PM Chapter 8: The Fourth Law of Motion

Reference: Postulate Mechanics (PM)

Planets in our solar system move around the Sun on their own, without being pushed. Similarly, the electronic field swirls around the nucleus on its own; and so does light that travels at a tremendous speed in a straight line. 

All these are instances of intrinsic motion. This is a natural property of substance. Intrinsic motion is visible in an environment where no friction and other external forces are present.

It is a misconception that substance has no intrinsic motion.

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Newton’s Laws of Motion

Newton’s three laws of motion apply to matter of fixed mass only. These laws may be stated as follows:

(1) “Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it.”

(2) “The change of motion is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.”

(3) “To every action there is always opposed an equal reaction: or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.”

Newton’s laws do not take into account any variations in mass. The variation in mass corresponding to the range of motion of matter is infinitesimal and cannot be measured.

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Inertia

Newton attributes to matter an “innate force” that makes each body persist in its state of rest or uniform rectilinear motion, yet he explicitly denies any active internal principle that can generate new motion without external forces. Newton thus introduces “vis insita, or innate force of matter” as a power of resisting changes of motion. This is what we now call inertia, codified in the First Law of Motion.

According to Newton, if a body is accelerated to a higher velocity, then the body shall continue to move at that higher velocity even after the accelerating force is removed. The removal of force shall not change the higher velocity, which shall be maintained due to inertia.

This is like saying that if a spring is compressed by putting load on it, then the spring shall remain compressed even after that load is removed. There seems to be something missing in this picture of inertia. 

For Newton, motion is explained by the interplay of inertia and forces in absolute space and time, codified in his three laws of motion and the law of universal gravitation. According to Newton, motion does not need a continuing cause; only changes in motion do.

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The Fourth Law

But Newton was not aware of the motion inside an atom, which is intrinsic to it. That motion is not being generated by some external force. From the center of the atom to its periphery, the volume increases, and with that increase in volume the mass thins out, and the intrinsic motion increases. There is some law hidden here that relates the two intrinsic properties of substance—mass and motion—to each other. If Newton had known this he could have come up with the following fourth law of motion:

(4) As mass of substance decreases its intrinsic motion increases; for the substance is now spreading over a larger volume.

There is a lot packed in this fourth law. It seems to define the mass (thickness) and intrinsic motion of substance in terms of each other. There appears to be an inverse relationship between the two, that maintains a natural balance.

This means that an external force may temporarily disturb this balance, but when that force is removed, the balance shall return. If Newton’s inertia resists the change caused by some disturbance, then it should also revert any change once the disturbance is over, provided the mass remains the same. If a body is accelerated to a higher velocity by an external force, then, upon removal of that force, the body must return to its “equilibrium” motion for its mass.

In other words, inertia is not just a one way street. If it resists an increase in motion by an external force, then it also restores the motion after the force is removed, provided the mass does not change. 

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Motion

Motion needs to be redefined under the fourth law:

Motion is intrinsic to substance just like the thickness is intrinsic. Motion is continuous yet finite like the surface of a sphere. This gives motion a cyclic nature. With the increase of cycles, the motion becomes increasingly centered. It then takes force to move it away from that centeredness. That resistance of motion to being changed is called inertia. 

Nucleus of an atom has very small surface; it has extremely finite and highly cyclic motion; and its inertia is very high. In comparison an electron has as big a surface as a hydrogen atom; its motion is high and less cyclic; and its inertia is lower. Light has an extremely large surface; its motion is extremely high with relatively low cycles; and its inertia is infinitesimal. 

In a galaxy, the central black hole is extremely dense. As the distance from the black hole increases, the average thickness of the galactic bodies decreases and their motion increases. The galactic bodies appear to rotate around the black hole. 

Change in intrinsic motion is the consequence of mass thinning out. If average mass does not change, the intrinsic motion shall not change either. It is restored after being disturbed by an external force.

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Considerations

The major concepts introduced in Chapter 7 is INERTIA. This concepts is defined in Glossary: Postulate Mechanics.

  1. Substance has intrinsic motion. 
  2. Intrinsic motion varies inversely with thickness of substance.
  3. Newton’s laws of motion apply to matter of fixed mass.
  4. Motion of matter may vary with infinitesimal change of mass.
  5. When the mass does not change, any change in motion is restored.

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