**Georgi Stankov, May 24, 2017**

Like mathematics, physics has failed to define the primary concept of space-time in terms of knowledge. This principal flaw has been carried on in all subsequent ideas which this discipline has developed so far. The method of definition of space-time in physics is geometry. It begins with *Euclidean space* of classical mechanics.

The substitution of real space-time with this abstract geometric space necessitated the introduction of two *a priori* assumptions on space and time by *Newton* that have not been seriously challenged since. Otherwise, we would not witness the parallel existence of *classical mechanics* and the *theory of relativity*. If Einstein’s theory of relativity were a full revision of Newtonian mechanics, the latter would no longer exist.

**In the new Axiomatics, we integrate all particular disciplines of physics into one consistent axiomatic system of physics and mathematics and thus eliminate them as separate areas of scientific knowledge.**

There is no doubt that we cannot develop any scientific concept about the physical world without establishing a primary idea of space and time. Newton’s primary notion of space and time is documented in his *Principles of Mathematics*:

*“Absolute Space, in its own nature, without regard to anything external, remains always similar and immovable. Relative Space is some movable dimension or measure of the absolute spaces; which our senses determine, by its position to bodies; and which is vulgarly taken for immovable space… And so instead of absolute places and motions, we use relative ones; and that without any inconvenience in common affairs; but in Philosophical disquisitions, we ought to abstract from our senses, and consider things themselves, distinct from what are only sensible measures of them. For it may be that there is nobody really at rest, to which the places and motions of others may be referred.”*

*“Absolute, True, and Mathematical Time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called Duration: Relative, Apparent, and Common Time is some sensible and external (whether accurate or unequable) measure of Duration by the means of motion, which is commonly used instead of True time; such as an Hour, a Day, a Month, a Year… All motions may be accelerated and retarded, but the True, or equably progress, of Absolute time is liable to no change.”*

From: *I. Newton*, Philosophiae Naturalis Principia Mathematica; translated from Latin by A. Motte, London, 1729.

Thus Euclidean space is the abstract reference surrogate of „absolute space“ to which all other physical motions are compared by the method of geometry according to the principle of circular argument. It is the primary inertial reference frame of all reference frames, in which **Newton’s law of inertia **(1st law) holds true. This law is an abstract tautological statement within geometry and cannot be applied to any real reference system – for instance, to a gravitational system which is always in rotation (*Kepler’s laws*) and exhibits a centripetal acceleration.

The reason for this is that Euclidean space has nothing to do with real space-time. Classical mechanics, which is based on this artificial space, contains no knowledge of the properties of space-time, as they are defined at the beginning of the new Axiomatics of the Universal Law.

According to Newton, space-time is “*absolute, empty, inertial”*, that is, free of forces, and can be expressed in terms of straight lines. These properties are summarized in his **law of inertia** postulating *immobility* (rest) or a *straightforward motion* (*translation*) with uniform velocity (*a* = 0) for all objects, on which no force is exerted. In this geometric space “*absolute time is liable to no change”*:** f = 1/t = const. = 1**.

In the Axiomatics I have proved that geometric space can only be built after we have arrested time within mathematics in an *a priori* manner. The *law of inertia* stays, however, in an apparent contradiction to **Newton’s second** and **third law**, and the **law of gravity** describing gravitational force as the origin of acceleration. While the first law is a mathematical fiction, the other laws of classical mechanics assess reality: there is no place in real space-time (universe), where no gravitational or other forces are exerted – for instance, we always observe rotations of celestial bodies (**Kepler’s laws**). As any rotation has an acceleration of *a* > 0, the law of inertia is not valid for rotations which are the only motions in space-time.

This paradox of classical mechanics justifies *Max Born‘*s estimation of Newton’s cardinal failure:

*“Here we have clearly a case in which the ideas of unanalysed consciousness are applied without reflection to the objective world.”*(1)

Since then, this remark can claim ubiquitous validity for the mindset of all physicists.

The question is why physics sticks to the law of inertia if it is an apparently wrong and abstract idea (idio) without any physical correlate, for instance, why it has not been abolished by Einstein in his theory of relativity? The explanation of this default is given by Max Born again:

*“In Newton‟s view the occurrence of inertial forces in accelerated systems proves the existence of absolute space or, rather, the favoured position of inertial systems. Inertial forces may be seen particularly clearly in rotating systems of reference in the form of centrifugal forces. It was from them that Newton drew the main support for his doctrine of absolute space.” *(2)

The basic paradigm behind the law of inertia is rather trivial: if a rotating body would move free of force in empty space, it would conserve its uniform tangential velocity expressed as straight line (vector) for ever. This property of the objects, called “inertia“, is regarded an *a priori* faculty that is inherent to matter.

This idea immediately evokes another principal objection:

*“The law of inertia (or persistence) is by no means as obvious as its simple expression might lead us to surmise. In our experience we do not know of bodies that are really withdrawn from all external influences: and, if we use our imaginations to picture how they travel in their solitary rectilinear paths with constant velocity through astronomic space, we are at once confronted with the problem of the absolutely straight path in space absolutely at rest…”* (3)

Let us recall that the existence of straight parallel lines has not been proven in geometry (check Euclid’s parallel postulate). As space-time is closed, all subsets of it manifest this property and perform** rotations**, which can be described by closed geometric figures, such as a *circumference* (closed [1*d-space*]) or a *spherical surface* (closed [2*d-space*]). This is a basic tenet of the new Axiomatics with which, in particular, quantum mechanics can be integrated for the first time with classical mechanics.

In addition, any rotation is a system of space-time that can be assessed in terms of *force, acceleration* (*electric field*), or any other abstract quantity of space-time = energy. This is another basic statement of the new Axiomatics which I have proved for all levels of space-time that have been described by physics so far.

This fact is reflected in **Lobachevsky’s geometry **(also known as** hyperbolic **or** non-Euclidean geometry)**, which reduces Euclidean space to a partial geometric solution.

From this analysis of the **space-time concept** of *classical mechanics*, we can conclude:

**1.** The introduction of *Euclidean space* for real space-time by Newton is the primary epistemological flaw of classical mechanics. The properties of this geometric space are:

a) emptiness (no forces, no acceleration);

b) homogeneity;

c) the existence of straight paths (lines)

d) absoluteness of space and time – no change of space and time magnitudes (immobility or translation).

**2.** These properties of Euclidean space are embodied in the *law of inertia*, which is an erroneous abstract idea without any real physical correlate. This law builds a basic antinomy with the other laws of mechanics, which assess real forces, accelerations and rotations.

**3.** While the absoluteness of space and time in classical mechanics is rejected by the *theory of relativity *(see the following publications), the homogeneity of space-time, which is tacitly accepted by the same theory, is refuted by *quantum mechanics*.

**4.** However, these disciplines make no effort to define the properties of the primary term of space-time in terms of knowledge. For this reason, classical mechanics still exists as a separate discipline, although the basic antinomy of physics appears in a disguised form in the **initial-value problem **(deterministic approach of classical mechanics) versus **Heisenberg uncertainty principle **of quantum mechanics (intuitive notion of the transcendence of space-time; see Volume II, chapter 7.3, p. 315).

This line of argumentation will be followed in the next publications discussing further blunders and contradictions in the concept of space-time of conventional physics.

**Notes:**

**1.** M. Born, Einstein’s Theory of Relativity, Dover Publ., New York, 1965, p. 57-58.

**2.** M. Born, p. 78

**3. ** M. Born, p. 29-30