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.
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