RANDOM DYNAMICS
RANDOM DYNAMICS TABLE OF CONTENTS SEQUENCE OF DERIVATIONS


RANDOM DYNAMICS

The ultimate goal of physics is to find the principles underlying all natural phenomena.
An essential guiding principle in the development of physical theory is symmetry, in the sense that most natural laws are symmetry laws, telling that the action representing the dynamics of the observed physics is invariant under some symmetry transformation. The highly successful Standard Model is an outstanding example of this.
Often people expect that beyond the Standard Model you will find a larger gauge group. In the search of the ultimate fundamental theory one favoured scenario is the Grand Unification approach, which so to speak repeats the Standard Model scheme. The idea is that we should search for a force corresponding to a larger symmetry group, which at lower energies breaks down to the symmetry group corresponding to the forces we see there.
In the Random Dynamics approach, it is however not assumed that the Standard Model tells you anything about its own extension.

If symmetry is one corner stone in the search for physical laws, another guiding principle is simplicity. As inheritors of Occam's razor we have learnt to look for the simplest scheme, and believe that the fundamental principles are by definition simple. That does however not imply that Nature itself is "simple" at a fundamental scale, on the contrary:
As we climb up the energy scale there are more and more degrees of freedom, not only the degree of symmetry, but also complexity increases with energy. What goes on at a fundamental scale, like the Planck scale, is probably enormously complicated and is most simply described in terms of randomness.
This is the punch line of Random Dynamics, a theory developed by Holger Bech Nielsen at the Bohr Institute, and his collaborators.
Unlike the Grand Unification scheme, in the Random Dynamics approach the natural laws are expected to get more complicated at higher energy. It is only by the formulation "the fundamental world machinery is essentially random" that the Random Dynamics model is simple. If one would formulate the details of the "laws", it would be exceedingly complicated!
The idea is that a sufficiently complex and general model for the fundamental physics at (or above) the Planck scale, will in the low energy limit (where we operate) yield the physics we know.
The reason is that as we slide down the energy scale, the structure and complexity characteristic for the high energy level, are shaved away. The features that survive are those that are common for the long wavelength limit of any generic model of fundamental supra-Planck scale physics.
The ambition of Random Dynamics is to "derive" all the known physical laws as an almost unavoidable consequence of a random fundamental "world machinery", which we take to be a very general, random mathematical structure ${\cal{M}}$, which contains non-identical elements and some set-theoretical notions. There are also strong exchange forces present, but there is as yet no physics: at some stage ${\cal{M}}$ comes about, and then physics follows.
The physics that we experience at our low energy level emerge from this primal mathematical set, but since we have no means to achieve precise knowledge about the structure at the fundamental scale, we postulate that ${\cal{M}}$ is merely a generic fundamental structure (possibly among many others) which gives rise to the world we observe.

A mathematical theory does not "mean" anything in itself, to interpret it means to relate it to concepts that emerge from one's own, sensory experience. These concepts are to be looked upon as "primitive", and in this sense Random Dynamics is more Aristotelian than Newtonian.
We believe that we do not talk about "what is always there", because we are in somehow genetically adjusted to "what is always there". Therefore we tend to describe not "what is always there", but the perturbations of "what is always there". Only in crazy theories like Random Dynamics do we try to formulate "what is always there". In this connection Aristotle is better than Newton - in the sense that there is always friction around, and what we really need to describe is the concept of dynamics, like in F=ma. Initially the energy concept is not that necessary - since we don't need the Hamiltonian to describe everything.

That the fundamental structure ${\cal{M}}$ comes without differentiability and with no concept of distance, that is, no geometry, not even topology, implies an apriori lack of locality in the model. We cannot put in locality by hand, since the lack of geometry forbids locality to be properly stated. Thus the principle of locality, taken say as a path way integration $\int {\cal{D}}e^{\int{\cal{L}}d^4x}$ with a Lagrangian density ${\cal{L}}$ only locally depending on the fields, cannot be put in before we have space and time.


Holger Bech Nielsen