Fractal Space-Time: Theory and Applications

[wolram]

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.

 

[MathematicalPhysicist]

Not new stuff, Nottale already had some publications on this.

Though I haven't looked at his research as of late.

 

[Entropia]

I find this contribution on the theory of scale relativity and its applications to be very intriguing. The idea of a fractal and nondifferentiable continuous space-time is a unique and interesting approach to understanding the laws of physics and their possible generalizations. The potential applications of this theory to various scientific fields, from physics and cosmology to Earth sciences and biology, demonstrate its versatility and potential for further advancement in our understanding of the natural world.

The fact that the theoretical predictions of this theory have been validated by new or updated observational and experimental data is a promising sign of its validity. The examples provided, such as the prediction of the QCD coupling and cosmological constant, demonstrate the potential usefulness of this theory in making accurate predictions in various scientific fields.

Overall, this contribution presents a thought-provoking and innovative perspective on space-time and its applications, and I believe it will be of great interest to other scientists and researchers in the field. Further exploration and experimentation with this theory could lead to new discoveries and advancements in our understanding of the universe.