Unification of the General Theory of the Relativity and the Quantum Mechanics

Quantum geometry of the Spacetime
Geometric Model of “Four Dimensions” of the Matter, the Energy, and
the Vacuum
Rafael Javier Martínez Olmo
www.gravityquantum.com
E-mail: Raf...@xxxxxxxxxxxxxxxxxx
Madrid
Spain
Madrid, on Sunday, March 09, 2008

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 simultaneous that are
incompatible as, 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 lives 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 zero dimension
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 has no time.
This incoherence is subtle and invisible like a virus. We know, of
its
consequences for 2600 years, but its origin always it happened
unnoticed. Historically it has appeared, in front of us, three times.
Always hidden 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 () 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 continuum mathematical (). 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 prove mathematically in punctual terms, only it is
possible of to prove 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 happened again unnoticed, and broke in
two 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
.


. 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, and 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 of the
astronomical observation.
The relative vacuum, which at least contains gravitational energy,
has
therefore, also four dimensions.
Not exist one physical example, (this is, measurable), of object in
our universe, that has the number of dimension different of four.
By Euclides we know which is not possible of to construct, by mere
addition, geometric objects of dimension different from that of its
elements of construction. If in the Nature uniquely exist elements of
four dimensions, the paltry and indivisible element of our universe
has to be of dimension four, a volume that exists in the time.
Also because in the 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 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.

G* h * c ^-2= 4,920 551 532 644 910E-55 cm^3/Sg

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 height are 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
object 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 260E-19 centimeters that it are 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 = 1,633
632
464 842 480E-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 are the paltry distance, in the Nature cannot exist a
wavelength shorter than Lmo, 4,897 506 921 037 260E-19centimeters. By
being the paltry wavelength it is equivalent the supreme value of
energy Emo = 253,177 660 585 902TeV.
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)
By the equivalence between mass and energy E = m • c^2, only we have
to divide by c^2 to obtain the value of the mass elementary paltry,
Mmo = 4,512 946 783 762 060E-19 grams, and any measurement of a mass
is equal to the product of Mmo by 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 on its own
dimensional units for example, the speed of the light is a length
divided by 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 are not used in this work, by considering
them it is unnecessary for its intention
The difference between the dimensional procedures of Max Planck, with
him established on 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 the work it is considered to be elementary, a volume of paltry and
indivisible spacetime of four dimensions. With a unique dimensional
formula the derivatives units are obtained of the Quantum Geometry of
the Nature. [G• h • c ^-2]
In the following list, we see the differences between both methods.
Max Planck This Work


Values (System cm, gr, sg)


5.39121 × 10-44 Seconds time Planck
1,63363 x 10-29 Seconds time this work


1.61624 × 10-33 centimeters distance Planck
4,89750 x 10-19 centimeters distance this work


2.17645 × 10-5 grams mass Planck
4,51294 x 10-19 grams mass this work


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 of 10E-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.
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 can be in the
correct way, and it is contrastable experimentally at present with
the
particle accelerators that 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 of Nature is scope of the
experimental physicists, who determine if the conclusions of this
work
is in accordance with the Nature or they are erroneous.

Extract.
If we understand the Differential calculus as a Physical Theory
(reality). Not like a mathematical model, this brings us near to this
one infinitely, but without reaching her. Using the mythological set
of the Real numbers (R). We see that it are 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, are volumes in the time (VT), of four dimensions (D4),
infinitesimal (e > 0) and of curved topology (Pi).
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 (OPi). It is 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 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
(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 has always failed by
the infinites. The origin of these is in an erroneous reading of the
"Calculus". Consequence of the error of expressing the continuity in
the term from points dimensional zero (D = 0; R) Las tentativas de
unificación de ambas teorías, esto siempre fallaba por el infinito..
El
origen de éstos está en una lectura errónea "del Cálculo".
Consecuencia del error de expresar la continuidad en el término de
puntos cero dimensional (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
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 are the result
of using the set of the real numbers out of context (scale). It are
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.
(It is supreme value of energy of an Elementary Quantum event).

Rafael Javier Martinez Olmo




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