Quantum_Geometry

The object of this work is the unification of the General Theory of the Relativity and the Quantum Mechanics, by means of the elimination of the randomness in the second one.

The motive by which it has been, until now, impossible to achieve this unification, is in an ERROR in the Logic. No physical object or ideal logical entity can possess two properties that are incompatible at the same time, to exist and not to exist, to be continuous and discreet, to be random and to be causal. This error infected the mathematics by means of the abstraction and this infection happened to the physics by the mere imitation.

Although the math, considering your abstract character, are almost immune to this virus, it same it do not happen with the Natural Philosophy, which today, we call Physics, considering its concrete character, being wanted for to describe the reality of the laws of the universe, and to submit it to the experimental contrast.

Not exist anybody, who could think about any object or quality, so much if it is ideal as if it is material, which exists and does not exist simultaneously, except naturally, the ideal concept of mathematical point of dimension = 0.

The point exists, because it has an exact and real position in the spacetime, which is determined by its four coordinates of spacetime.

The point does not exist, because it do not have dimensions (dimensions = 0). It has no height, it has no length, it has no breadth, and it does not in the time.

This incoherence is subtle and invisible like a virus. We know its consequences for 2600 years, but its origin has always happened unnoticed. Historically it has appeared, in front of us, three times. It always conceal in the concept of continuity.

The first time that presented its incoherence is in the four sophisms of Zenon de Elea, 2.600 years ago, and whose logic is perfect, closed, and conclusive.

These sophisms were presented to the local philosophers, in Athens. Perhaps in front of Socrates. (We know that Aristotle and Platon, lightly posterior, knew perfectly the discourse given by Zenon).

The second time that appeared again the contradiction is in the invention of the infinitesimal calculation. In that epoch, many intellectuals were against the logic of such a theory, since there is no way of explaining the movement, the speed, or the acceleration, on terms of the point.

The mathematical point has neither another point that is its following one, nor its previous one. The second point, the third point, the point quarter, etc. Not exist.

The motive is that the set of the numbers Real (R) lacks an ordinal number associated with its elements. In spite of being a completely tidy set, it lacks good order.

This contradiction, implicit in the “calculus”, and never solved, by being irresolvable, since it take implicitly the incoherence of the mathematical point (dimensional = zero) with that it is constructed the mathematical "continuum" (R). However, since that the calculation works, and the subtle contradiction was not discovered, the opinions opositoras had to be quiet unwillingly. By it, the movement entered the Incoherent Point Club. It is continuous (by definition) but it is not possible of to demonstrate mathematically in punctual terms, only it is possible of to demonstrate mathematically in terms of intervals (e> 0).

The third time that appeared the incoherence, it is in the birth of the Quantum Mechanics (Principle of suspense of Heisenberg). The incoherence of the point, it went unnoticed again, it broke in two to the Physics, introducing the randomness in the quantum world.

Since then the universe possesses simultaneously two qualities incompatible: it are random and it are causal, depending on the size of the object of the Nature that we are studying, random if this one belongs to the microcosm and causal if the object belongs to the macrocosm.

The matter always has three spatial dimensions (volume) and exists in the time, the energy always occupies a volume of space and exists in the time, and then both have four dimensions.

The absolute vacuum, in the sense of lacking both of matter and of energy, does not exist.

There is no way of isolating the gravity of a “volume of Spacetime”, by what we know experimentally and by the astronomical observation.

The relative vacuum, which, at least, contains gravity, has therefore, also four dimensions.

In our universe does not exist any example of a physical object with the number of dimension different of four.

According to Euclides, it is not possible to construct geometric objects of a dimension different from that of its elements of construction.

The paltry and indivisible element of our universe has to be of four dimensions, a volume that exists in the time.

Fundamentally because in Nature do not exist objects of less than four dimensions, except in the Platonic world of the ideas like mathematical abstractions.

To calculate its value we use the fundamental constants of the nature, c, h, y G, like Max Planck did one century ago, so that they give us a volume- time, that is to say, a volume during a unit of time

We know that the universe is isotropous do not exist spatial favorite directions, it present in any direction the same aspect and properties. The distinctions that we do between length, breadth and height are merely semantic, since we can interchange its names and they keep on representing the same physical reality.

If we associate the idea of the isotropy with the paltry element of the universe, this element can be uniquely a sphere

To the being a sphere we can calculate the radius Lmo=4,897506921037260E-19 centimeters, it is the paltry distance and any measurement of a distance is equal to the product of Lmo for a Natural number (N).

This distance is covered to the speed of the light in, Tmo = 1,633632464842480E-29 seconds. This is the interval of paltry time, and any measurement of time is equal to the product of Tmo by a Natural number (N).

Since it are the paltry distance, cannot exist a wavelength shorter than Lmo, 4,897 506 921 037 260 E-19 centimeters. Being the paltry wavelength it is equivalent the supreme value of energy. Emo = 253,177 660 585 902 TeV.

Likewise, the value of any measurement of a quantity of energy is equal to divide Emo by a Natural number (N)

For the equivalence between mass and energy E = mc^2, only we have to divide for c 2 to obtain the value of the elementary paltry mass Mmo = 4,512 946 783 762 060 E-19 grams, and any measurement of a mass is equal to the product of Mmo by a Natural number (N).

The dimensional procedure was established by Max Planck to determine the absolute units of the Nature, because it comes given by the universal constants, each of which comes expressed on its own dimensional units, for example, the speed of the light is a length divided per a time.

Max Planck considered, already one century ago, the length, the mass, the time, the electrical charge, and the temperature like fundamental. Using in addition to c, h, G, the constant of Coulomb, and the constant of Boltzmann, these two last ones are not used on this work, by considering that it is unnecessary for its purpose

The difference between the dimensional procedures of Max Planck, with him established on this work is at, what is fundamental? The question is debatable, in against of the idea established at present, reflected well in the following paragraph extracted from Wikipedia, Units of Planck:

“The system measures several of the fundamental magnitudes of the universe: time, length, mass, electrical load and temperature. The units Planck usually call (joking) for the physicists like the “units of God". This eliminates any arbitrariness anthropocentric of the system of units”.

On this work is considered to be elementary, a volume of space-time, paltry and indivisible and of four dimensions. With a unique dimensional formula (G h c^-2).

In the following table, we see the differences between the values of both methods.

Max Planck		This Work
Dimensional formulae	Values (System c, g, s)	Dimensional formula	Values (System c, g, s)
	5.39121 × 10^-44 Seconds		1,63363 x 10^-29 Segundos
	1.61624 × 10^-33 centimeters		4,89750 x 10^-19 centimeters
	2.17645 × 10^-5 grams		4,51294 x 10^-19 grams

The magnitudes calculated by Max Planck for the length and the time, are extremely small and it involve quantities of inaccessible energy to our technology. The costs necessary for its construction exceed the imagination, all this, without entering its size that would be cosmic. A wavelength of 10-33 cm is equivalent to an energy of 3,89626E+11 TeV approximately, one billion (of twelve zeros) of times the maximum energy of the current particle accelerators. On the contrary, the mass is big and accessible to the experimentation; nevertheless, we have not found any interrelation between its value and any experimental fact of importance.

Clearly it seems that the units of Planck are erroneous and do not have any physical meaning.

On the contrary, the magnitudes calculated in this work are in the correct way, and also, are contrastable experimentally at present with the particle accelerators which we have.

The maximum quantity of energy 253, 177 TeV, This one to two orders of magnitude of the last particle accelerators, probably the quantum geometry has been already photographed, but it have happened unnoticed because we did not know what it was necessary to search.

For the first time, the Quantum Gravitation is the scope of the experimental physicists, who will determine if the conclusions of this work are real or erroneous.

If we understand the Differential calculus as a Physical Theory (reality) [3] and not like a mathematical model, which brings us near to this one infinitely, but without reaching her. Using the mythological set of the Real numbers (R), we see that it is the logical way that shows us the elementary and quantum nature of the Geometry of the "Space-time"; whose elementary components, in the sense of without parts, are volumes in the time (VT), “ Four Dimensional ones ” (D4), infinitesimal (e > 0) and of curved topology (p).

This route based on the Differential calculus, is the Quantum Geometry. The writing tries to sit the bases and theoretical essentials of this way, which unifies the experimental results of the Quantum Mechanics with the theory of the General Relativity, by means of the hidden variables (Op). It is space temporary curvatures of the quantum events.

The model is of relation and independently from fund (Quantum Relativity), where so much the General Relativity like the Quantum Mechanics they are modified, the first one is specified in an elliptical geometry of radial dynamics (D = 4) The second one is completed introducing the causality, replacing the statistical treatment (random) with a geometric treatment (causal).

The Quantum Geometry he gives a causal explanation of the Quantum Mechanics, establishing an one to one connection, between the statistical results and the elementary geometries (without parts) of the "Spacetime", which contains the above mentioned quantum event. Likewise, he determines the geometry and the metrics of the Nature in your elementary scale, specifying the model of Quantum Relativity.

The attempts of unification of both theories, they have always failed for the appearance of the infinities. The origin of these indeterminations is in an equivocal reading of the "Calculus". Consequence of the error of expressing the continuity in terms of dimensional points zero (Dimensional = 0; R).

The set R they have allowed us up to today to represent the physical reality to our scale. But he sinks of unequivocal form on having faced the description of the elementary nature of the "Spacetime"; that can be described only in elementary (indivisible) terms, for geometric objects “ Four Dimensional ones ”, Volumes Time; (VT); and represented by the set of the natural numbers N, : 0 Ï N