INERTIA AND ITS SOURCE
Copyright © 2002 Richard J. Hanak
“I heartily beg that what I have here done may be read with forbearance; and that my labors in a subject so difficult may be examined, not so much with the view to censure, as to remedy their defects.” Isaac Newton (Preface of the Principia)
The following is a condensed paraphrasing of essential ideas in Chapter 8, INERTIA, and Chapter 14, THE SOURCE OF INERTIA, of my book A Journey Beyond the Universe Copyright 2001, Richard J. Hanak. You can read excerpts from my books for free by clicking on the above link. They are also available as inexpensive ebooks at Xlibris
End of commercial. [img]/phpBB/images/smiles/icon_biggrin.gif[/img] Note: the two paragraphs below involving the gamma factor are recent ideas and do not appear in the book.
Hold a weight in your hand with your arm extended and you will be very aware that you are exerting forces in several of your muscles. Those forces you exert are finally applied to the weight and resist the gravitational force between the weight and the Earth. The force you apply to the weight is equal in intensity and opposite in direction to that gravitational force. The situation is in accord with Newton’s third law that requires for every action of exerting a force, a reaction of exerting an equal and oppositely directed force.
Next, quickly withdraw your hand from under the weight. The weight falls. If nothing impeded the motion of the weight it would instantly fall to Earth, contrary to common experience. Therefore, something impedes that motion. As the weight falls, the gravitational force continues to exist between the weight and the Earth, so causing the velocity of the weight to increase as it falls.
We say that the inertia of the weight resists any acceleration that might be forced upon it during the time the weight falls. Despite that resistance, as Galileo would say if he were here, “it moves.” That being the case, perhaps we should think of inertial force as limiting or regulating the acceleration of the weight. The situation is analogous to electrical impedance regulating the flow of current in proportion to the impressed voltage. The inertial impedance of a body regulates its acceleration in proportion to the impressed motivating force. To find out why that is so, let us examine the nature of mass bodies, their inertia, and inertial force.
Not all bodies are electrically charged and externally surrounded by their own electric field; nor are all bodies magnetic and externally surrounded by their own magnetic field. However, all bodies possess mass, are externally surrounded by their own gravitational field, and have the property of inertia.
Newton's first law of motion tells us that an inert body cannot alter its own state of rest or motion and that such changes can only be brought about by an external force. His second law of motion describes the effect an external force has on an inert body; namely, that it causes an acceleration of the body. Laws one and two accurately summarize the meaning of the term inert body and what an external force does to an inert body. Whatever inertia is, we know at least that it is a property shared by all inert bodies.
Although Newton would not hypothesize, especially about the cause of gravitation, others speculated about the cause of inertia. Bishop Berkeley, observing that all motions could be referred to the 'fixed' stars, proposed that those distant stars cause the inertia of local objects. Berkeley reasoned that their great numbers would make up for their great distance. Much later Ernst Mach proposed that all the matter in the universe causes the inertia of local objects. Mach even suggested that if Newton's bucket of water were at rest and the universe were rotated about it, the water would form the same meniscus as when Newton rotated the bucket. It is surprising that Mach did not realize that if the Earth rotated around the bucket, let alone the whole universe, no mere meniscus would have been formed. The strongest tidal force imaginable would have emptied the bucket.
If distant bodies caused the inertia of a body, we should expect nearer bodies to cause directional variation in that inertia. Our observation of no such variation suggests that other bodies, near or far, do not cause a body’s inertia. The absence of any observed directional variation of inertia implies that the source of inertia must be uniformly distributed around an inert body. The one thing that every body has, a thing that is uniformly distributed around each body, is its own gravitational field.
The gravitational field, electrostatic field, and the magnetic field produce forces; they are force fields. All force fields store potential energy. Work must be performed to increase the intensity of a force field or to alter is spatial distribution. That work is stored in the field as potential energy. The force field resists increases to its intensity. The greater the intensity of the field, the greater is its opposition to further increases of its intensity. (It may help to think of those properties of a field in terms of an electrostatic capacitor.)
Consider a mass object sufficiently distant from other mass objects and at rest. Its gravitational field is spherically distributed in space with intensity inversely proportional to the square of the distance from the object. The intensity of the gravitational field is greatest at the surface of the object.
If a force from another body acts on that mass object it will begin to move and accelerate. As a consequence of that movement, its gravitational field will also move. However, the whole gravitational field will not move at once. A nearby forward region of the field previously at a lower intensity will now have a higher intensity pushed into it and the change will propagate through the field with a finite velocity. That change is a distortion of the field. But we have noted above that a force field resists increases to its intensity. In the case of a gravitational field, that resistance appears as a force exerted against the body, a force produced by the body’s own gravitational field. That resistance to change in the state of rest or motion is called inertial force. The source of inertia, then, is a body's own gravitational field.
Gravitational force is a manifestation of the static gravitational field of a body interacting with that of another body. Inertial force is a manifestation of the dynamic gravitational field of a body interacting with the body itself. Inertial force is not fictitious. It is a real force with a real source. Inertial force, a gravitational effect, is just as real and just as fundamental as gravitational force. Its behavior is independent of the frame of reference of an observer. It is equal and opposite to the accelerating force as required by Newton's third law. Einstein acknowledged the law equating gravitational mass and inertial mass. We now are aware that the forces by which we know them arise from the same source: gravity. They are not merely equal; they are identical.
The kinetic energy of a body, then, is stored as a distortion of its gravitational field. If such a distortion exists in a gravitational field, its body is moving. If the distortion is increasing the body is accelerating. Thus, the states of rest, unaccelerated motion, or accelerated motion of a body are potentially determinable from its own gravitational field. However, the gravitational field of a body is an attribute of a body, and is inseparable from the body. Therefore, the state of motion or rest of a body, being determined by an aspect of the body itself, and not by its relationship to any other body, is not relative rest or motion; it is absolute rest or motion.
The so-called relativistic increase in mass at high velocities, then, is not really an increase in mass. It is an increase in a body’s inertia as its gravitational field piles up ahead of it. The finite propagation velocity of a gravitational field disturbance limits the velocity of an accelerating body. There can be no such thing as a mass body without a gravitational field. A body cannot escape from its own gravitational field. That is what the Lorentz gamma factor (1-v²/c²)^(-½) is all about.
In that factor, c should now be interpreted as a variable representing the propagation velocity of a gravitational disturbance in space rather than the velocity of light. In my book I show that the propagation velocities of such disturbances decrease with increasing gravitational field strength, that electromagnetic radiation is also a propagating gravitational field disturbance, and that, therefore, the velocity of light cannot be constant.
This new interpretation of the gamma factor affecting inertia is not at all the relativistic increase in mass expressed in a different way. The relativistic increase in mass and increase in inertia concepts differ in at least two fundamental ways. The first is that if a body’s mass increases, its volume, density, or both must change. Increase in inertia requires no such changes. The second is that if a body’s mass increases, its gravitational field strength must increase in all directions. When inertia increases, the gravitational field increases only in the leading direction of the moving body.
Because this is an astronomy venue, I will close by calling to your attention that the information content in the Fraunhofer lines of starlight is independent of relative motions of source or observer. The kinds of atoms that caused those absorption lines are identifiable regardless of the amount of red or blue shift. Without those identifications the Doppler shift of starlight could not even be measured. Those identifications are also independent of red shift causes other than relative motion. Therefore, that information content of radiation is also absolute.
* Today’s against-the-mainstream has the habit of becoming tomorrow’s mainstream. – Hanak *