Although the motions of the objects in the gravity- and the spring model are similar, they differ significantly in terms of mechanical energy and so the Laws of Newton seem not to always apply, but with a slight modification they do, as we will see in the following.

In the gravity-model on the previous page, we can conclude that the mechanical energy of the objects in free motion remains constant. This is not the case in the spring-model, where an ongoing exchange of mechanical energy between the objects and the spring takes place. In this context it makes no difference if we would choose one object, or the other, as origin of the reference system of observation. By choosing different reference systems, in which an observer is at rest, we could give the course of the motions another appearance, but in all thinkable reference systems the readings of the accelerometers would remain the same. This indicates "absolute motion" - related to absolute energy (First Law of Thermo).

It is just this what all scientists, ever since the days of Newton, have missed to consider; they only considered the motions and so they came to the wrong conclusions. Nevertheless, their theories describe correctly what is observed, but the physical understanding of them is wrong, Mach's Principle being one of them, the misconception of centrifugal forces being an other, and so on.

By virtue of the invariance of the accelerometers' readings with any reference system of observation, the conclusion must be that inertia originates only and alone from changes in mechanical energy. I deliberately do not say 'kinetic' energy, because that would give the wrong idea about mechanically rotating or orbiting objects, having a constant kinetic energy, but yet inertia. This is because such motions lack potential energy and therefore 'mechanical' energy is the correct expression to cover ALL motions.
In consequence, inertia does not depend on the state of motion, the matter of the distant stars,⁽¹⁾ nor the properties of any reference system. Hence:

1) INERTIAL FORCES ARE CAUSED BY CHANGES IN MECHANICAL ENERGY ONLY AND ARISE IN THE OPPOSITE DIRECTION OF CAUSING EXTERNAL FORCES.

In consequence, we can extend the validity of the first law of Newton, without the need of relativistic or other amendments, simply by replacing the word "motion" with the expression "state of mechanical energy". So doing:

2) AN OBJECT THAT IS NOT AFFECTED BY EXTERNAL FORCES WILL MAINTAIN ITS STATE OF MECHANICAL ENERGY.

With "state of mechanical energy" is meant the amount of mechanical energy along the resolved components of the motion in any preferred reference system of observation and not just the numerical value of the object's mechanical energy. Although energy has no direction (is not a vector) in today's physics, when it comes to objects in circular motion, there is inertia if the moving object is mechanically fixed to the center of rotation (centripetal forces) and not if it is fixed by gravitation. The main difference here is, that in the case of an object in gravitational orbit, this object has potential energy as well, which an object in mechanical rotation has not (relative the center of orbit/rotation). In gravitational orbit, the potential and kinetic components take each other out, by which inertia does not arise and so we are bound to consider mechanical energy along the resolved componets of the overall motion. As we will see in the following, this condition is crucial in order to apply Newton's second law also on accelerated objects in free motion in gravitational fields.

In the following, this condition is understood in "change of mechanical energy". As a consequence, the a.m. definition(1) brings about a new definition of "force". As the state of mechanical energy of an object in free fall remains constant, preventing inertial forces to occur, we can no longer consider gravitational "attractions" as forces. Hence, the correct definition of "force" must be:

3) A FORCE IS AN ACTION THAT CAUSES, OR CAN CAUSE A CHANGE IN THE STATE OF MECHANICAL ENERGY OF AN OBJECT ON WHICH IT WORKS.

With these three definitions the validity of Newton's first and second law is extended to cover all types of motion we know. What about the third law?

The third law basically says that action = reaction, or in another words, you cannot lift yourself by pulling in your own hair. In my view, the third law is not directly related to inertia. A reaction force, that is not due to a change of mechanical energy of the object on which it works, is not an inertial one. Is it a force at all, according to a.m. definition(3) ? No, then it is not a force. If we for instance would be pushing against a heavy block on the ground, but not hard enough to move it, the driving force of the push is a force according to a.m. definition(3), because it would move the block if the latter had been movable (less heavy, or lesser friction). The reaction "force", that keeps the block unmovable and acts against the pushing force, does not have any potential to change the mechanical energy of the mass of the block; only the pushing force has that potential (it can do work)! This is why you can move a table, but the table cannot move you (on a flat floor).

To my knowledge, this distinction has never been made in physics, not even by Newton himself - action forces do not exist in our world of observations, only reaction forces exist there and are the ones we measure. This is how the notion of centrifugal forces arises, because we measure them - the centripetal forces cannot be measured. Hence, Newton's third law is only mathematically correct, but physically it is wrongly formulated, as it ignores the correct definition of "force". I therefore propose to use a new term to put Newton's third law into its right perspective. This term is "firce" instead of "force". ( the " i " relates to "imaginary" or "induced" ) Hence, Newton's third law formulates correctly as:

4) ACTION FORCE = REACTION FIRCE

Observe that these "imaginary" firces yet are the very real ones in our world of observations, as mentioned. Hence, we might call them "forces" again, but then the action "forces" should be called "firces". It seems arbitrary what we consider to be real; our illusionary observations, or the reality beyond observation? In order to avoid confusions, I prefer the latter alternative, as it will show in the following. In consequence, the a.m. definition(1) rewrites as:

5) INERTIAL FIRCES ARE CAUSED BY CHANGES IN MECHANICAL ENERGY ONLY AND ARISE IN THE OPPOSITE DIRECTION OF CAUSING EXTERNAL FORCES.