aspects within objects This unit discusses models for bound-state systems, including hydrogen-atom-like systems.
7
6.6.1 States of a system that includes elementary particles and/or other objects 8
This unit discusses a model for allowed states for, for example, atomic nuclei and, for example, for atoms.
1 This 2 This 3 This 4 This 5 This 6 This 7 This 8 This
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40
CHAPTER 6.
SYSTEMS, SUBSYSTEMS, AND MODELS
6.6.2 Objects similar to the hydrogen atom This unit correlates MM2 bosons with eects, such as ne-stricture splitting, that people measure re-
9
garding atomic physics.
6.6.3 Nuclear physics This unit notes possibilities regarding modeling aspects of nuclear physics for which people use the shell
10
model.
6.6.4 Neutron stars 11
This unit mentions possibilities regarding models for aspects neutron stars.
6.6.5 Possible generalizations to include more astrophysics and the entire G-family This unit discusses correlations and possible correlations between G-family bosons and known and hypo-
12
thetical phenomena.
6.7 Phenomena people model via general relativity This unit explores the possibility that people can model, using MM2MS2 techniques, phenomena people model via general relativity.
6.7.1 Models correlating with σSR+ symmetries This unit discusses possibilities that people can model, using MM2MS2 techniques, phenomena people model via general relativity.
13
6.7.2 Models correlating with σGR+ symmetries This unit explores model-centric aspects that may correlate with models based on general relativity.
9 This 10 This 11 This 12 This 13 This 14 This
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14
Chapter 7 Other phenomena, physics constants, and foundation topics
This unit discusses topics regarding so-called foundation of physics topics and regarding physics constants, elementary-particle phenomena, cosmology, astrophysics, and other phenomena.
7.1 Perspective - phenomena, constants, and foundation This unit summarizes results regarding so-called foundation of physics topics and regarding physics constants, elementary-particle phenomena, cosmology, astrophysics, and other phenomena and this unit provides perspective regarding MM2MS2, foundation topics, and physics constants.
7.1.1 Summary - foundation topics, physics constants, and phenomena This unit summarizes results regarding so-called foundation of physics topics and regarding physics constants, elementary-particle phenomena, cosmology, astrophysics, and other phenomena. People might say that we do the following. 1. Regarding physics-foundation topics, ... (a) Regarding the topic of arrow of time, we provide mathematical modeling that people might consider when discussing the topic. (b) Regarding the topic of entropy, we possibly point to possibilities for correlating the quantities
f2
(which has dimensions of
(energy)2 ), D∗ + 2ν ,
and/or
T +V
with concepts related to
entropy. (c) Regarding topics people correlate with terms such as numbers of dimensions or extra dimensions, we list some bases (for dimension-like constructs) that people might nd useful. (d) Regarding minimum quantities (such as a minimum unit of charge), we list some quantities that people might nd signi cant. 2. Regarding physics constants, ... (a) We discuss a formula relating the mass of the tauon to various physics constants including
GN
(or, the gravitational constant). We predict a more accurate tauon mass than people measure. i. We point to some possibly meaningful approximations regarding numbers that correlate with that formula. 41
42
CHAPTER 7.
OTHER PHENOMENA, PHYSICS CONSTANTS, AND FOUNDATION TOPICS
(b) People might say that we show at least one new (regarding uses in physics formulas) appearance of
α (or, the ne-structure constant).
This appearance correlates with a formula linking masses
of quarks and charged leptons. (c) We raise a question regarding the extent of physics-relevance for the Planck length. 3. Regarding elementary-particle phenomena, ... (a) We discuss interactions that contribute to neutrino oscillations. (b) We discuss possible phenomena correlating with photon lasing. i. We allude to possible practical applications regarding controlling or detecting polarizationrelated aspects of laser-produced light. (c) We discuss the extent to which people may be able to directly detect or produce dark matter. 4. Regarding cosmology and astrophysics, ... (a) We discuss mechanisms leading to CMB cooling. (b) We discuss concepts related to the proportions, in individual galaxies, of ordinary matter and dark matter. (c) We discuss mechanisms leading to the formation of quasars. (d) We discuss factors possibly contributing to the binding of (individual) galaxies. (e) We discuss the possibility that MM2MS2 provides bases for resolving the so-called spacecraft yby anomaly. 5. Regarding metals, semiconductors, and similar materials, ... (a) We note the possibility that models based on techniques paralleling MM2MS2
σ−
techniques
might provide useful insight.
7.1.2 Notes - physics-foundation topics and physics constants This unit provides perspective regarding MM2MS2, foundation topics, and physics constants. People might say that the following pertain. 1. The development of MM2MS2 is not necessarily designed to shed light on physics-foundation topics and/or physics constants. 2. Results from MM2MS2 ... (a) Have bases in models based on mathematics. (b) Seem to shed light on some physics-foundation topics. (c) Seem to point to non-traditional (or, new) relationships among physics constants. 3. Mathematically-based modeling contributions can impact people's thinking about physics-foundation topics and about a possible number (or, count) of physics constants that people might consider to be mutually independent.
7.2 Physics-foundation topics This unit discusses aspects of the topics arrow of time, entropy, numbers of dimensions, and minimum quantities.
1 This
1
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7.3.
43
PHYSICS CONSTANTS
7.2.1 Arrow of time This unit discusses possibly useful insight into the topic of arrow of time.
2
7.2.2 Entropy This unit mentions a possibility that aspects of our work may correlate with concepts correlating with
3
entropy.
7.2.3 Numbers of dimensions 4
This unit lists concepts that people might correlate with topics regarding numbers of dimensions.
7.2.4 Minimum quantities This unit mentions concepts that people might correlate with concepts of minimum non-zero values that nature exhibits.
5
7.3 Physics constants This unit explores approximate relationships between physics constants and speci c numbers, notes a possible numerical relationship within a set (that includes the mass of the tauon and the gravitational
6
constant) of physics constants, and notes possibly new roles (in formulas) for the ne-structure constant.
7.3.1 A correlation between mass(tauon) and GN This unit explores a possible numerical relationship within a set (that includes the mass of the tauon and the gravitational constant) of physics constants.
7
7.3.2 The ne-structure constant 8
This unit notes possibly new roles, in formulas, for the ne-structure constant.
7.4 Elementary-particle phenomena This unit discusses some details about neutrino oscillations, about light produced via lasing, and about possibilities for directly detecting or producing dark matter.
7.4.1 Neutrino oscillations 9
This unit discusses bosons that may intermediate interactions that produce neutrino oscillations.
2 This 3 This 4 This 5 This 6 This 7 This 8 This 9 This
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44
CHAPTER 7.
OTHER PHENOMENA, PHYSICS CONSTANTS, AND FOUNDATION TOPICS
7.4.2 G-family lasing This unit discusses possible features of light produced by lasers.
10
7.4.3 Detecting or producing dark matter This unit discusses the extent to which people may be able to directly detect or produce dark-matter elementary particles.
11
7.5 Cosmology and astrophysics This unit discusses aspects of various cosmology phenomena and astrophysics phenomena.
7.5.1 CMB cooling This unit discusses, regarding CMB cooling, a model that correlates with MM2MS2 and at space-time coordinates and that does not correlate with some traditional notions of an expansion of space-time.
12
7.5.2 Objects containing ordinary matter and dark matter This unit discusses conceptually statistics that may pertain regarding, within astrophysical objects, fractions of and distributions of ordinary matter and dark matter.
13
7.5.3 Quasar formation This unit discusses mechanisms that may correlate with some black holes forming quasars.
14
7.5.4 The galaxy rotation problem 15
This unit discusses phenomena that may correlate with solving the so-called galaxy rotation problem.
7.5.5 The spacecraft yby anomaly This unit discusses phenomena that may correlate with explaining the so-called spacecraft yby anomaly. People design trajectories for each of some spacecraft so that the spacecraft escapes the region in which earth's gravity dominates and then returns to the region so as to receive (via earth's gravity) a boost in kinetic energy. People observe variations (coming into the re-encounter with earth) in the timing
16
and speed of spacecraft compared to theoretical estimates.
7.6 Somewhat free-ranging σ− phenomena This unit mentions possibilities for applying
17
σ−
modeling techniques to semiconductors and other mate-
rials.
10 This 11 This 12 This 13 This 14 This 15 This 16 This 17 This
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Chapter 8 Models and modeling
This unit discusses relationships between and uses for MM2MS2 and traditional models.
8.1 Perspective - MM2MS2, traditional, and future models This unit summarizes aspects regarding relationships between and uses for MM2MS2 and traditional models.
8.1.1 Summary - MM2MS2 and traditional models This unit summarizes aspects regarding MM2MS2 and traditional models. People might say that we do the following. 1. We compare, between MM2MS2 and traditional physics, concepts correlating with the term action. 2. We compare advantages of using (and some technical aspects of ) MM2MS2 models and traditional models. 3. We discuss aspects regarding general relativity, including ... (a) Limitations on the applicability of general relativity. (b) Possible bases for extensions to general relativity. 4. We note that possibilities may exist to bridge between and integrate aspects of the Standard Model and aspects of MM2MS2.
8.1.2 Notes - current and future models This unit notes possibilities for integrating current and future physics models. People might say that we point to possibilities for integrating some current physics models and some future physics models.
TBD 1. To what extent might people use MM2MS2 techniques to integrate useful traditional physics models?
45
46
CHAPTER 8.
MODELS AND MODELING
8.2 Action This unit correlates concepts regarding action and concepts regarding mathematics based on harmonic oscillator equations and also notes that people might consider that aspects of MM2MS2 comply with
1
traditional notions of action.
8.3 MM2MS2 models and traditional physics models This unit discusses some aspects of MM2MS2 models and contrasts some aspects of MM2MS2 models with traditional models.
2
8.4 General relativity and MM2MS2 This unit discusses insights that MM2MS2 may provide regarding general relativity and uses of general relativity.
3
8.5 The Standard Model and MM2MS2 This unit notes possibilities for bridging between and integrating aspects of MM2MS2 and aspects of the
4
elementary-particle Standard Model.
1 This 2 This 3 This 4 This
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Chapter 9 Perspective - during and after this work
This unit discusses opportunities that people might want to pursue. Some of the opportunities arise within our work. Some of the opportunities spring from our work or might spring from follow on to our work.
9.1 Opportunities - physics and modeling This unit discusses some possible opportunities for research regarding physics and modeling.
9.1.1 Phenomena that people might try to detect, measure, or infer This unit discusses phenomena that people might try to detect, measure, or infer. Previous units allude to (and may provide details regarding) some of the possible opportunities this unit discusses. Previous units discuss other possible opportunities. People might say that people might want to attempt (soon or eventually) to conduct experiments, collect observational data, and/or make inferences {a} to verify (or rule out, to some degree of con dence) the existence of the following, {b} to measure properties of the following, and/or {c} to measure the following properties more accurately. 1. O-family particles, including the following. (a) Particle masses. (b) Charges of the 2O2 and 2O1 bosons. (c) O-family interactions that table
??
predicts.
2. Composite particles that include O-family bosons, including the following. (a) Composite particles that include of 0O0 bosons (and, for example, 1R fermions). (b) Composite particles consisting of quarks and 2O-subfamily bosons. (c) Composite particles that include 1R-subfamily fermions. (d) Threshold energies for producing composite particles. 3. CP-violations that correlate with 2O2 and 2O1 particles. 4. MM2MS2 predictions regarding conservation of generation and non-conservation of generation. 5. Ranges for interactions mediated by various WHO-family bosons. 47
48
CHAPTER 9.
PERSPECTIVE - DURING AND AFTER THIS WORK
6. Masses (to more accuracy than has been determined) of W- and H-family bosons. 7. Aspects regarding G-family elementary particles, including the following. (a) Interaction strengths (for other than 2G2&, 2G24&, and 4G4&). i. Perhaps, consider the particles' eects on the rate of expansion of the universe. ii. Perhaps, consider the particles' eects regarding simple atoms. (b) Possible interactions mediated by G-family bosons (other than 2G2& and 2G24&) that couple ordinary matter to the possibly-existing dark-matter copies of (a possibly somewhat extended list of {mostly}) 2016 Standard Model particles. 8. Aspects, regarding lasing of G-family elementary particles, including the following. (a) Correlations and/or anti-correlations between various particles and modes of those particles. (b) Possibilities for exciting, detecting, and/or gaining practical bene t from such correlations and/or anti-correlations. 9. 1R-subfamily fermions. 10. Neutrino masses. (a) Of special interest is the notion that MM2MS2 correlates with neutrinos having zero mass. 11. The tauon mass and/or
GN .
(a) Of special interest is the possibility that equation 9.1 pertains.
Based on 2016 PDG data
(Reference [3]), the equation predicts a tauon mass with a standard deviation of less than one quarter of the standard deviation correlating with the experimental result. Possibly, more accurate experimental determination of the tauon mass could predict a more accurate (than experimental results) value for the gravitational constant,
GN .
(4/3) × (mass(tauon)/mass(electron))12 = ((qe )2 /(4πε0 ))/(GN (me )2 )
(9.1)
12. Neutrino oscillations. (a) Of special interest are correlations (based on the surroundings through which neutrinos pass) with interactions mediated by various elementary bosons. 13. Ratios (during the evolution of the universe) of the density of dark matter to the density of ordinary matter. (a) Of special interest is the possibility that dark matter consists mostly of ve (in essence) copies of 2016 Standard Model particles (plus some additional elementary particles). 14. Ratios (for the cosmic neutrino background) of antimatter neutrinos to matter neutrinos. (a) Of special interest is the possibility that a preponderance of antimatter neutrinos (compared to matter neutrinos) could correlate with an MM2MS2 scenario for (if matter and antimatter charged particles were approximately in balance early in the history of the universe) creating the baryon asymmetry (or, charged-matter/charged-antimatter imbalance) people observe regarding much of the history of the universe. 15. The 3N subfamily of zero-mass elementary fermions. (a) Of special interest is the possibly for a contribution to the density of the universe.
9.1.
OPPORTUNITIES - PHYSICS AND MODELING
49
(b) Of special interest is the possibly for a contribution to galactic (so-called) dark-matter halos. 16. Inferred ratios (during the evolution of the universe) of the density of dark-energy stu to the density of dark matter plus ordinary matter. (a) Of special interest is the evolution of those ratios. The ratios may correlate with the strength of interactions intermediated by (at least) one Gfamily boson (and not with notions of {a} dark energy as a pressure or {b} creation, over time, of dark energy). 17. Aspects, within galaxies (and similar objects), pertaining to dark matter and ordinary matter. (a) Of special interest are statistics regarding ratios of ordinary matter to dark matter. (b) Of special interest are possibilities for clustering and/or anti-clustering {a} within and between clumps the feature ordinary matter, {b} within and between clumps that feature dark matter, and {c} between clumps that feature ordinary matter and clumps that feature dark matter. (Here, the term feature does not necessarily imply the notion of include only.) Such aspects may correlate with eects of G-family bosons.
9.1.2 Theory that people might enhance or develop This unit discusses theory that people might enhance or develop. Previous units allude to (and may provide details regarding) some of the possible opportunities this unit discusses. Previous units discuss other possible opportunities. People might say that people might want to enhance or develop theory regarding the following topics. Doing so could help determine {a} experiments and observations to attempt and/or {b} advances in techniques that may be needed in order to conduct useful experiments or to make useful observations. 1. Which (of the) possible MM2MS2 (or other possible) models most likely correlate with approximate O-family masses? 2. What would a better (than MM2MS2 includes) model for masses of non-zero-mass elementary bosons entail? 3. What minimum energies are required to produce composite particles that include O-family bosons? 4. Under what circumstances might people create O-family bosons or composite particles that include O-family bosons? 5. What are the sizes of coupling constants that pertain to producing and detecting phenomena correlating with O-family bosons? 6. What would lifetimes and decay products be for O-family bosons and for composite particles that include O-family bosons? 7. How best might people detect or infer the existence of (or rule out, to some con dence level, the possible existence of ) O-family bosons? 8. What would a better (than MM2MS2 includes) model for masses of non-zero-mass elementary fermions entail? 9. What values of mass (and other properties {other than spin}) would non-zero-mass spin-3/2 fermions (if they exist) have?
50
CHAPTER 9.
PERSPECTIVE - DURING AND AFTER THIS WORK
10. For interactions between gravity and each of various types of zero-mass elementary particles, which non-negative integer n (as in n-tensor) pertains (and likely correlates with
P
E
{or, the energy} and
{or, the momentum} of the zero-mass elementary particle) and what are the components of the
n-tensor? 11. To what extent (if any) do inferences rule out the existence of three generations of zero-mass neutrinos? 12. What (if any) perturbation theory pertains for MM21MS2 models? 13. What interaction coupling strengths pertain for G-family bosons other than 2G2&, 2G24&, (2G46&,) and 4G4&? 14. To what extent, regarding G-family lasing, might correlations and/or anti-correlations pertain regarding various G-family elementary particles and their modes? 15. To what extent, might people develop a (traditional physics eld-like) formulation for G-family physics such that there are four elds (correlating, respectively, with 2G, 4G, 6G, and 8G)? 16. To what extent do G-family (and possibly other family) interactions aect measurements regarding masses of WHO-family bosons? 17. What magnitudes of CP-violations correlate with interactions mediated by 2O2 and 2O1 elementary bosons? 18. What magnitudes of CP-violations correlate with interactions mediated by 2W1 and 2W2 bosons, in
σ−
environments?
19. What are the practical and theoretical implications for including or not including (in MM2 and MM2MS2) non-zero mass elementary particles with spins
S
for which
S ≥ 1?
20. To what extent might interactions split G-family (other than 2G2&, 4G4&, 6G6&, and 8G8&) bosons into components? (MM2MS2 does not include such possible interactions. Such interactions might appear to perform functions people attribute to {as yet hypothetical} axions.) 21. How can people more thoroughly (than does MM2MS2) integrate aspects of models relevant to non-zero-mass elementary particles into models relevant to zero-mass elementary particles? 22. How might people extend theory related to absorption (See table
??.)
or emission of elementary
bosons by elementary fermions to theory related to (elementary-fermion-) pair production and pair annihilation? 23. To what extent might theory link the 6 that (in ENS48 models and in ENS06 models) is the number of copies of 2016 Standard Model particles that might correlate with the span of one instance of 4G4& with the 6 that is half the exponent 12 in equation 9.1? 24. To what extent does work (similar to work regarding
σ(j, 0, k)−
symmetries) regarding possible
symmetries pertaining to hydrogen atoms (and similar systems) provide useful insight regarding atomic and molecular physics? 25. To what extent might eects of G-family forces (associated with G-family members other than 2G2&, 2G24&, and 4G4&) lead to black holes becoming quasars? 26. How might people harmonize or integrate MM2MS2 models and traditional models and theories?
9.2.
OPPORTUNITIES - GENERAL
51
9.2 Opportunities - general This unit discusses some possible opportunities for societal progress based on aspects of our work.
TBD 1. To what extent might people bene t from concepts that people might develop regarding circumstances, techniques, and so forth correlating with our work?
52
CHAPTER 9.
PERSPECTIVE - DURING AND AFTER THIS WORK
Bibliography
[1] Thomas J. Buckholtz, Models for Physics of the Very Small and Very Large, Atlantis Studies in Mathematics for Engineering and Science, Volume 14, Springer, 2016. (DOI 10.2991/978-94-6239-
166-6) [2] Particle Data Group, Electroweak (web page), The Particle Adventure, Lawrence Berkeley National Laboratory, (2014), http://www.particleadventure.org/electroweak.html. [3] C. Patrignani et. al. (Particle Data Group), Chin. Phys. C, 40, 100001 (2016). [4] Wolfram Alpha, http://mathworld.wolfram.com/DeltaFunction.html.
53
54
BIBLIOGRAPHY
Index
action, 45, 46
dark-energy stu, 10, 2327, 29, 49
ALG (a type of mathematical equation {and related
decay, 8, 35, 36, 39, 49
solutions} correlating with isotropic quan-
density (density of the universe), 9, 10, 23, 24, 26,
tum harmonic oscillators), 14, 39
48, 49
anomalous magnetic dipole moment, 37, 38
DES (dark-energy stu ), 24
arrow of time, 4143
dipole, 6, 8, 37, 38
astrophysics, 2, 3, 6, 31, 36, 38, 4042, 44
Dirac equation, 35
atom (atomic physics), 2, 6, 9, 19, 20, 24, 32, 3540,
Dirac fermions, 9, 15
48, 50
DMS (dark-matter stu ), 24
atomic nuclei, 2, 6, 8, 18, 20, 33, 36, 39, 40 ENS01 models, 2527, 29, 31
axion, 24, 50
ENS02 models, 2527, 29, 31 baryon asymmetry, 10, 32, 33, 48
ENS06 models, 2527, 29, 31, 50
big bang, 24, 3133, 38
ENS48 models, 2527, 31, 50
black hole, 18, 24, 26, 44, 50
ensemble, 18, 25, 26, 32, 33 entanglement, 35, 39
charge, 6, 8, 13, 18, 38, 41, 47
entropy, 4143
cloud of virtual particles, 7
expansion of the universe, 2, 9, 3133, 38, 44, 48
clumping, 32, 33, 49 CMB (cosmic microwave background), 23, 24, 42,
eld, 5, 6, 9, 50
44
ne-structure constant, 42, 43
color charge, 13
ne-structure splitting, 9, 3638
composite particle, 7, 8, 10, 1820, 25, 33, 35, 37,
at (as pertains intrinsically to space-time coordi-
39, 47, 49
nates), 36, 37, 44
conservation (of energy, momentum, and/or angular momentum), 17, 19, 31, 32, 37
galaxy, 23, 42, 44, 49
conservation of generation, 47
galaxy rotation problem, 44
cooling of CMB, 42, 44
general relativity, 1, 2, 19, 20, 36, 40, 45, 46
cosmology, 13, 5, 6, 31, 32, 41, 42, 44
generation, 27, 47
cosmology timeline, 1, 5, 31, 32
generator, 19, 2527, 31, 37
coupling constants, 49
gluon, 8, 10, 11, 13, 15, 18, 32
CP-violation, 47, 50
gravitational constant, 41, 43, 48
CPT-related symmetries, 17, 21
graviton, 2, 5, 6, 8, 11, 18
curvature (intrinsic curvature correlating with spaceHamiltonian, 4
time coordinates), 18
harmonic oscillator, 3, 4, 12, 46 dark energy, 2, 6, 10, 2327, 29, 49
Higgs boson, 2, 811
dark matter, 2, 6, 9, 10, 2327, 29, 32, 33, 4244,
hyper ne splitting, 3638
48, 49 dark-energy forces (or dark-energy pressure), 2325 55
in ationary epoch, 32
56
INDEX
instances (typically, for an elementary particle), 10, 11, 21, 2529, 50
SDF (spatial dependence of force), 8, 9, 27, 28, 33, 37, 38
interaction strength, 8, 4850
sea (for example, of quarks), 25, 32
isotropic (harmonic oscillator or pair of harmonic
shell model, 36, 40
oscillators), 3, 4, 12
σ + models, σ − models,
8, 9, 11, 17, 19, 35, 37, 39 8, 11, 18, 19, 37, 39, 42, 44, 50
Lagrangian, 4
spacecraft yby anomaly, 42, 44
Lamb shift, 3638
span (typically, for a force), 2528, 50
lasing, 4244, 48, 50
special relativity, 1, 2, 7, 17, 19, 21
lepton, 8, 10, 11, 18, 21, 32, 35, 36, 42
spin, 4, 69, 11, 13, 14, 18, 24, 37, 38, 49, 50
leptoquark, 11
Standard Model (elementary-particle Standard Model),
magnetic dipole moment, 6, 37, 38
sterile neutrino, 11
magnetic monopole, 11
strong interaction, 36
Majorana fermions, 9, 15
subsystem, 8, 12, 35, 37
mass, 6, 7, 1315, 17, 18, 21, 22, 35, 4143, 4750
supersymmetry, 11
13, 5, 18, 21, 25, 27, 29, 45, 46, 48, 50
monopole, 8, 11, 38 tauon, 41, 43, 48 neutrino, 711, 15, 24, 32, 42, 43, 48, 50 neutrino oscillations, 42, 43, 48 neutron star, 19, 20, 36, 40
TBD (to be determined), 24, 6, 10, 12, 14, 20, 24, 26, 27, 31, 32, 37, 45, 51 tensor, 50
non-point-like solution, 12, 13 nuclear physics, 2, 6, 36, 40 numbers of dimensions, 4, 4143 OME (ordinary-matter ensemble), 25 OMS (ordinary-matter stu ), 24 PDE (a type of mathematical equation {and related solutions} correlating with isotropic quantum harmonic oscillators), 14, 39 PDG (Particle Data Group), 48 photon, 511, 14, 18, 2426, 42 physics-relevance, 11, 12, 21, 27, 32, 42 Planck length, 18, 42 Poincare group, 7, 1719, 21, 25, 35, 37 point-like solution, 12, 13 polarization (or polarization mode), 5, 9, 42 primordial black hole, 24, 26 QCD (quantum chromodynamics), 20 QE-like, 2527 QED (quantum electrodynamics), 6, 10, 20 QP-like, 27 quadrupole, 38 quantum mechanics, 1, 2 quark, 8, 10, 11, 18, 21, 32, 35, 42, 47, 56 quasar, 42, 44, 50 range (of the weak interaction), 18, 21, 47 rate of expansion of the universe, 2, 9, 3133, 48
vertex (interaction vertex), 1015, 21 weak interaction, 18, 21, 36 weak mixing angle, 17, 18, 22 WIMP (weakly interacting massive particle), 24
