Mechanical quantum fractal?

Benoit Mandelbrot was saying that the geometry fractal teaches us to observe this old world with a few new eyes. The existence of all that of action that is intimately joined to the proper nature of the energy of the quantum fluctuations of the gap forces that his structure is discontinuous, staggered, fractal, for it the geometry fractal can teach us something that earlier we could not see.

I believe that there are objective arguments to consider a quantum mechanics to be a mechanical quantum fractal, that is to say under the point of view of the geometry fractal, but in science there exist a few tendencies or fashions of which it is difficult to turn aside, although it is to give a short walk. This can be one of the problems for which the current physics is stagnant.
And it is not a reflection of mine, some of the best physicists say it about the actuality, it is escaping from us a little that we must have it in front of our nostril and are not capable of seeing it. Sincerely, I believe that the fractales can help us to find it.
With the fractales, in certain way, we undo the abstraction that leads us to passing from a real object to ideal geometric objects for a line, a bucket or a sphere, and approach a little more the above mentioned real object. Benoït Mandelbrot uses the simple example of something real, as there are the coasts of the countries, to come closer the fractales. There are broken lines that keep on having a similar aspect when we change scale. Precisely these two properties are those who define a fractal: discontinuity (it plows, fractures, hence his name) and autoresemblance with the change of scale. We measure his grade of break and aberration with a simple number that we call a dimension fractal.
On this matter it is important to revise the structure concept fractal of Kenneth Falconer in his titled work “Fractal Geometry: Mathematical Foundations and Applications”, in 1990. In her it describes a structure concept fractal ‘F‘ as that satisfies someone (s) of the following properties:
(1). - “F“ it possesses detail to all the observation scales;
(2). - It is not possible to describe "F" with Euclidean Geometry, so much local as globally;
(3). - “F“ it possesses some class of autoresemblance, possibly statistics;
(4). - The dimension fractal of "F" is major than his dimension topológica;
(5). - The algorithm that serves to describe "F" is very simple, and possibly of recursive character.
Benoit Mandelbrot was saying that the geometry fractal teaches us to observe this old world with a few new eyes. The existence of all that of action that is intimately joined to the proper nature of the energy of the quantum fluctuations of the gap forces that his structure is discontinuous, staggered, fractal, for it the geometry fractal can teach us something that earlier we could not see.
Curiously, if we look in google "mechanical quantum fractal" or in English "Fractal quantum mechanics", practically we do not find anything. In Spanish I have found this marvelous linkage to Science Kanija. In my entry on "Ten dimensions, superropes and fractales" (*), you can read something more especially this. A greeting friends.
(*) The University of Chile, in his magazine Open Science, published to me the article “Stabilization of the quantum gap and rolled up dimensions”, (later other more finished two) on the possibility that the study of the energy of the quantum fluctuations of the gap should demonstrate to us, by implication, the existence of 6 rolled up dimensions that needs the superropes theory. The calculations seem to indicate that about the state in which there was adopted the configuration of 3 ordinary dimensions and 6 compactadas, the proper nature should be had decided of all that of action

Slightly more on fractales, his spatial dependency

The dimension of a fractal is intimately related to the way in which this one spreads over the space. His dimension gives us the aptitude of the fractal to cover a dimension space topológica superior to his, in fact, a trajectory fractal with dimension 2 it is capable of covering the plane, and of dimension 3 the three-dimensional space.

Let's imagine that in a space of three dimensions we meet a species of virtual devil moving randomly, with entire freedom, and trying to cover it completely. His trajectory will be a broken line, with infinity of bends, which end will be to happen for all the points of the space. As line of trajectory that is his dimension topológica will be the unit, but his aptitude to cover the space indicates us that we are before a geometric object different from the typical Euclidean objects that we have studied in the school, like the point, the line or the plane of dimensions zero, one or two. This type of objects is what Benoît Mandelbrot was calling in 1975 fractales objects, word that he invented from the Latin adjective “fractus“ (I rotate, fractured).
Dimension fractal. The dimension that defines the trajectory of the devil is already not the classic dimension of a line (the unit), but we must add to her a dimensional coefficient that indicates us his aberration grade. The sum of two coefficients gives us a new dimensional value to which we call dimension fractal. In this case we do the following sum: classic geometric dimension (1) + dimensional coefficient (2) = dimension fractal (3).
Dependency with the distance. There is a detail more than us it gives an idea of the movement that takes the devil. The entire distance that it covers after N of his steps must be only the cubic root of his effective alienation to an arbitrary point, that is to say an effective distance moves away d, of a point any, his entire trip will have to be d3. This exponent (3) is giving us, also, the dimension fractal of the movement. In certain form it is logical that it is like that, so the volume that intersect and the trajectory covers it performs the order of the bucket of his typical distance (Volume = Lado3).
In a spatial trajectory fractal:
(1) Covered entire distance = effective Distance (dimension fractal)

Being the dimension fractal equal to the dimension topológica more a more intricate the positive, so much major dimensional coefficient is the fractal, the expression (1) would stay:
(1) Covered entire distance = effective Distance (dimension topol. + coef. dimensional)

Can the geometry of the space modify the dimension fractal?. Let's imagine a trajectory fractal that happens from a space from 3 dimensions to other of 2. In the reality it might be the gradual step of 10 cm tubes. x 10 cm. to other one of 0,1 cm. x 1000 cm., of the same wealth. For, it depends that movement, the step might suppose changing, practically, from 3 to 2 dimensions. In the new situation the dimension topológica would have descended in a unit, therefore for the same dimensional coefficient (that depends on the aberration of the fractal), the new dimension fractal would be minor. The dimensions decrease topológicas acts of opposite form (remaining) to as it operates the dimensional coefficient (addend). In the end we would obtain, in practice, a less irregular and intricate movement.
And especially this, in somewhat informal plan, I add an articulito that was published in the web of the Real Spanish Society of Physics, in the forum of debate on Entertaining Physics. A few months earlier it had been published in the magazine ImasD of science and technology (magazine in role, later electronics and today eliminated: www.ImasD-tecnologÝa.com).Otro very simple later, also article, published by the Magazine Elements, of the Autonomous University of Puebla: The surprising quantum gap.

The devil Aleaxis and the effect of concealment of mass.

Aleaxis is a nice and unconscious devil that not of to pass, to fools and to madwomen of random form, in any direction of the plane. His trajectory is discontinuous, it can be represented by a broken line that would end up by covering the whole plane. In his awkwardness, to cover an effective distance of "n" steps it must give as it comes up n x n, that is to say n2 steps: his trajectory, in fact, represents a fractal, a broken and discontinuous dimension structure 2, the dimension fractal that cigar characterizes at random.
Of similar form, the fluctuations of energy of the gap (beginning of suspense) represent another devil, this real time and powerfully, that makes our universe much more interesting. Without him the gap would be empty, in addition to it seeming, it would be flat and it would be absolutely calm. This devil, somewhat slippery and not awkward at all, wrinkles the space - time and turns it into a fractal similar to the trajectory of Aleaxis. This time, so that we observe “n steps” of effective fluctuation of energy, the devil "gives" n x n x n steps, that is to say n3.
Observing, only, the effective Aleaxis steps and knowing that his trajectory is a fractal we can infer that there exists a “effect of concealment of steps”. Of the same form, on having observed the effective fluctuations of energy of the gap (there are the only ones that we can observe), we deduce that there is a powerful “effect of concealment of energy“ (or mass, for the beginning of equivalence between mass and energy).
The powerful devil of the fluctuations, in addition to wrinkling the space - time, coils part of his dimensions to accentuate the “effect of concealment”. If only it was limiting itself to wrinkling the fluctuations of the energy they would interfere the sufficient thing not to allow us to see the gap as such (on not having depended on the inverse one of the distance but of his cubic root). In the reality they depend on the inverse one of the distance: at big distances his value is despicable, at small distances it is impressively big, contributing to the impression of a paradoxical "superdense" gap. The devil acts like a real magician: he hides enormous mass quantities, behind his rolled up wrinkles, until the gap makes "appear". Only on having approached, “in the small distances“, we warn his trick.

What there hide the fractales and the dark energy, a hypothesis

The fractales hide under his "wrinkles" part of himself. Supposing the hypothesis of a quantum gap fractal, the slippery dark energy might be the consequence of the structure fractal of the quantum fluctuations of the gap that shape the whole space.

The measurement of the coast of Brittany
Benoït Mandelbrot was wondering how much was measuring the coast of Brittany, or any real coast that is usually irregular and intricate. A geographer would have answered it to himself perfectly, but it was not this it replenishes that he was looking for Mandelbrot. The geographer assumes that, on having measured the coast, it has to do it with a few certain practical criteria, abides by them, measures it and registers it forever in the geography books.
For Mandelbrot, the question was much more transcendent than it can seem to simple sight, because he realized that the measurement was depending on the unit of measurement with which it was going to be carried out. If the minimal unit of measurement to be taken was one kilometer, we would find a value, and if this minimal unit was the double would find a minor result. The same way as the used unit is minor, on having carried the measurement out, we approach better the aberrations of the area and find a major value. For a theoretical mathematical coast, de facto, we can make the measurement unit tend to zero as much as let's want and the result obtained will always be major. In the limit the length of any theoretical coast is infinite.
Fractional dimension of a coast
The coasts are simple examples of a few mathematical objects that Benoït Mandelbrot called fractales, because his structure is discontinuous, broken or fractured (of the Latin "fractus") and they support the same aspect to different scales. In contrast to the continuous geometric objects that we know as lines or planes, the fractales are capable of "filling" more space of the one that they should fill. The coasts fractales, as lines that are, should have the aptitude to fill a dimension, but really they fill 1.25, 1.30, 1.35 … etc. His dimension, which is fractional, is between the line and the plane, that is to say between 1 and 2, and similar sound more irregular major is his dimension, to which we call dimension fractal.

Classic gap and quantum gap
The classic and continuous gap is, in certain form, like a linear and regular coast, without inlets or protrusions. The quantum gap is very different, his fluctuations award an irregular structure that can remind the structure to us fractal of the coasts of the countries. Of “background“ it is not different from the classic gap, but of “fence“ it offers us a very different vision, the fluctuations gain leading role because they depend on the inverse one of the distance: over a distance half there are the double of intense. This difference between the classic gap and the quantum one can be observed, perfectly, trying to continue the trajectories of the subatomic particles. In the classic gap these are well definite and are continuous lines, in the quantum gap they do not exist as such, there are no properly trajectories since the same way as we try to observe them in a more detailed way, more irregular they appear. 2 are fractales with a dimension.
Quantum gap as a fractal?
All this makes to think about the possibility of considering the quantum gap to be a fractal, in which the energy of the quantum fluctuations would determine his aberration grade, and based on his value (one to climb) it might calculate the dimension fractal of these fluctuations that shape the whole space.
What there hide the fractales and the dark energy, a hypothesis
Between two points A and B of the space euclídeo it is possible to plan a straight line. The distance between two points following this straight line is the length of the same one. Nevertheless if we turn this straight line on a coast fractal real (without the infinite aberrations of a coast fractal mathematical), the distance between two points, following the coast, it is possible to do everything big that is wished depending on the quantity of aberrations of the same one.
If we observe this coastal line in the distance, the aberrations are hidden and his aspect approaches that of a much more regular line. His distance shows off also AB will be near to that of the straight line. We will know the real distance AB across the coast fractal and the distance shows off, dress the coast from a distance. In certain form it seems that it has eliminated a part of the coast, a part that from a distance we do not manage to observe, because she remains hidden between the aberrations of the fractal.
If we suppose the hypothesis fractal of the quantum fluctuations of the gap: might the part hidden by this immense fractal be the called dark energy?


In the figure: (representation of the gap
quantum), the most wide lines correspond with fermiones (quarks, electrons...) and his antiparticles, while the thinnest lines correspond to bosones (gluones, photons, W +, W - Z0...). In the relating thing to the color of the quarks and gluones, they correspond to the load of color of the same ones while the insensitive particles to the strong interaction appear in target or gray).
What we know till now about the dark energy
The exact nature of the dark energy is a speculation matter. It is known that it is very homogeneous, not very dense and the interaction is not known with any of the fundamental forces any more than the gravity. Since it is not very dense, approximately 10−29 g / cm, it is difficult to imagine experiments to detect it in laboratory. The dark energy can only have a deep impact in the Universe, occupying 70 % of all the energy, because on the contrary it fills uniformly the empty space.
Two possible forms of the dark energy are the cosmological constant, a thickness of constant energy that fills the space in homogeneous form and fields you will climb like the quintessence: dynamic fields which energy thickness can change in the time and the space. In fact, the contributions of the fields you will climb that they are constant in the space normally also they are included in the cosmological constant. It is thought that the cosmological constant originates in the energy of the gap. The fields you will climb that they change with the space they are difficult to distinguish of a cosmological constant because the changes can be extremely slow.
To distinguish between both there are needed very precise measurements of the expansion of the Universe, to see if the expansion speed changes with the time. The expansion valuation is parametrizada for the equation of the state. The measurement of the equation the state of the dark energy is one of the biggest challenges of current investigation of the physical cosmology.

The natural measurement of the things

The relation that we try to establish between two quantities can be deceitful. Sometimes the most logical values of the same ones remove us from the reality and from the phenomenon that we try to study. The common sense can give us an approach of the result capable of guiding us to find the correct solution, which adapts itself really to the reality.


Let's suppose that we want to relate two quantities that correspond to a palpable reality, for example two lengths of a certain object, and give us the following measurements: 2 and 1/2, 3 and 1/3, 4 and 1/4... n and 1/n. Being n a natural number. The division between them does not offer us any conflict, it will be 4, 9, 16... n2, the times quantity is giving us that a quantity is major than other one. Nevertheless there are relations that can give ambiguities if we allow ourselves to guide for the result purely mathematically. For example, if we concentrate on the figure that the classic fractal represents called flake of Koch and his construction, we see that in every iteration we replace a segment of 3 units with four segments of a unit: exactly the relation between log 4/log 3 gives us the dimension fractal of the figure, which is 1.261859 … If what we want to relate there are two lengths represented by any natural number N and his inverse one 1/N, on having found the relation similar to the previous one, of the flake of Koch, we are with a negative value,-1, a negative dimension for a fractal, when physically he has not any sense, since the dimension fractal is always equal to the topológica (or apparent dimension) more a more irregular the dimensional, so much major coefficient is the fractal.
Mathematician and logician, Kronecker was defending that the arithmetic and the analysis must be founded in the entire numbers doing without the irrational and imaginary ones. He was an author of a phrase much known between the mathematicians: "God did the natives; the rest is a work of the man" (Eric Temple Bell 1986, p.477. Men of Mathematics).
This is the question, in our case we must turn 1/N and N in two new natural numbers than on having been related, to express the value that represents the dimension of the object, us of a coherent result with the reality that we are observing. The figures that continue to this paragraph clarify to us the way to be taken to find a possible solution, for this particular case.
We see the construction of a figure when N=3, N=4 and N=5. In the first figure if we give the value 3 nearby, his perimeter will be 27 (33), but if we give him the value 1/3, his new perimeter will be 3. This way it happens for N=4 ó N=1/4, etc, and in general for any value N and 1/N (with N finite, although so big as let's want). It will always happen that if the side is N the perimeter will be N3 and if the side is 1/N the perimeter will be N, without for it it changing the form of the figure.
The natural conversion will be the one that the measurements couple transforms (1/N, N) in (N, N3) and the irregular value,-1, which we were finding for the dimension fractal of the curve would turn into 3. This value would give him to the curve the aptitude to fill the space. It is a fractal with entire dimension, of form similar to the case of a pure random movement, which from every N2 steps realized only moves away N, from any arbitrary point of reference that we consider, and therefore it has a dimension fractal equal to 2, capable of filling the plane.
In fact, for our case (1/N, N), infinite conversions exist, they answer to the expression:
Dim. fractal (*) = 1 + 2/logL (N), being L (N) the value of the side that we consider, like function of N. For L (N) = 1/N we have the value-1, for L (N) =N, the value corresponds to him 3, as we have said. For values of natural exponent more negatives (1/N2) and major the dimension approaches asintóticamente to l. For major values of N, as N2, N3, or of much major exponent the value asintótico will be also 1.
In the end we cannot trust blindly in the value that the mathematics give us, since the world that they represent is much wider than the real world and we will always need our common sense, in the analysis of the opposing results. On the other hand, paradoxically, sometimes the opposite happens: the common sense blinds us and prevents us to see a reality deeper that sublies in the mathematical results.
(*) Taking logarithms in base N
Duality T, (1/N, N)
Like simple curiosity, on the values exchange 1/N and N, and like culturilla on ropes theory, all this can remind the called Dualidad-T to us:

In the expression that represents the squares of the energies of the excitements of a rope in a space with a curved dimension or compactada, K. Kikkawa and M. Yamanaka in 1984, observed that the formula keeps on having the same aspect if we do the exchange R 1/R. Being R I remove microscopically of the dimension that bows.
From a physical point of view this indicates that the energies of the excitements of a rope, when there is an extra radio dimension R, it is the same that that of a rope when the radio is 1/R. Not already the energies, but all the physical properties of both systems are exactly the same ones. It attracts attention, so when R it increases 1/R it decreases, contradicting the experience of the daily life, which says to us that the small things differ from the big ones. For a rope it is not like that.
On "Unification and duality theoretically of ropes", to see the number of August, 1998 of Investigation and Science, of Luis E. Ibáñez Santiago. Watch The Good Wife S01E17 Heart now

The porcupine and the strange drafts of the fermiones

Of all the physical quantities the acquaintance as porcupine usually thinks like more "Meccano quantum". The word porcupine comes from English "spin", that means draft or to turn, and refers to a physical property of the particles (1) subatomic, as which any elementary particle has an intrinsic angular moment of fixed value. It is a proper characteristic of the particle as it it is the mass or the electrical load, and a magnitude that survives as the energy does it or the linear moment.

In contrast to what it happens with the angular moment of the macroscopic objects, to which we are accustomed, that can take very varied values depending on the actions to which they turn out to be subject, the magnitude of the porcupine of a particle is always the same one for this concrete type of particle. It is only the direction of the axis of draft the one that can change, although in a very strange way.

For an electron, proton or neutron the porcupine quantity is always 1/2 of the minimal value at the moment authorized (ħ). Precisely that's why this quantity at the moment angular would not be allowed for a compound object certainly number of particles orbiting without none of them being turn on itself. The porcupine can only appear because it is an intrinsic property of the proper particle, that is to say, that does not arise from the orbital movement of his parts concerning his center.

A particle that, like the electron, has an odd multiple porcupine of ħ/2 (ħ/2, 3 ħ/3, 5 ħ/2, etc) is called fermión, and presents a curious oddness: a finished rotation of 360th transforms his vector of the state not into himself but into the negative value of himself; he would need therefore a draft of 720th to remain just as before the draft. Most of the particles of the Nature are fermiones, the remaining particles for which the porcupine is a multiple point of ħ (ħ, 2 ħ, 3 ħ, 4 ħ, etc) they are called bosones. Under a rotation of 360th the vector of the state of a bosón returns to itself, and not to his negative.

If we take a porcupine particle 1/2, for example the electron, the space of the states Meccano quantum possible turns out to be two-dimensional, so that we can take a base of only two states that we can represent like [it arrives> and [below>, for the first one the porcupine turns to rights about the vertical direction up and for the second one it does it of the same way down. Likewise in an Euclidean plane any vector is a linear superposition of two bases ortonormales considered, in this case it happens equally, any possible state of porcupine of the electron is a linear superposition, for example:

w [it arrives> + z [below>, being w, z two complex numbers. Since the represented physical state remains unaltered if we multiply the component two by a complex number different from zero, the reason z/q will be the significant complex number that the state of the particle represents.
This complex number is represented on a Riemann of called sphere, as it appears in the figure. In the equator of the same one the singular points 1,-1 are, i and-i.

The Riemann sphere plays a fundamental role in any quantum system of two states, describing the set of the possible quantum states. For a porcupine particle 1/2, his geometric role is a particularly clear position that the points of the sphere correspond to the possible spatial directions for the draft axis. In other situations the role of the sphere of possibilities of Riemann is more secret enough, with a much less clear relation with the spatial geometry.
The strange draft of 720th of the electron to remain equal is the whole paradox. Frequently it seems to us that the quantum mechanics presents phenomena completely out of any logic, but on having analyzed infinity of completely normal situations for us in view of this amazing theory, we observe that without her they have no explanation. The proper cohesion of the matter, as we know it, or the existence of four fundamental forces they would not have sense. In the latter case in his essentials, paradoxically, is the proper beginning of suspense. A "bothersome" beginning that seems that only it serves to prevent us from measuring with infinite accuracy.
(1) It is admitted that a "particle" can possess individual parts with such that could be treated mecanocuánticamente like a quite simple one, with a well definite entire angular moment.

The infinite and further away, the numbers transfinitos Aleph

At the end of the XIXth century the original mathematician Georg Cantor proposed a beautiful theory on the finite numbers or transfinitos, according to which the entire number of fractions, entire numbers and natural numbers are the same number transfinito to the one that Aleph sub-zero called.
At first sight it does not seem slightly reasonable, since it might think that the number of points is major than the number of natives, since any natural number is a point while some points (the negatives) are not natural numbers. Of similar form it might think, also, that the number of fractions is major than that of points, but a thing is what seems and other one what is.
The key is in the strange properties of the infinite numbers and the relations that can be established between them. For finite objects of two different sets if we can establish a "mail one uno - or", between both, it is possible to deduce that they have the same number of elements. For a finite number of natural numbers it happens the same, but what is clear for finite numbers it stops being for infinites.
One one can establish a mail uno - or between the natural numbers and the entire numbers of the following form: 0 (point)-> 0 (native);-1 (I inform)-> 1 (native); +1 (point)-> 2 (native) and this way we continue indefinitely with the following table:

Every point and every natural number appear one and only once in the table. This mail between every pair of numbers point - native is what it establishes in the Singer's theory that the number of elements of the column of points is equal to the number of elements in the natives' column. Consequently, the number of points is the same that that of natives. Of similar form, although slightly more complicated, it is possible to prove that the set of (rational) fractions has the same number of elements as the set of points. The number is infinite, but it does not matter, it is the same number.
The big mathematician David Hilbert invented the metaphor of the Infinite Hotel to explain of intuitive form the paradoxes to which we are faced by the existence of infinity of infinites:
"There was a hotel that had infinite rooms. A new guest comes one day to stay there, but the caretaker says to him that it had no luck, that all floods were. The guest, infuriated calls the manager, and asks him how it was possible in a hotel with infinite rooms. The manager gives him the account, but he says that it cannot do anything, then the guest answers quickly: ' already what it is possible to do; there orders in that it is in the room 1 to the room 2, to that of the room 2 to 3 and this way successively, then the room 1 will remain free for me. The gerenteencontró ma ravillosa this solution and this way it did it".
"Some days later another guest comes and he asks of staying, to what they answer him that the hotel was full, but him not to worry, that they knew how to solve it. Then this guest says that there was a problem, that he was not alone, but with a group of friends … and that was an infinite group. The manager, again dismayed did not know what to do, but the guest, also very skillful says to him that he should not worry, that it should order that of the room 1 2, that of 2 4, that of 3 6 and this way successively. Thus all the rooms with odd numbers would remain free for his friendly infinites."
The sets that can be put in mail one uno - or with the natural numbers they are called numerables, so that the infinite sets numerables have aleph sub-zero element.
Surprisingly, although the system is extended from the natural numbers to the points and to the rational ones, we do not increase really the number of objects with which we work!.
Later all this we might think that all the infinite sets are numerables, but it is not like that, not only there is a type of infinite, so the situation is very different on having gone on to the real numbers. Singer demonstrated by means of the argument of the "diagonal court" that really there are more numbers real that rational. The number of real is the number transfinito C, constantly, another name that receives the system of the real numbers.
We might think of giving him to this number the name of aleph the sub-one, for example. But this name represents the following number transfinito major than aleph sub-zero and deciding if really C = Aleph constitutes the sub-one a famous not decisive problem, the called hypothesis of the continuous one.
Like curiosity, since we are speaking about infinites, the term gugol (in English googol) is an enormous number 10100 there was minted in 1938 by Milton Sirotta, a 9-year-old child, nephew of the American mathematician Edward Kasner. Kasner announced the concept in his book The mathematics and the imagination. Isaac Asimov said in an occasion on this matter: "We will have to endure eternally a number invented by a baby".
The gúgol is not of particular importance in the mathematics and neither it has practical uses. Kastner created it to illustrate the difference between a number inimaginablemente big and the infinite, and sometimes it is used this way in the mathematics education. The engine of search of google was called this way due to this number. The original founders were going to call it Googol, but they ended with Google due to an error of spelling of Larry Page, one of the founders of Google.

History, dignity and effect butterfly

We are crossing a serious world crisis of that nobody is sure how we will go out. Macroeconomic numbers are analyzed and plans are designed to stabilize the system, but nothing will work if there is not born in mind the principal factor that sublies in any crisis of a system: the human factor, a factor simultaneously estabilizante and destabilizing.
The amazing of the history
There is something amazing that has always attracted attention of me on the history. It happened earlier, it happens now and, possibly, it will always happen: the humanity seems neither to know, nor be able to control really, where it goes. The events happen and when everything seems stingy and in his place, there comes a new incident that spoils everything, wars, revolutions, economic crises or any another catastrophe. Before these situations the history, after happened, extracts his conclusions and helps us to prevent from repeating themselves again, but there is always something that escapes from us and everything derives again in some new catastrophe, everything begins again again.
Effect butterfly
In physics there exist a few systems that are extremely sensitive to the initial conditions. For very well that know the variables that are going to influence his development, for very sophisticated that there should become the instruments that measure them, there will always be a minimal suspense that will influence, decisívamente, the later development of the system. A minimal cause will be capable of unleashing big consequences. This effect is known, popularly, with the name of “effect of the butterfly”. Of exaggerated, but very graphic form, it is explained that the simple flight of a butterfly, in Africa, can unleash, with the time, a hurricane in China. The first one of these systems that was studied, somewhere near the sixties, was the time metereológico.
Effect butterfly and history
From the first moment, in which I had knowledge of this curious type of physical systems, he reminded to the proper one to occur of the history. We know thousands of small anecdotes that influenced, decisively, the later development of extremely important events. Any of these minuscule causes, on having developed in a different way, would have changed the destination of any country or of the world. The history has passed, during thousands of years, curdled with million with events of major or important minor, interlaced of random form or not. In many senses, it might be considered to be a system “very sensitive to the initial conditions”, not linear system and with infinity of feedbacks. Fortunately, the manipulators that try, and they will try, to change the destination of the nations, hardly, they will be able to bear in mind all the necessary variables to obtain his intention. Very short-term it is possible that his calculations are correct, but in average and long term they will be wrong. The small miscalculations, the same way as the events develop, they are having major influence in the results them up to going so far as to disfigure. The well-intentioned performances will come across, in principle, with the same disadvantages before the effect multiplier of the small miscalculations on the system. More now, that the effect of the globalization trasforma to the world in a more sensitive and unstable system.
Dignity and stability?
Apart from the factor purely “physical“, of the suspense, there is a cardinal element, in the historical development, which the manipulator stretches to forget and which is allied by the “effect of the butterfly” to spoil his plans. It can seem slightly scientific, even unreal, but, far from that, it obeys an observable and solid reality, and it is an essential element of the human factor: the dignity humanizes. It does not act like engine of the history but rather how "encauzador" of the real engine. This one, certainly, is not foreign to the egoism in his most diverse forms perverse in major or minor measurement.
The egoistic power tends to tread on everything, without any type of consideration. It is a coarse motive element, like a thunderstorm. But in contrast to the thunderstorm that acts without obstacles, obeying physical laws and conditionings purely mechanical, the power always has face to the dignity of the person. He will tread on it one and thousand times, will despise it, but in the end it will find it face to face, facing him, in the germ of any revolution or necessary change. And it will be capable of re-leading the proper current of the history. This is the difference between the physical, chaotic systems in the sense in which they can continue very different trajectories of future, the same way valid, and the “sensitive system” of the history which only stable final trajectory, after any chaotic change, goes on for the respect to the human dignity. The feeling that makes feel the only, different, with an intrinsic value, like center that we are of the world of which we perceive, of our world. It is a universal feeling and he is born of the proper conscience of being.
All the lovers of the physics and of the justice we can congratulate ourselves of that a "friendly" physical effect is allied of the social justice against the egoistic calculations of the power. These calculations organized by the most powerful of the computers that could exist in the future, are unable to gather all the information, potentially necessary and influential, in his smallest details. A simple flight, not foreseen, not calculated, of an insignificant butterfly it will be able to spoil the most perfect and pondered plans. This simple flight will be also capable of spoiling the well-intentioned plans that try to control any crisis if they are not provided with the factor of stabilization that introduces, in infinity of unstable points, the respect to the personal dignity.
Extracted Post of my collaboration with Book of notes, Sciences and letters.
HAPPY YEAR FRIENDS!!!

The mathematics and the physics

“The book of the Universe is written in mathematical language and his characters are triangles, circles and other geometric figures without whose mediation is a neither humanly impossible comprehension nor a word” (Galileo Galilei).
The existence of a particular relation between the physicist and the mathematics enjoy a public acknowledgement. Across the history of the physics the explicit testimonies abound in this sense, beginning for the famous affirmation of Galilean: "The philosophy is written in this immense book always opened before our eyes (the Universe), but it is not possible to comprise it if one does not learn to know firstly the language and the characters in which it is written. It is written in mathematical language and his characters are triangles, circles and other geometric figures without whose mediation is a neither humanly impossible comprehension nor a word.”
Three centuries later, the astrophysicist Jeans wrote: "The Big Architect seems to be mathematical.” There might be compiled a real anthology of appointments of this style. And any chapter of the physics seems good like example for such affirmations.
The physics uses successfully the mathematics. Nevertheless this statement, far from being as it feigns a strict observation, is loaded with budgets, although he sums up an immediate vision of the situation. But he leads to wondering straight for the causes of this success. How can it be that the mathematics reputed in general like study of pure abstractions, "work" in physical, considered like the science of the concrete thing excellent? The proper physicists give faith often, with an ingenuous surprise or in terms of an uncomfortable confession, of which this adequacy raises a problem:“ Nevertheless, it is notable that none of the abstract constructions that the mathematics realizes, taking exclusively as a guide his need for logical perfection and for increasing generality, seems that it has to remain without utility for the physicist. For a singular harmony, the needs for the thought, worried for constructing a suitable representation of the reality, seem to have been foreseen and anticipated by the logical analysis and the abstract esthetics of the mathematician” (P. Langevin). “The idea of that the mathematics could adapt, somehow, to the objects of our experience seemed extraordinary and exciting to me” (W. Heisenberg).
The mathematics constitute the language of the physics. Of Galilean two appointments can be added to him to the said text: "All the laws are extracted from the experience, but to enunciate them one is necessary a special language; the ordinary language is too poor, and it is also too vague, to express so delicate, so rich and so precise relations. This is the reason for which the physicist cannot do without the mathematics; these provide to him the only language in which he can speak” (H. Poincaré). “The mathematics constitute, for saying it this way, the language by means of which it can appear and a question be solved” (W. Heisenberg).
This conception of the mathematics as language of the physics can, nevertheless, be interpreted of several ways, according to which the above mentioned language should be thought like that of the nature, and which the individual who studies it will have to strengthen for assimilating; or that conceives him on the contrary, how the language of the individual, to which the facts of the nature will have to be translated so that they turn out to be understandable. The first position seems to be of Galilean, also it is that of Einstein: "In accordance with our experience until now, we have right to be sure that the nature is the achievement of the ideal of the mathematical simplicity. The construction purely mathematical allows us to find these concepts, and the beginning that relate them, that give us the key to understand the natural phenomena.” The second point of view is that of Heisenberg:“ The mathematical formulae already do not represent the nature, but the knowledge that of her we possess”. Nevertheless, both attitudes, far from being opposed, are not but the extreme points of a continuous bogey, and of what it is a question it is of scientists - laws find a breakeven inside a structure that supports on the pairs of opposite notions nature - man, experience - theory, concrete - abstract, done scientific.
For the big physicist - mathematician Roger Penrose, in certain form, the mind seems to have “access“ to the world of the ideas to which Platón was referring. Revising some of the affirmations that does in his book “The new mind of the emperor”: Until point are "real" the objects of the world of the mathematician?. From a certain point of view it seems that there can be nothing real in them. The mathematical objects are only concepts; there are mental idealizations that there do the mathematicians often stimulated by the apparent order of certain aspects of the world that surrounds us, but mental idealizations in any case. Can there be anything more than mere arbitrary constructions of the human mind? At the same time it seems that some deep reality exists in these mathematical concepts that goes beyond the mental lucubrations of a particular mathematician. Instead of it, it is as if the mathematical thought was being guided towards some exterior truth — a truth that it has reality as itself and that only we are revealed partially to some of us.
To be able: "To think more the mathematics”, of the series Metabe afraid directed. For Jorge Wagensberg de Tusquets Editores. There are articles of several authors. The post alludes to the article of J.M Lévy-Leblond, teacher of the University of Nice and big popularizer of the mathematics.
On Penrose and the mathematical Platonism: To see linkage.
It seems that it was yesterday, but today it has been one year since my father died. D.E.P.

Particles, fields, classic and quantum theory

The quantum theory was not anything that the theoretical ones were wishing. Most of them were led, to his sorrow, to this strange vision of the world because the classic theory, despite his haughty nobility, has some deep difficulties.
The principal cause is the fact that two types of physical objects must coexist: the particles, each of them described by means of a finite number of parameters, three positions and three moments; and the fields that need an infinite number of parameters. This dichotomy is not physically consistent. So that a system with particles and fields they are in balance all the energy of the particles must be transferred to the fields. This is a consequence of the called phenomenon "equipartición of the energy": in the balance the energy is distributed equally between all the grades of freedom of the system. Since the fields have infinite freedom grades to the particles they cannot have left at all by no means.
The classic atoms would not be stable since the whole movement of the particles would be transferred to the undulatory ways of the fields. When an orbital electron moves alededor of the nucleus it should express electromagnetic waves of an increasing intensity up to infinite in a small second fraction. At the same time it would describe a spiral that would close and would sink in the nucleus. Nevertheless nothing of that is observed. What is observed is quite inexplicable on the base of the classic theory. The atoms can express electromagnetic waves (light) but only in twinkles of specific discreet frequencies: the sharp spectral lines observed and typical of every type of element. Also, these frequencies satisfy rules that have not anything in common with the classic theory.
Another declaration of the instability of the field coexistence and particles is the phenomenon known as “radiation of the black body”. In 1900 Rayleigh and Jeans had calculated that all the energy would be absorbed by the field, without limit, in what it has been called “an ultraviolet catastrophe”. The energy would keep on flowing incessantly towards the field with every time major frequencies.
Max Planck, in the same year, proposed a revolutionary idea to eliminate the ways of high frequency of the “black body”: that the electromagnetic oscillations only happen in “all that“ whose energy E supports a relation defined with the frequency f, given for: And = h f, being h a new fundamental constant of the Nature, now known as constant of Planck. With this extravagant ingredient, Planck could obtain a surprising theoretical agreement with the dependency experimentally observed of the intensity with the frequency, now called law of radiation of Planck.
In the end the electromagnetic radiations could only present in discreet bundles called photons to themselves. The light, after everything, as he had insisted Newton two centuries earlier must be formed of "particles", although at the beginning of the XIXth century Thomas Young demonstrated that it was consisting of waves. Waves or particles?. In 1923 the French physicist Louis de Broglie proposed that the proper matter particles were behaving sometimes like waves. The frequency of the wave of Broglie f, of a particle of mass m, satisfies the relation of Planck, combined with the relation Einstein's mass / energy.

The dichotomy between particles / waves or oscillations of the field, which had been a characteristic of the classic theory, is not respected in the Nature. The Nature manages to construct a world consisting of that the particles and the oscillations of the field are the same thing.
To know more:
- "The new mind of the emperor". Roger Penrose.
- "The light, something on his history". LBT.
- "The quantum physics is easy". LBT.

The modular function of Ramanujan and the theory of ropes

The ropes theory supposes that every way or vibration of a fundamental rope represents a different elementary particle, and can explain simultaneously the nature of the matter and of the space - time (the particles instead of being punctual happen to be unidimensionales). It is the first quantum theory of the gravity: When there were calculated for the first time the ties of autoconsistency that imposes the rope on the space - time, it was observed by surprise that Einstein's equations (theory of the gravity) were emerging of the rope, in fact, the gravitón or all that of gravity was the minor vibration of the closed rope.
We do not know yet why the ropes theory is defined only in 10 and 26 dimensions, although it seems sure that this theory might not unify the fundamental forces with only three dimensions. The ropes break and form in the N-Dimensional space dragging with them a series of terms that destroy the wonderful properties of the theory. Fortunately, these terms turn out to be multiplied by the factor (N-10), what it forces us to choose N=10 to eliminate them.
On having tried to manipulate the diagrams of bonds KSV (Kikkawa-Sakita-Virasoro) created by the ropes in interaction, the ropes theoretical ones find a few strange functions called modular that appear in the most distant and "unconnected" branches of the mathematics ((Yutaka Taniyama (Japan, 1927-1958) observed that every modular function is related to an elliptical curve. This forms the base of the conjecture Taniyama-Shimura that demonstrated to be an important part in the demonstration of the Last Theorem of Fermat of Andrew Wiles)). A function that appears continuously in the theory of modular functions is named a Ramanujan function, in honor to the mathematician Srinivasa Ramanujan, born in 1887 in Erode, India, close to Madrás.
Ramanujan, being employed at entire isolation (and without formation, all his mathematical instruction obtained it of the reading of darkly and forgotten I free of mathematics written by George Carr), it was capable of re-discovering for himself the most valuable of hundred years of western mathematics and of leaving to us a work, which consists of 4.000 formulae on four hundred pages densely full of theorems of incredible force but without any comment or demonstration. It had such an intuition that the theorems simply were flowing of his brain, without the minor apparent effort. He usually said that the goddesses Namakkal were inspiring the formulae to him in sleep.
It was employed at the frank port of Madrás, at a servile work with a wretched pay, but it had enough freedom and time to continue with his mathematical sleep. After sending several letters to three well-known British mathematicians, it achieved that the brilliant mathematician of Cambridge Godfrey H. Hardy realized his immense mathematical genius and brought it to Cambridge in 1914. Trying to estimate the mathematical Ramanujan capacity, Hardy was granting 80 to the big mathematician David Hilbert, 100 to Ramanujan and 25 to himself.
The Ramanujan function contains a term risen up to the potency twenty-four. This number is the origin of the miraculous cancellations that happen in the ropes theory, since each of twenty-four ways of the Ramanujan function corresponds to a physical vibration of the rope. When the Ramanujan function is generalized, the number 24 remains replaced by 8. If we bear in mind that two more dimensions are added to the entire number of vibrations that appear in a theory relativista, we will obtain 8+2, ó 10: The rope vibrates in ten dimensions because it needs these Ramanujan functions generalized to remain autoconsistent.
Pure geometry to explain everything, Einstein's sleep. And the strangest mathematics imagined by a genius, without scarcely basic instruction, to get in a theory of ropes that he needs from mathematics that we do not know yet. Einstein had the mathematics invented by Riemann for his theory of the general relativity, the theory of ropes perhaps need the mathematics, which they rest in the notebooks full of theorems without demonstrating, of Ramanujan. In the fund, always, a beautiful connection between the most distant and unconnected branches of the mathematics and the proper reality that the physical laws represent.
To know much more: "HIPERESPACIO", of Michio Kaku, (1996 CRÍTICA-Grijalbo Mondadori, S.A. Barcelona) teacher of theoretical physics in City University of New York. He is a specialist on a global scale in the physics of the top dimensions (hyperspace). The book dismisses with one beautiful words: "Some persons look for a meaning to the life across the personal benefit, across the personal relations, or across proper experiences. Nevertheless, I believe that being bendecido with the intellect to foresee the last secrets of the nature gives sufficient meaning to the life”.
Edition of one of my classic post, published initially on October 12, 2006.