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BOOK: Creative Education

BOOK: The Disturbance Theory

BOOK: The Mindfulness Approach

A Critique of Scientology Philosophy


Remedial Math Level 2


Middle School Review 2

Lesson 1: Integers

For exercise: Integer Problems from Dubb

For certification solve 3 randomly selected problems each 

(1) From mixed problems 57 to 75 in 10 minutes.

Lesson 2: Arithmetic Expression

For exercise: Arithmetic Expression Problems from Dubbs

For certification solve 3 randomly selected problems each 

(1) From word problems 1 to 25 in 10 minutes.

(2) From word problems 26 to 50 in 10 minutes.

Lesson 3: Factoring

For exercise: Factoring Problems from Dubb

For certification solve 3 randomly selected problems each

(1) From Article 87 (1 to 21) in 5 minutes.

(2) From Article 88 (1 to 22) in 5 minutes.

(3) From Article 89 (1 to 35 – 1 word problem) in 10 minutes.

(4) From Article 90 (1 to 37 – 1 word problem) in 10 minutes.

(5) From Article 91 (1 to 21 – 1 word problem) in 10 minutes.

Lesson 4: Fractions

For exercise: Fraction Problems from Dubb

For certification solve 3 randomly selected problems each

(1) From Article 103 (1 to 20) in 10 minutes.

(2) From Article 104 (1 to 30) in 10 minutes.

(3) From Article 105 (1 to 30) in 10 minutes.

(4) From Article 106 (1 to 25) in 10 minutes.

(5) From Article 107 (1 to 30) in 10 minutes.

(6) From Article 108 (1 to 40) in 10 minutes.

(7) From Article 108 GCD (1 to 12) in 10 minutes.

(8) From Article 108 LCM (1 to 12) in 10 minutes.

(9) From Article 111 (1 to 34 – 1 word problem) in 10 minutes.

(10) From Article 114 (1 to 38 – 1 word problem) in 10 minutes.

(11) From Article 115 (1 to 21) in 10 minutes.

(12) From Article 118 (1 to 35) in 10 minutes.

(13) From Article 119 (1 to 42 – 1 word problem) in 10 minutes.

(14) From Article 120 (1 to 20) in 10 minutes.

(15) From Article 121 (1 to 14) in 10 minutes.

(16) From Article 122 (1 to 20) in 10 minutes.

(17) From Article 129 (1 to 102) in 10 minutes.

Lesson 5: Decimals

For exercise: Decimal Problems from Dubb

For certification solve 3 randomly selected problems each

(1) From Article 135 (1 to 50) in 5 minutes.

(2) From Article 136 (1 to 18) in 5 minutes.

(3) From Article 141 (1 to 31) in 10 minutes.

(4) From Article 142 (1 to 30) in 10 minutes.

(5) From Article 143 (1 to 20 – one word problem) in 10 minutes.

(6) From Article 144 (1 to 30 – one word problem) in 10 minutes.

(7) From Article 147 (1 to 35 – one word problem) in 10 minutes.

(8) From Article 150 (1 to 37 – one word problem) in 10 minutes.



To be used for students needing more details.

MS B1 Mixed Operations

MS B2 Integers

MS B3 Factors

MS B4 Frac Props

MS B5 Frac Ops

MS B6 Decimals


Einstein’s Theory of Quantum

Qunatum Mechanics

Reference: Disturbance Theory


The Fundamentals

In 1900 when Planck was trying to find a relationship between the intensity of the electromagnetic radiation emitted by a black body and the frequency of the radiation, he could not come up with a theory using the classical approach that explained the experimentally observed black-body spectrum. In desperation he took a statistical approach, making an arbitrary postulate that energy of the emitted radiation is proportional to its frequency. This provided a curve that fitted the experimental data. [See Black-body radiation (Notes)]. Since frequency has a discrete nature, it meant that energy was discontinuous for radiation. This went against the classical notion of Maxwell’s theory that electromagnetic energy is a continuous function in space. Planck looked at his proportionality postulate as a mathematical convenience. He did not believe in the quantum interpretation of his postulate.

About this time Einstein was investigating the factors underlying the atomic phenomena. He was impressed by the success of statistical mechanics in this area, especially with kinetic theory of gases. He decided to apply statistical approach to the atomic theory to derive other material properties. Einstein estimated the accuracy of his assumptions by using them to calculate the Avogadro’s number. He thus verified his theoretical approach to the determination of viscosity (molecular attraction) and distribution coefficient in liquids. This approach has since been found very useful by molecular physicists and chemists.

Einstein was thus testing his assumptions as they applied to the yet theoretical domain of atoms and molecules through the calculation of Avogadro’s number. He then analyzed the Brownian motion of microscopic particles suspended in liquid, which appeared to be “self-induced”. He developed an original statistical approach to determine the relationship between the mean square fluctuation of suspended particles and the distribution coefficient of liquid. Once again, Einstein confirmed his assumptions by calculating the Avogadro’s number. This time his work was immediately verified experimentally. This helped establish the physical reality of atoms and molecules for scientists who were very skeptical before.

Simultaneously, Einstein looked into the distribution of energy density in the blackbody radiation. He analyzed the work of Planck and Wien and showed mathematically that the energy density of radiation, which appeared to be continuous at lower frequencies, became particle-like at higher frequencies. The postulate of Maxwell’s theory that the energy of radiation was a continuous function in space was valid at lower frequencies only. At higher frequencies the behavior of energy density of radiation could be compared to the results from kinetic theory of gases. Einstein thus verified Planck’s postulate that energy of radiation was proportional to its frequency. But Einstein then did something more. He proposed the idea of “light quanta” based on Planck’s postulate and used it to explain the photoelectric effect. He proposed an energy equation for the photoelectric effect that could determine the Planck’s constant experimentally. (See Einstein’s Conception of Light Quanta).

Robert A. Millikan, who vehemently disagreed with the idea of “light quanta”, spent some ten years testing Einstein equation and he did the most exacting experiments. He found that “Einstein’s photoelectric equation · · · appears in every case to predict exactly the observed results.” This turned Planck’s theoretical idea of “energy quanta” into the physical reality of “light quanta”, which came to be known later as “photon”. Einstein also established equivalence between energy and matter that later gave rise to the harvesting of nuclear energy.

In 1905 Einstein published these researches in four different papers. He basically established a relationship between energy and matter. It showed that energy of electromagnetic radiation coagulated with increasing frequency. Thus light became particle-like at higher frequencies, and at the upper reaches of frequency spectrum the limiting condition appeared to be matter. This conclusion supported the idea of particles, such as electrons, in the Gamma range of the electromagnetic spectrum. Thus electromagnetic field was a more fundamental substance than matter. Einstein thus established the fundamentals of the quantum theory.


The Theory of Relativity

It was the increasing frequency that coagulated energy into matter. Therefore, Einstein’s fifth paper in 1905 investigated the fundamentals of motion. The obvious questions were, “Is there an absolute rest point? What happens to electromagnetic radiation as frequency reduces to zero? What is the limiting condition then?”

In Newtonian Mechanics the absolute rest point was assumed to be the stars fixed in the firmament. Maxwell’s theory also declared the velocity of light to be absolute, and this was confirmed by most exacting experimental evidence. Material velocities did not seem to add or subtract to the velocity of light. When the velocity of light was taken to be an absolute constant, the Lorentz transformations showed that the very characteristics of space and time were affected.

Einstein observed that the simultaneity of time could not be maintained when there were vast differences in the velocities, such as those between light and matter. In his view time could not be treated as absolute. He gave up on the idea of an absolute rest point and advance a theory of relativity based on the following postulates.

  1. All physical laws have the same form in all inertial frames (i.e. frames of references which move rectilinearly with a constant velocity with respect to each other);

  2. The velocity of light is same in all inertial frames.

With these postulates Einstein could derive the Lorentz transformations newly. He then showed that as the difference in velocities between two inertial frames increased, the characteristics of space and time changed in the form of “length contraction” and “time dilation”.

In other words, space and time become “diluted” with increase in relative velocity. 


The Glitch

Einstein’s theory of relativity was extremely successful in explaining previously unexplained phenomena in the cosmological realm where light interacted with matter. But, when it came to the quantum realm, where light interacted with atomic structure, Einstein could not apply his theory of relativity successfully in spite of a lifelong of efforts. Einstein was very troubled by this failure.

Thus, a new subject of Quantum Mechanics came about that lacked a theoretical basis of physical explanations, and which was based entirely on mathematical relationships.

Theoretical physics seems to be stuck at the postulates that Einstein made to derive his theory of relativity. These postulates must be examined closely.


Einstein’s 1905 Paper on Light Quanta

Light quanta

Reference: Disturbance Theory


In his very first paper published in 1905 Einstein establishes the concept of “energy quanta” or “light quanta”. The manifestation of light quantum (photon) becomes more pronounced as the frequency of radiation increases.

Einstein’s original paper translated by D. TER HAAR

Einstein’s original paper with comments

In his paper Einstein analyzes the work done by Wien and Planck on Black Body radiation [see Black-body radiation (Notes)] and makes the following fundamental observations.

  1. According to Maxwell’s theory, the energy must be considered to be a continuous function in space for all purely electromagnetic phenomena, thus also for light.

  2. According to Kinetic Theory of gases, the energy in a volume can be written as a sum of energy of a finite number of particles localized in space, which move without being divided.

  3. The classical treatment of energy as a continuous function in space fails to predict the energy spectrum observed for the black body radiation.

  4. Max Planck’s postulate, “energy is proportional to the frequency of radiation” completely predicts the energy spectrum observed for the black body radiation.

  5. Planck’s equation provides the classical results for low frequencies, showing that radiation energy is a continuous function in space at low frequencies only.

  6. Using Wein’s law that matches experimental observations of black-body radiation at high frequencies, Einstein proves the energy behavior of radiation to be particle-like. From this arises Einstein’s proposal of “energy quanta” or “light quanta”.

  7. Use of “statistical probability” by Boltzmann is compatible with the principles of physics, and they can be used to estimate the magnitude of such energy quanta.

  8. The idea of energy quanta is compatible with the observations made in photoluminescence resulting in the Stoke’s Rule.

  9. The calculated magnitude of “energy quanta” is in line with the experimental data obtained from photoelectricity.

  10. In conclusion, the concept of energy quanta is also compatible with ionization of gases by ultraviolet light.


The Quantum Phenomena


Reference: Disturbance Theory


The electromagnetic cycles are packed so closely in the nucleus of an atom that they may be considered to be “collapsed”. By “collapsed” we mean that that the electromagnetic cycles have become infinitesimal and they cannot be distinguished one from another. Therefore, these cycles form a continuum within the nucleus.  This condition is identified as “mass”.

The Newtonian mechanics is applicable within the material domain where it treats space and time as absolute and independent of each other.  This is possible because the continuum of mass provides constancy to space and time. Thus, arbitrary material units may be used to measure the distance between two points, and the time interval between two events.

Underlying the material domain is the domain of electromagnetic field. In this domain the frequencies are smaller and the variations in them are depicted as a spectrum (see The Spectrum of Substance ). The cycles of these frequencies may be distinguished from one other and counted. In short, we do not have a continuum in the electromagnetic domain; and no constancy of space and time. The theory of relativity identifies this condition as “length contraction” and “time dilation” from the perspective of the material domain.

The quantum phenomenon arises in the electromagnetic domain due to the absence of continuum.

In the electromagnetic domain, length and time are determined by counting the number of cycles between two points. Thus, each electromagnetic cycle is a quantum entity, and length and time do not exist within the cycle.

The fundamental quantum entity is the electromagnetic cycle.

Since both length and time are “counted” by the number of cycles, they are not independent of each other. They are related by the universal constant “c” known as the speed of light.

This quantum characteristic of the electromagnetic cycle may also explain the phenomenon of quantum entanglement. At very low frequencies, one electromagnetic cycle may extend to hundreds of miles when it is superimposed on the material domain. Any action within the span of this cycle will appear as simultaneous and instantaneous from the perspective of material domain.

Quantum entanglement will then be a phenomenon that will occur at very low frequencies. The lower is the frequency the farther will the effects be observed.


Anxiety & Resolution

Reference: Mindfulness Approach


Anxiety comes when a person is not certain or confident about the outcome. He is lacking confidence because he does not have clear guidelines or principles to follow. The basic guideline is logic consisting of a sense of continuity, harmony and consistency. In its place this person has confusion, which goes back to past experiences. Such experiences contain confusion that caused anxiety in the past.

The resolution of anxiety requires that one looks at past experiences of anxiety as far back as possible. The person spots the precise confusion present in each of those experiences and compiles a list of those confusions without trying to resolve them. This may take hours if not days.

A complete and precise list of all such confusions must be made first, before any effort is made to resolve.

The next action would be to meditate on that list with mindfulness to see if all these confusions point to a single basic confusion! The person meditates and spots the confusion that is uppermost in his mind. He then simply meditates on that confusion with mindfulness.

Reduce all those confusions to a basic confusion that must be resolved.

The person isolates things from that basic confusion that do not make sense. Such things are illogical because they contain discontinuities, disharmonies or inconsistencies. He traces each discontinuity, disharmony or inconsistency to gaps in awareness.

Meditate on the basic confusion to discover gaps in awareness.

The person looks at each gap more closely. If something comes up then fine, otherwise he moves on to find another gap to examine. All such gaps are interrelated anyway. As he continues to examine these gaps a missing piece will fall into place and, sooner or later, his anxiety will start to lessen.

Let the realization occur by itself without being forced.

The person then continues with this process until all anxiety is gone.