Melody
25 Oct 2004, 10:52 AM
i found a book in a nearby library that pointed out that general relativity did not take something into account and einstein recognized it as a trouble
ima havfta look for that book again it was interesting because it seemed to meld quantum physics and general relativity via fractal geometry (all three of which i am interested in)
and it used a particular value related to the properties of scale
The book is Fractal Space-Time and Microphysics: Towards a Theory of Scale Relativity by Laurent Nottale.
From section 2.1
At small scales, the "standard model" of elementary particles, based on quantum chromodynamics and electroweakdynamics, is able to include in its framework the observed structure of elementary particles and coupling constants (i.e., charges). But it seems, up to now, unable to predict on purely theoretical grounds either the number of elementary particles, or their masses, nor the values of the fundamental couplings. This failure is certainly related to the main failure of electrodynamics (classical and quantum): the divergence of self-energy and charge at infinite energy. Renormalization was only a partial solution to the problem. By replacing in calculations the theoretical infinite charges and masses by the observed ones, it allowed physicists to predict with high precision all the other physical quatities of interest. But the problem of masses and charges was left open.
At the other end, that of very large scales, even though the current cosmological theory has known great successes, one must not forget that general relativity, being a purely local theory (its fundamental tool, the metrics element, is differential), tells us nothing about the global topology of the Universe. This is, with the problem of sources of gravitation (why does inertia curve space-time?), one of the limiting domains where general relativity is an incomplete theory, as recognized by Einstein himself: an indication of this incompleteness may be its inability to include Mach's principle, except in some particular models, while observations seem to imply that it is effectively achieved by Nature.
From section 1
Then the introduction of a Lorentz-like renormalization group, in conjunction with the breaking of the scale relativity symmetry at the de Broglie scale (transition from scale-dependence to scale-independence), leads to a demonstration of the existence of a universal, lower, limiting scale in Nature, that is invariant under dilations and plays the same role for scale as that played by the velocity of light c for motion. It is identified with the Planck scale (Λ = (ħG/c^3)^1/2 ~ 1.6 x 10^-35 m; T = Λ/c = (ħG/c^3)^1/2 ~ 5.4 x 10^-44 s), which, in such a new framework, owns all the properties of the previous perfect zero point. The de Broglie and Heisenberg relations are generalized: energy-momentum now tends to infinity when the length-time scale tends to the Planck scale. Although the largest effects of such a new structure are expected at the Planck scale, at which space-time would become totally degenerated, it also has observable consequences in the domain of energy presently accessible to experiment.
It seems good to me for various reasons, one of which is that I do not believe in "dimensions," and fractal geometry does not limit itself by integral dimensions. For example, it is possible for a fractal construct to have a dimension of 1.4. Also, I have been looking into fractal geometry since I was a twig. In addition to being pretty, it is natural.
The book covers the basics of fractal geometry, so the prerequisites are a good knowledge of quantum physics and relativity.
It seems significant to me, but I have heard nothing about this idea anywhere else. I wonder why. It could be I'm just out of the loop.
ima havfta look for that book again it was interesting because it seemed to meld quantum physics and general relativity via fractal geometry (all three of which i am interested in)
and it used a particular value related to the properties of scale
The book is Fractal Space-Time and Microphysics: Towards a Theory of Scale Relativity by Laurent Nottale.
From section 2.1
At small scales, the "standard model" of elementary particles, based on quantum chromodynamics and electroweakdynamics, is able to include in its framework the observed structure of elementary particles and coupling constants (i.e., charges). But it seems, up to now, unable to predict on purely theoretical grounds either the number of elementary particles, or their masses, nor the values of the fundamental couplings. This failure is certainly related to the main failure of electrodynamics (classical and quantum): the divergence of self-energy and charge at infinite energy. Renormalization was only a partial solution to the problem. By replacing in calculations the theoretical infinite charges and masses by the observed ones, it allowed physicists to predict with high precision all the other physical quatities of interest. But the problem of masses and charges was left open.
At the other end, that of very large scales, even though the current cosmological theory has known great successes, one must not forget that general relativity, being a purely local theory (its fundamental tool, the metrics element, is differential), tells us nothing about the global topology of the Universe. This is, with the problem of sources of gravitation (why does inertia curve space-time?), one of the limiting domains where general relativity is an incomplete theory, as recognized by Einstein himself: an indication of this incompleteness may be its inability to include Mach's principle, except in some particular models, while observations seem to imply that it is effectively achieved by Nature.
From section 1
Then the introduction of a Lorentz-like renormalization group, in conjunction with the breaking of the scale relativity symmetry at the de Broglie scale (transition from scale-dependence to scale-independence), leads to a demonstration of the existence of a universal, lower, limiting scale in Nature, that is invariant under dilations and plays the same role for scale as that played by the velocity of light c for motion. It is identified with the Planck scale (Λ = (ħG/c^3)^1/2 ~ 1.6 x 10^-35 m; T = Λ/c = (ħG/c^3)^1/2 ~ 5.4 x 10^-44 s), which, in such a new framework, owns all the properties of the previous perfect zero point. The de Broglie and Heisenberg relations are generalized: energy-momentum now tends to infinity when the length-time scale tends to the Planck scale. Although the largest effects of such a new structure are expected at the Planck scale, at which space-time would become totally degenerated, it also has observable consequences in the domain of energy presently accessible to experiment.
It seems good to me for various reasons, one of which is that I do not believe in "dimensions," and fractal geometry does not limit itself by integral dimensions. For example, it is possible for a fractal construct to have a dimension of 1.4. Also, I have been looking into fractal geometry since I was a twig. In addition to being pretty, it is natural.
The book covers the basics of fractal geometry, so the prerequisites are a good knowledge of quantum physics and relativity.
It seems significant to me, but I have heard nothing about this idea anywhere else. I wonder why. It could be I'm just out of the loop.