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The size and the unity of physics

Our reality is defined by the three spatial coordinates and the concept of time, or the four dimensions that govern our existence. However, to understand the most complex theories of physics, and move the limits of experience (and research) to the actual knowledge of the universe, these four variables are not enough: it needs at least ten. How can they be convinced

string theorists (theoretical physicists who study string theory) that their theories work? The answer lies in the work of the seventeenth century French mathematician René Descartes (Descartes said), who showed that the real space geometry can be converted into abstract algebraic equations. Given a line of fixed length, for example, we can derive an equation that will tell us on what the x and y will pass the ends of the line if it is rotated. We have thus a circle, which is described in mathematical form. The idea is powerful because it can be extended to how many dimensions you want, simply by adding more details. In three dimensions, a sphere is described by equations similar to that of the circle, adding a set of coordinates z So why not go further, and write an equation for a ' "hypersphere" four, five, or six dimensions? In 1854, the German mathematician Bernhard Riemann taken the brave step, three-dimensional geometry generalizing to an arbitrary number of dimensions. After all, it was realized that this was not a big deal: "It's not that difficult to work with these results," says String theory and Field medal Edward Witten of the Institute for Advanced Study in Princeton. But what these objects look like high-dimensionality? The physical Gia Dvali of New York University believes it is important to be able to find some effective mental representation: "The essence of an equation is included and stored more easily in terms of images and animations." For Dvali, Newton's gravity is represented by an object with mass from which branch off in all directions, to infinity, the lines of gravitational field. This image works regardless of the number of dimensions to which you are thinking, "The representation has nothing to do with a multi-dimensional space real, "says Dvali," but the law facilitates the generalization to higher dimensions. "physicist Roger Penrose states that" Space and time are not concepts to be considered independently of each other. "In the theory of special relativity ( or restricted) by Albert Einstein, they dissolve into a single entity. Two objects that appear to a person separated only in space, another may appear separated in space and time. Similarly, only two events that seem to separate Time may, from another perspective, also occur in different places. The discrepancies between the perceptions of two observers become evident when their relative velocity is close to the speed of light - The universal speed limit. The physics of Einstein, now confirmed by numerous experiments, reveals a profound truth: the space and time are only "threads" of a single infinite fabric called space-time. And the force of gravity in this context is simply a measure of "curvature" of space-time itself.

Consider the time as the fourth dimension then gave way to Einstein's special relativity and has served to develop its generalization: the theory of general relativity. The German mathematician Theodor Kaluza had an idea even more impressive: in 1919, soon after the development of general relativity, Einstein sent a paper to the which argued that adding a fifth dimension to space-time, it was possible to show that gravity and electromagnetism were two manifestations of one same force. A few years later, a Swedish mathematician, Oscar Klein, took the idea of \u200b\u200bKaluza and developed the best: answer the obvious objection against the existence of a fifth dimension could be argued that this tiny, wrapped around itself at of each point of the four-dimensional spacetime.

Using string theory, Lisa Randall of Harvard and Raman Sundrum of Johns Hopkins University in Baltimore, showed in 1999 that a fifth dimension could explain a nagging mystery: because the gravity is so much weaker than the other fundamental forces of nature (strong nuclear, weak nuclear and electromagnetism). Their model has four dimensions of our family that "float" in a fifth dimension infinitely large and negative curve. While the electromagnetic and nuclear forces would be "fixed" within a so-called "brane" in four dimensions, gravity leach out in the fifth. At the same time, Paul Wesson of the University of Waterloo in Ontario, Canada, thought that the real world does have five dimensions, which can be articulated in our familiar four dimensions plus the mass that fills our world. This theory not only free from the physical problem of why things have mass - which thus becomes a product of geometry - but also the singularity of the Big Bang, which, seen through the perspective of the entire universe to 5 scale, is nothing more than a "visual illusion". Always remaining in terms of 5 dimensions, in one of the greatest achievements of string theory, the theoretical physicist Juan Maldacena suggested in 1997 that some string theories in five large, including gravity, are equivalent to ordinary quantum field theories in four dimensions without gravity. They both would be "holographic projections" of the other - which potentially makes our ethereal world as a "hologram" projected from the edge of the universe. This correspondence has recently been applied to difficult computational problems in many areas, including the physics of superconductors at high temperatures. In the depiction of Maldacena, the 4D theory is not a description of "more real" than the 5D.

With ten sizes we obtain, finally, the "landscape" of string theory. This theory is currently the only race when it comes to trying to combine quantum mechanics and general relativity into a theory of everything ". The theory holds that all particles of matter, or transmit the forces created by the vibrations of tiny strings. These strings are one-dimensional, but the space in which it is not vibrate at all, indeed, it has as many as 10 dimensions: nine space and one time (the superstring theory). Even a primitive version of string theory (the theory of bosonic string) covered 26 dimensions. There are five general categories of string theories in 10 dimensions which compete to explain the universe. These various theories can be unified into a comprehensive theory, known as M-theory. The M-theory has 11 dimensions. It is assumed that the extra dimensions of M-theory must somehow be "compressed" (or "compactified") to a size that we can not see (the compactification of extra dimensions lead to the creation of a variety - Or space - called Calabi-Yau, which, unlike a circle resulting from the compactification of the fifth dimension, is an "object" much more complex math). The surprising thing is that there is practically a very large number (10 ^ 500) of ways in which this can be done (so there are 10 ^ 500 possible Calabi-Yau). The most extreme idea that physicists have had the vision of the "multiverse", then "all" possible universes actually exist and that this is part of what is called the "landscape" (landscape) of string theory.

recent years string theory has had two further developments: the model-Palumbo Nardelli and the connections between solutions of different sectors of string theory and the golden number phi or its fractional power (Phi ^ n / 7). With the model

Palumbo-Nardelli (2006a) has been shown that bosons (energy carriers) and fermions (particles) are dual aspects of energy:

- ∫ d ^ 26x √ g [- R / 16πG - 1/8g ^ ^ μρg νσTr (GμνGρσ) f (φ) - 1/2G ^ μν ∂ μφ ∂ νφ] =
= ∫ 1 / 2 (κ10) ^ 2 ^ 10x ∫ d (- G) ^ 1 / second-2Φ ^ [R +4 ∂ μΦ ∂ μΦ ^ - ^ 2 1/2H3 - (Κ10) ^ 2 / (g10) 2Trν
^ (F2 ^ 2)] (1)

(the first integral in the right-hand side goes from 0 to infinity) for which the mass is another category of 'energy. The minus sign in the formula of the model Palumbo-Nardelli (1) indicates that the particles (fermions) are moving in the opposite direction to the propagation of energy. This formula is an interaction and then the equals sign should more correctly be replaced with that of the survivor, used in chemical reactions. This would imply that the bosons transform into fermions and vice versa. This is a theoretical representation in processing experimental verification in nature of an electron, which has a mass in a photon, which do not possess it, or would have a mass 10 ^ 5 times smaller than that of the electron. Another example is the difference (equal to 4 times the mass of the electron) between the theoretical mass of deuterium and the experimental one, a very small amount, at the base of the enormous energy released during the fusion of lighter nuclei and division (or fission) of the heaviest. On the other hand, the spontaneous appearance of particles was observed in the various energy colliders. The report (1) says that carriers of the potential energy (Ep), ie the ways in which it occurs, will come true geometrically and structurally defined (particles) and keep the characters. Bosons are the language (carriers) by means of which evolve to become Ep fermions, ie material particles, while fermions are expressed in a language made up by the kinetic energy and in particular by the gravitational interaction, ie the attractive force among the masses. In the universe, forms are often linked to the golden ratio φ equal to 0.61803398 ... = (√ 5 - 1) / 2, and then the corner aureus arccosφ = 51.827292 °, just as there are many shapes (spherical and circular) related to the number π equals 3.14159265 .... Therefore, π and φ are the fundamental signs featuring many works of art and all forms of nature. The relationship between π and φ, ie between 3.14 and
... 0618 ... can be obtained from the simple relationship

arccosφ arccos = 0618 = 0.2879 π. (2)

values \u200b\u200bof π and Φ (where Φ = 1.61803398 ... is called the golden ratio) are also bound by the report of the famous mathematical genius S. Ramanujan:

π = F (n) / [(√ 5 + 1) / 2] ^ n = F (n) / Φ ^ n, (3)

linking the nth number in the series of Fibonacci to the nth power of Φ, from number 5 (5, 8, 13, 21, 34, 55, 89, ...). For example 13, which is the third number in the sequence from 5 divided by 3 ^ Φ approaches the value of π. The number 55, which is the sixth number in the sequence from number 5, divided Φ ^ 6, is even closer to the value of π. The golden ratio Φ π appears implicitly in (1), which binds to the particle energy and extend the dependence on Φ of all forms of micro-and macrocosm (Palumbo and Nardelli 2007). It, that has fascinated thinkers of the past who considered the Φ basis of all cosmic and aesthetic forms, finds its physical meaning, is the root of all natural forms. The reason why among the many universes, the real one is based on φ = 0.61803398 ..., lies in the individuality, or uniqueness of the golden ratio φ to be mathematically related to both the π to be two fundamental entities, the first is the foundation of numbers and the latter because all natural forms are based on π, the indispensable basis of geometric shapes. The numerical relationship between π and φ is given by (2), that between the golden ratio φ, or between its inverse Φ factor (gold) and the unit comes from the following reports: 1618 = 1 / 0618 = 1 / 1 to 1618 and 1618 ^ 2 = 2618 = 1618 + 1 which shows that, by subtracting the number 1 from 1618 gives its inverse value, adding the number 1 to 1618, you get its square. Since all the original body of the universe, from celestial to the atoms have a structure related to the logarithmic spirals, it follows that all natural forms are based on φ. This model unifies the gravitational forces of the two other fundamental forces of physics (nuclear force and electromagnetic force). This is confirmed by the binding of π and Φ to the factor γ of the universal gravitational constant (6.67 x 10 ^ -11) by the relation: π ^ 2 - 2Φ = γ which provides a degree of approximation greater the greater the number of decimal places of two irrational numbers used. The common bond of the Newtonian constant and that of the fine structure (α = 2πe ^ 2 / (hc), which as we see, is related to π) in π implies that between these two latter constants α and γ. In addition, by 432 / π = 137 = 1 / α it follows that α = π/432 = 1 / 137 (where 432 is the frequency of the natural) and similarly, from γ = π ^ 2 - 2Φ obtained γ = 0.0155 x 432. Both the microcosm, governed by the fundamental atomic constants, the macrocosm, governed by the gravitational constant is then related to the natural frequency, which in turn is related to the fine structure constant and π by the following inverse formula 432 = π / α.

Michele Nardelli