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Appendix 3 Erection Coordinates
Description / Excerpt Below
Appendix 4 Cylindrical Figures
Description / Excerpt Below
|List Of Appendices||Page|
|Appendix 1, Particle Physics Primer||3|
|Appendix 2, Decisions On How Not To Approach this Work||17|
|Appendix 3, Erection Coordinates||30|
|Appendix 4, Cylindrical Figures||35|
|Appendices List Of Figures|
|Appendix 1, Harmonic Spirals||4|
|Appendix 1, Harmonic Waves||7|
|Appendix 1, Exponential Curve & Mirror Image||10|
|Appendix 1, Wave function & Mirror Image||12|
|Appendix 1, Spiral & Mirror||15|
Appendix 1 Particle Physics Primer (excerpt)
The objective of this report is to give a brief orientation on the topics of discussion, LEPTONS and PHOTONS, found in the other core reports of this body of work. What are these “objects” and how do they fit in with other scientific information of modern technological societies?
The research presented in the other reports of this overall work was pre-screened by persons with technical, scientific, and engineering backgrounds. While these people clearly had the necessary intellectual where-with-all and also had great knowledge concerning their own particular fields of specialty, most were only vaguely familiar with the terminology used in particle or subatomic physics. Thus occasionally after reading these reports and apparently easily following the mathematics and analyses, there several of them asked, “What is a lepton”? Oops, such a question makes reading these research reports a bit disconcerting, if someone doesn’t know what the subject of the discussions is. Thus this particle physics primer is presented so that technical persons who are not familiar with the current realm of subatomic physics can follow the presentations in these reports with more ease.
2 What Is A Lepton – The Short Version
Leptons and photons are elementary subatomic particles, wave forms. They are from the world and size realm of the physicists. This is many orders of magnitude smaller than the realm where the elements of chemistry are found. And that in tern is of course many orders of magnitude smaller that the consensus world realm which humans inhabit. The lepton series is comprised of the well known electron and its two bigger but highly unstable brothers, the muon and tau. The photon is of course a single or discrete electromagnetic wave. Persons in modern societies are familiar with visible photons seen when turning on a light switch or invisible ones used when when opening a cell phone. There are several good publicly available primers at web sites which describe the features found in this subatomic realm of the particle physicists. These can be found at the following two sites, plus many more.
Wikipedia.org, any and all of the search words; neutrinos, leptons, quarks, photons, elementary particle, etc at this site will give an essential part of the picture.
Particleadventure.org has a wonderful pictorial chart.
Appendix 2 Decisions On How Not to Approach this Work (excerpt)
In Methodology the overall constraints for the entire project were set. What the project objectives were or what results were expected. How these objectives would be reached. What starting data would be the permitted. What constraints or criteria would be placed upon any candidate descriptive equations for the target measured subatomic physical properties. Thus in the Methodology report, the vast bulk of the discussions focused upon how the research of this overall work would be or was in fact done.
What was only briefly alluded to in Methodology was what manner of research others have done. This topic is long, immensely long, and covers at least 30 years of endeavors in particle, high energy, and hypothetical physics. What others have done in these sub realms of the broader science of physics covers tens-of-thousands of papers, tens-of-millions of research hours, and billions of dollars. Additionally extremely few of these efforts have any relevance to the mathematical physics research efforts of this overall work. Thus only very limited references were made in Methodology to what others have done in these realms. This was intentional to keep that report focused on what would be done in this overall work.
Thus to be fair some discussion is needed in this overall work as to what others have done. This is particularly true since such discussions are absolutely required in the formal published papers of others in the field. In fact such discussions are the first item of business from which a logical flow is made to the entire body of the remainder of such papers. Thus readers from the academic realms will automatically look for such discussions upon starting this body of work. Further they will tend to become extremely disoriented, confused, and frustrated when they cannot an item required as a part of their habitual way of thinking and doing things. Thus this report has been created to soften the impact of this “missing” item.
This report will give a brief overview of what other have done in the field of hypothetical or calculational particle physics. Again essentially none of this prior work is relevant to the research conducted here. Thus what others have done will NOT be examined for specific concepts, calculational procedures, or resultant answers which can or will be used as trail heads for this current work here. This prior work will be examined in general to determine various methodologies and calculational practices. These procedures will be highlighted as being something which is NOT done in this work. Thus essentially every thing which others have done will be contrasted with what is done in this work, and will not be used to supplement or support the work here.
The main objective here is NOT to negate what others in academic particle physics have found useful for the last 30 years. The intention of this report is to show a different way of viewing and “doing” calculational particle physics which has either been overlooked or forgotten. Specifically what will be found repeatedly in this report, is that when the required trappings of the hypothesis-first methodology are throw off, then great intellectual freedom and creativity can arise. This is the emphasis and message here and is the hope for what the reader carries away from this report.
Appendix 3 Erection Coordinates (excerpt)
Erection coordinates or generalized n-spherical angular coordinates are necessary when considering work in more than 3 dimensions. The usual declination spherical coordinates do not set a pattern, can not be generalized, and thus are useless in more than 3 dimensions.
The reasons are simple. In basic algebra books when students are introduced to graphing, the independent variable is called X, the first variable and axis of the discussion. The dependent variable is represented by Y and the second axis and variable of discussion. Trigonometric angles are introduced by drawing an angle q out away from this first axis X of discussion. Polar coordinates, 2 dimensional radial-angular coordinates, follow this same convention, simply renaming the X axis to be the polar line. When 3 dimensions are introduced Z is created as the third variable and axis of discussion. When shifting to spherical coordinates, 3 dimensional radial-angular coordinates, the second necessary angle is referred to this third Z axis or variable or discussion. An angle φ is dropped down, declined, from the traditional vertical axis to become angle 2. Thus in 3 dimensions one has the first angle referred to the first rectilinear axis and the second angle referred to the third rectilinear axis. The second axis of discussion is left out as an angular reference. This declination system had legitimate historical roots in the navigation of sailing ships, but as seen has created a long enduring mathematical anomaly.
The problem when continuing on to more dimensions immediately becomes obvious. For n-dimensional spherical coordinates, there is always a radius, the first dimension, and n-1 angles and angular dimensions. On referring back to n-dimensional rectilinear coordinates to obtain reference axis or lines, there are always one less angle than there are dimensions or reference axis-lines. The question only needs to asked, “Which dimensional axis or variable of discussion gets left out”. With the 3 dimensional declination system it is the Y or number 2 axis. In 4, 5, or 6 dimensions which axis gets left out; Y number 2, Z number 3, Number 4, Number 5, or Number 6? Always the second of discussion Y? Always the next to last, in the case of 6 dimensions, Number 5? Thus the system breaks down and cannot be generalized. Thus there needs to be a system which can be immediately generalized as more dimensions are added to a discussion without the disruption of formulas and patterns already established.
Appendix 4 Cylindrical Figures (excerpt)
Cylindrical figures were first discussed in Part 2 Chapter 2.1, the lepton paper. There the groundwork was laid for the application or use of some of the vector properties of these mathematical forms in explaining the origin of the value of the elementary charge of the leptons, e = 1.602,177,33 x 10-19C. The purpose of this appendix is to rigorously develop some of the results used in Chapter 2.1, Sections 3 and 4.1. Such a step-by-step derivation of the two vector quantities curvature к and torsion τ is given in Section 3 in this appendix.
Much of the work in the lepton paper bases off of properties of the generalized cylindrical figure. In particular the derivation of, and final mathematical formulas for, the curvature к and the torsion τ. The importance of these quantities, both for the specific case of the cylindrical helix and for the generalized figure, is that;
1 Both quantities are free from or independent of the original transcendental trigonometric functions.
2 Both are independent of the original functions of F(t) and G(t).
3 Both are independent of the free standing original implicit variable t.
4 As such both are numerical constants.
5 Both by their calculational definitions are scalar quantities and not still vectors. Thus they are free from the unit vectors i, j, k.