TO RETURN

 

 

 

QUANTUM GEOMETRY OF THE SPACE-TIME

 

 

Model “Dimensional Four” of Matter, Energy and Vacuum

Rafael Javier Martínez Olmo

E-mail: Rafael@gravityquantum.com

Madrid

Spain

Madrid, on Wednesday, April 22, 2009

 

   Philosophical prologue.

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 is 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 its abstract character, is 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 Zenón 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 Sócrates. (We know that Aristóteles and Platón, lightly posterior, knew perfectly the discourse given by Zenón).

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 is random and it is causal, depending on the size of the object of the Nature that we is studying, random if this one belongs to the microcosm and causal if the object belongs to the macrocosm.

.    Physical prologue.

The universe and all its content has four dimensions.

The Spacetime has four dimensions.

The universe, up to where we know experimentally, also has four dimensions.

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, 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 ”, for what we know experimentally and of the astronomical remarks.

The relative vacuum, which, at least, contains gravity, has therefore, also four dimensions.
There does not exist any physical example, (this is, measurable), of object in our universe, that they have a number of dimensions different from four.

Following Euclides, it is not possible to construct, for mere addition, geometric objects of dimension different from that of its elements of construction. If in the Nature only elements of four dimensions exist the paltry and indivisible element of our universe has to be four dimensions, a volume that exists in the time.

Also because there 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 was already doing one century ago, so that they give us a volume - time, that is to say, a volume during a unit of time.

In System Cegesimal (centimeter, gram, second)

Since we know, the universe is isotropous, that is to say, it do not have spatial favorite directions, it present in any direction the same aspect and properties. The distinctions that we do between length, breadth and high place is merely semantic, since we can exchange to will its names and they keep on representing the same physical reality.

If we associate it the idea of isotropy with the elementary and paltry objento of the universe, this can be only, clearly, a sphere.

To the being a sphere we can calculate the radius Lmo = 4,897 506 921 037 260 E-19 centimeters that 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 at 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 for a Natural number (N).

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

Any wavelength is equal to the product of Lmo for a Natural number (N).

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 = m • c^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 for a Natural number (N).

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

Max Planck considered, already one century ago, the length, the mass, the time, the electrical load and the temperature as the fundamental elements to describe the Nature, and using in addition to c, h, G, the constant of Coulomb and the constant of Boltzmann.

These last two constants is not used in this work, for considering them to be unnecessary for its intention.

 The difference between the dimensional procedure of Max Planck, with him established in this work, is in the response to: “What is fundamental?” Question that is humanly opinable, against of the idea established at present, reflected well in the following paragraph:

“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 " God's units ". This eliminates any anthropocentric arbitrariness of the system of units”.

Extracted from Wikipedia, Units of Planck.

In this work it is considered to be elementary, a volume of paltry and indivisible spacetime of four dimensions. With a unique dimensional formula, the fundamental units is obtained of the Quantum Geometry of the Nature. [G• h • c ^-2]

 In the following table, we see the differences between 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 Seconds

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, is 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 concerning 10E-33 cm is equivalent to an energy of 3,89626E+11 TeV approximately, one trillion 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.

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

On the contrary, the magnitudes calculated in this work can be in the correct way, and it is contrastable experimentally at present with the particle accelerators which we have.

The supreme quantity of energy 253, 177 TeV; it is to only 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 there is scope of the experimental physicists, who will be those that they determine if the conclusions of this work is in accordance with the Nature or it is erroneous.

   Extract.

If we understand the Differential calculus as a Physical Theory (reality). 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 "Spacetime"; whose elementary components, in the sense of without parts, is volumes in the time (VT), of four dimensions (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). Spacetemporary 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 it is 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 (chance, random) with a geometric treatment (grounds, determinist).

The Quantum Geometry it give 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, it determines the geometry and the metrics of the Nature in its elementary scale, specifying the model of Quantum Relativity.

The attempts of unification of both theories, it 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 bug of expressing the continuity departing from points dimensional zero (D = 0; R).

The set of the real numbers (R) 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 of “ Four Dimensions ”, Volumes in the Time (VT); and represented by the set of the natural numbers. N: 0 ÏN

Consequently, the continuous term is put up only to discreet under the concept of mathematical point (D = 0; R) (infinite divisibility). Physical singularities do not exist in the Nature, it is the result of using the set of the real numbers out of context (scale). It is mathematical singularities (division for zero) and Not physical.

This model is finite, quantitative, and predictive. Contrastable experimentally at levels of energy between 1 and 8 TeV. It will be irrefutable at a level of energy lower than 253,177 660 585 902 TeV.

(Supreme value of energy of an Elementary Quantum event).

 

 


INDEX

 

                                  I.       Current  situation

                                 II.     “Spacetime” and Causality

                                III.               The last route

                                                               a.       The  Foundation

                                                               b.      The Principle of “ Spacetime ” paltry

                                                               c.       The principle of “ Paltry information ”

                                                               d.      The first prophecies

                                                               e.       The first Calculations and Results

                              IV.                 The Development of the Quantum Geometry

                                                                a.       The Real Numbers (R)

                                                                b.       We will have walked from R up to N. The Art of To Measure

                                                                c.       The continuity  

                                                                d.       The Sophism. Parménides  and Zenón de Elea

                                                                e.       What is the error?

                                                                 f.        The Implicit Presumptions

                                                                g.       The ambiguity of the concept “Point”

                                                                h.       The ambiguity of the Vacuum

                                                                 i.        The ambiguity of  the “Calculus

                               V.                    The Hypothesis Basic of the geometry of “ Spacetime “

a.         The  Infinitesimal Calculation

b.        The Inventory

c.         The Objection

                          VI.                    The Quantum Geometry - the first Part

a.      The Elementary Geometry of the Nature.

b.     The Paltry "Spacetime", The Dynamics 4D

                      VII.                      The Quantum Geometry - the second Part

a.         A sketch of Geometry Source

b.        The Compatibility with Newton's Gravity

c.        The Modifications in the “ Calculus

d.        The General Theory of the Relativity (R.G.)

e.         The Quantum Mechanics (M.C.)

                   VIII.                      The Cosmological Geometry

                                                            A.          The Quantum Geometry or Elementary

                         IX.                       A Bibliographical Base

 

 

 

 

I.             Current situation

At present the Physics it is divided in two; two models for two fundamental theories of all our physical knowledge of the nature, and both is contradictory between yes. To admit the essentials of one of them, he means to invalidate other one.

We search from 1930 a theory of unification; that he manages to obtain a model “The last one”, which assembles both theories, Mechanics Quantum (M.C.) and General Relativity (R.G.) to be explained like particular cases inside the new model, and this till now, he has been impossible to manage.

This situation is very unsatisfactory at theoretical level, where both theories is opposite. In the General Relativity, the constant of Planck is not born in mind, arguing its smallness and therefore, its insignificance in the calculations and essentials of the theory.

On the other hand, the Quantum Mechanics he does not bear in mind to the gravity, arguing of equal form its smallness, in this case, the extreme weakness of its associate field, which makes her, in fact, undetectable at small distances, that is to say, in which there demonstrates the whole phenomenology described in the experiments of the Quantum Mechanics.

The essential difference is in that for the Relativity Special and General, the idea of causality is essential. On the contrary, the Quantum Mechanics he does not bear it in mind by no means; it is more, it proclaims the nonexistence of causality in the quantum world, everything materializes in functions of probability on events.

The experimental physicist could have verified the validity of the General Relativity up to scales of the order of the millimeter, but from there and considering its extreme weakness we do not know anything. Although the scientific community inclines for thinking, that at the distances at which the particle accelerators is employed, the component gravitational must be paltry and certainly without relevancy to quantum effects. He has gone over in the particle accelerators at distances of the order of 10E-16 cm.

The situation is disconcerting, both theories is loaded with good arguments, both is supported by the experimentation and also with amazing precisions, but it is not possible that the two is true, because they rest on fundamental contradictory concepts, or one of them or the two is erroneous

For the General Relativity (R.G.) the "Spacetime" is relational with regard to its content, the matter and the energy, (he influences and is influenced).

The "Spacetime" is curved by the presence of these, and mass and energy move following these curvatures. For the Quantum Mechanics (M.C.) is only a frame of reference (absolute or of Newton) and he has a secondary importance, let's remember that it is a statistics, and in the statistics the variables “ spacetime “ is regarding external, neutral, not related to the events. (They neither influence they is not even influenced by them.)

Both lose its prophetic power, when he changes the scale of distances between the point A and the point B. what is badly, he is related to the magnitude distance and the ends of its scale .

 

II. “ Spacetime “ and Causality

The "Spacetime" has been, usually, considered like a stage or system of reference, inside which the physical phenomena happen, and although we can measure to (compare) from ancient, up to the theory of the relativity, few ones had thought about a "Relational" stage that should influence and be influenced by the physical phenomena that he contains.

The General Relativity he shows that the "Spacetime" is not only a neutral stage. That a "volume - time" it is indistinguishable from any other "volume - time". To having taught us that the curved matter to this one, and in turn the "Spacetime". This way curved, governs the movement of the matter and the energy. With which, it stops being a frame of neutral reference to describe the physical phenomena, to the being another active component of the nature, since he influences the mass and the energy and in turn it is influenced by them.

For it is reasonable to think that the geometry of the "Spacetime", which contains the quantum event, is the causal person in charge of the quantum phenomena, to the being the geometry inside which they happen.

It must be labeled in terms of the physics like of “hidden variable”, "relational", “independently from fund”, “determinist “and "quantum"

1.    When the Quantum Mechanics this proposed the nonexistence of causality in the quantum world he supposed a finished revolution in the same base of the classic physics, where the principle of causality is out of discussion, any effect has a cause and any cause creates an effect and there did not exist physical experiment that was demonstrating the opposite.

Nevertheless, in the experiments in quantum mechanics the same cause always produces different effects. The same ones in quantity and each of them with a probability that is always the same. Following the lead let's say that the expressed results meanwhile per cent they is 1st 12 %, 2nd 18 %, 3rd 40 %, 4th 8 %, 5th 3 %, 6th 9 %, 7th 10 %, so many times as we always repeat the experiment will give themselves 7 results and each of them in the aforesaid proportion. This with an extreme precision let us say with not major change of 1 between one trillion 10E+12 of events.

This leads us to asking us why this mistake happens in the law of the causality that he says that the same cause always produces same effect, imagine Vd. that supports an object with the hand and releases it, the object will always fall down and also following the same direction perpendicular to the soil [[1]]. It always happens thus, as he confirms our daily experience.

Now it be imagined that it is the quantum experiment of the previous example. when we were releasing the object he would fall down in seven different directions, and only in seven, and if we were repeating the experiment a much raised number of times, we would verify that each of these directions recurs in an exact proportion to earlier described, but before to release the object we will never know that this time is going to happen in particular: in whom of seven directions he will go? We do not know it any more than in terms of probability.

The first thing that was thought is that perhaps, the mistake in the causality, owed not to have born in mind anything, let's call him "x", that is to say a variable, or perhaps several, and that once found it would know, thanks to its value, which of the possible events would be produced and everything would be again like he was always.

So many Einstein as many people others searched and searched which might be this or these “ invisible variables ” because he is really difficult to admit, since it can be the nature to small aleatory scale and to our scale to be a determinist, being our scale a mere sum of the quantum states.

However, for much that nothing is searched he was, and one to an all the proposed ideas, which have been formulated, they have been dismantled for the Mechanics Quantum, quite which seems to indicate that God, not only plays the given ones, but it should be a finished Ludópata.

This supposed a rupture of the theoretical structure of the physics, which gives like result that the physicists think to the “way relativist” when they treat of the nature of the macrocosm, and of “quantum way” when they treat of the nature of the microcosm.

Although as they see, they is completely opposite; and one of the two, or perhaps the two, has to be erroneous, since the nature cannot be simultaneously two mutually exclusive things, aleatory and determinist.

2.    "Relational" model. With this adjective I want to indicate that the model shares the idea of the general relativity of that the "spacetime" is intimately related to the mass and the energy and vice versa, being influenced mutually.

3.    Model “independent background”. With this expression, he wants to indicate that the model does not depart from any preconceived idea of the geometric structure of the "spacetime". In the sense from if it is a space of Hilbert, Mikonski, Riemann, hyperbolic, elliptical, Euclidean, “almost-Euclidean” or from any other name and on this mathematical base to construct the theory, much on the contrary it is the theory the one that generates in a simple and natural way the quantum or elementary geometry of the universe.

4.    “Determinist” shaped. I believe that I have already been sufficiently explicit, he consists of the fact that the model considers fundamental and I validate the principle of cause and effect or of causality, as the Relativity or the classic physics.

5.    “Quantum” model. With it I want to express that there is essential for the theory the constant of Planck and the principle of suspense of Heisenberg. Moreover, the central idea of its construction is based on the constants of the nature and in the way of operating of dimensional formwith them that Planck used.

           III.        The Last one Route

a.           Foundation

Bases of the model:

1.                      The Infinitesimal calculation as physical theory “Natural Calculation” is a hypothesis, very guessed right, on the infinitesimal and discreet nature of the quantum geometry of the "Spacetime". It is the base of this model of Quantum Geometry.

2.                      The “Natural Calculation” confirms the physical hypothesis of which it is possible to describe with major great precision and mathematical generality, the curved and volumetric nature of the geometry of the "Spacetime", if we always suppose that the dimensional variables have a very small, infinitesimal value.

3.                      Planck operating in a dimensional way with the fundamental constants of the nature; speed of the light in the vacuum (c), gravitational constant (G), and of Planck (h); calculated a series of units of measurement that take its name Length, Mass, Time of Planck. Whose values we understand like absolute, in the sense of generated by the proper Nature, and that today we use, for example, to predict at the distances and energies where the quantum gravitation must show its effects. None of these units of Planck is a volume time, it turns out to be clear that Planck did not think that a "volume - time" had a fundamental and elementary character, yes on the contrary, he considered as such: the length, the mass, and the time.

Following the same dimensional process of Planck, we calculate the natural unit of "Volume - time". It is necessary to multiply the gravitational constant G by the constant of Planck h and to divide by the square of c (speed of the light) and we obtain, if it is allowed me, the "volume - time" of Planck who have the consideration of elementary and paltry "volume - time", fundamental brick of the geometry and dynamics of the Universe.

               (c.g.s.)

With only this universal constant, we can calculate other dimensional "elementary" magnitudes length, mass, time, curvature of the space-time… and with values very different from those of Planck and very near to our current reality.

 

The existence of this VT of paltry value, he supposes likewise, for the size of the dimensions of the "spacetime" a paltry and elementary value [[2]]. . This value has the physical meaning of being the paltry distance - time to which two volumes can be placed time, that contain elementary mass, (Mmo), these elementary values is geometric constants of the Nature and fundamental parameters of the structure and dynamics of the "Spacetime", both to the quantum scale and to cosmological scale. [6].

4.                      We have the physical evidence of which the geometry of the nature always appears to “Dimensional Four” and us finite (D = 4). The universe possesses four dimensions, both the energy, and the matter, like the proper "Spacetime" that contains them there is “Four Dimensional ones” (D = 4). Nobody knows any object or physical entity, which should possess minor number of dimensions. Nobody knows any form to change the number of dimensions of the physical previously mentioned objects not also. Yes we can on the other hand, diminish the value (length) of any of the dimensions of the "spacetime", but for the previous reflection we cannot equal them to zero, since he would eliminate the dimension.

5.                      Since the universe does not present favorite directions, of a paltry, indivisible value  exists and irreducible, of the size of any of the dimensions of the "spacetime", we would come to a spherical "volume - time",  of "Spacetime", paltry, elementary and “Dimensional Four” (D = 4).

6.                      The Nature he detests the mathematical concepts zero and infinity, to the effect that they lack physical reality. They do not exist in the Nature.

7.                      If finally the Nature it is constituted only by volumes - times (VT), and we reason with Euclides who is not possible to construct geometric objects of dimension different from that of its constituent elements, the elementary brick of our universe has to be also, with all certainty, a VT (4D).

Thanks to its spherical form we can calculate the radio, obtain 4,897 506 921 037 470 And-19 cm. (Lmo) Distances Paltry, that is late in is covered at the speed of the light 1,633 632 464 842 480 E-29 Sg. (Tmo). It is Paltry Time.

Finally the supreme curvature (Cma) is the inverse one of the radio of the sphere 4,897 506 921 037 470 E+19 cm-1. This is the maximum value of curvature that a VT has, and it is the supreme level of energy of a quantum elementary event 253,177660585902 TeV Mmo of 4,512 946 783 762 060 E-19 corresponds with the elementary mass gr.

Notice that this geometric property of the "Spacetime", has to take the matter as an origin, since it is the matter the one that generates the "Spacetime" for radiation and on account of its mass, hence the principle of minimal distance only affects to the volumes time occupied by elementary material particles (with mass).

In physical terms we can define this property of the geometry of the "Spacetime", saying that the elementary masses (Mmo), Lmo believe a "volume - time" of radio around him that he prevents no other Mmo from being able to be over a distance lower of her.

8.                      Any elementary mass (Mmo), it is a geometric and energy origin of the geometric spherical creation, with radial dynamics of the "Spacetime", to the scale of Planck, (quantum geometry).

Being the geometry of any "volume - time" VT.

Where, it is a function defined on a new set of numbers that we will name (), both concepts is specified further on, whose elements is provided with good order. They possess ordinal.

Every elementary VT with mass believes in the unitary time (Tmo), a spherical and concentric field around him that he determines a "volume - time" in the shape of spherical ring [[3]] of section Lmo, which is a place of the "Spacetime" where no other particle with mass can be, since he would infringe the principle of paltry "Spacetime" (ETmo)

The only way of achieving this, it is radiating energy to a very short and energy wavelength 253,177 660 585 902 TeV to support its "private" inviolable "volume - time". The wavelength is of 4,897506921037260E-19 cm

This spherical radiation that comes from every elementary particle with mass (Mmo) expands around him, of spherical form, at the speed of the light, creating and giving form to the "Spacetime", in the sense of dividing this one in volumes time elementary (spherical rings) that Mmo can be occupied by other masses. Without break the principle ETmo.

b.           The principle of “Spacetime paltry”

Every elementary VT with mass believe around him for emission of gravitational radiation and on account of its mass, a spherical field, volumetric and concentric of radio the paltry length (Lmo) 4,897506921037260E-19 cm. in the time also paltry Tmo. This establishes, agree Tmo is spending the unitary moments, a foliation volume time spherical of the "Spacetime", about her and he forces to any other particle (with mass) in the neighborhood, to occupy a spherical elementary ring, being therefore at a distance multiply native, of her.

 

c.           The principle of “ Paltry information ”

Every elementary VT only possesses paltry information of the Nature.

See (F )  Page. 22

N=1

Every elementary VT only possesses a paltry instruction to process the information of the nature.

See [F ] Page. 22

N=1


d.          The First Prophecies

1.      The Quantum Mechanics he describes the universe when the radio of the volumes - times, which contain the event, tends to 4,897506921037260 And-19 cm. paltry distance Lmo. At this distance of an elementary mass Mmo, the universe has the supreme curvature, or of equivalent form, it is the supreme energy of a quantum event. This wavelength corresponds at a level of energy of 253,177660585902000 TeV. This level of energy has an asymptotic character, in the sense of unattainable or supreme.

2.      The hidden variables of the Quantum Mechanics they is in the geometry, to paltry scale, of the "volume - time" that contains the quantum event. Up to today, we have thought that the curvature spacetime to this scale was almost flat, therefore, of almost void influence.

For against, the quantum geometry, he places the origin of the curvature and therefore of the geometry, in any particle with mass, therefore the supreme curvature or maximum energy is over a distance paltry Lmo, of any "volume - time" occupied by an elementary mass (Mmo). The supreme curvature is 1/Lmo. = 4,897506921037260E+19 cm.-1.

3.      Since we know for Feynman, the quantum electrodynamics (Quantum Electrodynamics Q.E.D.) were suffering in its beginning of that all the results that he was giving were infinite. The motive is that the sum of histories must bear in mind all the possible, and these ways depend on the distance between particles, this distance becomes zero, the zero introduces the infinity in the results.

Feynman determined not to take the calculations up to zero to avoid the indetermination, replacing it with a very small number 10E-100 cm. and stopping the sums on histories in this value. This supposed a solution to the indeterminations, but other problems appeared, the uniqueness of the probability gets lost; in addition to infinitesimal terms appear with negative energy.

These problems eliminate, if instead of using a small arbitrary distance we use the paltry Natural distance, 4,897506921037470 And-19 cm. to interrupt the sums on histories. Both problems appear of adding probabilities of nonexistent interactions. Concretely all calculated for distances lower than Lmo.

4.      The geometry “ Dimensional Four ” at quantum level behaves as if there was two-dimensional, since the radio determines three spatial dimensions and the time the dynamic evolution, also the radio, he has the same ordinal that the time, (there coincides the tag of the spherical ring and the time since it was radiated).


c.     The first Calculations and Results

 

 

A

B

C

D

1

Constante

Constante

Constante

Operaciones

2

(c) Velocidad

(G) Gravedad

(h) Planck

h*G/c^2

3

2,997924580000000E+10

6,674200000000000E-08

6,626069300000000E-27

4,920551532644910E-55

4

cm·Sg. -1

cm+3·gr.-1·Sg. -2

cm+2·gr.+1 ·Sg. -1

cm^+3*gr.^0*Sg.^-1= cm^+3*Sg.^-1

5

c2

6,674200000000000E-11

6,626069300000000E-34

VT =(Olmo) c.g.s

6

8,987551787368180E+20

m.+2Nw·Kg.-2

6,62608E-34 j*Sg. -1

Comprobaciones m.k.s

7

cm2 / Sg. 2

M+3·Kg-1·Sg. -2

1,000000000000000E+07

Comprobaciones

8

Hipótesis

Hipótesis

Dimensión

Resultados Numéricos

9

2

G·h/c^2

cm+3/Sg. +1

4,920551532644910E-55

10

2,387324146378430E-01

1,174695148738260E-55

4,897506921037470E-19

4,897506921037470E-19

11

Constante

Constante

Constante

Operaciones

12

(c) Velocidad

(G) Gravedad

(h) Planck

h*G/c^2

13

2,997924580000000E+10

6,674200000000000E-08

6,626069300000000E-27

4,920551532644910E-55

14

cm·Sg. -1

cm+3·gr.-1·Sg. -2

cm+2·gr.+1 ·Sg. -1

cm^3/Sg.

15

c2

6,672660000000000E-11

6,626069300000000E-34

VT =(Olmo) c.g.s

16

8,987551787368180E+20

m+2Nw·Kg-2

6,62608E-34 j*Sg. -1

Comprobaciones m.k.s

17

cm2 / Sg. 2

m+3·Kg-1·Sg. -2

m^+2*Kg^+1*Sg. ^+1

Comprobaciones

18

Hipótesis

Hipótesis

Dimensión

Resultados Numéricos

19

2

G·h/c^2

cm+3/Sg. +1

4,920551532644910E-55

20

2

3/(4Pi) de E14

2,387324146378430E-01

1,174695148738260E-55

21

2

radio

cm

4,897506921037260E-19

22

2

G·h·c^ -2

m3/Sg.

4,920551532644910E-65

23

2

Tiempo - Luz

Sg.

1,633632464842480E-29

24

(c) Velocidad

(G) Gravedad

(h) Planck

masa  Planck

25

2,997924580000000E+10

6,672660000000000E-08

6,626070000000000E-27

5,456180000000000E-05

26

cm. / Sg.

cm^3* / Sg. ^2 * gr.

cm^2*gr. / Sg.

gr..

27

r de Schwarzschild = 2G•m

masas en gramos

Radio(Schwarzschild) en cm

Máximo Actual.<2 TeV

28

Masa de Planck

5,456180000000000E-05

7,281450000000000E-12

 

29

Masa Olmo=Lmo/2G*=gr.

1,633969926586420E-26

4,897130209679920E-19

 

30

Masa Olmo=Lmo/2G*=gr.

4,512946783762060E-19

6,023135827094970E-26

Energía en eV

31

E = h*v = ergios;  E/c^2 = gr.

4,056034721762770E+02

4,512947260524770E-19

2,531776605859020E+14

32

Lmo

h

E = h·v

Energía Ergios

33

4,897506921037260E-19

6,626070000000000E-27

4,056034293269820E+02

405,603429326982000

34

Longitud de Onda cm.

Energía en TeV

Frecuencia v

1 Ergio= 6,242E+11 eV

35

4,897506921037470E-19

253,177660585902000

6,121327908945680E+28

6,242000000000000E+11

36

2,041855205358660E+18

1,000000000000000E+12

6,121327908945680E+28

2,531776605859020E+14

 


IV.      The development of Quantum Geometry

In the essentials of the theory these affirmations have done:

1)            The existence of a paltry VT like natural principle.(OLmo) (not reducible, not divisible).

2)            That the infinities that is obtained when we work with R.G. and M.C., their have its origin in the use, in both, of the set  for to give form the Physical reality.

3)            In the Nature not existed (absence of reality) of the mathematical concepts, zero and infinity.

These three questions is more that related between if, and since we will see, its clarification happens for understanding and fixing some ambiguous concepts of an unequivocal way. For it we go away to support like essentials in the logic, the theory of numbers and the infinitesimal calculation and like example the sophism of Parmenides and Zenón.