Finbar

The following are musings not hard statements.


In fundamental physics there seems to be some interplay between the closely related principles of locality/non-locality and causality. While causality is vital for any theory, locality is not so essential it would seem. The reason for this is clear since by violating causality a theory can soon be shown to be inconsistent; on the other hand locality is only important such that it preserves causality. In other words a theory can...

The Wheeler-Dewitt equation also known as the Einstein-Schrodinger equation. Makes a profound statement about Quantum gravity: In quantum gravity there is no time.
The equation reads
Hf=0

H is the Hamiltonian.
f is the wave function of the universe.

1) classical theory is described by an action
2) By minmising the action we find the equations of motion
3) With boundry conditions we can find unique solutions to these equations.(be they analytical or numerical)
4) All classical theories in nature are geometrical theories, hence the solutions 3) are in general geometries
5)Quantisation can be understood through the renormalisation group as going from a single classical action to a set of actions parameterized by some...

Fractal dynamics is an idea in which the the quantization of a classical field theory is reformulated as the "fractalization" of a geometry. That is we take a classical solution to classical field theory interpreted as a geometry and then convert it into a fractal. This could well be understood as taking a tree level feynmann diagram and then adding more loops as we increase the energy scale which in turn corresponds to moving along the renormalization group flow in theory space.
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Fractal dynamics is the name I give to a research program I hope one day to embark on. My idea is that nature is actually a dynamical fractal in the following sense: there are many scales on which we can describe nature if we stick to a single scale then we can describe the physics using some form of field theory that has a classical geometrical interpetation i.e. classical gravity is intepretated as riemannian geometry, QCD can be understood as fibre bundles. In this sense we have a "geometrodynamics"...