Pre Galilean, Aristotelian Physics considered immobility as steady state of a body on which no force was acting. Under action of force the body moved at speed proportional to the force. When force ceased to act, the body returned to immobility. It may look strange to us, but this model was universally accepted during 2000 years until Galileo discovered that the steady state of a body is not immobility, but uniform movement at constant (in value and direction) speed: A body on which no forces act moves at constant speed in an unchanged Euclidian direction. Galileo called such a body associated with concrete or virtual Observer an "Inertial Referential" (IR). This definition excludes absolute movement: all IR's move relatively to one another at constant speeds and none is in any way privileged.

Question arose if concept and laws describing mechanical and dynamic phenomena in some IR keep their validity transformed to other IR's and, if they do, than by being invariant or covariant. (A construct is "invariant upon a transformation" when after being transformed it stays unchanged; it is "covariant" when upon the transformation it undergoes linear modification entirely determined by the transformation. This notion of "covariance" should not be confused with "vector covariance" defined in "Vectors".) Invariant physical constructs are considered as absolute within the concerned Model. Relative constructs are Covariant upon the Transformation of the concerned Relativity Model. Galilean Relativity and Newton's Model are partially based upon an absolute construct, the Galilean #Space.

Galilean #Space is in contradiction to usual commonplaces, four dimensional: an event is determined by 1 Time and 3 Space values. It's indeed a TimeSpace, a 4D #Space encompassing two sub-#spaces of our Raw View:

-the 1 dimensional Time
-the 3 dimensional euclidean Space.

The confusion attributing "TimeSpace" to Einstein is due to Galilean Time and Space being incommensurable or Affine ("Space. Affine and Metric"), while Einstein's 4D continuum, as we shall see in the next chapter, is the Metric "LighttimeSpace" where the Galilean component "Time" is replaced by "Lighttime" having the measure of distance commensurable with the components of Space.

Incommensurability of Galilean Time and Space excludes the notion of Time-Space Interval and, consequently, of Transformation involving the entire Galilean TimeSpace. On the other hand, constancy of speed among IR's excludes Rotation and we are left with two Translations, one in Time and one in Space, which accounts for Galilean Relativity being sometimes called "Translational Relativity" as opposed to the "Rotational Relativity" of Einstein, which latter term we justify in the next chapter.

Given two IR's: R(O, X, Y, Z, T) and r(o, x, y, z, t) moving with respect to one another along the common axe X-x at speed V the Time and Space Translations from R to r are respectively: t = T; x = X + a + VT; [1] where a is the distance of o, origine of r from O at T = 0.

[1] is called the Galilean Transformation. It supports invariant or absolute Time and distance, i. e. Space. Indeed, distance DX in R DX = X2 - X1, transforms into Dx in r: Dx = x2 -x1 = (X2 + a + VT) - (X1 + a + VT) = X2 - X1 = DX

Intervals of Time and Space are Invariant under the Galilean Transformation, or in epistemological terms, GALILEAN TIME AND SPACE ARE ABSOLUTE.

A Detector moving along X/x at VDx with respect ot r moves at VDX = VDx + V with respect to R:

Speed is additively Covariant under Galilean Transformation, which, after a few simple mathematical operations results in the rule:

MECHANICS AND DYNAMICS ARE COVARIANT UNDER GALILEAN TRANSFORMATION

Galilean Relativity reached its apogee in Newton's Model. In order to investigate it from the point of view of RD we shall start by trying to assign it to one of the basic classes: Continuous or Discrete.

At first glance the answer seems obvious: Discrete. At Newton's time and for centuries afterwards the fabric of Universe was considered to be corpuscular. Newtonian #Space was compactly filled with corpuscules acting directly on one another, like billiard balls thus supporting Mechanics, Local Action and Causality. However, such corpuscules have never been observed, nor was there even any hint to their conceptual features such as size or mass. They have appearance of an ad hoc "crutch", of a hypothetical corpuscular "matter substance", introduced in order to formulate a microscopic model based intuitively upon macroscopic billiard. Now, hypothetical or not, this corpuscular "matter" accounted well for the laws of Mechanics.

However, serious difficulties arose with Optics. In agreement with the postulate of discrete Universe, light was mapped as a flow of corpuscules thus introducing an additional ad hoc crutch, a "luminiferous" corpuscular substance. It supported rectilinear progression and reflection of light, as well as refraction (with help of hypothetical interactions between "material" and "luminiferous" substances). In order to account for dispersion, or separation of white light into spectral components, it was necessary to split the "luminiferous" substance into several substances, one per colour, propagating for some reason each at different speed through various "material" substances. One accumulated uncountable ad hoc crutches, all hypothetical and not supported empirically. One grew a habit to add for each new problem some new "substance" which indeed looks more like tautologies than solutions.

Finally, realizing that no conceivable new "substances" could possibly account for such phenomena as diffraction and interference patterns, physicists abandoned the corpuscular theory of light to the advantage of wave theory which, in conjunction with the discrete view of Universe, ushered in the Aether concept which dominated Physics till the beginning of the 20th century. The corpuscular theory fell into oblivion until it apparently resurrected in the Quantum Theory, at an incomparably higher level of complexity and in a form having nothing to do with rudimentary mechanistic thinking.

Leaving for the moment Optics we shall move to Newton's Dynamics. It's based upon 3 Laws of Motion:

1. In absence of force any object moves at constant speed.
2. Accelaration of an object is directly proportional to force acting on it and inversely to its mass.
3. For every action, there is an equal and opposite reaction.

Let's note that only 2. and 3. are original. 1. is a redefinition of Galilean Inertial Referentials.

On the other hand, a fundamental concept is missing, that of kinetic energy. It has been conceived and formulated at age of 16 by Pierrette Paulze - Lavoisier who, astounding as it may seem, fell into almost complete oblivion. Maybe not so astonishing after all: she was a woman; she did not belong to any Academy, none would accept a woman in 17th Century; and married to Lavoisier she was overshadowed by him. Not by his fault. She married him at age of 13 and from the first day became his full-fledged collaborator, which he emphasized at every occasion so that the rare cognoscenti who heard about her call them "Father and Mother of modern Chemistry". But there it is, hardly anybody heard about her.

Thus, if we consider Newton as founder of modern Physics and perhaps the greatest scientist of history, it's not due to his unconvincing Optics, nor to his Dynamics, certainly great, but incomplete and amended by a nearly unknown 16 years old girl. His outstanding significance is named "Gravitation", to which we shall further refer as to "Newton's Model".

It boils down to the following Law of Gravitation:

Attracting gravity force between two masses F(r)=G(m1*m2)/r^2 where G: gravity constant, m1, m2: respective masses, r: distance.

Let's start with our basic question: Is Newton's Model Continuous or Discrete? On the face of it it seems Discrete, according to the contemporary view of Universe and to his own explicit statements. However, this assumption leads immediately to paradoxes:

The law of Gravitation assumes Action at Distance thus clearly contradicting all principles of the corpuscular billiard-like view as well as the Local Action and Causality. [3]

#Space (distance) determines the Gravity Force, without this Force impacting in any way the #Space, which contradicts the action/reaction principle. [4]

Paradox [3], Action at Distance in a Discrete Model, is not just a contradictory detail, but an essential inconsistency which casts doubt upon the very base of the theory. Consequently, question arises if Newton's Model was not de facto Continuous, perhaps implicitly, against author's own explicit belief in the universally accepted discrete fabric of Universe.

Indeed, taking the formula of gravitational Force: F(r)=G(m1*m2)/r^2, we may combine G*m1/r^2 into g(r)=G*m1/r^2 and define "g(r)" as "Gravity Field in any point r of #Space".

Then, F(r)=g(r)*m2 and replacing m2 with detector of mass m2=1, we get F(r)=g(r) - Gravity Force exerced by Field g(r) on a unit mass in every point r of #Space.

Once we replace corpuscules acting paradoxically at distance, with Continuous Field acting locally in all points of #Space, Newton's Model becomes Continuous as well as consistent with Local Action and Causality; a pertinent foundation of modern Physics, precursor of Einstein's Relativity and of the Quantum Field Theory.

In this light, the paradox [4] involves Field rather than Force. Indeed, #Space being a Continuum and Force a point event, the original version of [4] simply does not make sense. In the Field version, on the contrary, both Field and #Space being Continua, it becomes a meaningful albeit yet unsolved inconsistency.

Now, Field is a factual construct and #Space an abstraction, so by virtue of the Principle of Preponderance of Facts, it's Newtonian #Space that is primarily called into question by [4] and should be reexamined in the first place. We shall see below that [4] has been indeed considered and solved in that sense by the General Relativity.

Finally, let's recall that a major part in the acceptance of Newton's ideas was due to Euler's re-writing of his entire family of ideas in the language of the calculus, which Newton had done so much to invent but largely left out of the Principia.

And who says calculus, talks about Continuity. This argument seals our conviction that Newton's Model was, at least implicitly, the first pioneering Continuous Field Model which founded and determined the subsequent progress of Physics till our own days.