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## Main Question or Discussion Point

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" associated with each scale so when we probe different scales we see a new geometry. So in this sense actually have a fractal (picture in your mind some geometical shape then if you look at a small bit with a microscope you see it is made up of a new geometry, you could then zoom further in ad see yet another geometry).

Remember though that these geomtries don't describe a static physical state but a dymanical process(spacetime not just space). This is important as I believe it to be an explaination of the uncertainty principle. Consider for a secound classical physics such that there are no quantum effects. In this instance we could describe the classical dynamics by a single geometry. This would be the same as looking at just one scale(call it A) on this single scale we could have a well defined dynamics but dues to the fact that we are only looking at the one scale we will always have an uncertainty in the momentum and position ;we don't care about actally where the particle is because we're only concered with a given length scale say a metre so if two particles are 1.0001 meters apart we could just call that a meter. But when we look at the same phyical system at a new maller scale(call it B) we see a new set of dymanics associated with a new geometry and the concepts of lengths and momentums on the old geometry no longer apply. From this we see that the uncertainties associated with scale A were real because geomery A was only valid at scale A. Its importantant to note that this makes sense in terms of the unceratity princple. The equation states:

delta x delta p > 2 pi

working in units such that Plancks constant and the spped of light are one. x has mass dimension [x]=-1 and p has mass dimension [p]=1. This implies that the uncertainty pricplle is scale independent i.e one can choose the mass unit we measure p and x in and the constant just cancels.

Now curreently all this is in some way all ready understood in terms of QFT and the renormalisation group. What I would like to explore is a new frame work. The current frame work is that we take a classical action and "quantize" it such that we then have a QFT. If we then look at that QFT at different energy scales we see that we can define an effective action which describes the physics at that level. The renormalisation group is the set of transformations that take us from one scale to another. My idea is that prehaps we can circumvent the quatization procedure and instead of starting with a classical theory given by a geometrodynamics we start with a quantum theory given by a fractal dynamics. This will involve understanding how fractal could ultimatly describe the universe in an analogy to how cosmogolgists currently understand the unverse as a geometry.

I think though that there maybe a consequence of what im saying...If my explaination of the unceratinty principle holds and we assume that the unertainty principle applies on all scales then there must alawys be a scale smaller i.e. there is no smallest scale! This may seem to be at odds with the idea of a smallest area in loop quantum gravity. But as loop gravity does not present itself as a final theory there is no real contdriction. The concept of a smallest area only makes sense when you look at a single geometry when you go to a smaller scale you can no longer define that area...as such there should be a smallest are in QG as gravity is the theory that defines areas.

Something I like about my idea is that it explains quantum mechanics but only in the light of relativity inparticular one needs the notion of locality lacking in newtoinan physics which essentially lead Einsten to a geometrical interpretation of gravity. One then extends this idea of locality such that it has some scale dependence.

A small note: when i say geomery I really mean in the most universal way possible not just geomeries defined by metrics (probably). Also I'm not really sure what I mean by fractal more than something that can be well approximated by a geometry at a single scale. Again what I mean by "scale" may also come into question sense geometry could be seen as defing scale so one should understand it as an energy scale i.e associated with the relative dynamics of geomery(where a lower energy scale would desribe the local area of a point in the fractal as smooth the higher energy scale would describe the local area as more dynamic ie more energtic.

Remember though that these geomtries don't describe a static physical state but a dymanical process(spacetime not just space). This is important as I believe it to be an explaination of the uncertainty principle. Consider for a secound classical physics such that there are no quantum effects. In this instance we could describe the classical dynamics by a single geometry. This would be the same as looking at just one scale(call it A) on this single scale we could have a well defined dynamics but dues to the fact that we are only looking at the one scale we will always have an uncertainty in the momentum and position ;we don't care about actally where the particle is because we're only concered with a given length scale say a metre so if two particles are 1.0001 meters apart we could just call that a meter. But when we look at the same phyical system at a new maller scale(call it B) we see a new set of dymanics associated with a new geometry and the concepts of lengths and momentums on the old geometry no longer apply. From this we see that the uncertainties associated with scale A were real because geomery A was only valid at scale A. Its importantant to note that this makes sense in terms of the unceratity princple. The equation states:

delta x delta p > 2 pi

working in units such that Plancks constant and the spped of light are one. x has mass dimension [x]=-1 and p has mass dimension [p]=1. This implies that the uncertainty pricplle is scale independent i.e one can choose the mass unit we measure p and x in and the constant just cancels.

Now curreently all this is in some way all ready understood in terms of QFT and the renormalisation group. What I would like to explore is a new frame work. The current frame work is that we take a classical action and "quantize" it such that we then have a QFT. If we then look at that QFT at different energy scales we see that we can define an effective action which describes the physics at that level. The renormalisation group is the set of transformations that take us from one scale to another. My idea is that prehaps we can circumvent the quatization procedure and instead of starting with a classical theory given by a geometrodynamics we start with a quantum theory given by a fractal dynamics. This will involve understanding how fractal could ultimatly describe the universe in an analogy to how cosmogolgists currently understand the unverse as a geometry.

I think though that there maybe a consequence of what im saying...If my explaination of the unceratinty principle holds and we assume that the unertainty principle applies on all scales then there must alawys be a scale smaller i.e. there is no smallest scale! This may seem to be at odds with the idea of a smallest area in loop quantum gravity. But as loop gravity does not present itself as a final theory there is no real contdriction. The concept of a smallest area only makes sense when you look at a single geometry when you go to a smaller scale you can no longer define that area...as such there should be a smallest are in QG as gravity is the theory that defines areas.

Something I like about my idea is that it explains quantum mechanics but only in the light of relativity inparticular one needs the notion of locality lacking in newtoinan physics which essentially lead Einsten to a geometrical interpretation of gravity. One then extends this idea of locality such that it has some scale dependence.

A small note: when i say geomery I really mean in the most universal way possible not just geomeries defined by metrics (probably). Also I'm not really sure what I mean by fractal more than something that can be well approximated by a geometry at a single scale. Again what I mean by "scale" may also come into question sense geometry could be seen as defing scale so one should understand it as an energy scale i.e associated with the relative dynamics of geomery(where a lower energy scale would desribe the local area of a point in the fractal as smooth the higher energy scale would describe the local area as more dynamic ie more energtic.