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THE ORIGIN OF INERTIA
By: Rudolph N.J. Draaisma (l) Bangkok, June 24,1996
..But if we consider the earth to be at rest and the steady stars rotating
around it, there will be no flattening at the earth poles and no experiment
of Foucault and so on, at least according to our perception of the law of
inertia. We can solve the problem in two ways: either all motion is absolute
or our law of inertia is not correctly formulated. I prefer the second way.
The law of inertia must be formulated in such a manner that it concludes
exactly the same from the second assumption as from the first one. Herewith
it will be clear that we must take the masses of the universe into account.
1872, Ernst Mach
Let us consider two objects that move towards each other under the influence
of their mutual gravitational attraction and that no other forces are working
on these objects. For convenience we further assume that the objects are
of equal mass and thus move with equal accelerations towards the geometrical
middle of the distance between them. Without dispute we can postulate that
these objects are not subject to inertia, meaning that accelerometers placed
on them would give no reading until the objects collide with each other.
Let us further assume that a collision between the two objects would be
fully elastic. During the deformation period from such a collision, in which
the objects strongly retarded will come to a halt against each other, the
accelerometers will read the inertial forces that arise. At the moment in
which the objects momentarily are at rest, the readings will be zero and
immediately after increase with the same polarity during the onfollowing
reformation phase of the objects, in which they accelerate away from each
other. As soon as the objects loose mechanical contact with each other,
after completed reformation, and their motion away from each other has changed
from a accelerated one to a retarded one under influence of their gravitational
attraction, the accelerometers will read zero again and will show no further
reading during the continuing motions away and towards each other, until
the next collision occurs.
The situation becomes totally different however, if we instead would perform
the experiment in a manner by which the two objects are moving by the action
of a contracting / expanding spring attached between them and any gravitational
interaction is neglected. When the objects are accelerated towards each
other by the action of the contracting spring, accelerometers attached to
them would show a reading during the whole cause of that motion. Only in
two cases, one of which is when the objects have come to a halt relative
each other, when the spring is fully contracted or stretched (loaded), the
readings of the accelerometers will momentarily drop to zero and then indicate
again with the same polartity.
The other case is when the spring is fully unloaded and the objects move
at their maximum speed in the cycle (momentarily constant), the readings
of the accelerometers will instantly go through zero and change polarity.
Observe that the direction of motion, away from or towards each other, has
no influence on the readings of the accelerometers: only the direction and
magnitude of the accelerations have that effect.
In summarizing we have performed two experiments in thoughts about objects
in motion that, as far as the motions are concerned, are identical. For
the sake of good understanding I must emphasize that the de- and reformation
phases in the gravity-system are equivalent with the according contraction
and expansion phases in the spring-system. In both cases we have two objects
that move accelerated towards and away from each other and as such move
in a similar oscillating cycIe However, in one experiment inertial forces
occur where they do not in the other. As both experiments can be performed
in any environment, the choice of what ever environment or reference system
can not have an influence on the character in which the accelerometers react.
For this reason neither the laws of Newton, the Principle o+ Mach, nor Einsteins
Relativity theory can explain the occurrence or non-occurrence of inertial
effects in the above described experiments. The explanation is therefore
and obviously to be found within the systems of the moving objects themselves.
On considering the motions of the objects in the gravity-system we can without
further dispute postulate that the mechanical energy of these objects remains
constant while moving. It makes in this concept no difference if we would
consider one of the objects as being the origin of an inertial or non-inertial
reference system or assume any other arbitrary reference system. By choosing
different systems we could give the course of the motions an other appearance,
but in all thinkable reference systems the mechanical energy of the objects
in motion would remain constant. In the spring-system however, de mechanical
energy of the objects in motion is not constant. A continuous exchange of
mechanical energy between the objects and the spring takes place and also
here the choice of whatever reference system can not change anything about
that.
Let us now take a closer look at the inertial forces that occurred during
the elastic collision between the objects under gravitational influence.
When the objects are maximum deTormated and as such come to a halt against
each other, they have lost their mechanical energy; it has been transformed
to "deformation or contraction energy" that is stored in the molecule
structure of the objects. Upon this loss of mechanical energy, inertia occurs.
When the objects then reformats and regain this stored energy in Term of
kinetic energy, once again inertia cccurs.
During the following motion away from each other this kinetic energy is
gradually transformed to potential energy but the total mechanical energy
of the objects remains constant, also during and after turning on the way
back and no inertia occurs.
In view of these events we can conclude without reservation that inertia
only and alone originates from changes in mechanical energy and as such
not depends on the matter of the fixed stars or of the properties of any
other reference system. Hence:
1) INERTIAL FORCES ARE CAUSED ONLY BY CHANGES IN MECHANICAL ENERGY AND ARISE
IN THE DIRECTION OF WORKING EXTERNAL FORCES.
In consequence we can extend the validity of Newtons first law, without
the need of relativistic completions, simply by replacing the word "motion"
with the expression "mechanical energy". So doing:
2) AN OBJECT THAT IS NOT AFFECTED BY EXTERNAL FORCES WILL MAINTAIN ITS MECHANICAL
ENERGY.
With this formulation the law also applies on accelerated objects that freely
move in a gravitational field It then also brings about a new definition
of force. As the mechanical energy of freely moving objects in a gravitational
field remains unchanged, we can no longer consider gravitational attractions
as being forces. Hence, the correct definition of force must be:
3) A FORCE IS AN ACTION THAT CAUSES OR CAN CAUSE A CHANGE OF THE MECHANICAL
ENERGY OF AN OBJECT ON WHICH IT WORKS.
With these three definitions also the validity of Newtons second and third
law is extended to cover all types of motions we know.
However, the events in the above described experiments seem to be in conflict
with the widely acknowledged equivalence between gravity and inertia. As
I will show in the following, the contrary is true.
Let us first consider the so called centrifugal forces that arise when an
object rotates around a center to which it is mechanically connected. In
fact, centr1Iugal forces do not exist: there is only a centripetal force
that keeps the object in its circular trajectory. If both centripetal AND
centrifugal forces would exist simultaneously- taking each other out, there
would be no resulting force to keep the object in circular motion. Such
a rotating object simply is NOT in balance of forces. How is then the situation
for objects in gravitational orbit, f.e. a satellite orbiting around the
earth. It is a known fact by experience that astronauts are weightless in
their orbiting space capsules. For a to me ununderstandable reason it is
claimed that the cause of this is that the gravitational orce is taken out
by the centrifugal force working on the object in orbit.
If that is so, which force then is keeping the object in orbit ? As centrifugal
forces do not exist, there can be no such balance with gravitational forces
whatsoever. The conclusion can only be that there are no gravitational forces
acting as centripetal forces.
The motion of an object in gravitational orbit IS balanced, not in terms
of forces but in terms of mechanical allergy. It is simply moving according
to the general laws of inertia as 1 stated above.
This should not surprise us if we closely consider what actually happens
in Einsteins accelerated cabin in free space, without any gravitational
influence. A test person in that cabin who drops a ball will surely observe
the ball to fall to the floor of the cabin, but we can all agree that there
are no forces working on that ball; it simply moves according to Newtons
first law or better, according to definition (2) above. The ball is not
attracted by the floor of the cabin and by equivalence, neither is an object
in free fall in a gravitational field attracted by the center of that field.
Once the floor of the cabin makes contact with the ball it will increase
the mechanical, in this case the kinetic energy of the ball, causing inertia
by which the ball gains weight. By equivalence, the same thing happens in
a gravitational field; we have weight because the surface of the earth increases
our mechanical energy, causing inertia !
At this point we can find an answer as to why inertia occurs with centrifugal
rotations. The centripetal force is definitely an inertial one, but the
mechanical energy of the rotating object remains apparently constant. But
this is only apparent. If we resolve the motion of the rotating object on
the axes of the reference system of consideration, we see that the mechanical,
in this case the kinetic energy, constantly changes between zero and maximum
along these axes. Because there is no potential energy component that compensates
for these changes, as is the case with objects in gravitational orbit (!),
inertia arises. It is for this reason that gravitational orbits can not
be circles but MUST be ellipses in order to resolve the components energy
along the leading radius of orbit (!) One may object that f.e. ballistic
trajectories are parabolic ones. This is only true as long as the surface
of the earth is considered to be flat. If we take account for the curvature
of this surface, the eccentricity of the trajectory becomes smaller than
1, which makes it an ellipsoidal trajectory (!)
Let us for clarity consider such a ballistic trajectory ( assume flat earth
surface) in which a projectile is launched with a certain initial speed
and at a certain leading angle. When we resolve the speed vector in horizontal
and vertical components, we see that the horizontal component remains constant
throughout the whole of the trajectory.
The vertical component changes through zero to inverted polarity, but the
mechanical energy in the direction oi this component remains constant as
kinetic energy is fully converted to potential and vice versa. If forces
would be acting on the projectile between launch and impact, they could
only work vertically ( flat earth surface), it we neglect air resistance.
Because there is no change of mechanical energy in that direction, there
is no inertia either !
Let us now repeat the experiment but instead we launch the same projectile
with the same initial speed frictionless through a circular (!) curved pipe
between the same points of launch and impact as previously and at the same
leading angles. First of all we can observe that the highest point of this
curved pipe lies below the highest point of the previous ballistic trajectory.
This means that in the highest point of the pipe the projectile must have
a higher speed than it had in the highest point of its previous ballistic
trajectory ( because it has gained less potential energy and the total mechanical
energy must remain constant). This means that the vertical component of
the motion is in unbalance of energy; not all the kinetic energy in the
direction of that component is converted to potential energy, but part of
it has been added to the horizontal component. Because of this unbalance,
inertia will arise and as forces only can act perpendicular against the
upper inner surface of the pipe (no friction, no air resistance) this inertia
will appear as the centripetal force we know from every day experience.
This Iully complies with the definition as stated above under (1).
We have thus reached the same conclusion, that gravitational forces do not
exist, in three different ways:
1 The a.m. experiments in thoughts
2. The non-existence of centrifugal forces.
3. The equivalence between gravity and inertia.
What is new is that inertia does not follow the Principle of Mach and as
such not the General Relativity Theory in which it is incorporated, but
is caused only and alone by changes in mechanical energy and as such is
invariable with transformations between reference systems.
In addition, I feel it adequate to remind and emphasize that a true theory
must explain what is and by necessity exclude what is not. I claim that
my theory as revealed above fulfills this criterion.
Last Updated: March 17, 1999
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