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From: Q_Gravity on 9 Jul 2010 12:05
Quantum Geometry of Spacetime

Tetra Dimensional Model of Quantum Relativity

Author: Rafael Javier Martínez Olmo

E-mail: Rafael(a)gravityquantum.com

www.gravityquantum.com

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

this 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) size =

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.

To 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 tiny

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 mo

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 c2 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.

Dimensional formulas
Values (System c, g, s)
Dimensional formulas
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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