## Motion & Force

##### Reference: A Logical Approach to Theoretical Physics

With the understanding of substance as matter and radiation, we have a better understanding of particle and void. As we break down the particle of matter it ultimately reduces to radiation.

DEFINITION II: The quantity of motion is the measure of the same, arising from the velocity and quantity of matter conjunctly.

The motion of the whole is the sum of the motions of all the parts; and therefore in a body double in quantity, with equal velocity, the motion is double; with twice the velocity, it is quadruple.

A body of matter moves in space at a uniform velocity. This velocity is shared by all particles that make up that body. The total motion of the body is the sum of the motion of all its particles. The measure of a velocity is consistent only when it is relative to the velocity of a standard reference body.

Velocities are absolute when measured relative to a reference-body at absolute rest.

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## The Immovable Space

The background of stars appears to be fixed against which the planets move. Newton, therefore, used this background of stars as the reference-body at rest. Newton, however, was not sure if the stars were at rest; so he postulated the background of space to be immovable.

The background of stars, however, appears to be fixed because of their remoteness and fixity. We observe bodies of lesser mass revolving around bodies of larger mass. Theoretically, a body of infinite mass shall be fixed relative to all bodies of lesser mass. The absolute space of Newton, then, must consist of infinite mass to be immovable.

Theoretically, infinite mass provides us with a reference-body at absolute rest.

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## Inertia

DEFINITION III: The vis insita, or innate force of matter, is a power of resisting, by which every body, as much as in it lies, endeavours to persevere in its present state, whether it be of rest, or of moving uniformly forward in a right line.

This force is ever proportional to the body whose force it is; and differs nothing from the inactivity of the mass, but in our manner of conceiving it. A body, from the inactivity of matter, is not without difficulty put out of its state of rest or motion. Upon which account, this vis insita, may, by a most significant name, be called vis inertia, or force of inactivity. But a body exerts this force only, when another force, impressed upon it, endeavours to change its condition; and the exercise of this force may be considered both as resistance and impulse; it is resistance, in so far as the body, for maintaining its present state, withstands the force impressed; it is impulse, in so far as the body, by not easily giving way to the impressed force of another, endeavours to change the state of that other. Resistance is usually ascribed to bodies at rest, and impulse to those in motion; but motion and rest, as commonly conceived, are only relatively distinguished ; nor are those bodies always truly at rest, which commonly are taken to be so.

The body, when pushed, changes in velocity; but this change is inversely proportional to the mass. The velocity of a body of large mass may only be changed with difficulty. Newton viewed this as a resistance put up by the body and called it the “force of inertia”. He then postulated that the inertia keeps the body moving at a uniform velocity in a straight line, in the absence of external forces. In other words,

Inertia smooths out the deviations from the uniform velocity of the body.

But deviations from uniform velocity can occur only when the body is being pushed around randomly. This means that mass of the body is smoothing out deviations from uniform velocity.

The body settles upon a certain uniform velocity because of the measure of its mass.

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## Force

DEFINITION IV: An impressed force is an action exerted upon a body, in order to change its state, either of rest, or of moving uniformly forward in a right line.

This force consists in the action only; and remains no longer in the body, when the action is over. For a body maintains every new state it acquires, by its vis inertia only. Impressed forces are of different origins as from percussion, from pressure, from centripetal force.

The impressed force, or push, will definitely influence the uniform velocity of the body, but that velocity shall be restored back by inertia soon after the push is over. This restoration shall occur as argued in the section above. But, according to Newton, the velocity increased by the momentary push is now maintained by inertia. This could only mean that the momentary push has somehow overcome part of the inertia for the time being.

External force overcomes a body’s inertia when the body undergoes acceleration.

The body, however, returns to its uniform velocity when the force is removed as argued in the previous section. This means that the absolute uniform velocity of a body is determined by its mass. This conclusion is supported by following observations:

• A body of lesser mass uniformly revolves around a body of greater mass.
• Radiation with no mass has velocities much greater than bodies with mass.
• A body of infinite mass shall be completely fixed relative to all other bodies.

When the external force is removed, the body’s inertia is restored, and so is restored its absolute uniform velocity.

This conclusion is supported by Faraday’s principle of Conservation of Force. Both mass and absolute uniform velocity is manifestation of force, and the total force is conserved.

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## The Cosmic Geometry

DEFINITION V: A centripetal force is that by which bodies are drawn or impelled, or any way tend, towards a point as to a centre.

Of this sort is gravity, by which bodies tend to the centre of the earth; magnetism, by which iron tends to the loadstone; and that force, whatever it is, by which the planets are perpetually drawn aside from the rectilinear motions, which otherwise they would pursue, and made to revolve in curvilinear orbits… It is necessary, that the force be of a just quantity, and it belongs to the mathematicians to find the force, that may serve exactly to retain a body in a given orbit, with a given velocity; and vice versa, to determine the curvilinear way, into which a body projected from a given place, with a given velocity, may be made to deviate from its natural rectilinear way, by means of a given force…

A centripetal force requires a fixed location. Therefore, we need to examine the subject of location.

Locations in real space correspond to the points in mathematical space. The space occupied by rigid matter has locations that are approximated by uniformly spaced grid points of a Euclidean space. This space is treated as homogenous.

Only the space occupied by matter comes close to being fixed and homogenous like the mathematical space of Euclidian Geometry.

Such homogenous space was also the idea underlying the postulate of aether. Newton assumes space to be immovable from his observation of the fixed stars. Stars did not move because they were far and had much greater mass. Relative to these stars planets moved because they were closer and had lesser mass. For space to be immovable, it must be fixed everywhere like stars. This requires infinite mass (like stars) filling the void. This is not so.

Space not occupied by matter is not homogenous as observed by fixed and moving locations in the sky.

That is why the idea of aether is rejected. In reality, only those locations in the void are fixed that are infinite in mass. Locations lesser in mass are less fixed.

The fixity of a location in the void depends on the mass at that location.

The positions in the void are not fixed automatically. A moving location, such as a planet of finite mass, does not mean that it is changing position in space. It is the position in space that itself is changing as location relative to more fixed locations. The locations in the void, whether fixed or moving, are the positions that define the space.

The geometry of the real space has mass and motion integral to it.

When the mass at a location in space is less than infinity, there is a certain degree of uncertainty associated with that location. This uncertainty is expressed in terms of its distance from a completely fixed point of infinite mass, as well as its absolute uniform velocity.

Uncertainty of locations shall determine their distances and velocities from completely fixed locations (axes).

By the very nature of this geometry, a less fixed point will revolve around a more fixed point at a distance with velocity determined by its mass. The radiation of void has no mass; therefore, its location is completely uncertain. Its radius of revolution would be infinite. It would appear to move in a straight line at near infinite velocity. That is light.

Light quanta of no mass shall appear to move in straight lines at near infinite velocity by virtue of this geometry.

In general, the points in the void shall be fixed in proportion to their mass or inertia. The location of a body is determined by its center of mass.

The uncertainty of a location is expressed by its curvature and velocity.

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## Summary

A location in the void is as fixed as its mass or inertia. Radiation has no mass but it is a substance and, therefore, it has some inertia. Since this inertia is very small compared to the inertia of mass, the velocity of radiation is many degree of magnitude greater than the velocity of bodies with mass.

Newton, essentially, chose his reference-body (the background of fixed stars) as a body of near infinite inertia and near zero velocity. Einstein, on the other hand, chose his reference-boy (light) as a body of near zero inertia and near infinite velocity.

Newton’s approach gives us a near absolute scale of velocity. Einstein’s approach gives us a near absolute scale of inertia.

Finally,

The universe is so arranged that any perturbation will right itself. This law of inertia modifies Newton’s laws of motion.

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