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Quantum Interval Mechanics (QIM), Part 3: Wave-Based Modeling of Mass, Charge, and the Unified Four Forces M. J. Lindeman August 31, 2017 Abstract Most professional physicists have neither time nor motivation to read the original writings of the early theorists. Even major theorists such as Heisenberg identified all previous theories but general relativity as “closed”—uninteresting except to use in calculations. However, physicists’ inability to unify mainstream physics indicates the hindrances are cognitive mismappings between the theories. This Part 3 paper of a three-part series describes the systematized process that yielded the unified mathematical results reported in Parts 1 and 2. For several masterpiece theories, including electromagnetism and special relativity, the original conceptual models of the theorists were changed significantly by later physicists. A common practice was to make the theories more pragmatic. For electromagnetism, Heaviside and Hertz completely eliminated Maxwell’s primary focus on the A field of vector potentials that is now central in quantum mechanics. Minkowski changed Einstein’s lightlike Euclidean version of special relativity to a theory of the timelike motions of objects in curved spacetime. Also, physicists now have access to experimental information (e.g., from superconductivity) that was not available to earlier theorists. Together these opened the door to the creation of the unified theory, Quantum Interval Mechanics (QIM). The new results reported in this paper are wave-based visualizations of (1) mass and charge as they relate to the Higgs field, and (2) the unified model of the four forces (gravity, electromagnetic, weak nuclear, and strong nuclear).

Contents 1 The Problem Statement . . . . . . . . . . . . . . . . 2 The Unification Process. . . . . . . . . . . . . . . .

8 Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Method: Find Treasures in the Literature 8.2 Method: Create a Unified Dictionary . 8.3 Method: Implement Schrödinger’s Idea

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I: Describe (Purpose & Vision) 3 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Vision . . . . . . . . . . . . . . . . . . . . . . . . . . .

IV: DO (Explore, Identify, Select, Create) 3 4

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II: Discover (Goals & Issues) 5 Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Issues. . . . . . . . . . . . . . . . . . . . . . . . . . . .

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V: Done (Deliver & Close) 13 Deliver. . . . . . . . . . . . . . . . . . . . . . . . . . . 21 13.1 Modeling Rest Mass and Charge . . . 21 13.2 The Spin-0 Field of Darkness . . . . . 24 13.3 Modeling the Spin-2 Unification of Forces 25 13.4 Gravitational Waves . . . . . . . . . . 29 14 Close . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

III: Determine (Tasks & Plans) 7 Tasks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 7.1 Choosing the Methodological Approach 8 7.2 Identifying the Theories and Physicists 10 7.3 Identifying the Foundation . . . . . . . 10

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M. J. Lindeman: Quantum Interval Mechanics (QIM), Part 3

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The Problem Statement

As early as the 1920s, Heisenberg, Schrödinger, and Einstein suggested that physics needed a new foundation. Heisenberg argued that physics needed “entirely new conceptual structures, for instance those introduced by relativity theory or quantum mechanics.” [46, pp. 97-98] Schrödinger suggested that theoretical physics go back 300 years and start over in a new direction for theory development. [21, pp. 41-42] It is probably justified in requiring a transformation of the image of the real world as it has been constructed in the last 300 years, since the re-awakening of physics, based on the discovery of Galileo and Newton that bodies determine each other’s accelerations. . . . One must therefore go back 300 years and reflect on how one could have proceeded differently at that time, and how the whole subsequent development [of physics] would then be modified. Schrödinger noted that physicists had focused on the time integrals of acceleration (velocity and positional displacement). These variables were the “instantaneous properties of anything real”. Early physicists’ focus on accelerated motions in the universal frame of reference had been lost. Now accelerated (rotating) motions are attributed to “fictitious forces” in local inertial frames of reference. In what ways would physics be different if the fundamental concepts were acceleration and its changes? Cognitive psychologists know very well that “people’s views of the world, of themselves, of their own capabilities, and of the tasks that they are asked to perform, or topics they are asked to learn, depend heavily on the conceptualizations that they bring to the task.” [71]∗ Other Nobel Laureates, such as Bohr and Born, related physics and mathematics to everyday thinking, particularly in terms of language and everyday experiences. Bohr wrote: [7, pp. 9-10] Mathematics is therefore not to be regarded as a special branch of knowledge based on the accumulation of experience, but rather as a re∗

The belief that Schrödinger’s equation could not be logically derived was one of the major cognitive blocks that was hindering progress in physics. That belief was published by Born as early as 1935. [9, p. 132] However, its rigorous mathematical derivation is now available. The identity equation +1 = (−1)(i)(i) is used to convert from real to complex numbers. [59]

finement of general language, ... Physics is to be regarded not so much as the study of something a priori given, but rather as the development of methods of ordering and surveying human experience. Born noted that “Mathematics is just the detection and investigation of structures of thinking which lie hidden in the mathematical symbols.” [10, p. 227] Einstein stated there is no “general theoretical basis for physics, which can be regarded as its logical foundation.” [24, p. 110] He also wrote: The whole of science is nothing more than a refinement of everyday thinking. It is for this reason that the critical thinking of the physicist cannot possibly be restricted to the examination of the concepts of his own specific field. He cannot proceed without considering critically a much more difficult problem, the problem of analyzing the nature of everyday thinking. [25, p. 290] Bohr specifically relates the thinking problem to quantum theory: [46, p. 209] Only by using a whole variety of concepts when discussing the strange relationship between the formal laws of quantum theory and the observed phenomena, by lighting this relationship up from all sides and bringing out its apparent contradictions, can we hope to effect that change in our thought processes which is a sine qua non† of any true understanding of quantum theory. If quantum theory is to be unified with general relativity and the other theories in physics, there must be a change in thinking. In other words, there needs to be a new conceptual model that provides a logical foundation for all of theoretical physics. To summarize these statements from Nobel Laureates, theoretical physics needed to go back to Galileo and start over with a focus on accelerated motion. Also, if physics is to proceed, it must “analyze the nature of everyday thinking” and effect a change in our thought processes (conceptual models) . †

Latin translated literally is ‘without it, not’. Therefore without a change in our thought processes, there will not be any true understanding of quantum theory.


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The Unification Process

The systematic-design process that guided this unification project is an application of design thinking for creating interactive systems. [88] As a solution-focused methodology, it is an iterative process. It uses both analysis and synthesis to create the optimal [or approaching optimal] solution. As a consultant I learned it was beneficial to surprise a prospective client by providing valuable information in very early discussions of a proposal. To help do this, I created several mental processes to guide me in quickly identifying core issues, whether they were organizational or technological. I also created a “Five-finger” approach to understanding a project and achieving its goals. The steps are easy to explain, remember and use. They are (1) Describe, (2) Discover, (3) Determine, (4) Do, and (5) Done.∗ It fits user-interaction design into a client’s governing process for a project, ranging from the largest waterfall to the smallest agile project. These systematic processes were applied to theoretical physics to create the unification results. An overview of the Five-finger process is shown in Figure 1. The iterative substeps in “Do” are for knowledge research rather than software design.

Describe

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The Five-finger process as it was applied to physics is the outline for the rest of this paper. In sequence: Part I

Describe

Purpose and vision

Part II

Discover

Goals and Issues

Part III

Determine Tasks and Plan(s)

Part IV

Do

Explore, Identify, Select, Create

Part V

Done

Deliver and Close

Part I Describe (Purpose & Vision) 3

Purpose

A “hunch” is a guess based on intuitional feelings rather than logical facts. Some scientists claim they only use logic, but Einstein’s approach was intuitive and visual. It was obviously successful multiple times, including the photoelectric effect, special relativity, and general relativity. Bridgman, the 1946 Nobel Laureate in Physics, suggested a psychologist might better understand why and how Einstein was so successful at creating new theories. [12, p. 160] It is perhaps for the psychologist rather than the physicist to attempt to recapture the full flavor of Einstein’s intuitive drive . . . [that] put itself in the place of different observers in different circumstances, no matter how strange. This intuitional drive is even more manifest in Einstein’s general theory of relativity than in his special theory.

Purpose & Vision

Discover

Goals & Issues

Determine

Explore

Identify

Do

Tasks & Plan(s)

Create

Select

Done

Deliver & Close

Fig. 1: The “Five-finger” iterative process for a research

project. The Do step circles around the ring finger. The more complex the project, the more iterative and messier the search for the solution. Because this series of papers is a completed-project milestone, they do not report the many iterations needed to complete this project. ∗

For a project planning to meet a deadline date, the time estimates start with Done and then work backwards to identify the time available for each step. This allows a quick assessment of whether or not a project is realistic.

I am a cognitive psychologist who specialized in the mathematical modeling of cognitive processes. [89] I also have expertise in historical research, theoretical physics, and designing interactive systems so they are easy to learn and use.† For as long as I can remember, I have been curious how reality works. Science has been a primary interest since high school—the transcript lists my goals as becoming a chemist and going to MIT. Through the many twists and turns my life has taken instead, my interest in how reality works has continued to grow stronger. †

https://www.linkedin.com/in/marthalindeman/


Ernst Mach was a cross-disciplinary researcher who left his mark on both physics and psychology (Mach’s principle for inertia, Mach number for speeds, and Mach bands for visual perception). He strongly believed physicists and some psychologists study the same domain of reality. He wrote: [60, pp. 17-18] Thus the great gulf between physical and psychological research persists only when we acquiesce in our habitual stereotyped conceptions. A color is a physical object as soon as we consider its dependence, for instance, upon its luminous source, upon other colors, upon temperatures, upon spaces, and so forth. When we consider, however, its dependence upon the retina (the elements K L M. . .), it is a psychological object, a sensation. Not the subjectmatter, but the direction of our investigation, is different in the two domains. The purpose of this project, however vaguely it was originally worded, was to understand more about physical reality. Returning to college as an adult, understanding reality became a deep academic focus, particularly to understand the mind-matter relationship. That guided my undergraduate studies, and it was the agenda I took into my graduate work (NSF Graduate Fellow, Ph.D., Harvard University, 1985). 4

Vision

The vision for this project was to provide an alternative representation (conceptual model) of theoretical physics that is easy to learn and easy to use. It is based on Mach’s belief that physicists and some psychologists study the same subject matter from different points of view. The unified theory uses the same descriptive physical dimensions as human perception. Feynman knew the benefits of having multiple psychological representations of a theoretical domain: [35] Theories of the known, which are described by different physical ideas may be equivalent in all their predictions and are hence scientifically indistinguishable. However, they are not psychologically identical when trying to move from that base into the unknown. For different views suggest different kinds of modifications . . . I, therefore, think that a good theoretical physicist today might find it useful to have a

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wide range of physical viewpoints and mathematical expressions of the same theory. . . For example, Thorne devotes an entire chapter to two valid alternative descriptions of general relativity— the “curved spacetime paradigm” and the “flat spacetime paradigm”. He compares them to using 1/1000 and 0.001 to represent the same number. [84, Chap. 11] Another example of alternative conceptual models is the “Copenhagen interpretation” and “Bohm-deBroglie interpretation” of quantum mechanics. There are numerous valid interpretations of the quantum-mechanical mathematical formalism, so many that a Wikipedia page called “Interpretations of Quantum Mechanics” is needed to discuss them. In summary, the vision was to design a scientifically valid and mathematically testable unified view of theoretical physics. It would be limited to the same dimensions as human perception, and would not require any newly hypothesized particles or alternative universes.

Part II Discover (Goals & Issues) 5

Goals

This unification project is at the intersection of three domains of information: Cognitive psychology (how physicists think), Theoretical physics (what they think about), and Systems engineering (how to design excellent systems). Usability is the extent to which people can use a product or system to achieve their goals effectively, efficiently and be satisfied within a particular context of use.∗ The overall design goal for this unification project was increasing the usability of physics. In other words, to make physics easier for people to learn and use. Understanding how people and systems interact is fundamentally important to the three knowledge areas named in Figure 2: • Cognitive psychology: The study of mental systems (structures and processes), and their effect on how people interact with other people and physical objects. ∗

The users, goals and context must be specified in a complete statement of usability. The author was a member of the committee who wrote the first drafts for ISO Usability Standard 9241 and coauthored the draft for Part 11: Usability.


Cognitive Psychology

Usability of Physics

User Content (Theoretical Physics)

Systems Engineeering

Fig. 2: Three information domains determine the usabil-

ity of physics. The definition of “interaction” is fundamental to each of the named areas in the diagram. • Theoretical physics: The creation and use of conceptual and mathematical systems (theories) to define, describe and explain observable interactions within our Universe. • System engineering: Defines how to design and document a system’s interactions internally and with external systems∗ (including people). Because the theories of physics have been developed by many different people over centuries of time, some of the current forms of the theories are inconsistent or contradictory.† Also, their complex descriptions do not achieve Feynman’s and Einstein’s goal of simplicity—that the theories of physics should be easily explained to first-year college students [36, Special Preface] and, without the mathematics, to children. [15, p. 184] There are three goals embedded within increasing the usability of physics: 1. Simplicity: It was noted previously that Feynman and Einstein believed theories should be easily explained without difficult mathematics. Einstein wrote, “nature is the realization of the simplest ∗

A system is a set of principles, methods, procedures and practices that governs how a bounded set of objects interact with each other and with external systems. † The strongest contradictions in physics are between general relativity and quantum mechanics. Bohm and Hiley [5, p. 351] state they “are qualitatively in complete contradiction.” General relativity is a strictly local theory that requires strict causality and continuity. In contrast, quantum mechanics implies the opposite at all times and in all places.

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conceivable mathematical ideas.” [23, p. 274] Heisenberg used these words: “Mathematical simplicity ranks as the highest heuristic principle in exploring the natural laws in any field . . . the inner relations seem to be understood only when the determining laws have been formulated in a simple mathematical way.” [45, p. 58] 2. Symmetry: The perfect symmetry of the pure radiation that existed at the beginning of the BigBang must be conserved. Perfect symmetry is not physically observable. Symmetry must be broken to produce observable material objects. 3. Visualization: The results had to be visualizable in the classical spacetime of a human perceptual observer. The complex fragmentation of physics has made it difficult for physicists to create a unified picture of physical reality. That much fragmentation in a computersystem project would require a focused analysis of the project’s core documents. Its goal would be separating the system’s fundamental concepts from its functional logic and its surface-level features (Figure 3).

Surface

Features (words)

Functional Logic (math) Substrate

Concepts (ideas)

Fig. 3: The three levels of reality and the cognitive de-

scriptions of them. This also applies to theoretical physics. The functional logic of theoretical physics is expressed in mathematical equations. The surface-level features of physics are the words used to interpret the meanings of its equations. For this project, the conceptual models were buried in the writings of the physicists who originally created and proved the theories. This included Galileo, Kepler, Newton, Faraday, Maxwell, J. J. Thomson, Planck, Einstein, de Broglie, Schrödinger, Dirac, and Feynman. (The first five died before 1900. The last seven are Nobel Laureates in Physics.) Notice that images are not included in the three levels in Figure 3. They can convey information at all of the levels, and thus are useful for understanding relationships between levels. It is often easier to sketch a


picture before attempting the same description in words. Einstein described how pictures came first in his thinking, even before the mathematics. The words came later.∗ The creative sequence he described is the upward path in the levels of reality. The bottom-up cognitive path is from conceptual models to mathematical logic to surface-level features (the words). Other theorists in the list also argued strongly that visualization (or hands-on experimenting for Newton and Maxwell) was crucial for progress. Dirac focused more on the mathematics, but to him it was a form of play similar to how others used visualizations. It is important to visualize concepts and their relationships when attempting to understand a system.† An inability to visualize processes within a system makes it a “black-box” with only inputs and outputs identified. Einstein and Infeld describe a black-box system with these words: [29, p. 31] In our endeavor to understand reality we are somewhat like a man trying to understand the mechanism of a closed watch. He sees the face and the moving hands, even hears its ticking, but he has no way of opening the case. If he is ingenious he may form some picture of a mechanism which could be responsible for all the things he observes. . . In summary, the goal was increasing the usability of physics by providing an alternative view that is mathematically valid and testable. As subgoals, it was necessary to increase (1) conceptual-model simplicity, (2) the symmetry of physical representations, and (3) the ability to create visualizations of theories and what they represent. Thus the major results reported in this paper are visualizations of conceptual models for quantum mechanics. ∗

Einstein’s dry spell after general relativity until his death was because he focused on differential equations without any mental pictures to guide him. Einstein’s words describing the important of visualization are in the Appendix of Hadamard’s book. [40] Also, an excellent discussion of Einstein’s approach is in Michio Kaku’s Einstein’s Cosmos: How Albert Einstein’s Vision Transformed Our Understanding of Space and Time. † Visualization is discussed in the paper describing the rigorous mathematical derivation of Schrödinger’s quantum-wave equation from a classical equation.

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Issues

Theoretical physics is a “knowledge infrastructure”, a network of people (with their organizations and technologies) that “generate, share, and maintain specific knowledge about humans and the natural world.” [17, p. 5] A knowledge infrastructure has several or many subsystems (domains), each with its own origin, interests, practices and procedures. This is similar to Kuhn’s definition of “paradigm”. [55] [54] In this project, the people included were Nobel Laureates (or earlier) who originated masterpiece theories. Each theorist had personal mental models, interest, practices and procedures. The theories are in different domains, including classical mechanics, electromagnetism, relativity theory, and quantum mechanics. This description of theorists is similar to a description of major stakeholders in a new computer-system project. Major stakeholders have different types of expertise and are prioritized in their importance to the continuance and success of the project. For an interactive system, it is crucial that the userinteraction designer merge the ideas of the principal and major stakeholders‡ into a unified view of the system. Then that unified view can be adjusted as needed to integrate the needs and wants of other stakeholders. Although the end goal is to satisfy end users, the initial goal is creating a unified overview of what the system is supposed to do, who will be its users, and what will be their methods of access.§ Theoretical physics is already an interactive system with many types of users and many access points. The users include expert physicists, engineers, students at all levels, and ‘outsiders’ who want to understand how physical reality works. Major knowledge domains include Newtonian mechanics, Faraday-Maxwell’s electromagnetism, Einstein’s special and general relativity, Schrödinger’s quantum-wave mechanics, and others. Technological access points include every communication channel currently in use, ranging from printed textbooks to virtual-reality systems. The works of the ‡

Principal stakeholders are people who can kill a project will a single decision. This project had one principal stakeholder, the author of this paper. Major stakeholders have the power to affect the design of the new system, both in functionality and in appearance. § More than once when using this approach, a project’s sponsors discovered they needed to reconsider who would be using the system. Often that meant broadening the system scope to include additional user roles.


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theorists were originally described in what Weinberger calls “stopping points,” [85] fixed products of the past such as printed journal articles and books. In the past, getting a reference listed in a text meant a trip to a store or a library. Now much of a researcher’s reading is done online. Following a reference trail is often a click on a link or a Google search for the fulltext. When a document is not available online, it usually requires only an electronic request sent to a library to get the needed document(s). It helps to live in a city with multiple universities, a state consortium that provides borrowing privileges from almost 100 college and university libraries, the state library, a city library that is often ranked #1 in the United States, and multiple good suburban libraries. They have online databases of their holdings. In this new electronic world, “We can now be as smart as our new network allows—but we will be smart differently.” [85, Back Cover] Researchers also can obtain new and old (e.g., library discarded) books from sources across the world. Deep-knowledge research is no longer limited to academic environments. Historical research [13] can be applied to any domain and be done from anywhere, anytime, and by anyone who can learn to understand and evaluate the content. Historical research is not for the weak or hurried. As Kuhn wrote, it requires “The wrenching experience of entering into an older mode of thought”. [53, pp. 362-363] For this project, the researched period starts with Galileo in the 1600s and ends with a description of the properties of the Higgs field. The issue of limited access to information was not a major issue for this project. An active issue was the difficulty in getting constructive feedback on unusual ideas prior to making them public. Similarly, there was no opportunity for collaborative work on the project, even though possible opportunities were identified and explored. The academic pressure of “publish-or-perish” forces academics to focus on what is publishable and can win grants from funding agencies. It is also why I chose industry rather than academia for a career. Other selffunded scientists have made the same choice. This issue could be addressed with open-innovation approaches, such as crowd-sourcing. It is going to be necessary to include non-academics and academics with unusual ideas in scientific research teams. Much faster

progress could be made by collaboratively working together to explore new ideas and create new results. Another issue can be described in Kuhn’s words. He wrote, “If we can learn to substitute evolution-fromwhat-we-do-know for evolution-toward-what-we-wishto-know, a number of vexing problems might vanish in the process.” [53, p. 362] But professional physicists have neither time nor motivation to read the original writings of the early theorists as part of what-do-we-know. Closing off this historical information is losing valuable data. It assumes the current form of a theory is the only valid form, without considering alternative forms and interpretations. There is often the assumption that the current form is an improvement and that the older information is outdated. To glance ahead, that assumption was proven false. For example, Maxwell defined the vector-potential A field as the fundamental field of electromagnetism. But Heaviside removed all reference to the A field from Maxwell’s theory. He reduced Maxwell’s 20 equations to the four equations now called “Maxwell’s equations”. His goal was pragmatic, to make the theory easier to apply to his work in telegraphy transmission. However, the A-field later appeared elsewhere, as the field used in Schrödinger’s quantum-wave equation. Thus Maxwell’s electromagnetism and quantum mechanics use the same fundamental field. Further, in 1931 Dirac demonstrated that the Planck constant has two equal electromagnetic components. Those components are the product of unit charge and unit magnetic pole strength. Dirac’s value is now in common use in superconductivity.∗ The rediscovery and use of Maxwell’s fundamental A field is only one example. In a later section a table lists five other major theories that physicists significantly changed in ways that blocked their unification. Another issue is the method used by members of a domain to change its theories. The current push by physicists is to go beyond the Standard Model. Few, if any, look inside the Standard Model. This three-part series of papers looked inside the Standard Model and discovered there is no need for new dimensions, new particles, or other universes. This relates to the methods physicists use to change their theories. Heisenberg argued the method for creating progress in physics is very different from the method ∗

Citations provided with detailed discussion in a later section.


for creating progress in engineering: progress in physics requires replacing old theories with “entirely new conceptual structures”. [46, pp. 96-98] In his words, “All we can do is to adopt an entirely new conceptual system, in which the old system is contained as a limiting case.” For example, classical laws apply to “matter in bulk” as the limiting case of quantum theory, which has to do with fine structure. [11] This is in deep contrast to how he describe theoretical changes in engineering. For the engineer, “all technical terms retain their old significance; at most, the formulae are adjusted or corrected so as to cover previously neglected factors.” The engineering approach was used in this project. To glance ahead, Pauli’s argument [72, p. 98] that the domains of classical physics have ~ = 0 was proven false. The quantum of action ~ decomposes into two electromagnetic unit waves, the product of unit charge and quantum magnetic flux. Classical mechanics subsumes quantum mechanics as part of its domain.∗ Einstein’s summary of a fifth issue could have been written by a cognitive psychologist. [27, Doc. 29, p. 142] Concepts that have proven useful in ordering things easily achieve such authority over us that we forget their earthly origins and accept them as unalterable givens. . . . The path of scientific progress is often made impassable for a long time by such errors. Heisenberg vividly described the difficulty of proposing new conceptual models that challenge an established mindset: [43, p. 162] And now a word about the strong resistances that have arisen to every change in the pattern of thought. . . . For the demand for change in the thought pattern may engender the feeling that the ground is to be pulled from under one’s feet. . . . I believe that the difficulties at this point can hardly be overestimated. Once one has experienced the desperation with which clever and conciliatory men of science react to the demand for a change in the thought pattern, one can only be amazed that such revolutions in science have actually been possible at all. ∗

Refer to another paper by this author, “The Rigorous Derivation of Schrödinger’s Equation as the First Step towards Visualizing Quantum Mechanics”, DOI: 10.13140/RG.2.2.32647.19365.

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Dirac expressed the issue similarly:

[16, p. 1]

These big [theoretical] jumps usually consist in overcoming a prejudice. We have had a prejudice from time immemorial; something which we have accepted without question, as it seems so obvious. And then a physicist finds that he has to question it, he has to replace this prejudice by something more precise, and leading to some entirely new conception of nature. Schrödinger expressed a similar belief:

[79, p. 60]

The question is, whether after having had all the experience about Nature we have had, it is possible to re-build it in such a way from primitive principles of thought, in a way which suggests that it could hardly have been different from what it was; in a way, to understand it— In summary, numerous issues were identified in this project. They include (1) access to information, (2) availability of constructive feedback and collaboration, (3) physicists’ elimination of fundamental aspects of theorists’ original conceptual models, (4) physicists’ requirement to replace current models rather use the engineering approach of drilling deeper into them, and (5) the difficulty of accepting ideas that require rethinking “unalterable givens” and releasing a “prejudice from time immemorial”. We have the freedom to explore new ways of modeling physical reality. As Einstein wrote, “Physical concepts are free creations of the human mind, and are not, however it may seem, uniquely determined by the external world.” [29, p. 31] Thus he could think that spacetime is Euclidean and also write that four-dimensional spacetime is “merely a system of concepts”. [27, p. 217]

Part III Determine (Tasks & Plans) 7 7.1

Tasks Choosing the Methodological Approach

Knowledge infrastructures are ”robust networks of people, artifacts, and institutions that generate, share, and maintain specific knowledge about the human and natural worlds.” [17] A knowledge infrastructure has several


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or many subsystems (domains), each with its own origin, interests, practices and procedures. This is similar to Kuhn’s definition of “paradigm”. [55] [54] The current state of theoretical physics is similar to knowledge infrastructures in general. Edwards et al. wrote, “The result is a patchwork of unsatisfactory kludges, contradictions, and inconsistencies that may undermine the prospects for change.” [17] Pauli wrote: [65, p. xxv]

electromagnetism. He describes [50, pp. 2-3] how Heaviside, Devon, Lodge, and FitzGerald were “engaged in the 1880s and 1890s in the lively business of remaking Maxwell’s theory”. He notes that the dramatic changes to Maxwell’s theory are

Though we now have natural sciences, we no longer have a total scientific picture of the world. Since the discovery of the quantum of action, physics has gradually been forced to relinquish its proud claim to be able to understand, in principle, the whole world. Other physicists have expressed frustration at the lack of progress towards understanding the world. For example, Woit wrote that “the field has stagnated and worked itself a long way down a blind alley.” [93, p. 255] In The Trouble With Physics, Smolin wrote “what we know for certain about these laws [of nature] is no more than what we knew back in the 1970s.” [80, p. viii] Physicists are smart and they work hard. Therefore the block(s) to progress must be psychological rather than mathematical issues or logical reasoning. This same type of wicked problem occurs in projects designing large new computer systems. These projects involve numerous major stakeholders with very disparate views of the same physical system. For this knowledge-research project in physics, the disparate stakeholders groups were (1) physicists who died prior to 1900, such as Galileo and Maxwell, and (2) physicists who won a Nobel Prize for their work. These men provided multiple views of the domain that are in some ways inconsistent and conflicting. When the current forms of some of the theories were considered, some of their views appeared to be irreconcilable., [54, pp. 293-319] [55] In a new afterword to his Black-Body Theory and the Quantum Discontinuity, 1894-1912, Kuhn describes the need to understand the mental models (“modes of thought”) of a theory’s creator. [53, pp. 362-363] These are often central to understanding the fundamentals of their discoveries. They provide information that may have been lost in communication as the theory evolved to its present day form. Hunt studied the history of Maxwell’s theory of

a striking example of a process quite common in science . . . a theory is likely to be so refined and reinterpreted by later thinkers that by the time it is codified and passes into general circulation, it often bears little resemblance to the form in which it was first propounded. Because current experts have thoroughly learned a changed theory, it is difficult for them to understand the original form of the theory. As previously mentioned, Kuhn described it as “The wrenching experience of entering into an older mode of thought”. This is why novices and outsiders often are the source of creative breakthroughs. They can study older concepts and use them to create new models without experiencing severe mental conflicts. Understanding the creative process is in the domain of cognitive psychology. Figure 4 shows the cognitive model for solving what Ackoff calls a “mess”, a set of two or more interdependent problems. [1, p. 52] This describes why the unified theory has been so difficult to achieve—physicists have addressed the issues as independent problems. A “mess” has to be addressed as a whole. Considering the problems or parts independently conceals their interactions and blocks creating a solution. Solving a single problem may make other problems worse and may cause new problems. There are six levels of cognitive issues to understand when resolving a mess into a coherent structure for identifying solutions. A new and unified conceptual model for the domain must be created before the problems can be solved. It is almost impossible to jump directly from the problem (mess) level to a new conceptual model. If there is only one conceptual model on the problem level, then some of its concepts and actions are fundamental in that view of reality. However, the mess in theoretical physics has multiple conceptual models: electromagnetism, special relativity, general relativity, Newtonian mechanics, quantum mechanics, thermodynamics, optics, etc. There are also experimental contexts such as superconductivity and particle accelerators.


Problems & Issues to be solved

An Ackoff “mess” is a set of interdependent problems within a system.

Principal & major stakeholders

Physicists

10 Table 1: Major partial-unification theories in physics.

Each theorist combined two or more disparate concepts into a unified theoretical structure. Physicist

Overlaps among mental models Primary Concepts that define frames

Theory

Unified Concepts

Einstein

Special Relativity

Einstein

General relativity

Space & time & light Inertia & gravity & geometry of spacetime

de Broglie & Schrödinger

Quantum (matter) waves

Dirac

Quantum symmetry Quantum electrodynamics

Feynman

Subdomain Frames

Organizing Principle (Thing, Task, Tool, or Time)

Quantum Mechanics

Electromagnetics

Relativity Theory

A-field Substrate & Strings

Fig. 4: There are six levels to understand when resolv-

ing a set of interdependent problems into a coherent structure for identifying solutions. Solving the interdependent problems requires creating a unified conceptual model as the foundation for the domain. Trying to solve a mess is hazardous if all the relevant stakeholders are not identified at the beginning of the project. Each stakeholder added at a later time brings in the risk of making previous decisions incomplete or invalid. Thus the first major task was choosing to use a cognitive-psychology approach to resolving a mess. 7.2

Identifying the Theories and Physicists

Because physics has massive fragmentation at the problem level, the second major task was deciding what to unify. Table 1 lists major theories that had completed partial unifications within theoretical physics. Each of these theories unified two or more major concepts (right-hand column). For example, FaradayMaxwell’s theory of electromagnetism unified three conceptual models: light, magnetism, and electricity. Einstein’s general-relativity theory unified inertia and gravity.

Light waves & matter Particles & antiparticles Light particles & matter

Physicists have found that two theories in Table 1, general relativity and quantum theory, are especially difficult to unify. According to Born, they both are “generalisations of the classical laws of mechanics and electrodynamics.” [11, p. 533] However, they are very different in their assumptions: dynamic or static spacetime, and continuous or discrete variables. Thus the third major task was identifying or defining a logical foundation that supported unification. 7.3

Identifying the Foundation

For quantum theory, Planck’s quantization of the linear operator “provided the starting point for the entire theory”. [63, p. 584] Bohr postulated that Planck’s quantum was indivisible, [6, pp. 108, 114] and its indivisibility became a conventional belief passed down through generations of physicists. Also according to Bohr, “Only in terms of the classical electromagnetic theory is it at all possible to give a tangible content to the question of the nature of light and of matter.” [6, p. 16] Electromagnetic radiation (light) was the only thing existing at the first instant of the Big Bang, and everything else came into being from that. Einstein strongly argued, “There is no such thing as an empty space, i.e., a space without a field. Space-time does not claim existence on its own, but only as a structural quality of the field.” [26, p. 155] Thus Newton’s static background of absolute space and time can be replaced with the dynamic electromagnetic A field. Feynman wrote: The fact that the vector potential appears in the wave equation of quantum mechanics (called


11

Contextual Theory: Electromagnetism

the Schrödinger equation) was obvious from the day it was written. That it cannot be replaced by the magnetic field in any easy way was observed by one man after the other who tried to do so. This is also clear from our example of electrons moving in a region where there is no field and being affected nevertheless. But because in classical mechanics A did not appear to have any direct importance and, furthermore, because it could be changed by adding a gradient, people repeatedly said that the vector potential had no direct physical significance. As Hunt observes, [50, pp. 126-127] Maxwell’s “preferring to work entirely with the vector potential” is very obvious in his original writings. For example, Maxwell wrote that the state identified as the vector-potential A field “may even be called the fundamental quantity in the theory of electromagnetism. [62, p. 187] ” But unfortunately “few readers of twentieth-century textbooks of electromagnetism would ever guess that Maxwell had built his theory on A and ψ [the magnetic and electric potentials, respectively].” Maxwell’s original theory of light describes light waves in terms of the vector potential. [62, Chapter XX] The particle for the field in the Standard Model is the photon. The quantum waves in the A field are the ‘electromagnetic strings’ of Einstein’s lightlike Interval.∗ The theories in Table 1 were unified into a new theory called Quantum Interval Mechanics (QIM)† . The Faraday-Maxwell theory of electromagnetism is its foundation. As described in the previous papers in this series, it posits that real electromagnetic strings are the fundamental objects in physical reality (Figure 5). In summary, the project can be summarized under four primary tasks: • identifying and understanding the interdependent problems that could not be addressed separately, • identifying and exploring the existing theories to be included in the unification, • identifying the theoretical foundation for the new conceptual model, and

Lightlike

Special Relativity

(electrodynamic)

Intervals

General Relativity

Electrodynamic Dirac’s Strings Vector equation (QIM) Potential

components

A Field

Quantum Mechanics

Fig. 5: The relationships among theories that combine

to create the study of electromagnetic strings and their interactions. The new theory is called Quantum Interval Mechanics (QIM). • identifying and working a plan to create the new unified theory. 8

Plans

In a well-defined and well-organized project there would have been a ‘plan’ guiding the work. However, this project was not well-defined nor well-organized. There were no firm time deadlines. Thus the optimal plan could only define the methods that would be used to achieve the project’s goals. Three methods were used: (1) finding treasures in the historical physics literature, (2) creating a common dictionary, and (3) following Schrödinger’s suggestion to (a) start over with Galileo’s work and (b) focus on accelerated motions. Schrödinger’s suggestion was one of the last treasures found in the historical literature. 8.1

Method: Find Treasures in the Literature

The systematic process previously discussed for userinteraction design includes instructions for what to look for when analyzing historical documents. There are two questions to continually keep in mind: • What to look for?

∗

The details were provided in the previous papers in this threepart series. An oscillation that does not lose energy (not damped) is called a harmonic oscillator. [39, p. 40] These can be modeled as circularly polarized waves. † QIM is pronounced as the ‘qui’, in quick and the ‘im ’ in swim.

• What can be done with newly discovered information? When considering what to look for, hindrances to unification are often discovered by identifying hidden


12

and/or invalid assumptions. For example, Bohr’s assumption that the quantum of action ~ was indivisible was not based on logical reasoning or experimental evidence. It was a postulate, an assumption, without a foundation. Also look for (1) discarded concepts and explore why they were discarded, (2) theoretical branching introduced as a late (more modern) version of the original theory, and (3) old ideas that can identify new relationships among existing concepts. What can be done with discovered information? For example:

servable Euclidean background that Feynman defined for his graviton derivation of general relativity. • New relationships: Sommerfeld’s fine-structure velocity constant α = electron lightspeed c is the inverse of the refractive index for ground-state electron waves in a Hydrogen atom. This was used in the definition of the unit mass-energy for calculating the three generations of particles in the Standard Model of particle physics.

• Assumptions can be proven false. • Valid equations can be rearranged into different forms to make obvious new conceptual definitions or relationships. • Disregarded (forgotten) concepts can be revived and given new usefulness in different contexts. • Old mathematical formalisms can be given new interpretations. • Open issues and problems can be found and resolved, particularly if new information (e.g., from superconductivity) is available. • Conflicting approaches or data can be understood as the views of two different observers. They may have different conceptual models and/or different frames of reference. The following list provides some examples. These and numerous others of the same types were blocking attempts at unification: • Invalid assumption: Bohr’s assumption that the quantum unit of action ~ is indivisible was disproved by Dirac in 1931, but the physics literature does not reference that fact. The components of ~ are two electromagnetic unit waves (the product of unit electric charge and quantum magnetic flux). • Discarded concept: Maxwell’s magnetic vector potential A field that was discarded by Heaviside is the field described by Schrödinger’s wave equation for quantum mechanics. • Theoretical branching: When Minkowski required positive-value (timelike) intervals for Einstein’s special-relativity equation, he introduced spacetime curvature into physics. Reverting to Einstein’s 1905 lightlike interval provided the unob-

8.2

Method: Create a Unified Dictionary

Creating a unified theory for physics involves several intense challenges. A unified theory has to reconcile fundamentally different paradigms. [54, pp. 293-319] It has to acknowledge and address differences in assumptions, definitions, symbols, assignment of directions to handedness, domains of physical objects (e.g., sizes), etc. For example, the subdomains of physics, such as general relativity and quantum mechanics, do not agree on fundamental definitions of words such as “reality”, on the appropriateness of visualization, and if the results of individual experiments can be predicted (rather than a statistical result across numerous experiments). Lindsay writes, “A study of the history of physics clearly indicates that the first impression of any natural phenomenon is almost always one of disorder and confusion. Only gradually do the careful and thoughtful investigators transform chaos into order.” This is even more true for the unified theory—it has been through multiple simplifications and can be simplified even more. It is important to realize that dictionary definitions are not limited to words—they may be visual diagrams and they may be mathematical equations. However, the interpretations of equations must be expressed as either words or pictures or both. There are numerous examples in physics where the same equations are used to justify very different interpretations. The first paper of this three-paper series defined the primary physical constants and their relationships. Several constants, such as Newton’s gravitational G and the fine-structure constant, were given electromagnetic definitions as theoretical values. There are other challenges in designing a unified theory because the existing theories were each independently created. Often a new theory succeeds by challenging and invalidating a fundamental assumption un-


derlying a previous theory. There are also simpler issues to address, such as multiple meanings for the same symbols. In a unified context, it is not easy to determine which meaning is to apply. Other examples include: • Size Differences: Individual physical objects exist in a wide range of sizes, ranging from the tiniest subatomic particle to the largest star. The unified scale for size is so large it is communicated in powers of 10. The views shown in the 1977 video Powers of TenTM range from 0.000001 angstroms (10−16 meters) to 100 million lightyears (1024 meters). This identifies 1040 as the required span for size. The smallest view is within the realm of quarks. The largest view has “the galaxies like dust”.∗ • Internal or external coordinate systems: At the extreme ends of the scale all coordinate systems must be internal to the object—there is nothing to externally establish what is up-down or left-right. Feynman argues that each physical object must have its own coordinate system. • Coordinate scaling factors: The theoretical value of Newton’s G was defined in the Part 1 paper [57] and used in the Part 2 paper [58] as a scaling constant for the precessions of planetary orbits. • Handedness: There are two conventions for identifying the direction of circular polarization of light: the right-hand rule convention, and the screw convention. The difference is in the relative position of the observer. When the thumb of the right hand is pointed in the direction of propagation of the light wave, the fingers will curl in the direction of rotation of the electric field. In the right-hand rule, this is “right-handed”. In the screw convention and with the observer in the same location, the polarization is “left-handed”. The conventions agree if and only if the Observer views the wave as incoming (absorption) for the right-hand rule and outgoing (emission) for the screw convention. ∗

Some physicists gave up on creating an intuitive (sense experience) understanding of physical reality. For example, Heisenberg wrote, “We must therefore come to agree that the experimental findings on the very small and very large scale no longer provide us with an intuitive picture, and must learn to manage there without intuitions.” [44, p. 83]

13

8.3

Method: Implement Schrödinger’s Idea

As described in the Section 1, Schrödinger suggested that physicists go back 300 years and start over in a new direction for theory development. In a 1950 letter to Einstein, he wrote: It is probably justified in requiring a transformation of the image of the real world as it has been constructed in the last 300 years, since the re-awakening of physics, based on the discovery of Galileo and Newton that bodies determine each other’s accelerations. [21, pp. 41-42] According to Schrödinger, the standard approach had worked well for Newtonian physics, but it was no longer working. Physicists had focused on velocity and position [displacement] rather than focusing on acceleration and its changes. One must therefore go back 300 years and reflect on how one could have proceeded differently at that time, and how the whole subsequent development [of physics] would then be modified. Einstein did not disagree. In fact, he proposed the concept of field might be successful, but he was not sure. He summarized the state of physics as a newborn baby and that “the fellows struggle against admitting it (even to themselves).” [21, pp. 43-44] This involved searching through old books and articles to discover how the original theorists described their own work. Secondary sources were primarily used to find quoted references and references to little known works of the original theorists. Some, such as Bondi for Einstein, [8] provided useful interpretive information.

Part IV DO (Explore, Identify, Select, Create) Figure 6 provides a more detailed view of the Do cycle for knowledge research. Although the arrows show a linear sequence, the arrows actually go in every possible direction. A new decision in any step at any point in time can trigger reevaluation of decisions made in any previous and/or following step. The four sections in this part are the four substeps in the Do process: Explore, Identify, Select, and Create. The details provided here are only summary overviews


EXPLORE to identify (a) invalid assumptions, (b) redefined concepts, & (c) disregarded concepts. IDENTIFY ESSENTIALS (Analysis)

Interesting concepts Primary concepts

DO

CREATE RESULTS (Synthesis)

Physical expressions

14 Table 2: Changes in emphasis as modifications to the

masterpiece theories. In each case, both the original view and the modified alternative are valid. Creator

Unknown

Heaviside. Hertz, Gibbs

Emphasizing only linear B and E fields instead of universal curvilinear force field of magnetic vector potential A field

Minkowsky

Emphasizing only perceptual timelike (positive) intervals instead of Einstein’s lightlike (zero) intervals of electromagnetism

Einstein’s general relativity

Feynman and others

Emphasizing only massless (spin-2) ton” particles of spacetime try [38, p. ix]

de BroglieSchrödinger

Born

Emphasizing only probability instead of matter-wave motions in spacetime

Dirac

Multiple authors

Emphasizing only quantum fields instead of Dirac’s function “ψ” for a real particle in spacetime

Logical relationships Conceptual definitions

SELECT CONCEPT(S) TO USE OR MODIFY Fig. 6:

The iterative tasks in the DO cycle of a knowledge-research project. Although shown as a linear sequence, a decision in any step can trigger an change in a previous step and cascade its results though the following steps. of the actions included in those steps and the results from them for this project. 9

Einstein’s special relativity

Explore

The historical journey through through the literature reported in the previous paper [58] uncovered the information reported in Table 2. Later physicists reinterpreted each theory and dropped crucial information from the original theorists’ conceptual models. These later reinterpretations usually eliminated the visualizations and focused on how to pragmatically apply the mathematics. This created a dual view of reality for each theory: (1) the original view of the creator(s), and (2) the modified view that was created later. Both the original and modified forms of each theory are needed for unification. For example, Einstein’s 1905 special-relativity equation and Minkowski’s modifications in 1908 are both included in general relativity. Similarly, Heaviside’s vectors and Maxwell’s A-field that Heaviside eliminated are both needed for unification. Minkowski’s focus on physical motion is an example of a major conceptual-model shift. In Einstein’s original 1905 model for only lightlike intervals, any two points in spacetime could be connected by a sin-

Later Modification Emphasizing only straightline motions instead of accelerated (rotational) motions as absolutes

Galileo, Kepler, and Newton

FaradayMaxwell Fundamental concepts

Modifier

field of “graviinstead geome-

gle light ray. Light waves, not material objects, defined the criterion for measurements. The two points can be in different galaxies. In any case, the interval between them is the same straightline length in space and in time (multiplied by lightspeed c). An observation has perfect symmetry because it measures equal separation distances in space and in time. Thus Einstein defined the universal background of freely moving light as the criterion for all measurements. In 1908 the mathematician Minkowski modified Einstein’s equation to require positive timelike values for all observed intervals. This focused special relativity on the motions of material objects rather than using light as the standard. This view formalized a curved-spacetime model for describing distances. Spacetime observations have broken symmetry because they measure unequal


15

separation distances in space and in time. Minkowski’s change eliminated the Newtonian background field of light waves that Einstein had defined for all observers at all places at all times. His modifications converted Einstein’s 1905 universal special relativity into the 1908 theory of local events. Einstein then used Minkowski’s local model to include gravity in general-relativity theory. Thinking only about local regions of spacetime allowed Einstein to break out of his Newtonian model of an absolute background field. This enabled him to define a dynamic background field (the gravitational field) as spacetime. This is why general relativity and quantum mechanics have seemed irreconcilable. However, the validity of general-relativity’s curved-spacetime model does not mean that spacetime is a observable object that is physically curved. Misner, Thorne and Wheeler [66, pp. 417-428] describe five “routes” to deriving the general-relativity equations in addition to the route used by Einstein. The Feynman route has an unobservable straight-line (Euclidean) spacetime that can be used for both quantum mechanics and general relativity. This fits with cosmological observations. Physicists studying our Universe consider it puzzling that their measurements (within the range of error bars) indicate spacetime is not curved. Precise measurements of the electromagnetic radiation field (cosmic microwave background radiation) left over from the Big Bang creation has a flat or almost flat structure. Thus a major problem defined while exploring was how to model general relativity with the A field used by quantum mechanics. The key was using Feynman’s derivation of general relativity based on the particle of gravity, the graviton. [66, pp. 417-428] In general relativity Einstein posited that measurements of space and time could not be done with rigid bodies. There is no way to define a “quite definite length, which is independent of the locality and orientation of the body, and is also independent of the time.” Nor can there be “an interval of time of a definite length, which is independent of time and place.” [28, p. 148] Also, “The laws of physics must be of such a nature that they apply to systems of reference in any kind of motion.” “We therefore reach this result:—In the general theory of relativity, space and time cannot be defined in such a way that differences of the spatial co-ordinates can be directly measured by the unit measuring-rod,

or differences in the time co-ordinates by a standard clock.” [28, pp. 149-153] For the law of motion, Einstein introduced a frame of reference that had arbitrary local coordinates within a gravitational field. He wrote: [28, p. 156] the motion of the free material point will present itself in the new coordinates as a curvilinear non-uniform motion, and the law of this motion will be independent of the nature of the moving particle. We shall therefore interpret this motion as a motion under the influence of a gravitational field. The inability to use standard rulers and clocks requires non-rigid measuring instruments for space and time. “Instead, light rays and freely falling test particles are considered as the basic tools for setting up the spacetime geometry.” [18, p. 85] In this model used in QIM, particles become a set of “events”. The local values of the gravitational field gµν determine the metric of spacetime and therefore the clock readings and the paths of test particles and light rays. Using a radar∗ model to define distance, units of time (such as light-years and light-seconds) are used to measure distance. [8, pp. 34-38] The radio waves emitted and returned from the distant object travel at the speed of light. Therefore the time interval between emission and absorption multiplied by lightspeed c measures twice the length of the distance between the source and the target object. This corresponds to Einstein’s special-relativity definition of local lightspeed as two one-way trips between spacetime Points A and B: [22, p. 127] Speed of light =

2AB t2 − t1

(1)

Then the events that comprise a particle (which are observers carrying clocks) are described by a real time that is “nonmetric, but smoothly varying time, determined only up to smooth and smoothly invertible transformations.” [18, pp. 85-87] Close (observed) events “are required to be connectible to the particle by precisely two light rays”. The first ray is the emission ray from the particle to the event, and the second ray is the return ray absorbed by the particle. In other words, the particle and event ∗ The word “radar” is an acronym for RAdio Detection And Ranging.


16

can be modeled as the initial and endpoints of a light ray path defining a lightlike (null) interval. That timeline can be decomposed into a three-dimensional spatial to obtain spatial coordinates with the source at the origin. A common event is related to two “particles” by the radar-time of each observer. The particle (again, observer) is “uniquely determined by an event and a direction (initial velocity) at that event”. These parameters determine the path-structure of the local combined inertial-gravitational field. This approach makes the real spacetime geometry more fundamental than the metric used to measure it. The “geometry appears as the natural framework for the kinematics of light rays and free particles independently of and more basic than a metric.” [18, pp. 85-87]

are a static subset of Maxwell’s fully dynamical theory.∗ It has “lost its dynamical basis.” [3, p. 9]† Restoring the A field to its original prominence returns Maxwell’s theory to its emphasis on dynamical change.‡ It also provides a dynamic background that fits the requirements of general relativity. Defined as “electrokinetic [or electromagnetic] momentum”, [62, pp. 224,232,247,256-257] the A field is the only field that provides a completely wave-based theory of physical reality. The concept of momentum is also crucially “important because it applies to a system as a whole, regardless of what may go on inside the system”. [8, p. 162] The A field is also the central focus of Schrödinger’s wave equation in quantum mechanics.§ Feynman wrote, “It is interesting that something like this [the ‘real’ A field] can be around for thirty years but, because of certain prejudices of what is and is not significant, continues to be ignored.” [32, ’15-12] This is true even though it has been proven to cause physical effects (e.g., the Aharonov–Bohm effect). [87] Konopinski attributes the A field’s indispensable role in quantum electrodynamics (QED) theory to its ease of use: “The variational principle is also applicable to quantum-mechanical descriptions, which only require operator values for Aν .” [52] As mentioned previously, the product of the A field

10

Identify

The exploration process drilled deeply into Einstein’s definition of spacetime structure. It identified the fundamental issue as the geometrical representation of spacetime. It focused the Identify step to search for an existing theoretical field that could be used as the fundamental field. Traditional physics was built using particles as the conceptual model. In contrast, major theorists such as Faraday, Maxwell, Schrödinger, and Einstein focused on fields. Einstein created special relativity as an amalgamation of Maxwell-Lorentz’s electrodynamics and classical mechanics. [20, p. 113] As was detailed in the previous paper, [58] Maxwell defined six different fields that he organized in pairs. The product of each pair (AJ, ED, and BH) is energy density, the amount of energy per unit volume. Further, he defined the A field of the (magnetic) vector potential as the fundamental field. This was how Maxwell’s continued Faraday’s emphasis on a field of force. [61, pp. viii-xi] Its potential values are the “electrokinetic momentum at a point” in spacetime. [62, p. 232] The A field models the lines of curved magnetic force that fill all space. [62, p. 282] Faraday-Maxwell identified this universal field as a state of stress. Similarly, Misner, Thorne and Wheeler use the A field to diagram the parallel structures of electrodynamics and general relativity (“geometrodynamics”). [86, pp. 218-219] The four equations currently written in textbooks

∗

Hertz rejected Maxwell’s use of the vector potential, calling it “scaffolding” and removing it from the equations. He also wrote, “Mr. Oliver Heaviside . . . removes the same symbols as myself; and the simplest form which these equations thereby attain is essentially the same as that at which I arrive. [48, pp. 195-197] ” † Barrett writes, “Although the term ‘classical Maxwell theory’ has a conventional meaning, this meaning actually refers to the interpretations of Maxwell’s original writings by Heaviside, Fitzgerald, Lodge and Hertz. These later interpretations of Maxwell actually depart in a number of significant ways from Maxwell’s original intention. In Maxwell’s original formulation, Faraday’s electrotonic state, the A field, was central, making this prior-to-interpretation, original Maxwell formulation compatible with Yang-Mills theory, and naturally extendable. [3, p. 2] ” ‡ Refer to Konopinski [52] for details explaining why the A field is fundamentally real. § It has been mathematically described as follows: “The vector potentials Aαµ are connection coefficients on a principal fiber bundle where the structure group is the gauge group (U(1) for electromagnetism, SU(2) for Yang-Mills, and SU(3) for classical chromodynamics). The field strengths Fµν (i.e., the electric and magnetic fields in electrodynamics) are the curvatures associated with the connections (the potentials). The charged matter that the fields couple to are associated vector bundles”. [74, p. xxxii]


17

and its current field J is energy density. As the universal substrate, the A field’s gauge-free harmonic oscillators exactly compensate for local phase changes (rotations). This compensation keeps the electron’s kinetic energy constant. [75, pp. 34-36] This is the application of Newton’s third law of action and reaction in the universal substrate. The Afield’s harmonic oscillators act to conserve spacetime structure by removing states of stress. The mean energy of any harmonic oscillator is the same as counting the number of photons—“up to any number n of particles, one finds that this system behaves for all quantum mechanical purposes exactly like a harmonic oscillator.” [33, pp. III-4-9 & 10] A-field values are ambiguous (not set within a specific gauge) because the field can change locally without having to make the same change at all points. Gauge transformation is changing from one vector potential to another without changing the value for the magnetic field B that is derived from the A-field vectors. Both the electric field E and the magnetic field B are derived from the vector and scalar potentials. To quote Heaviside about the vector potential: “its spacevariation has to furnish the magnetic force, and its timevariation the electric force;” [68, pp. 91, 93] [42, p. 491] The A field can be Fourier-analyzed in terms of the different frequencies (energies) it contains. In Heisenberg’s view, an electron “jumps” from one stable state (Sommerfeld’s “orbit”) to another and emits a wave for each transition between neighboring states. Each possible emitted wave (a term in the Fourier series) is modeled as a “harmonic oscillator”. The possible values for emitted waves define an infinite table of rows and columns. Emitted waves create the “spectral lines” that identify each type of atom. The intensities of the spectral lines can be calculated as the squares of the amplitudes of the terms shown in Heisenberg’s table. Jumps must be between neighboring states, and therefore a jump of any size is the sum of the unit jumps that comprise it.∗ Figure 7 shows how the A field and its J field current density relate to stress (force per area) in observable reality. The two rows are for Maxwell’s two systems of units. For electromagnetic units (EMU), the value of lightspeed is the integer “1”. For electrostatic units (ESU), its value is the standard value of lightspeed c.

Maxwell’s fundamental variable has the dimensions of the square root of the moment of inertia per unit p 2 length ( ML /L). The EMU A-field value is that value per unit time, and the ESU value is that value per unit length. The square of an EMU A-field value is force, and the square of its ESU value is mass per radial length. The A-field’s current density is called the J field. Its square is the rate of change in the rate of change of spacetime stress. Those changes are space-dependent for EMU units and time-dependent for ESU units.

∗

Refer to Baggott

[2, pp. 47-50]

for more details.

Source: (A Field)2

EMU units

ESU units

Effect: (J Field)2

Force

Stress / length2

 ML  ≡ ML  T  T2 

 ML  ≡ ML  L2T  L4 T 2  2 M LT Stress ≡ ≡ 2 Area L

2

2

=

(

Mass Velocity Radius

)

2

Radial mass density

Stress / time2

 ML  ≡ ML  L  L2 

 ML  ≡ ML  LT 2  L4T 2  2 M LT Stress

2

≡ M L ≡ Mass Radius

2

≡

T

2

≡

2

Time

Fig. 7: The equations that relate the A and J fields to the

dimensions of physical reality. There also are traditional mathematical reasons for using the vector-potential field as the fundamental field: “without it, we could not express the principle of stationary action, or the Lagrangian, Hamiltonian, and Poisson formulations of mechanics for particles in magnetic fields.” [81, p. 197] Schrödinger was aware of the relationship between A-field potentials, his ψ waves and the Maxwell-Lorentz equations. [77, pp. 59-60] He stated a question: An especially important question—perhaps the cardinal question of all atomic dynamics—is, as we know, that of the coupling between the dynamic process in the atom and the electromagnetic field, or whatever has to appear in the place of the latter. Then he answered his own question in these words: the mechanical field scalar (which I denote by ψ) is perfectly capable of entering into the unchanged Maxwell-Lorentz equations between the electromagnetic field vectors, as the “source” of the latter; just as, conversely, the electro-


dynamic potentials enter into the coefficients of the wave equation, which defines the field scalar [ψ]. Schrödinger defined ψ waves as the “source” of the Maxwell-Lorentz electromagnetic field vectors. His verbal description is diagrammed from the bottom up as: Electromagnetic field vectors (energy) ↑ Unchanged Maxwell-Lorentz equations ↑ Mechanical field scalar (matter wave ψ) ↑ Coefficients of the wave equation ↑ Electrodynamic field (potentials) Schrödinger’s ψ waves are de Broglie matter waves. A matter wave’s phase velocity is always greater than lightspeed c because its associated particle’s velocity must be less than lightspeed c. The product of the two speeds (wave phase and particle) always equals c2 , the square of lightspeed c. Schrödinger’s equation describes the transmission of power in terms of potentials (the A-field) rather than observable energy. “The correct quantum mechanical equation for the motion of an electron in free space was first discovered by Schrödinger. . . . [It] has the same form you get for the limiting case of an electron moving along a line of atoms.” [33, p. III-16-4] In summary, the A field of the magnetic vector potential is the universal substrate for everything else in the universe. Its current densities move power across distances between points. This is the original FaradayMaxwell electromagnetic theory of light. 11

18

Feynman’s further analysis defined the action∗ (the weighted sum of kinetic energy minus potential energy within a duration of time) as the transformation function. [37, p. vi] In other words, energy (ML2 /T 2 ) extended in (multiplied by) time T is action (ML2 /T ). Unit action is unit angular momentum in atomic units. Feynman used a spinning pointer as his measuring instrument for spacetime. As a clock it counts the number of complete 2π rotations between a path’s ‘start’ (emission) and ‘finish’ (absorption). [34, p. 27] The arrow starts spinning at the instant of emission and stops at the instant of absorption. The frequency of the light wave defines the number of completed 2π cycles per unit time. The length of the arrow (its magnitude) is the amplitude of the wave. In quantum mechanics the amplitude is the square root of the probability of the event. Adding all the arrows for all possible ways the event could happen models the probability of the event. [34, p. 53] The differences in phase (partial rotations) are also important. For example, a particle with a wave path that started at 12 and ended at 6 would interact differently (or not interact) with a particle whose wave path started at 3 and ended at 9. An example spinning arrow (a vector called a phasor) is shown in Figure 8. It provides a mechanism for quantizing spacetime by counting only complete 2π cycles. When de Broglie discovered matter waves, he made complete cycles a requirement in his description of electrons’ ‘orbits ’. or Phas π

Identifying the A field as the universal substrate raises the issue of how to represent it as a conceptual model. If there were no existing models, then the Create process would come into play. However, Feynman provides an existing model that was Selected for use in QIM. Feynman’s integral over all paths (sum of all histories) approach is based on “action”. Dirac defined the exponential function eit as the coefficient that defined the evolution of quantum waves in time.

5π

2π 4π

3π

Select

0

Unit Time

6π

Time

Fig. 8: An example rotating arrow (vector) representing

a phasor of three spatial cycles (2π) per unit time. ∗

Technically, the exponent of the time integral of the Lagrangian.


19

Feynman [38, p. 31] identified three types of potential fields based on the spin values of their particles (Table 3). (The right column was added as a descriptor for each type of particle.) He then constructed a spin-2 theory as the background field in general relativity. He noted this was possible because of hindsight developed during the fifty years since Einstein’s original work. Table 3: Feynman’s three integer-spin particles.

Spin Spin 0 Spin 1 Spin 2

Symbol X Aµ hµν

Type Scalar Vector Symmetric tensor

Particle? Higgs boson Photon Graviton

Phasor models can have a real physical significance. When each 2π cycle represent one unit of angular momentum, the phasor models the equation Planck constant/2π = Energy / 2πFrequency,

(2)

The amount of energy observed for frequency equal one is the unit energy for that Observer’s local frame of reference. The rate of spin is a measure of the strength of the proximal gravitational field. The field strength changes as the freefall continues, and the pointer will spin faster during each unit of fall time. Feynman points out that gravity can be described in three very different ways that are mathematically equivalent: (1) for descriptions of causality, use Newton’s Law; (2) for force fields, use descriptions of local potential fields; and (3) for motions in time, use the minimumaction principle. [31, pp. 49-53] Because all physical objects are in continual motion, there is no state of absolute rest. Consequently, Einstein defined the freefall state as the state of relative rest. In Figure 9, the hammer and the man are at rest relative to each other however fast they are moving. Objects in freefall feel no force of any kind because their accelerated motions offset the local gravitational field. This is why general relativity posits any observer can choose to arbitrarily define the local coordinate system as the state of rest. A phasor can be used to represent the acceleration necessary to offset gravity at any point. Each time unit during a freefall is represented by a different phasor according to Galileo’s law of acceleration. The phasor for the first time unit completes one cycle per unit time.

Fig. 9: Einstein’s visual model of the freefall frame in

general relativity. The hammer and the man are at relative rest and neither is experiencing any force—at each location in space and time the effect of gravity is precisely offset by the freely falling object’s acceleration. The phasors for other time units increase the number of completed cycles by two for each additional time unit. For example, the phasor for time unit two of the freefall is drawn in Figure 8. The phasor time unit three would have a frequency of five, and the phasor for time unit four a frequency of seven. Used in this way, phasors represent the strength of the gravitational field. In discussing his spinning arrows, Feynman defined specific [per mass] angular momentum as “the area generated per second by objects moving about.” [31, p. 77] He notes that angular momentum hidden in the local field is manifested as rotation only when the local currents are removed. [31, p. 79] That was Maxwell’s original description of the angular momentum hidden in the A field. [62, p. 232] The vector A (English A) represents in direction and magnitude the time-integral of the electromotive intensity which a particle placed at the point (x,y,z) would experience if the primary current were suddenly stopped. We shall therefore call it the Electrokinetic Momentum at the point (x, y, z). It is identical with the quantity which we investigated in Art. 405 under the name of the vector-potential of magnetic induction. The electrokinetic momentum of any finite line or circuit is the line-integral, extended along the line or circuit, of the resolved part of the electrokinetic momentum at each point of the same.


20

It is important to note that Maxwell did not view electrical charges as separate entities. He viewed “charge as simply a manifestation of discontinuities in the displacement of the field.” [50, p. 222] The electron as a particle was invented by later theorists. Maxwell also wrote, “The vector A [A] and its constituents F, G, H depend on the position of ds in the field, and not on the direction in which it is drawn. They are therefore functions of x,y,z, the coordinates of ds, and not of l,m,n, its direction-cosines.” Think of the electrokinetic momentum at a point as the potential energy (per unit length of current) that is stored in spacetime as accelerated light waves. It is a stress in what Einstein called the “ether” (gravitational field) of general relativity. All physical reality ultimately reduces to light waves and their interactions.

The ±S value indicates the direction up (+S ) or down (−S ), and the ±ct indicates left or right circular polarization (like the circular face of a clock). For example, the {+S-ct} wave is an Up wave with a left-handed rotation coming towards the Observer.

12

Create

The Universe at the beginning of its beginning (the “Big Bang”) was only electromagnetic radiation (light waves). Those light waves now dance in patterns that create and recreate matter as regions of concentrated energy held together by electromagnetic and gravitational fields. In Einstein’s search for a new physics, he declared, “The new physics will not have to consider fields and matter; its only reality will be the field . . . ”.∗ A stone falling to the ground is a region of concentrated energy shifting locations in a field. The displacement of the energy per unit time is measured as the velocity of the stone. Again, Einstein said it best: “Hence the material particle cannot possible be a fundamental concept in any field theory.”† This requires the definition of the fundamental field, the A field, as a field of light waves. In a little-known equation, Einstein posited that all of the energy comprising matter is field energy. Specifically, “of the energy constituting matter three-quarters is to be ascribed to the electromagnetic field, and onequarter to the gravitational field.” [19, p. 88] The factoring of Einstein 1905 lightlike interval into four symmetrical waves (Equation 3) divided the field energy into fourths. That allowed calculation of the standard general-relativity values for gravitational effects with only basic algebra and no free parameters. [58] ∗ †

As quoted by de Broglie in [15, p. 144]. As quoted by de Broglie in [15, p. 143].

s21 + s22 + s23 =

3 X

s2i − (ct)2 = 0

(3a)

1

v u t Define

3 X

s2i = +S 2 for cube’s diagonal2

(3b)

1

and then factor S 2 − (ct)2

(3c)

Two interval solutions +S solution waves: (+S +ct)(+S –ct) –S solution waves: (–S +ct)(–S –ct) The two interval solutions in Equation 3 conserve the perfect-symmetry structure of the Big Bang, which contained only electromagnetic radiation (light). The four entangled waves may be grouped in three ways: (1) the interval with four waves, (2) a solution (two waves with the same sign for origin in space), and (3) a cycle wavepair (two waves with the same sign for rotation in time). The direction of travel (propagation) of a wavepair may be forward or backwards, and it is not determined by the equation. Only wavepairs with the same direction of propagation were used in the results of this paper. However, when both wavepairs propagate in the same direction, one of them is traveling forward in time as matter, and the other is traveling backwards in time as antimatter. This provides the non-local theory of particles because measuring one value identifies the state of its ± entangled opposite. A ± entanglement remains until one of them participates in an interaction, even if the entangled partners have traveled to different galaxies. In other words, special relativity is the classical expression of Dirac’s equation. The four-component wave functions are known as Dirac spinors, and the twocomponent ones are known as Weyl spinors.‡ . The interval waves are Maxwell’s A-field potentials that cannot be created and observed as single waves. ‡ [56, p. 327]

equation.

Chapters 36-38 (pages 322-347) focus on the Dirac


21

A virtual particle requires the intersection of the two waves in a solution. Detection requires one traveling wavepair and its matching wavepair in the detector completes the interval when it arrives. Also, a unit wave with angular frequency ω = 1 deh fines the vacuum’s zero-point energy as 1/2 ~(ω=1) = 4π . This explains why Heisenberg’s uncertainty principle h defines 4π as the lower limit of the universe.

This equation can be rearranged to define the total moment of inertia without any reference to the object’s mass. N X Moment o f inertia mi ri2

Part V Done (Deliver & Close) 13 13.1

Deliver Modeling Rest Mass and Charge

The four waves follow their helical paths around the same axis of rotation. When the full interval is modeled, different pairs of waves intersect at different times and places. The directions and signs have been arbitrarily chosen because there are different conventions in different subdomains of physics. At this point it is necessary to define mass. However, mass works only for point particles and, as Born points out, point particles cannot exist if Maxwell’s equations are taken literally. [11] In addition, Jammer points out that any valid theory of mass must give a non-mechanical theory priority over any mechanical theory. If not, the theory will be caught in circular logic. [51, p. 144] Einstein’s 1905 lightlike special-relativity is the nonmechanical theory given priority in the unified theory. Its four interval waves intersect to create mass (and charge), and therefore mass is a derived concept. The universal default motion is curvilinear motion around an axis of symmetry. Therefore rotational inertia, called the “moment of inertia”, is a centrally important variable for the unified theory. In the traditional view, a rotating object is defined as a rigid assembly of point masses at ri distances from the axis of rotation. The rotational kinetic energy of the object is defined in Equation 4. [90] Rotational kinetic energy Ek N

X 1 = (Angular speed ω)2 massi · radius2i (4) 2 n=i

n=i

2 · rotational kinetic energy Ek = (angular speed ω)2

(5)

In words, the moment of inertia is the ratio of twice an object’s rotational kinetic energy to the square of its angular speed. Work is a change in the rotational kinetic energy. Power, which is work per unit time, is the scalar product of torque and angular velocity. In SI units, power is in watts, torque is in newton metres and angular speed is in radians per second. [92] When the rotational speed is in revolutions per time (rather than angular speed in radians/time), the power is increased by a factor of 2π per revolution (Power = torque x 2π x rotational speed). The torque on an object equals the first derivative of its angular momentum with respect to time. [92] The atomic unit of angular momentum is also the atomic unit of action (the quantum of action ~). [14] Although the mass of the unit photon is tiny, its tremendous velocity allows it to carry a measurable angular momentum. The unit wave is the zero-point energy of the quantum vacuum, and it carries h/4π angular momentum. This is also the value of Heisenberg’s uncertainty principle, and thus it also defines the lower limit of measurable physical reality. The mass of a unit wave pair is twice that amount. As shown in Figure 10 on page 22, unit proper mass can be calculated using different physical constants because unit mass is fundamental to all of physics. When visualizing these equations, the local definition of lightspeed c defines the ‘unit’ circle. For SI units, that value is 299,792,458 meters. There are three panes of equations in Figure 10. (a) For unit proper mass, the quantum equation uses Einstein’s Mass = Energy/c2 . The second equation, for unit-mass flow rate, can be visualized as one unit wavepair per unit time passing through a circle with a radius lightspeed c. (b) This classical-electron equation uses the electron’s observed mass and an old electromagnetic constant known as the classical electron radius. The coefficient (multiplier) is the inverse of Sommer-


(a) Unit Proper MassUnitPhoton = Energy = 2 c

Unit Mass Flow RateElectromagneticWaves =

(b) Unit Proper MassClassicalElectron =

22

h sec 1.054 571 726 x 10-34 sec = = 1.1733692 x10-51 kg c2 (299, 792, 458m) 2 -34 unit electromagnetic wave ½ h ½ (6.626 069 57 x 10 J s ) kg = 1.1733692 x10-51 = 2 = SI unit circle s p (299, 792, 458m) 2 pr

cSI _units Classical electron masse radiuse * = 1.1733692 x10-51 kg 299, 792, 458m c Atomic_units

Note: The inverse of the lightspeed ratio (SI units / Atomic units) is the Fine-Structure Constant.

(c) Unit Proper MassForce / Acceleration =

1 4pe0

2

æ UnitCharge ö÷ çç ÷ çè 299, 792, 458m ø÷ 1 sec

c AU

2

æ1.602176565 x10-19 C ö÷ 1 çç ÷÷ -12 2 2 ç 4p (8.854187817 x10 s / m ) è 299, 792, 458m ø÷ = = 1.1733692 x10-51 kg 1 6 2.1876912633 x10 m / s sec

Numerator: Coulomb's force law for electromagnetic charge Denominator: (Angular velocity in radians per sec)(Classical electron linear velocity) = Centripetal acceleration of electrical pair

Fig. 10: Four equations that use different standard constants all reduce to a calculation of the unit proper mass.

(Current NIST values may have changed slightly since when this figure was done.) feld’s original definition of the fine-structure constant. (c) This force equation is the ratio of Coulomb’s electrical force to the centripetal acceleration for the wavepair. Notice that the four equations using different standard constants all yield the same result. In other words, they are different coordinate systems used to measure the same object, the rest mass of one half-cycle occurrence of the unit photon. This tiny (10−51 ) value is why the mass of the photon could be traditionally defined as zero. Figure 11 on page 23 models an interval with frequency of two for its four waves. Because the wavepairs intersect twice per 2π cycle, there are two instances of each of the four possible intersections (particles). For the unit interval, these particles are the four components of the Dirac equation. Four different types of virtual particles (wave-pair intersections) occur during one 2π unit cycle. There could be only matter, such as the electron, and antimatter, such as the positron. However, the Weyl equations and the interactions with the Higgs field require an additional variable (another degree of freedom). [83] That variable is often called “handedness”, but in technical physics terminology that can be either chirality or helicity. Given that the interval waves have spin chirality (±ct), the additional degree of freedom will be

identified as helicity. If a particle’s spin and momentum are parallel, it has +1 (right-handed) helicity. A particle with opposing spin and momentum has -1 (left-handed) helicity. Table 4 on page 23 identifies the four particles in the traditional organization of Weyl’s equations. [83] The path of a physical electron alternates between a virtual electron e− and a virtual anti-positron /e+ . The path of a physical positron alternatives between a virtual positron e+ and a virtual antipositron /e− . The Higgs field mixes the right-handed electron and its left-handed anti-positron alternative into the physical electron. Similarly, the virtual positron and its antielectron alternative into the physical positron. The two zigzag paths in Figure 11 agree with two findings in the literature: (1) it models the “trembling motion” of the electron Schrödinger called “zitterbewegung”, [64] [49] and (2) it models the mass mixing of the Higgs field for the electron. [67, p. 6] In the Higgs approach, mass is the interaction between the two directions of handedness. However, handedness in the Higgs model is helicity [73, p. 630] rather than chirality (spin). Spin is an internal property of the wavepair. For a particle ‘at rest’, the zigs and zags in Figure 11 are the Compton length [~/(mass · lightspeed c)]. Thus the value of the Compton length is angular momentum / linear momentum. This is also the definition of the


23

Higgs Mixing of Interval-Wave Solutions Side view of helical paths. Lighter shade is front; darker is back.

–S –ct -S solution

e–

/e–

e–

/e–

/e+

e+

/e+

–S + ct +S + ct +S solution e+

+S – ct e– is electron e+ is positron /e– is anti-electron with positive charge /e+ is anti-positron with negative charge

Paths in Higgs mass field − charge: Solid line (fronts) + charge: Dotted line (backs)

Fig. 11: The QIM retarded and advanced wave-pairs, the particles they create, and the zigzag paths of charges

through the Higgs field. Table 4: Traditional quantum mechanics. Weyl’s two equations provide the solutions to the Klein-Gordon equation.

The solutions are two-component wave functions. Each solution combines matter and antimatter.

First Weyl Equation Property

Second Weyl Equation

Solution 1a

Solution 1b

Solution 2a

Solution 2b

Matter

Antimatter

Antimatter

Matter

Energy

>0