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From: Rafael Javier Martínez Olmo on 11 Jul 2010 14:58
Quantum Geometry of Spacetime
Unification of the General Relativity Theory and the Quantum Mechanics
Model
Author: Rafael Javier Martínez Olmo
E-mail: Raf...(a)gravityquantum.com

Web Page http://www.gravityquantum.com
PDF http://www.gravityquantum.com/Geometría Cuántica.pdf
Madrid
Spain
Updated: Vigo, Saturday May 22, 2010

Philosophical Prologue.

The purpose of this work is the unification of the General Theory of
Relativity and Quantum Mechanics, by eliminating the randomness in the
second.
It is unacceptable the current state of physics, it is clear that
what
we know about the workings of the Universe are biased, do not answer
some important
questions such as those involving dark energy or dark matter, and
wrong when it comes to the
very small In the case of General Relativity (GR), and when not
talking about the very small,
in the case of quantum mechanics (MC).
We know that the two fundamental theories about our knowledge of the
universe, General Relativity and Quantum Mechanics, are not
successful, then describes
two antagonistic
worlds, opposites, one of them or perhaps both, must (n) be
fundamentally wrong (s).
These theories do not get along, are not united in a more general
theory, the explanation we have this problem is fundamentally
mathematical general relativity is
not renormalizable, this unorthodox mathematical technique (not
accepted by some) was used
for the elimination of the infinite of quantum electrodynamics, nor
have we ever
considered a new idea (mathematical model) that takes the same effect
(elimación of the
infinite). Does not seem possible a mathematical model that integrates
both theories in a
single.
The reasons given for the impossibility of unification are several:
(RG) and (MC) are built with different principles, some totally
opposed to the principle of
causality. Fundamental in General Relativity. Every effect has a cause
and every cause has an
identical effect identical.
This is not fulfilled in quantum mechanics, the same cause has many
different effects, always the same, both in number of events such as
the probability that
each event is given, in addition each of the effects or experimental
results given
statistically, with an accuracy greater than one part in one trillion
(10+12).
The second reason is that they do not take into account the existence
of the other, General Relativity does not take into account the Planck
constant (h) and
quantum mechanics does not take into account the existence of
gravity.
The third reason is the space-time model they use. In the model of
General Relativity, spacetime is relational, influences the behavior
of matter and energy
and the latter in turn affect the geometry of spacetime. For quantum
mechanics the space-time
is neutral, has no bearing on the matter or energy it contains and is
not influenced by
them.
These reasons are known and accepted by most physicists.
However, there is, in my opinion, a fundamental mathematical reason
and after, which must be resolved to achieve the unification of both
models, the replacement of
all real numbers (R) for the set of natural numbers (N) to represent
physical reality.
We use the set of real numbers (R), for both theories. Which is
totally wrong as it introduces mathematical concepts in physics, which
are not measurable
(physical), as the concepts zero point or infinity. Recall that R is
an infinite set of
second order (Cantor), ie that satisfies the property that any part of
R is equal to all,
obviously, this property does not exist in nature.
The reason why the infinite appear when we joined General Relativity
and Quantum Mechanics and can not be eliminated, (General Relativity
is not renormalizable),
has its origin in the use of the set (R) to describe physically
Nature.
This choice introduces the infinite power (infinite second order) in
measurements and calculations, allows the value of a physical variable
can claim
infinite (being a singularity), such as gravity or electromagnetic
force are inversely
proportional to the square of the distance between the masses or the
electrical particles,
these forces increase with decreasing distance, if distance is zero,
the value of the
variable gravitational physics or electromagnetic force is infinite
(division by zero). These
are the infinite prevent unification, this is the error that we carry
a BUG in the
essence of logic. No physical object can have two exclusive properties
simultaneously,
such as exist and not exist, be continuous and discreet, be random,
yet deterministic.
This error by the mathematical procedure of abstraction, giving rise
to lower dimensional geometric objects to which it has a physical
nature, ie, four, three
spatial dimensions and one time dimension. I refer to the mathematical
concepts of zero-
dimensional point, line (one dimension) and map (dimension two). Just
as the mathematical
concept and physical meaning of zero.
While mathematics given its abstract nature, are almost immune to
this
error, not so with the Natural Philosophy or Physics, given its
particular character by
having to describe the reality of the laws of the universe and submit
it to the experimental
contrast. This failure is in the ambiguity of the mathematical point,
when
applied to physical concepts as distance, speed, acceleration ...
The concept of point is physically absurd. Since it has two exclusive
properties simultaneously, there and there.
It is not possible to think of physical objects that exist and not
exist at the same time, however, the mathematical concept of dimension
= 0 point, when applied
to physics presents his apparent paradox:
The point there, because it has a real and exact position in any
space-
time reference system, which is determined by its four coordinates in
space time, in
fact the point is used
to indicate a position in space-time (R4) unequivocally. The point
does not exist, because it has no dimensions (dimension =
0). No high, not long, not wide, and also there in time. This
inconsistency is subtle, but
evident after a brief reflection.
Historically this inconsistency was brought to us three times. Always
hidden under the concept of continuity. The first time was the
inconsistency is in the four fallacies of Zeno
of Elea, 2,600 years ago and whose logic is perfect, closed and
conclusive. These fallacies
were presented to the local philosophers in Athens. Perhaps before
Socrates himself, we know
that Aristotle and Plato, somewhat later, knew well the speech made by
Zeno. To pursue
the subject.
The second time he appeared again a contradiction, is the invention
of
calculus. At that time, many intellectuals were against the logic of
this theory, since
there is no way to explain the movement or its associated variables,
velocity and
acceleration, in terms of zero-dimensional points.
The mathematical point has another point to be your next, or the
previous. There is no point second, fifth ... nor the next or previous
item at any given point.
Because the set of real
numbers (R) is not an ordinal number associated with its
elements.Despite being a completely ordered, no good order. (How to
explain the movement from
point A to point B, if we are unable to leave because there is no next
point).
The contradiction is implicit in the mathematical inconsistency of
point (dimensional = zero) which is built the continuum mathematical
(R).
But as the calculation works and works, and the subtle contradiction
was discovered, the opposing views had to reluctantly silent.
Whereupon, the movement and its associated quantities, velocity and
acceleration entered the club of the inconsistencies, then: the set of
real numbers (R) is
continuous (by definition) but the infinitesimal calculus can not be
demonstrated mathematically
in terms points
(dimension = 0), can only be demonstrated mathematically in terms of
intervals (e> 0) dimension = 1

1. The third time was the inconsistency appeared in the birth of
quantum
mechanics (Heisenberg uncertainty principle). The reality of the
concept incoherent point,
again unnoticed and broke in two physics, introducing randomness in
the quantum world.
Since then the universe has both two mutually exclusive properties:
is
random and is causal, depending on the size of the object we are
studying nature, random if
it belongs to the microcosm and determines whether the object belongs
to the macrocosm.
Prologue and First Physical Predictions
The universe and all its contents has four dimensions.
Space-time has four dimensions.
The universe, as far as we know experimentally, also has four
dimensions.
The subject has always three-dimensional space (volume) and exists in
time, and energy is always a volume of space and time exists, then
both have four
dimensions. The perfect space, in the sense of lacking both matter and
energy,
does not exist. There is no way to isolate the gravity of a "volume of
space-time."
The relative vacuum, ie that at least contains gravity, has
therefore,
four dimensions.
There is no physical example (that is, it can be measured), objects
in
our universe, having a number of dimensions different from four.
Following Euclid can not be constructed by simple addition,
dimensional geometric objects different from that of its building
elements.
If in nature there are only four elements of size, the tiny and
indivisible part of our universe has to have four dimensions. That is
a volume that changes
with time.
There are no objects in nature in less than four dimensions, only
exist in the Platonic world of ideas as mathematical abstractions of
reality.
o calculate the value of the lowest volume-time we use the
fundamental constants of nature, c, h, and G, similar to as it did a
century ago, Max Karl Ernst Ludwig
Planck, the combine looking for in this case a volume-time , ie, a
unit of volume in a
unit time. This can be done with the following combination of
fundamental constants, which is
also unique:


G·h·c^-2= 4.920 551 532 644 910.10-55 cm+3No SG-1


Temporary Volume ïnfimo


Centimetre gram second system (centimeter, gram, second)


As we know, the universe is isotropic, ie has no preferred spatial
directions, in either


direction has the same appearance and properties.


The distinctions we make between length, width and height are merely
semantic, because we can share with their names and will continue to
represent the same
physical reality. If we associate the idea of isotropy elementary and
tiny object in the
universe, this can only be, of course, a sphere.
As a sphere is easy to calculate the radio: Lmo = 4.897 506 921 037
260E-19 cm distance is negligible and any measurement of distance is
the product of Lmo for a
Natural number (N) This distance is traveled at the speed of light, mo
= 1.633 632 464
842 480 E-29 seconds.
This is the time interval negligible, and any measurement of time is
equal to the product Tmo for a Natural number (N).
As the distance is very small, there can be a wavelength shorter than
Lmo, 4.897 506 921 037 260E-19 inches. As the tiny wavelength is the
supreme value of energy
Emo = 253.177 660 585 902 TeV.
Any wavelength is equal to the product of Lmo for a Natural number
(N).
The value of any measurement of a quantity of energy is equal to
divide Emo for a Natural number (N).


On the equivalence of mass and energy of Einstein E = m • c2, we just
divide by c^2 to obtain the value of the tiny elementary mass Mmo =
4.512 946 783 762 060E-19
grams, and any measurement of a mass is Mmo the product of a Natural
number (N).
This dimensional procedure was devised by Max Planck to determine the
absolute units of nature, because they are derived from the universal
constants, each of
which is expressed in its own dimensional units, for example the speed
of light is divided
by a length time.
Max Planck considered a century ago, the length, mass, time, electric
charge and temperature as key elements to describe the nature, and
using c, h, G, Coulomb's
constant and steady Boltzmann.
These last two constants are not used in this work, as unnecessary
for
the description of quantum geometry (elementary = not divisible) Space-
time.
The difference between the Max Planck dimensional procedure, with the
establishment in this work is that we consider elemental. For Planck
are the length, mass
and time. That it is quite debatable question, contrary to the
currently
accepted idea that is well reflected in the following paragraph:
"The system measures several of the fundamental values of the
universe: time, length, mass, electric charge and temperature. Planck
Units are called (in jest) by
physicists as "units of God." This eliminates any arbitrariness
anthropocentric system of
units. " Excerpted from Wikipedia, Planck units.
This paper considers such magnitude Elementary, a volume of spacetime
of four dimensions, tiny and indivisible. With one dimensional formula
can calculate the
trace amounts and supreme Quantum Geometry of spacetime.

VT = [G • h • c^2]
The following table shows the differences between the two
calculations.
Values (System c, g, s)

Max Planck t= 5.39121 × 10-44 seconds
This Work>>t = 1.63363 × 10-29 seconds
Max Planckl= 1.61624 × 10-33centimeters
This Work>>l = 4.89750 × 10-19 centimeters
Max Planckm = 2.17645 × 10-5 grams
This Work>>m = 4.51294 × 10-19 grams

The magnitudes calculated by Max Planck length and time, are
extremely
small and involve amounts of energy inaccessible to our technology.
A wavelength of about 10E-33 cm is equivalent to an energy of 3.89626
E +11 TeV approximately one trillion (10E +12) times the maximum
energy of
current particle accelerators.
In contrast, the mass is large, comparable to the mass of a bacterium
2.17645E-5 gr. and therefore accessible to experimentation, however,
have found no
correlation between its value and any quantum experimental fact.
Clearly it seems that Planck units have no physical meaning.
By contrast the magnitudes calculated in this work may be on the
right
track, and are experimentally testable energy levels of current
particle accelerators
such as CERN (LHC).
The highest amount of energy 253, 177 TeV. It is only two orders of
magnitude from the previous particle accelerators, quantum geometry
has probably already
been photographed, but has gone unnoticed among the billions of events
and data obtained in
the experiments of these large accelerators.
For the first time, quantum gravity be viewed by experimental
physicists, particularly those currently working at CERN (LHC), which
are those that may determine if
the predictions of this work are in agreement with nature or
erroneous.
Extract from the model.
If we understand the differential calculus as a physical theory
(reality). Not as a mathematical model, which leads us to it
endlessly, but without
achieving it. Using the Mythological and physically absurd set of real
numbers (R). Proven to
be the logical way that shows the elemental nature and quantum of the
Geometry of Space-
Time ", whose basic components, in the sense without parts, are
volumes in time (VT) in
four dimensions (D4) ,infinitesimal (e > 0), topology curve (p.) And
represented only by the
set of natural numbers (N)
This route based on the Differential Calculus, Geometry is the
quantum. The paper lays the
foundations and theoretical foundations of this road, which unifies
the experimental results of quantum mechanics with the theory of
general relativity, by
including the variable Op, a variable hitherto invisible, hidden,
Op = curvature of space-time elementary quantum Event
The relational model is independent of the fund (Quantum Relativity),
where both the General Theory of Relativity and quantum mechanics are
modified.
Neither the structure nor the variables, the results of both models
can be expressed as belonging to the set of real numbers (R), all
these belong to the set
of natural numbers (N).
General Relativity can not be expressed as a hyperbolic geometry, but
an elliptical geometry of topology spherical (p) and radial dynamics.
Quantum mechanics is also introducing causality completed, replacing
the statistical treatment (casual, random) by a geometric treatment
(causal,
deterministic) to include the variable Op . This variable Op gives a
causal explanation of quantum
mechanics, establishing a two-way connection between the statistics
and the basic geometries
(without parts) of the "Spacetime" containing those quantum events.
Also, determine the geometry and the metric of nature in its
elemental
scale, tiny and indivisible, specifying the model of Quantum
Relativity.
Attempts to unify the two theories, they have always failed by the
appearance of the infinite. The origin of these uncertainties is a
misreading of
"Calculus." Result of the error to express the continuity based on
zero-dimensional points (D =
0, R.) The set of real numbers (R) have allowed us to date represent
the
physical reality to our scale, but sinks to confront unequivocally the
description of
elementary and indivisible nature of the "Spacetime", which can only
be described in elementary
terms, for tetra-dimensional geometrical objects, Temporary volumes
(VT) and be
represented by the set of natural numbers (N).
The term continuous as opposed to discrete only if we use the concept
of mathematical point that continuing to build (D = 0, R) (infinite
divisibility). There are no physical singularities in nature, are the
result of using
the set of real numbers out of context (quantum level). They are
therefore
mathematical singularities (division by zero), not physical.
Other Predictions.
1 .- Quantum mechanics describes the universe when the radio-temporal
volumes, containing the event, tends to 4.897506921037260 E-19 cm. Lmo
paltry distance. At
this distance of an elementary mass Mmo, the universe has the highest
curvature, or
equivalently, is the supreme power of a quantum event. This wavelength
corresponds to an energy
level 253.177660585902000 TeV. This energy level has an asymptotic
nature in the sense of being
unattainable or supreme.

Energy Supreme of an elementary quantum event = 253.177660585902 TeV

2 .- The hidden variables of quantum mechanics are in the geometry, a
very small scale, space-time that contains the quantum event. Until
now we thought that
the spacetime curvature on this scale was almost flat, therefore,
influence
negligible. In contrast, the quantum geometry, places the origin of
the curvature and hence the
geometry, any particle with mass, hence the supreme or maximum
curvature energy is negligible
Lmo distance of any "time-volume" occupied by elemental mass (Mmo).
The ultimate curvature
is:
1/Lmo = 4.897 506 921 037 260 E +19 cm -1
3 .- As we know from Feynman, quantum electrodynamics (QED Quantum
Electrodynamics) suffered in the beginning that all the results given
were infinite. The reason
is that the sum of stories must take into account all possible paths,
and they depend on
the distance between particles, this distance becomes zero, enter zero
to infinity in the
results. Feynman decided not to carry the calculations to zero to
avoid
uncertainty, replacing it with a very small number 10E-100 cm. and
stopping sums over histories
in that value. This was a solution to the uncertainties, but other
problems appear, you
lose the uniqueness of probability, in addition to appearing with
energy infinitesimal terms
negativa. Estos problems go away, if instead of using a very small
distance and
arbitrary, we use the paltry distance Nature, Lmo = 4.897506921037470
E-19 cm. to interrupt the
sums over histories. Both problems appear to add interactions likely
exist. Specifically, all
calculated for distances less than Lmo.
4 .- The tetra dimensional geometry at the quantum level behave like
two-dimensional (only two degrees of freedom) as the radius determines
the three spatial
dimensions and time dynamic evolution, the radio also has the same
ordinal that time (line
label spherical ring and the time since it was irradiated). This model
is finite, quantitative and predictive. Experimentally
testable energy levels between 1 and 8 TeV. It will be compelling to a
lower energy level to
253.177 660 585 902 TeV. (Value Supreme Elemental energy of a quantum
event.)

October 12, 2005
All Rights © Rafael Javier Martínez Olmo
 | 
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