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BOOK: The Mindfulness Approach
BOOK: The Disturbance Theory
BOOK: Education in Information Age
Remedial Math
A Critique of Scientology Philosophy
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When there is confusion in a subject, the first thing to do is to isolate the area of confusion and check the understanding of the words used to explain that area. Hopefully that would handle the confusion or, at least, narrow it down.
Words and symbols form our basic understanding.
A word can have not only many definitions but also many shades of definitions. It is not only a missing definition but also a missing correct definition that generates confusion. Different contexts may require different definitions, or shades of definitions, for the same word.
It is the tendency of the mind to fill the missing definitions by preconceived notions. This leads to contradictions and conflicts in the mind. Therefore, it is very important to examine the definitions of the words in the context at hand. Correct definitions bring continuity, harmony and consistency to the understanding of the materials.
The following procedure helps determine correct definitions for words in study materials.
Look up the word that is not quite clear to you. You may find the broad concept listed under ‘history’, ‘origin’, or ‘derivation’ of the word in a dictionary.
The following broad concepts for some words are taken from “Dictionary of Word Origins” by John Ayto
The word STUDY comes from a Latin word meaning “eagerness, intense application”.
The word MATHEMATICS comes from a Greek word meaning “something learned”.
The word ARITHMETIC comes from Greek, ARITHMOS number + TECHNE skill, which means “number skill”.
Next you may look up the definitions provided for that word. A good but simple dictionary is very useful.
Please note that small words like “a”, “of”, “in”, et cetera, have many different definitions. A wrong interpretation of such words may completely alter the idea expressed.
Visualize the definitions as you look them up. To get a better idea you may bring up the images for that word on the Internet. Make examples of different definitions to understand the differences. Make sentences to get further clarity on a definition. Relate the different definitions to your experiences to make them real.
If a definition contains a word that is not quite clear then look it up following this procedure. This may sometime get you in a long word chain. Keep an account of the words that you are looking up. Cross out the words from the list as you clear them up.
NOTE: It is okay to look up the same word as many times as necessary. Each time you look up a word you may pick up a new dimension of its meaning.
Once you have understood the basic concept, and have adequately examined all the definitions of the word, determine the definition that fits the context the best. Then review that area to see if the confusion has cleared up.
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Keep examining the definition of words in that area until the confusion clears up fully. If the confusion persists in spite of your best efforts at “word clearing” then apply the procedure of “subject clearing”.
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This is continuation of the examination of Einstein’s postulates underlying his theory of Relativity, specifically, how these postulates were translated into his mathematics.
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Einstein takes up a system of coordinates in which equations of Newtonian mechanics hold well. These he calls inertial frames in which a body remains at rest or moves with constant linear velocity unless acted upon by forces. This property of a body is called inertia.
Inertia represents the resistance to change in motion of a body in space. When this resistance is overcome there is acceleration. We have assumed all along that space is completely permeable to matter. This is not so as evidenced by inertia.
Therefore, matter is ‘stationary’ relative to space when there is no acceleration. All inertial frames in “uniform motion” are actually stationary relative to space. This we identified earlier as the space reference frame (SRF).
A particle is essentially a disturbance propagating through space. This particle of disturbance has a configuration. As the complexity of this configuration increases, the inertia of the particle also increases, and its speed of propagation decreases. A light particle has the simplest configuration and its speed of propagation is ‘c’. An electron is a particle of complex configuration, whose speed is less than 1% of the speed of light. A neutron is a still more complex particle whose speed is thousand times still less.
Einstein’s “material point” refers to a matter particle that has a configuration more complex than that of a neutron. In its most complex configuration a matter particle shall have a speed that is infinitesimal compared to ‘c’. Euclidean geometry and Cartesian co-ordinates apply only to this extreme case of a matter particle. They do not apply to light particles.
All motion considered by Einstein is in reference to matter. This we identified earlier as the material reference frame (MRF). MRF represents a limiting case of a more general SRF that addresses a much wider range of particle configurations.
The natural speed of propagation in space then depends on the complexity of configuration of a disturbance as particle. This we perceive as motion that is balanced by the inertia of the particle. Any change in this balance is perceived as acceleration. Acceleration implies presence of force.
Motion is described by the property of TIME. Time essentially describes the sequence of change. A change is referred back to the previous step in the sequence. Thus, time lies in the continuity of a sequence, and it is unique to the configuration of that sequence.
To compare two time sequences in terms of simultaneity they must have comparable configurations. This is reflected in comparability in terms of inertia of the particles. The property of time shall then be a function of inertia. The “time” that we are used to is tied with the material level of inertia. In other words, our experience of time depends on the inertial characteristic of MRF (material reference frame).
The “time” associated with light shall depend on the configuration of the light particle or its inertia. To consider simultaneity of time for matter and light particles, their relative inertia shall have to be taken into account.
The “time characteristics” of particles of different inertia shall be measurable from a “particle” that has no inertia. Such a particle may be postulated as “undisturbed space”. We can then assess the “simultaneity” of two particles by determining their “time characteristics” in terms of their inertia.
The complexity of configuration, and thus the inertia of a particle may be measured in terms of “disturbance levels” as described earlier in The Disturbance Theory. On this scale the disturbance level of zero is a frequency of 1. The disturbance level of 77.6 represents a neutron. All higher disturbance levels represent matter. Earth has a disturbance level of about 235.
At the disturbance levels of matter the wavelength, period and speed become infinitesimal; and the sinusoidal variations in time and space become imperceptible. Time and space then acquire an appearance of constancy that does not exist at electrodynamic and quantum levels.
The idea of observer basically represents the characteristics of the reference frame that is being used to interpret motion. The time measured by Einstein’s clocks follows the inertial characteristics of matter. To combine the velocity of light with material velocity would be equivalent to assuming light to have same inertial characteristics as matter. Any mathematics that combines the velocity of light with material velocity using simple addition or subtraction shall lead to erroneous results. It would be like adding a penny to a dollar and calling it two coins of same magnitude.
Unfortunately, Einstein’s mathematics does just that in the rest of this section. We shall skip this mathematics and focus on those aspects of Einstein’s theory that make correct predictions of physical phenomena. Hopefully, a closer look at such aspects will provide better insight into Einstein’s thinking.
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This examination of Einstein’s 1905 paper on relativity (see the link above) is being carried out to see if Einstein’s original postulates can be modified to bring better consistency among the Theory of Relativity and Newtonian Mechanics.
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This introductory paragraph from the paper mentions asymmetry observed in the relative motion between a magnet and a conductor. This asymmetry occurs in the reference frame of the lab, which results in different interpretation of the same phenomenon.
This “asymmetry” disappears when we use the magnetic lines of force, which are attached to the magnet, as the reference frame. The conductor moves relative to these lines of force the same way in either case producing the same result.
This paragraph states that no motion of the earth relatively to the “light medium” has been discovered. This is incorrect because the very fact of radial acceleration due to inertia is a proof of motion relatively to the “light medium”.
This “light medium” is the space itself as established by Maxwell’s equations. The very fact that the speed of light is determined exclusively by the permeability and permittivity of space establishes space as the “light medium”. Light is a disturbance in space.
It was assumed that space could not be a medium because it could not be rigid to electromagnetic waves, while being completely permeable to matter. It was not realized that space puts up resistance to motion relative to it in the form of inertia. Thus space is not completely permeable to matter. Space resists the motion of matter. This resistance shows up as inertia.
Any motion relative to space requires force and it is accompanied by acceleration. Moons are always accelerating toward their planets. Planets are always accelerating toward their stars. Stars are always accelerating toward the center of their galaxies and so on. There may appear to be no acceleration in the direction tangential to an orbit. But there is always a radial acceleration toward some center. When there is no force or acceleration, there is no motion relative to space.
There is no uniform motion without acceleration that travels in straight line. All Newtonian or Einstenian inertial frames are actually a single frame, which is at rest relative to space. This nicely explains the Principle of Relativity.
Any motion in this single frame is resisted by inertia. A fixed velocity in this frame shall result from a balance between acceleration and inertia. The velocity of light is finite and constant because there is a balance between an electromagnetic push of disturbance and the inertia of disturbed space.
If a Michelson-Morley experiment is conducted to compare the speed of light in the direction tangential to earth’s orbit and also normal to it, it is likely to observe a difference due to the centripetal acceleration of earth. Einstein’s assumption that there is no motion of the earth relative to the “light medium” is not fully justified.
An absence of inertia may be used as an absolute rest point from which to measure motion. Any motion relative to space will manifest some force due to inertia as acceleration.
The phenomena of electrodynamics as well as of mechanics, has inertia as a property common between them that can be referenced from the idea of undisturbed space.
Einstein postulates as the Principle of Relativity: “The same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good.”
This postulate assumes that light has same inertial characteristics as matter. This assumption is not justified.
Einstein makes another postulate: “Light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body.”
This postulate assumes that there is no property shared by light with the body that emits it, which control their respective velocities. This assumption is also not justified because the velocities of light and the emitting body are related by their respective inertia relative to space.
Essentially, Einstein uses RIGID MATTER as its reference frame. We may call it the Material Reference Frame or MRF. This reference frame does not properly account for the inertia associated with light and sub-atomic particles. It actually considers inertia of light particle (photon) to be zero.
The proper reference frame would however be SPACE. We may call it the Space Reference Frame or SRF. This reference frame shall account for the inertia associated with light and sub-atomic particles. It would not represent space by rigid coordinates. The SRF coordinate system shall take into account the varying characteristics of inertia of the particles being considered.
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On June 9^{th}, 1952, Einstein stated in the preface of the 15^{th} edition of his “Relativity–The Special and General Theory”,
“In this edition I have added, as a fifth appendix, a presentation of my views on the problem of space in general and on the gradual modifications of our ideas on space resulting from the influence of the relativistic viewpoint. I wished to show that space-time is not necessarily something to which one can ascribe a separate existence, independently of the actual objects of physical reality. Physical objects are not in space, but these objects are spatially extended. In this way the concept of “empty space” loses is meaning.”
The Disturbance Theory is based on the postulate that space, when disturbed, breaks into electric and magnetic fields. In other words, when space and time come together they transform into energy of disturbance. This transition is seamless, meaning that space, time and energy are intimately related. They show up as wavelength, period and frequency of the disturbance.
The electromagnetic spectrum represents increasing state of disturbance, which ranges from low frequency radio waves to high frequency gamma rays. The disturbance starts to condense in the range of gamma rays until it transforms into matter. In this sense, space, time, energy and matter are fundamentally related.
All stages of the electromagnetic spectrum may be found in the structure of an atom, if we consider the atomic boundary to extend all the way to space. The most condensed disturbance forms the nucleus of the atom.
Atoms may be looked upon as tiny whirlpools in the sea of electromagnetic field of disturbed space.
The above shows that not only space, time and energy are intimately related, the energy appears as mass at very high disturbance levels.
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The undisturbed space has no bounds or form. It acquires a form only when it is disturbed. The disturbance appears as a dynamic electromagnetic field that has gradients of disturbance levels. A gradient of disturbance levels has the form of acceleration, force or gravity. Within a uniform disturbance level there is stillness or constant velocity.
The disturbance levels are defined by their wavelength, period and frequency. The wavelength and period maintain a constant ratio ‘c’. The frequency is the inverse of period. This may be shown symbolically as
λ / T = c
f = 1/T
Where, λ is the wavelength associated with space;
T is the period associated with time;
c is a universal constant referred to as speed of light;
and, f is the frequency associated with energy
The electromagnetic spectrum covers a large range of frequencies as radio and micro waves, infra-red, visible and ultra-violet light, X and Gamma ionizing radiation, and subatomic particles. These frequencies may be expressed more conveniently on a logarithmic scale of base 2. The logarithmic form of frequency is referred to as Disturbance Level (D).
D = log_{2} (f)
So we have a fundamental relationship among space, time, energy and matter.
By equating space-time with energy-mass, the Disturbance Theory hopes to bring about an interpretation that makes the theory of relativity consistent with quantum mechanics and Newton’s theory of motion.
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We live on a material plane, and so we view space, time and energy from the viewpoint of matter. Our reality is the fact of matter.
Matter appears at the upper end of the electromagnetic spectrum. It is highly condensed disturbance. If we look at the wavelength of disturbance as the unit of space, it is infinitesimal at the level of matter. Similarly, the unit of time as period of disturbance is also infinitesimal at the level of matter. This makes the calculus of space and time possible. But this is so at the level of matter only and not at other parts of the electromagnetic spectrum. There is continuity at disturbance levels lower than matter but it is of a different sort. At these parts of the electromagnetic spectrum the wavelength and period is finite and the reality can be very different, but we do not get to experience it ordinarily.
We live on earth. We are connected to matter all the time. Therefore, we perceive space and time in infinitesimal increments. This brings smoothness of continuity to our physical senses. It forms the basis of our knowledge. Euclidean geometry and Newtonian mechanics has its basis in it.
But how is it out in the interstellar space? How does one experience space and time away from matter—even away from the matter of the spaceship that carried us there, or away from the matter that constitutes our bodies? What is space and time like when its units in terms of wavelength and period are no longer infinitesimal?
How do we visualize an electromagnetic field spread over vast interstellar space in which finite wavelength, period and frequency are changing dynamically. Here the gradients in frequencies bring about the sense of acceleration, force or gravity. It is like living within Faraday’s lines of force that come together, and then spread out in an eternal cosmic dance.
Like a blurred vision, the location in space and time gets blurred far from material surface of a planet. A location can be defined with pin-point precision on a material surface only. The GPS signals that travel to a satellite and back require relativistic correction. This is because the location of satellite is a bit blurred relative to the locations on earth.
The theory of relativity gets it right about the blurring of the very nature of space and time.
Dark energy and matter in the interstellar space has no reasonable explanation at the moment. The concept of disturbed space might be able to provide an explanation.
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Relativistic mathematics of Einstein is based on MRF (material reference frame). The Disturbance Theory proposes mathematics based on SRF (space reference frame). SRF math is yet to be developed. It should lead to similar space-time correction.
MRF math uses the concept of velocity, which is applicable only for a specialized view of space and time near the surfaces of planets.
SRF math shall use the concept of disturbance levels, instead of velocity.
The concept of disturbance level is applicable to all locations near or far from planets.
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