Reference: Postulate Mechanics (PM)
Newton’s own definition of MASS in his Principia is: “The quantity of matter is the measure of the same, arising from its density and bulk jointly.” In modern notation that is , i.e., mass equals density times volume. In everyday and much of classical physics, mass is thought of as “how much matter” an object has.
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Classical Mechanics
In classical mechanics, mass is looked upon asa fundamental property of physical objects that measures how much they resist changes in their motion (their inertia) and how strongly they participate in gravitational interactions.
Inertial mass measures resistance to acceleration when a force is applied (the mass in F= ma). Gravitational mass appears in the law of gravitation and measures how strongly an object creates and responds to gravitational fields. These two types of mass are assumed to be the same because change in mass is undetectable when motion changes.
In free fall (Einstein’s elevator experiment) if objects drift away from each other after some time, then it would mean that gravitational mass is not exactly the same as inertial mass. But this difference is extremely small. This equivalence of inertial and gravitational mass forms the basis of general relativity.
Mass is quantified more precisely by how hard it is to accelerate it. If the same force produces less acceleration, the object has more mass.
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Postulate Mechanics
In general, mass is viewed to add up in terms of some atomic unit, whether such units are assembled tightly or loosely. Mass exists as an assembly of atoms and molecules. In this view mass is strongly associated with atoms of matter. However, this view starts to change as we look at subatomic particles and radiation.
Mass represents the thickness of substance. Inside the atom, this mass is highest at the center of the atom, and it dilutes towards the periphery of the atom. This dilution of mass occurs as the layers of substance around the center increase in volume. This dilution of mass was described brilliantly by Faraday in terms of “lines of force.” These lines start from the center of the atom and spread out in space, thinning in that process. There is no limit to which these lines can thin out.
Subatomic particles are made up of diluted mass. The more diluted is the mass, the larger is the size of the subatomic particle. Ultimate dilution of mass takes place in radiation. The mass in radiation becomes undetectable, but if the “wavelength” associated with substance denotes the circumference of its particle, the “frequency” may be seen as the spin that imparts centeredness to that particle. This centeredness then expresses itself as the inertia of the particle, which is measured by mass.
So, the radiation may not have “mass,” but it has inertia that influences the linear motion of the particle. For example, the speed of light is very large but it is still finite because of its very small inertia.
The idea of intrinsic mass is thus tied strongly to the ideas of intrinsic motion, centeredness, and inertia. Actually, these concepts are so much tied together that they cannot be separated. The higher the mass the smaller is the velocity as in case of the black hole at the center of a galaxy. The smaller is the mass the higher is the velocity as in case of light.
Thus, mass and velocity of a particle seem to “balance” each other in a dynamic manner. This equilibrium may be called “inertia” for a single particle, and “gravity” for a system of particles. This view may redefine both inertia and gravity as dynamic internal forces, and not some passive phenomena.
The classical view of these concepts has not been changed. It is simply enhanced. For example, when a particle is pushed to a higher velocity and let go, instead of keep moving uniformly at that higher velocity, its velocity is adjusted by the internal force of inertia. In case of a system of particles, the velocity is adjusted by the internal force of gravity.
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Force
In Postulate Mechanics there are no external forces. An “external” force is the “internal” force of a larger system. When there is an “external” pull or push on a particle, the particle has become part of a larger system, and being subjected to its internal forces.
When the internal forces of a particle are in equilibrium, we have inertia and mass of the particle. When the internal forces of a system of particles are in equilibrium, we have gravity and “mass” of the system.
From the viewpoint of the Universe, there is no external force. The universe is all that there is. IT IS ONE!
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Considerations
No new concepts are introduced in Chapter 12; instead existing concepts are further refined. These concepts are defined in Glossary: Postulate Mechanics.
- An existing concept needing refinement is the concept of mass.
- Mass is tied with the concepts of intrinsic motion, centeredness and inertia..
- The uniform velocity is maintained by the internal force of inertia.
- Inertia acts as the internal restoring force of a particle.
- Gravity acts as the internal force of a system of particles
- Mass is a quantitative measure of these internal forces.
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