General Foundation of Mechanics

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Index:
The First Law of Nature
Inertia as identification of existence
What is force?
The Second Law of Nature
Basic laws of conservation and of wholeness
Mechanics and quantum mechanics

The First Law of Nature

When our experience leads us to the conviction that a predictable natural science is possible, our assumption is that Nature is governed by necessity, rather than by chance, i.e. nothing happens without a cause. Such an understanding of nature is a causal one.

The cause of change we call "force". And what inanimate things do when not acted by a "force"? Right: they remain unchanged! The last joint in a chain of causal understanding is the acceptance:

"Everything remains, as long as it depends on itself, in its state."

This does not mean that things possess by themselves a state; they only maintain - in an acausal manner - their state! René Descartes (1596-1650) has already formulated a very similar inherence of preservation, calling it "the first law of nature". Since it is irreducible, I shall call it "the fundamental law of conservation".

And what do things acted upon by forces? Right: they try, again by themselves, to preserve their state, a fact experienced by us as inertia and force, respectively.

Causality founded on the acausality, who not need a external cause.

Without acausality, no causality. Those, for whom everything is a consequence of external agents, overlooks that the external agent (i.e. an acting force) is also generating by something which ties to preserve by itself its state, therefore becoming a cause/force, too.

Laws, rather than being imposed upon nature, are expressions of nature as it is.

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Inertia as identification of existence

The fundamental principle of conservation expresses our experience that every change needs a cause.It is an empirical principle which cannot be scientifically derived, but, on the other hand, is confirmed by the irreducible conservation principles. Its content is so straightforward and we trust it so much, that it penetrates forcefully our consciousness and we undertake it almost without reflection. Conservation being the most basic phenomenon related to inanimate things, it has to underlie mechanics generally.

The tendency of physical objects to preserve their state is observable during interaction through inertia. Objects possess inertia by themselves, since they have themselves the tendency to preserve their state (of motion). Inertia is, therefore, a manifestation of the existence of interacting objects. To doubt the existence of inertia is the same as doubting the existence of objects. No science of material objects is possible if their very existence is put in question.

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What is force?

Force is no thing, but rather an aspect of things. Newton defined "force" in his second axiom as the agent capable of changing "motion". Dynamically it is not motion, but rather its change, which is relevant. The first axiom holds independently on the state of "motion", or of "rest" of the observer, provided motion is rectilinear and uniform. rest or motion become apparent to an observer, when referring an object to a (for him) fixed point and comparing the change with time of its relation to it. Thus, only forces represent a real aspect of things. Causes originate in things, rather than in the relationships of an observer to things. Einstein´s problem, which was his reason for formulating the relativity theory, consisted in the absence of evidence for the falsely accepted reality of movement. (It vanishes when one undertakes a causal analysis.) This doesn´t have to first eliminate ´v´, in order to get an objective (i.e. relevant for the object) statement. Following the "reality principle", namely to formulate judgements on the object-level instead of the relation-level, one obtains equations valid for all real systems not acted upon by forces (which doesn´t mean that such systems really exists), quite independently on how observers look upon their own motion. The "reality principle" is already there, where Einstein´s relativity principle would like to be; to prove that the motion of a (closed) system doesn´t matter -since it comes into being first in the head of the observer, as shown by a century of movie.

The origin of a mechanical force is the inertia of an object. This is formulated in a most clear manner in Newton´s third definition of force: "This force is always proportional to the respective object and differs from the inertia of mass only through the way of treatment....The naive observer associates a force of resistance with objects at rest and "impetus" with objects in motion. Rest and motion, as commonly understood, differ, however, only with respect to the point of reference." The following axiomatic needs "rest" and "motion" only to establish the correspondence with Newton´s mechanics.

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The Second Law of Nature

Since any object manifests both inertial and gravitational effects, one has (to my mind) to include gravitation in the axiomatics from the very beginning. My starting point will be a Parmenidean concept of wholeness, for me still the deepest understanding of the phenomenon of gravity. In my essay "Gravity as an argument for a holistic approach", I proposed, relying upon Descartes, "The Second Law of Nature":

"Each existing object has to complementary aspects: one of his own and one of the whole. The first is manifested -when acted upon- by inertia, the second by its share to gravity. The two are proportional to each other."

Due to their double nature and double action of objects, one has to take into account both principles, of conservation and of wholeness, respectively. like inertia, gravitational action is an evidence for the existence of an object, too.

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Basic laws of conservation and of wholeness - their applications and consequences

1. Basic Law of conservation

1.1. Each object maintains from itself its state.
1.1.1. Conservation is irreducible, therefore conservation principles are supreme.
1.2. Conservation, in temporal approach, manifests itself as endurance (of a thing).

2. Persistence and motion

2.1. The observer-related relativization of behavior allows to him to see each thing as either "in motion", or "motionless".
2.2. Both persisting (resting) and free-falling objects appear to a resting, or, respectively, to a co-moving reference frame as "at rest", or in rectilinear and uniform motion. (This is, in fact, the definition of a force-free situation.)

(Persistence is a reality. Motion and no-motion (rest) are relational estimates of the observers, thus relativities. Had motion and rest have a reality status too, Newton had not been able to write without contradiction: "Each object persists in his state of rest or motion", since an object cannot be at the same time at rest and in motion! However, they are at rest for themselves and in motion (or not) for the observer, a hint for giving up the illusion that "neutral" observations were possible.)

The effectiveness of a thing is determined by what it is by itself. It is, therefore, decisive for its understanding, to distinguish between its own and the observer-related states. The reality principle is useful in this respect.

3. Persistence/Conservation as a precondition for causality an force

3.1. Self-conservation implies that every change of state of a thing necessitates a cause.
3.1.1. The change of state (acceleration) and its direction are caused by a force, which is proportional to them. (Definition of force.)
3.1.2. The intensity and the direction of a force on a system are recognizable with the help of rulers which are not influenced by the force.¹⁾
3.2. The source of both inertia and of inertial force, is the tendency of state preservation.

(But: every thing is by itself, not for itself, inert or forceful, and always for another thing: "This force acts only when the thing is acted upon" (Newton, Def.IV.) Force is an operational aid, helping us to determine the consequence of conservation in the presence of interaction.)

¹⁾ Newton has expressed the necessity of constant measurement conditions for an experimental science by calling space and time "absolute", i.e. independent from the investigated forces. Only constant and everywhere valid scales can guarantee the reproducibility of technical and scientific activity. To guarantee this is the task of metrology, which defines and checks the measurable quantities and their units. Without both definitions, without the object of measurement and the measurement procedure -with units not influenced by the act of measurement- there is no act of measurement deserving its name.

4. Law of interaction

4.1. According to 3.2. force is something secondary, which manifests itself only during interaction. Nothing is a force by itself.
4.1.1. The existence of a thing can manifest itself as inertia or force, as far as acted upon by another thing. The reciprocal actions of two things are, therefore, always equal and opposite. (Origin of force.)
4.2. Things bring their masses and their -one upon the other oriented- behavior as impulses during interaction.
4.2.1. The end-result is proportional to the impulse (i.e. linear momentum) involved.

(Newton formulated first his third axiom as monocausal: "Action and reaction are always opposite and equal", although actually there is no objective distinction between action and reaction. Just after that, he gave the proper formulation:"or, the reciprocal actions of two objects, each upon the other, are always equal and opposite.")

5. Basic Laws of wholeness

5.1. Every thing is an un separable part of the whole.
5.2. Its non-separability is recognizable as gravity-generating centripetal force.

(Centripetal force, too, is a "force", as far as he acts upon other things. If things, and therefore actions, are missing, we talk about a field of force of an object - as a description of its potential ability to accelerate a test-body.) A thing acts neither directly, nor indirectly at-a-distance. It is merely the center of its permanently existing, spatially distributed potential. Thus, Newton´s Def.VIII states: "The accelerating force has to be traced back, as an ability of action, to the position of the object, distributed in the space surrounding that position." The repeatedly expressed opinion, Newton were believing in action-at-a-distance, unmasks only somebodies own erroneous ideas about gravity, namely that the inertial mass acts as cause of centripetal action; Newton treated it only as the center of its action.)

6. Origin and law of gravity

6.1. The centripetal force is one of the two forms of interaction of an object. Both are proportional to its mass, as a measure of its inertia.
6.1.1 Energy has inertia, too.
6.2. The force of inertia originates in every quantum of matter and distributes isotropicaly in space, i.e. it displays only radial dependence.¹⁾
6.3. The "fall" initiated by the centripetal force is independent on the falling body, therefore "everything falls".

(Inertia is the locally passive, while the centripetal force the universally-active aspect of a thing called mass-energy. To one thing belong two arts of action, determined by the same measure. The "inertial mass" is not the thing in itself, but rather the measure of the inertial resistance of a thing. The "gravitational mass" is the thing under the action of the gravity field of other masses. The carrier of the characteristics "mass" is matter, either condensed, or radiant. Einstein's famous equation E = mc² represents a relationship between condensed and radiant matter, as the inverted relation m_E = E/c² shows. The populistic interpretation of E = mc² as a measure of the conversion of mass in energy, confirmed supposedly, by the atomic bombs, betrays an alchemistic thinking and is untenable, as already hinted at by Heisenberg. During nuclear fission it is merely bounding-energy released. Einstein himself talked only about "equivalence" between mass and energy, using one of his dear veiled expressions. The author is not informed to which degree this claimed relationship holds, or not.)

¹⁾The isotropic distribution of the gravity force (lines) is a consequence of a conservation principle (in this case of the product between volume and force ), too. Newton's gravitational force-law holds rigorously for two point masses/quanta! Since the action of the centripetal force shows a power-law decrease, the linear shift of the mass - producing the field in the geometrical center of an extended body - a lower change of linear momentum in the vicinity of the body. (The center of gravity for things on the surface will be rather on the half-way between surface and geometrical center.) Although Newton observed that "the solar gravity consists of the gravitational action of the individual parts of the Sun", he has, nevertheless calculated the centripetal force from the center. I think that the linear impuls difference resulting from this procedure, could account for the claimed (by Einstein) influence of "space curvature" in the vecinity of large masses. Since the description of gravity by Newton was purely geometrical, the interplay of gravity and space is not something new. We have to be conscious that "force" - as analog of the force of muscles - "field" and "space" are only metaphorical description facilitating our understanding.
²⁾The interaction is, however, given, since the falling thing from its part, acts upon the accelerated thing through its gravitational field. Would fields interact between themselves, the dismissal of fields in the vecinity of the relevant masses, could possibly result in new effects. Perhaps there is something there which could be described as "curving of space", oder "perihelion precession" of the planets closest to the Sun? This is just a stimulating idea, trigerred by my efforts to clarify scientific concepts and to provide stimulating ideas by changing points of vie.

What as „Law of Nature“ counts is the representation of the nature - as - such in categories of scientific though, as formulated in principles, these categories allowing a (spiritual) intellectual treatment.

_{(Categories belong always to men, rather than to things.)}

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Mechanics and quantum mechanics

The basic laws of mechanics are the instrument of the physicist and are valid in all fields of mechanics and its applications. A classical mechanics eliberated from the superfluous, contradictory, respectively built-in assumptions, should not differ qualitatively from quanteum mechanics, as Heisenberg used to emphasize, even if the macroscopic, respectively microscopic research differ necessarily in what scale is concerned. Since Heisenberg in a lonely night in spring 1925 realized that his energy matrix obeys the principle of energy conservation, he had "the sensation that through the surface of atomistic phenomena we could look into the inner beauty of a deeper level of reality....". Our certainty in the validity of conservation principles in quantum mechanics serves as a warning that the holistic principle has to be involved in what is called the problem of quantum gravity. Since gravity, as a complementary force, belongs to the quanta themselves, this problem is only historical, rather than fundamental. This has much to do with the fact that, out of respect for Einstein's famous reputation, the assumptions and ideas patterned by him are by all means preserved. It would, however, be much more in the spirit of Einstein, to take care on the unit of physics, rather than on names.

Literature:
First of all are Newton's "Principia" (Meiner Verlag, Philosophische Bibliothek Nr. 394) to be mentioned, Werner Heisenberg's "The Part and the Whole" (dtv); also my GPS (German Physical Society)-lecture: "The reality-principle as epistemological strategy" (DD 1995) and "Gravity as argument for a holistic approach" (DD and GR 1996)

translated by Dr. George Galeczki (Cologne/Germany)

Lecture at the 61th Conference of the German Physical Society, 1997, Berlin, FV DD, Proceedings pp. 766-771

The Meaning of Axioms