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The World of Atom (Part XII)

Reference: Boorse 1966: The World of Atom

Chapter 62: The Principle of Least Action (William Rowan Hamilton 1805 – 1865)

On a General Method of Expressing the Paths of Light, and of the Planets, by the Coefficients of a Characteristic Function. Hamilton’s mathematics was based on the analogy between the behavior of light of very short wavelength and the behavior of ordinary particles of matter. He demonstrated that the dynamical problem may be solved by considering the motion of a system as though it were a gradual unfolding of a series of states, each one derived from the preceding one by an infinitesimal transformation similar to what we have when a ray of light advances from one wave front to the next.

Chapter 63: The Wavelengths of Particles (Prince Lois V. de Broglie 1892 – 1987)

The Undulatory Aspects of the Electron. At small scales, there is dualism in Nature between waves and corpuscles. The wavelength associated with a corpuscle is as concrete a physical quantity as its mass. The velocity of the corpuscle is equal to the group velocity of its associated wave. Planck showed that energy is connected to frequency, E = hv. It can also be shown that momentum is connected to wavelength, p = h/λ. This is a fundamental relation of the Theory.

Chapter 64: A Wave Equation for Particles (Erwin Schrodinger 1887 – 1961)

Derivation of the fundamental idea of wave mechanics from Hamilton’s analogy between ordinary mechanics and Geometrical Optics. At close range, the particle appears to be a wave motion represented mathematically by a continuous manifold of wave functions. Using this approach, Schrodinger could derive the arbitrary integers assigned to electron’s energy-levels in the Bohr’s Atomic model.

Chapter 65: Statistics and Waves (Max Born 1882 – 1970)

Wave Corpuscles. The waves do not represent physical vibrations but rather the unfolding of the probabilities of future events from a given initial state. The complex amplitudes of the waves obtained as solutions to Schrodinger’s wave equation can be interpreted better as the probability of finding the electron at a location.

Chapter 66: The Uncertainty Principle (Werner Karl Heisenberg 1901 – 1976)

Critique of the Physical Concepts of the Corpuscular Theory of Matter. Heisenberg discovered the foundation of quantum mechanics—the uncertainty principle.The uncertainty principle refers to a limit on the accuracy with which we can measure certain pairs of quantities simultaneously. Heisenberg introduced his square arrays or matrices, which depict the electron as existing simultaneously in all possible Bohr orbits.

Chapter 67: The Barrier around the Nucleus (George Gamow 1904 – 1968)

Quantum Theory of the Atomic Nucleus. While Gamow’s paper explains the spontaneous emission of particles (alpha decay) from radioactive nuclei, it also validates Schrodinger’s wave equation inside the nucleus and demonstrates the correctness of Born’s concept that the Schrodinger wave function is the probability amplitude for finding a particle in a given small neighborhood of space.

Chapter 68: Electron Waves (Clinton J. Davisson 1881 – 1958, George Paget Thomson 1892 – 1975)

Diffraction of Cathode Rays by a Thin Film. Davisson: Electrons reflect from crystalline surfaces. The relationship between the angle of maximum intensity, the speed of the electrons, and the lattice spacing in the crystal are the same as that for a wave. Thomson: The rings arising from diffraction show the wave properties of the electron. The radius of the rings is inversely proportional to the velocity of the electrons. These experiments provided evidence supporting the De Broglie equation.

Chapter 69: The Electron and Relativity (Paul Adrian Maurice Dirac 1902 – 1984)

The Principle of Superposition. All one needs to know about the observable properties in order to understand their physics is the algebra that governs them (theory of operators). A system in quantum mechanics must be looked upon as simultaneously being in a whole set of states rather than in some particular state. The electron is forced in one of these states due to the perturbation of measurement. Dirac’s idea of states very brilliantly connected the Schrodinger wave function with the probability concept ascribed by Born.

Chapter 70: “Holes” in the Dirac Theory (J. Robert Oppenheimer 1904 – 1967)

On the Theory of Electrons and Protons. Dirac’s theory predicts the existence of an infinite continuum of negative energy. Dirac proposed that all but few of these negative-energy states are filled with electrons with negative energy; negative-energy states that do not have electrons represent protons. Oppenheimer pointed out that this hole theory gave a different mass dependence and led to insurmountable difficulties. He proposed to retain the picture of the electron and the proton as two independent particles of opposite sign and dissimilar mass and to picture all of Dirac’s negative-energy states as filled.

Chapter 71: Complementarity (Niels Bohr 1885 – 1962)

Discussion with Einstein on Epistemological Problems in Atomic Physics. The discussion led to the Principle of Complementarity: There are always two complementary and mutually exclusive ways of looking at a physical phenomenon, depending on how we arrange our apparatus to measure the phenomenon. When we deal with an electron, we must use both the wave picture and the particle picture; one is complementary to the other in the sense that the more our apparatus is designed to look for the electron as a particle, the less the electron behaves like a wave and vice versa.

MAIN POINTS

The behavior of light of very short wavelength approximates the behavior of ordinary particles of matter.
The wavelength associated with a corpuscle is as concrete a physical quantity as its mass.
The velocity of the corpuscle is equal to the group velocity of its associated wave.
Energy is connected to frequency, and momentum is connected to wavelength.
At close range, the particle appears to be a wave motion.
The “waves” represent the unfolding of the probabilities of future events from a given initial state.
The electron seems to exist simultaneously in all possible Bohr orbits.
The mathematics applied to electrons seems to work inside the nucleus as well.
A quantum system is simultaneously in a whole set of states rather than in some particular state.

THEORY
The mathematical development seems to confirm that electrons are a wavelike flow that has variable consistency. Even the nucleus is a pattern of a very condensed flow.

March 6, 2021 – 9:30 PM Categories: Physics Book | Post a comment

The SLC Policies

Reference: Course on Subject Clearing

The following policies apply broadly to all SLCs.

POLICY # 1: The study materials for a subject follow the logical sequence in which the concepts are developed.

This policy is followed in developing the math materials from Level 00 to Level 2 at Course on Mathematics. Later levels provide materials that are selected per this policy.

POLICY # 2: The study materials are presented on a gradient such that they are suitable for a student studying them for the first time.

These math lessons were developed to address the “holes” in the understanding of High School dropouts, but they are written in a manner that they can be used at earlier levels. The students are encouraged to read and understand these lessons under the supervision of trained supervisors who have already completed these lessons.

POLICY # 3: Each lesson is accompanied by a large number of exercise problems with answers provided for them.

All lessons of this math curriculum are supported by plenty of exercises with answers provided at the bottom. The student does these exercises to practice the concepts of that lesson, and then checks his or her answer. The correct answers reinforce the students’ confidence. The incorrect answer provides an opportunity to find and correct the error. The errors decline rapidly as the student becomes aware of how he made the error.

POLICY # 4: The SLC course room provides access to course materials on electronic tablets.

The SLC course room is a single large space with tables and chairs, and a white board with markers and eraser for lecture purposes. All course materials are accessed through individual electronic tablets provided to the students.

POLICY # 5: The course room may also provide pencil and paper and dictionaries.

Students may also be provided with pencil and paper for doing exercises, and dictionaries to clear up the meaning of words. Students are encouraged to utilize the resources available with care, so that there is enough for everybody.

POLICY # 6: The students teach themselves directly from their course materials, with the use of “Word Clearing”.

The students learn to use the procedure of Word Clearing to self-learn. They apply this procedure to their course materials.

POLICY # 7: The students are assisted in their self-learning by the “Word Clearers”.

A Word Clearer is fully trained on word clearing, and is familiar with the courses being studied. He ensures that the students understand the procedure of word clearing and are applying it. He assists any student having difficulty in understanding their course materials by helping them find the word they don’t understand and clear up the area of confusion. NOTE: The senior students in the course room may act as “word clearers” for junior students.

POLICY # 8: The SLC course room is run by a “Course Supervisor”.

The person in charge of the SLC course room is called the Course Supervisor. He (or she) is fully trained on all the courses that are being studied in that Course room. He manages the Course room and its supplies, and ensures that the students are making progress and completing courses.

POLICY # 9: New students are started with introductory lectures on their course and the word clearing procedure.

New students go through a lecture by the Course Supervisor that introduces them to the course room, the supplies, the use of electronic tablets to access their course materials and the word clearing procedure. Additionally, the new student may be given introductory lectures on the subject he is going to study, such as, the two lectures provided at the link for Level 1 Math. There are some Diagnostics too at that link, which the new student may do while waiting for the lectures. After the lectures, the student starts on the course.

POLICY # 10: Throughout the course the student is spot-checked intermittently for his understanding of the study materials.

The discipline of word clearing is vital for a self-learner and it is reinforced on the course. The Word Clearers in the course room randomly spot-check the students on the materials they have already studied. This check is for understanding and not for memory. The student is asked to demonstrate how a concept could be applied in a given situation, or how a word representing a certain concept could be used in a sentence. This gives the student feedback in real time on his comprehension of the materials. He also learns to improve his comprehension if it is lacking.

POLICY # 11: After completing a lesson, the student is examined by the Course Supervisor for his ability to apply its contents.

When the student has completed a lesson he goes to the Course Supervisor to be examined for his skills learned on that lesson. If the Course Supervisor finds some minor things missing he tutors the student on the spot and then verbally quizzes him again on the whole lesson. If major understanding is found to be missing, the student is sent back to restudy the lesson under closer supervision of a Word Clearer. The Word Clearer spot checks the student’s skills (especially in math) by giving exercises to do. The student must be able to do three exercises correctly in a row before he is sent to the Course Supervisor to be examined again. Upon passing, the student is recognized for this accomplishment in front of the class. He then moves to the next lesson.

POLICY # 12: After completing a course, the student must pass a written examination 100%.

The written exam must be objective in testing the concepts and skills taught in that course. Basically, the student is being examined in his ability to think critically in that subject. All questions asked are on contents covered in that course. None of the questions should fall outside the course. If the student scores less than 100%, he must restudy what he missed and sit for another written exam. Upon passing the written exam, the student is awarded a certificate for course completion. The course completion is announced in the course room.

POLICY # 13: The study materials for a subject may exist in the form of simple to complex modules for different levels.

The study materials of a subject may be developed as a series of modules starting from introduction to fundamentals to advanced levels in a subject. Each module is then delivered as a course. Before one can start on a course module, he must have completed all earlier modules in that subject. The lower skills must be mastered before the student moves to learning higher skills. When a student has completed all available course modules in a subject, he may learn the tool of Subject Clearing to make further progress in that subject on his own using the data available on Internet and elsewhere.

POLICY # 14: The SLC’s focus is on High School dropouts, but anybody able to follow the discipline of word clearing may be enrolled.

If middle and primary school students want to enroll on SLC courses, they may do so if they can at least follow the discipline of word clearing. They all share the same space. Pre-K and Kindergarten level children may not be enrolled. Instead their parents may enroll themselves on Course Modules for Pre-K and Kindergarten levels so they can teach their young children on those levels at home.

POLICY # 15: There is no competition among students in the course room. The only contest is against ignorance.

The whole focus in the SLC course room is on overcoming one’s lack of knowledge. Students are not segregated by their age or level. The students on a course may be of any age. If a ten year old can handle calculus then so be it. And if an eighteen year old still needs to complete the course module on fractions, then he stays on that module until complete. There can be students studying different subjects in the same course room. Even on the same subject, the students may be on different modules. The students progress at their own pace. They are spot-checked, quizzed and examined individually for their understanding. The progress is strictly based on their knowledge and skill.

POLICY # 16: The product of an SLC is a student who is able to learn from materials by himself.

The student is encouraged at every step to apply word clearing. He is helped with troubleshooting his difficulties. When a hole becomes visible it is traced back to earlier holes in understanding until it is handled completely. The result of all this effort is that the student starts to get a first-hand experience of what it takes to be a self-learner. On top of this, if the student does the course on Subject Clearing, he is certified as a self-learner.

March 4, 2021 – 6:58 PM Categories: Education | Post a comment

The Postulates 31 … (old)

Please refer to Course in Subject Clearing.

When we apply the method of SUBJECT CLEARING to the general knowledge we inevitably end up with the following postulates.

POSTULATE # 31: Underlying an anomaly there is fixation of attention.

COROLLARY: Fixed attention generates anomalies.

Most people have their attention fixated on the body and identity. This leads to fixations on survival and politics. All reactions, as in obsessive-compulsive behavior, are fixations. When you are trying to locate an anomaly, follow the trail of fixation of attention. When you are trying to resolve an anomaly, work out the anatomy of fixations involved. Illusions arise when there are fixations. When you recognize fixations for what they are, you free yourself from them.

Fixations on body appear in the belief that one is just the body. Such a person is fixated on taking care of the body. He rarely have “out-of-body” experiences. Attention gets centered on the body as new sensations are encountered; but when that attention is suppressed it gets fixated there. Attention definitely gets fixated on the body when there are shocks, accidents, and illnesses.

In Scientology, attention gets fixated on individuality when one makes an effort to resolve present and past identities. The attention naturally settles in exploring the environment. For remedies of fixated attention refer to the POSTULATES 26, 27 and 28.

[To be continued…]

February 26, 2021 – 6:17 AM Categories: Postulates | Post a comment

The Postulates 26 – 30 (old)

Please refer to Subject Clearing Self.

When we apply the method of SUBJECT CLEARING to the general knowledge we inevitably end up with the following postulates.

POSTULATE # 26: The ability to resolve anomalies increases as the viewpoint becomes broader.

COROLLARY: The viewpoint is as broad as it is not fixated and is free to consider.

The narrowest viewpoint is one that is stuck in some mystery. The biggest mystery is when the viewpoint is unconsciousness. As the viewpoint starts to become conscious it becomes aware of the mystery. It finds itself waiting for something to come up, or happen. As it becomes aware of waiting it starts to feel anxious about its survival, and its attention gets fixated on reproducing itself. As it moves beyond the anxiety of sex, its attention gets fixated on eating. It even consumes thoughts and ideas in their literal, symbolic form. It must then overcome its fixation on “figure-figure” type of thinking. As it moves beyond this level, it makes effort to collect data and analyze it. Beyond that it simply starts to rely on emotions. As the attention gets freed up from these fixations the viewpoint is increasingly able to see things as they are, to directly know about them, to become aware of what it does not know, and finally, to know fully.

The technique of meditation that helps this broadening of viewpoint is provided at Meditation from Mystery to Knowing. The viewpoint, ultimately, becomes free of all fixed ideas, biases, prejudices and other filters and, knows things in their totality.

POSTULATE # 27: Meditation with the discipline of mindfulness helps solve anomalies.

DEFINITION: The discipline of mindfulness helps overcome filters that one may be looking through.

Anomalies exist because the viewpoint is unable to get full and clear picture of a situation. This is partly because it is unwittingly looking through certain filters. We know these filters as prejudices, biases, fixed ideas, etc.; but the person is simply not aware of them. In meditation, the Discipline of Mindfulness allows the person to view the subject of meditation clearly without such filters. This discipline is essential when meditating on “mystery to knowing” as covered in Postulate # 26.

POSTULATE # 28: Resolution of anomalies is further supported by Subject Clearing.

DEFINITION: Subject Clearing is detecting the basic postulates, assumptions and erroneous ideas present in a subject.

Anomalies also exist partly because the information is not sorted out fully. In the Information Age of today, there is plenty of data available, but skill is required to sort out the relevant data from deceptive, misleading and irrelevant information. One must identify what is really missing and be able to research it. A person can very quickly learn this skill by using the procedure of Subject Clearing. This procedure helps detect and clear up assumptions and erroneous ideas present in a subject. Subject clearing and meditation with the discipline of mindfulness go hand-in-hand.

POSTULATE # 29: The attention field continues while the identities disintegrate and regenerate.

COROLLARY: The recycling of identities supports the evolution of the attention field.

Death is the disintegration of identities into energy. From that energy new identities are generated. This recycling of identities is essential for the evolution of the attention field, which is the true self. Only the discrete identities (made up of bodies and mental matrices) die and take birth. The continuum of attention field, which is the integrated awareness of the universe, never perishes. The true eternal self is the attention field. Anomaly comes about when the self starts to believe that it is an identity. When this happens, the self gets trapped into worrying about life and death.

A soul is the idea promoted by some religions that your identity continues after death. What continues is the attention field. A religion giving hope for a finite identity to survive forever is an anomaly. One should let the identity live and die with dignity.

POSTULATE # 30: The root cause of all human troubles is the attachment to an identity (individualism).

COROLLARY: Trouble arises when individualism is given priority over the natural goals of family, groups, state, country, mankind, life, and the universe.

Ideally, the goals of an individual should be consistent with the natural goals of family, groups, state, country, mankind, life organisms, etc. When individual goals are in conflict, but still given a higher priority, then we have individualism at play. A good example of individualism is the anomalies in politics that undermine the natural growth and well being of a country. Whenever selfish intentions take priority over the welfare of family and the community, we have trouble. Peace and prosperity arise when individual goals and actions are consistent with the natural goals of family, groups, state, country, mankind, life organisms, etc.

February 24, 2021 – 5:51 AM Categories: Postulates | Post a comment

PLATO: The Psychological Problem

Reference: The Story of Philosophy

Note: The original Text is provided below.
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Summary

But behind these political problems lies the nature of man; to understand politics, we must, unfortunately, understand psychology. The state is what it is because its citizens are what they are. Therefore we need not expect to have better states until we have better men.

Human behavior, says Plato, flows from three main sources: desire, emotion, and knowledge. Desire is a bursting reservoir of energy, fundamentally sexual. Emotion is the organic resonance of experience and desire in the flow and force of the blood. Knowledge is the eye of desire and can become the pilot of the soul.

Some men are but the embodiment of desire; restless and acquisitive souls. These are the men who dominate and manipulate industry. Some are temples of emotion, who are pugnacious rather than acquisitive. These are the men who make the armies and navies of the world. And last are the few whose delight is in meditation and understanding; who yearn not for goods, nor for victory, but for knowledge. These are the men of wisdom, who stand aside unused by the world.

An effective individual action implies strong desire, warmed with emotion, and guided by knowledge. So, in a perfect state, industrial forces would produce, the military forces would protect, and the forces of knowledge would rule. Unguided by knowledge, the people are a multitude without order, like desires in disarray. Statesmanship is a science and an art; one must have lived for it and been long prepared. Only a philosopher-king is fit to guide a nation. This is the key-stone of the arch of Plato’s thought.

Comments

Plato’s division of various functions in the society parallels the caste system in Hinduism. It is as if the Shudras are disarrayed desires, brought into focus by Vaishyas, who operate in an environment protected by Kshatriyas, under the overall guidance by the Brahmins.

Original Text

But behind these political problems lies the nature of man; to understand politics, we must, unfortunately, understand psychology. “Like man, like state” (575); “governments vary as the characters of men vary; … states are made out of the human natures which are in them” (544); the state is what it is because its citizens are what they are. Therefore we need not expect to have better states until we have better men; till then all changes will leave every essential thing unchanged. “How charming people are!—always doctoring, increasing and complicating their disorders, fancying they will be cured by some nostrum which somebody advises them to try, never getting better, but always growing worse. … Are they not as good as a play, trying their hand at legislation, and imagining that by reforms they will make an end to the dishonesties and rascalities of mankind—not knowing that in reality they are cutting away at the heads of a hydra?” (425).

Let us examine for a moment the human material with which political philosophy must deal.

Human behavior, says Plato, flows from three main sources; desire, emotion, and knowledge. Desire, appetite, impulse, instinct—these are one; emotion, spirit, ambition, courage—these are one; knowledge, thought, intellect, reason—these are one. Desire has its seat in the loins; it is a bursting reservoir of energy, fundamentally sexual. Emotion has its seat in the heart, in the flow and force of the blood; it is the organic resonance of experience and desire. Knowledge has its seat in the head; it is the eye of desire and can become the pilot of the soul.

These powers and qualities are all in all men, but in divers degrees. Some men are but the embodiment of desire; restless and acquisitive souls, who are absorbed in material quests and quarrels, who burn with lust of luxuries and show, and who rate their gains always as naught compared with their ever-receding goals: these are the men who dominate and manipulate industry. But there are others who are temples of feeling and courage, who care not so much what they fight for, as for victory “in and for itself”; they are pugnacious rather than acquisitive; their pride is in power rather than in possession, their joy is on the battle-field rather than in the mart: these are the men who make the armies and navies of the world. And last are the few whose delight is in meditation and understanding; who yearn not for goods, nor for victory, but for knowledge; who leave both market and battle-field to lose themselves in the quiet clarity of secluded thought; whose will is a light rather than a fire, whose haven is not power but truth: these are the men of wisdom, who stand aside unused by the world.

Now just as effective individual action implies that desire, though warmed with emotion, is guided by knowledge; so in the perfect state the industrial forces would produce but they would not rule; the military forces would protect but they would not rule; the forces of knowledge and science and philosophy would be nourished and protected, and they would rule. Unguided by knowledge, the people are a multitude without order, like desires in disarray; the people need the guidance of philosophers as desires need the enlightenment of knowledge. “Ruin comes when the trader, whose heart is lifted up by wealth, becomes ruler” (484) ; or when the general uses his army to establish a military dictatorship. The producer is at his best in the economic field, the warrior is at his best in battle; they are both at their worst in public office; and in their crude hands politics submerges statesmanship. For statesmanship is a science and an art; one must have lived for it and been long prepared. Only a philosopher-king is fit to guide a nation. “Until philosophers are kings, or the kings and princes of this world have the spirit and power of philosophy, and wisdom and political leadership meet in the same man, … cities will never cease from ill, nor the human race” (478).

This is the key-stone of the arch of Plato’s thought.

February 22, 2021 – 5:10 AM Categories: Philosophy | Post a comment