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.
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