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Quantum Geometry of the Space-Time

Model of Unification of General Relativity and Quantum Mchanics

Author: Rafael Javier Martínez Olmo
E-mail: Rafael@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 mutually exclusive properties simultaneously, such as exist and not exist, be continuous and discreet, and yet be random deterministic.

This bug appeared through the process 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 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 exist. Because it has a real and exact position in any frame of reference space temporary which is determined by its four coordinates in space time, in fact the point is used to indicate a position in space-time 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, were well aware of the speech given by Zeno.

The second time he appeared again the 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 points zero-dimensional.

The mathematical point has no point that is next or the previous. There is no point second, fifth ... nor the next or previous item to any given point. Because the set of real numbers (R) Is not an ordinal number associated to 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)

This 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 whole of real numbers (R) Is continuous (by definition) but the infinitesimal calculus can not be demonstrated mathematically in terms of points (dimension = 0), can only be demonstrated mathematically in terms of intervals (e > 0) dimension = 1.

The third time was the inconsistency appeared in the birth of quantum mechanics (Heisenberg uncertainty principle). The reality of the concept incoherent point v.olvió to remain unnoticed and broke in two physics, introducing randomness in the quantum world.

Since then the universe has both two mutually exclusive properties: it 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 if the object belongs to the macrocosmo.

Prologue Physical - First 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, it is possible to build, simply by adding, geometric objects of different dimension from that of its building elements.

If in nature there are only four-dimensional elements, the tiny and indivisible part of our universe must 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. You can do this with the following combination of fundamental constants, which is also unique:

G ·h·c^-2= 4.920 551 532 644 910.10-55 cm⁺³sg^-1
Unit of Spacetime (Indivisible, without parts).
Centimetre gram second system.

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 paltry object of the universe, this can only be, of course, a sphere.

When an area 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 by a Natural number (N)

This distance is traveled at the speed of light, Tmo = 1.633 632 464 842 480 E-29 seconds.This is the infinitesimal time interval, and any measurement of time is equal to the product of Tmo by 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. All the wavelength is equal to the product of a number Lmo Natural (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 have to 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 mass is equal to the product of a number Mmo Natural (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 their 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, using addition of c, h, G and constant Coulomb's constant Boltzmann.

These last two constants are not used in this work, as unnecessary for a description of quantum geometry (elementary = not divisible) of 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 often 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 elemental, A volume of spacetime of four dimensions, tiny and indivisible. With one dimensional formula can calculate the trace quantities and supreme Quantum Geometry of spacetime.

VT = [G • h • c^-2]

 The following table shows differences between the two calculations.

The magnitudes calculated by Max Planck length and time, are extremely small and involve amounts of energy inaccessible to our technology. The costs needed for its construction overflowing imagination, all this without entering its size that would be cosmic.

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. By 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 physical 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), curve topology (p) And represented only by the set of natural numbers (N)

This means based on differential calculus, quantum geometry is. 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 variable Op, A variable 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", that only can be described in elementary terms, for tetra-dimensional geometric objects Volumes Temporary (VT) and be represented by the set of natural numbers (N)

The term continuous is only opposed to discrete, if we use the concept of mathematical point to build the ongoing (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 equivalent, 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.

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 at this scale was almost flat, therefore, almost nula.Por influence against, quantum geometry, places the origin of the curvature and hence the geometry, any particle mass, therefore the supreme or maximum curvature energy is negligible Lmo distance of any "time-volume" occupied by an elementary 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) 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 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 the 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= 4.897 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 geometry tetra dimensional quantum level behaves as if it were 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 radiated).

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.)

++++++++++++++++++++++

First hundred levels of energy, in yellow attainable energies in the LHC.

Nivel de Energia	Energia en TeV	Nivel de Energia	Energia en TeV	Nivel de Energia	Energia en TeV	Nivel de Energia	Energia en TeV
1	253,177660585902	26	9,73760233	51	4,964267855	76	3,331285008
2	126,588830292951	27	9,376950392	52	4,868801165	77	3,288021566
3	84,392553528634	28	9,042059307	53	4,776936992	78	3,245867443
4	63,294415146476	29	8,730264158	54	4,688475196	79	3,204780514
5	50,635532117180	30	8,439255353	55	4,603230192	80	3,164720757
6	42,196276764317	31	8,167021309	56	4,521029653	81	3,125650131
7	36,168237226557	32	7,911801893	57	4,441713344	82	3,087532446
8	31,647207573238	33	7,672050321	58	4,365132079	83	3,05033326
9	28,130851176211	34	7,446401782	59	4,29114679	84	3,014019769
10	25,317766058590	35	7,233647445	60	4,219627676	85	2,978560713
11	23,016150962355	36	7,032712794	61	4,150453452	86	2,943926286
12	21,098138382159	37	6,842639475	62	4,083510655	87	2,910088053
13	19,475204660454	38	6,662570015	63	4,018693025	88	2,87701887
14	18,084118613279	39	6,491734887	64	3,955900947	89	2,844692816
15	16,878510705727	40	6,329441515	65	3,895040932	90	2,813085118
16	15,823603786619	41	6,175064892	66	3,83602516	91	2,782172094
17	14,892803563877	42	6,028039538	67	3,778771054	92	2,751931093
18	14,065425588106	43	5,887852572	68	3,723200891	93	2,722340436
19	13,325140030837	44	5,754037741	69	3,669241458	94	2,693379368
20	12,658883029295	45	5,626170235	70	3,616823723	95	2,665028006
21	12,056079075519	46	5,503862187	71	3,565882543	96	2,637267298
22	11,508075481177	47	5,386758736	72	3,516356397	97	2,610078975
23	11,007724373300	48	5,274534596	73	3,468187131	98	2,583445516
24	10,549069191079	49	5,166891032	74	3,421319738	99	2,557350107
25	10,127106423436	50	5,063553212	75	3,375702141	100	2,531776606

October 12, 2005

All Rights © Rafael Javier Martínez Olmo