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In the classical physics observed in everyday life, matter is any substance that has mass and takes up space by having volume. This includes atoms and anything made up of these, but not other energy phenomena or waves such as light or sound. More generally, however, in (modern) physics, matter is not a fundamental concept because a universal definition of it is elusive; for example, the elementary constituents of atoms may be point particles, each having no volume individually.
Matter represents substance. Substance is something that can be felt and experienced. It is the essential aspect of any interaction. Without substance there can be no interaction, feeling and experience. Matter is one aspect of substance. The other aspect is field. An interface occurs between field and matter within an atom. In the atom we observe the field increasing in frequency toward the center, where it ends up as matter with mass.
Space is a manifestation of the extension property of field and matter. Without field and matter there is no space. The gaps between material objects are filled with gaseous matter and field. A vacuum is not entirely empty even when there are no atoms and molecules of gaseous material in it. There is still field in that vacuum for space to appear.
The idea that the fundamental constituents of atoms may be point particles is a mathematical conjecture. In reality, matter in atom reduces to field. The “volume” of matter reduces to cycles of field.
All the everyday objects that we can bump into, touch or squeeze are ultimately composed of atoms. This ordinary atomic matter is in turn made up of interacting subatomic particles—usually a nucleus of protons and neutrons, and a cloud of orbiting electrons. Typically, science considers these composite particles matter because they have both rest mass and volume. By contrast, massless particles, such as photons, are not considered matter, because they have neither rest mass nor volume. However, not all particles with rest mass have a classical volume, since fundamental particles such as quarks and leptons (sometimes equated with matter) are considered “point particles” with no effective size or volume. Nevertheless, quarks and leptons together make up “ordinary matter”, and their interactions contribute to the effective volume of the composite particles that make up ordinary matter.
Matter has shaped science’s viewpoint of reality. Even when field is discovered as a more basic substance, Science still uses matter as its reference point. This has led to considerable confusion in theoretical physics, which is now taken over by increasingly compartmentalized mathematical theories of Newton, Einstein and Quantum Mechanics.
Atom is not made up of point particles, but of field that is increasing in frequency toward the center of the atom. The “point particles” are high frequency regions of the field. The cycles of very high frequencies get compacted and appear as mass. Thus we have protons and neutron as regions of very high frequency and compactness at the core of the atom. The electrons are regions of relatively lower frequency and compactness that surround the nucleus of the atom.
Rest Mass is best understood as the inertia of a “particle”. Volume is best understood in terms of the cycles that make up the “particle”. Photons may be massless, but they are not inertia-less. They may not be matter but they are made up of cycles, which is the substance of field. Science, with its fixation on matter tries to evaluate field properties in terms of classical material properties of mass and volume. It refuses to go for a deeper understanding in terms of inertia and cycles. “Particles” such as quarks and leptons are mathematical conjectures that have not been encountered in reality.
Matter exists in states (or phases): the classical solid, liquid, and gas; as well as the more exotic plasma, Bose–Einstein condensates, fermionic condensates, and quark–gluon plasma.
These states of matter are essentially hybrids of field and matter.
For much of the history of the natural sciences people have contemplated the exact nature of matter. The idea that matter was built of discrete building blocks, the so-called particulate theory of matter, was first put forward by the Greek philosophers Leucippus (~490 BC) and Democritus (~470–380 BC).
Matter has been contemplated upon since the beginning of human consciousness.
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The invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is that portion of the total mass of an object or system of objects that is independent of the overall motion of the system. More precisely, it is a characteristic of the system’s total energy and momentum that is the same in all frames of reference related by Lorentz transformations. If a center of momentum frame exists for the system, then the invariant mass of a system is equal to its total mass in that “rest frame”. In other reference frames, where the system’s momentum is nonzero, the total mass (a.k.a. relativistic mass) of the system is greater than the invariant mass, but the invariant mass remains unchanged.
Due to mass-energy equivalence, the rest energy of the system is simply the invariant mass times the speed of light squared. Similarly, the total energy of the system is its total (relativistic) mass times the speed of light squared.
The word “rest” means that mass is not being pushed through the surrounding field. The surrounding field is a continuation of mass. When the mass is pushed through the surrounding field there is the resistance of inertia and acceleration. When there is no manifestation of acceleration the mass is “at rest”. A mass moving at uniform velocity is “rest mass”. When a mass is accelerating, there is force and energy in addition to the mass. This may be looked upon as “equivalent additional mass”.
The Lorentz transformations look at field from the viewpoint of matter and gives it a “mass” that is equivalent to its energy.
Systems whose four-momentum is a null vector (for example a single photon or many photons moving in exactly the same direction) have zero invariant mass, and are referred to as massless. A physical object or particle moving faster than the speed of light would have space-like four-momenta (such as the hypothesized tachyon), and these do not appear to exist. Any time-like four-momentum possesses a reference frame where the momentum (3-dimensional) is zero, which is a center of momentum frame. In this case, invariant mass is positive and is referred to as the rest mass.
A field is defined as having cycles and not mass (tight cycles at the upper end of the electromagnetic scale). Therefore, a field is massless but not “cycle-less” or “inertia-less”. To be able to move faster than light, a particle must have less inertia than a photon. The above description in terms of “four-momentum” is part of a mathematical theory.
If objects within a system are in relative motion, then the invariant mass of the whole system will differ from the sum of the objects’ rest masses. This is also equal to the total energy of the system divided by c^{2}. See mass–energy equivalence for a discussion of definitions of mass. Since the mass of systems must be measured with a weight or mass scale in a center of momentum frame in which the entire system has zero momentum, such a scale always measures the system’s invariant mass. For example, a scale would measure the kinetic energy of the molecules in a bottle of gas to be part of invariant mass of the bottle, and thus also its rest mass. The same is true for massless particles in such system, which add invariant mass and also rest mass to systems, according to their energy.
Here the definition of “invariant” or rest mass is based on a center of momentum frame. An absolute definition of “rest mass” is possible only from the reference point of zero inertia.
For an isolated massive system, the center of mass of the system moves in a straight line with a steady sub-luminal velocity (with a velocity depending on the reference frame used to view it). Thus, an observer can always be placed to move along with it. In this frame, which is the center of momentum frame, the total momentum is zero, and the system as a whole may be thought of as being “at rest” if it is a bound system (like a bottle of gas). In this frame, which exists under these assumptions, the invariant mass of the system is equal to the total system energy (in the zero-momentum frame) divided by c^{2}. This total energy in the center of momentum frame, is the minimum energy which the system may be observed to have, when seen by various observers from various inertial frames.
An isolated massive system moving at uniform velocity has zero acceleration same as a system at rest. This is the center of momentum frame. The uniform velocity is not relevant because it is based on an arbitrary reference frame.
Note that for reasons above, such a rest frame does not exist for single photons, or rays of light moving in one direction. When two or more photons move in different directions, however, a center of mass frame (or “rest frame” if the system is bound) exists. Thus, the mass of a system of several photons moving in different directions is positive, which means that an invariant mass exists for this system even though it does not exist for each photon.
The “rest mass” basically boils down to a measure of INERTIA in the reference frame of Emptiness, which provides the reference point of zero inertia.
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The biggest challenge to education is the stressed child, or the stressed student. When a child is stressed his attention is introverted onto his personal issues and he cannot learn.
The education at SLS is successful because it is addressing the challenge of stress successfully through its special curriculum. Learning requires extroverted attention. The SLS environment is very extroverting.
The general stress in the current society is increasing. It is inevitable that a certain percentage of children coming to school have stressful situations that are holding their attention. Their introverted attention then does not allow them to learn.
It is absolutely necessary for school to provide a stress-free extroverting environment so that learning can take place. If the school’s environment is also stressful then the student becomes conditioned and robotic.
At SLS, the first half hour of the day is devoted to activities that extroverts attention. The following exercise may also be used to extrovert attention.
This exercise may be conducted with a group of students, or it could be applied to a student who has difficulty learning.
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The SLS Math curriculum is designed with the following rule in mind.
The subject of mathematics starts with COUNTING. The next concept is PLACE VALUE. Place values allow one to write large numbers in a concise manner. The student must learn how to read and write large numbers before proceeding to the next concept of ADDITION.
Mathematics introduces the student to systematic learning. Counting and place values provide ways to think systematically.
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The SLS Math curriculum consists of lesson plans that are concise, relevant and easy to follow. The students are encouraged to read and understand the lessons on their own. Supervisors are there to help him as needed.
Each math lesson is followed by a large number of exercises for practice. Answers are provided for all exercise problems. The students are encouraged to do the exercises and check their answers. The correct answers reinforce the students’ confidence.
The students are encouraged to trace the incorrect answers back to the exact error made. Supervisors are there to assist them in this effort. Once a student becomes aware of the exact error he is less likely to make it again.
The student works to get the correct answers first, and then works on the speed. He learns the methods of arithmetic that make computations easier and faster.
The student may do every fifth or every tenth problem first to sample problems of different level of difficulties. He may then practice the problems that are at the right level of difficulty for him..
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When the student has studied and practiced a lesson plan he asks the supervisor to check him. The supervisor spot checks him on the concepts of the lesson and have him solve some exercise problems. If the student fails the spot-check the supervisor sends him back to study and practice some more, and come back for another spot-check. When the student passes the spot-check he goes to the class tutor to be examined on his understanding of the lesson plan.
The class tutor examines the student’s knowledge from the viewpoint of skill. He makes sure that the student has required skills. If the tutor finds some minor things missing in the student’s understanding then he tutors him on the spot. If he finds something major missing then he sends the student back to the supervisor with exact instructions on what the student must restudy and practice.
In the end, the class tutor requires the student to do three exercise problems correctly in a row. When the student answers all three problems correctly, the class tutor announces him complete on the lesson plan.
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Classes are divided by the levels of the curriculum. Levels Pre-0 and 0 are written for skill levels learned in Pre-kindergarten and Kindergarten respectively. Similarly, Levels 1 and 2 are written for skills learned in primary and middle school respectively. Each level consists of a number of lesson plans. When a student has completed all lesson plans for a level, he moves up to the next level.
If the student is found lacking the skills of a level he is assigned to that level. He is then examined for completion of each lesson plan on that level.
The SLS math course is performance based. The students can move through these levels rapidly. He is not held back because of age. Normally a student is allowed to advance through these levels at a pace most suitable for him. By the time a student has completed Level 2 he is deemed to be a self-learner. He then continues up through Level 3 and above rapidly with minimal supervision..
A higher level student is also trained on supervisor skills. He supervises at least one lower level student through to completion.
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Mass is both a property of a physical body and a measure of its resistance to acceleration (a change in its state of motion) when a net force is applied. It also determines the strength of its mutual gravitational attraction to other bodies. The basic SI unit of mass is the kilogram (kg).
In physics, mass is not the same as weight, even though mass is often determined by measuring the object’s weight using a spring scale, rather than balance scale comparing it directly with known masses. An object on the Moon would weigh less than it does on Earth because of the lower gravity, but it would still have the same mass. This is because weight is a force, while mass is the property that (along with gravity) determines the strength of this force.
In Newtonian physics, mass can be generalized as the amount of matter in an object. However, at very high speeds, special relativity states that the kinetic energy of its motion becomes a significant additional source of mass. Thus, any stationary body having mass has an equivalent amount of energy, and all forms of energy resist acceleration by a force and have gravitational attraction. In modern physics, matter is not a fundamental concept because its definition has proven elusive.
There are several distinct phenomena which can be used to measure mass. Although some theorists have speculated that some of these phenomena could be independent of each other, current experiments have found no difference in results regardless of how it is measured:
The mass of an object determines its acceleration in the presence of an applied force. The inertia and the inertial mass describe the same properties of physical bodies at the qualitative and quantitative level respectively, by other words, the mass quantitatively describes the inertia. According to Newton’s second law of motion, if a body of fixed mass m is subjected to a single force F, its acceleration a is given by F/m. A body’s mass also determines the degree to which it generates or is affected by a gravitational field. If a first body of mass m_{A} is placed at a distance r (center of mass to center of mass) from a second body of mass m_{B}, each body is subject to an attractive force F_{g} = Gm_{A}m_{B}/r^{2}, where G = 6.67×10^{−11} N kg^{−2} m^{2} is the “universal gravitational constant”. This is sometimes referred to as gravitational mass. Repeated experiments since the 17th century have demonstrated that inertial and gravitational mass are identical; since 1915, this observation has been entailed a priori in the equivalence principle of general relativity.
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