wolram
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http://arxiv.org/PS_cache/arxiv/pdf/0812/0812.3857v1.pdf
Quote.
In the first part of this contribution, we review the development of the theory of
scale relativity and its geometric framework constructed in terms of a fractal and
nondifferentiable continuous space-time. This theory leads (i) to a generalization
of possible physically relevant fractal laws, written as partial differential equation
acting in the space of scales, and (ii) to a new geometric foundation of quantum
mechanics and gauge field theories and their possible generalisations.
In the second part, we discuss some examples of application of the theory to
various sciences, in particular in cases when the theoretical predictions have been
validated by new or updated observational and experimental data. This includes
predictions in physics and cosmology (value of the QCD coupling and of the cosmological
constant), to astrophysics and gravitational structure formation (distances of
extrasolar planets to their stars, of Kuiper belt objects, value of solar and solar-like
star cycles), to sciences of life (log-periodic law for species punctuated evolution,
human development and society evolution), to Earth sciences (log-periodic deceleration
of the rate of California earthquakes and of Sichuan earthquake replicas, critical
law for the arctic sea ice extent) and tentative applications to system biology.
An accidental find i thought may be of interest.
Quote.
In the first part of this contribution, we review the development of the theory of
scale relativity and its geometric framework constructed in terms of a fractal and
nondifferentiable continuous space-time. This theory leads (i) to a generalization
of possible physically relevant fractal laws, written as partial differential equation
acting in the space of scales, and (ii) to a new geometric foundation of quantum
mechanics and gauge field theories and their possible generalisations.
In the second part, we discuss some examples of application of the theory to
various sciences, in particular in cases when the theoretical predictions have been
validated by new or updated observational and experimental data. This includes
predictions in physics and cosmology (value of the QCD coupling and of the cosmological
constant), to astrophysics and gravitational structure formation (distances of
extrasolar planets to their stars, of Kuiper belt objects, value of solar and solar-like
star cycles), to sciences of life (log-periodic law for species punctuated evolution,
human development and society evolution), to Earth sciences (log-periodic deceleration
of the rate of California earthquakes and of Sichuan earthquake replicas, critical
law for the arctic sea ice extent) and tentative applications to system biology.
An accidental find i thought may be of interest.