Can fractals make sense of the quantum world?

[Nahee_Enterprises]

A fascinating article in the "New Scientist" talks about resolving Quantum Theory with fractals:

    http://is.gd/pFiD]http://is.gd/pFiD
or:
    http://www.newscientist.com/article/mg20127011.600-can-fractals-make-sense-of-the-quantum-world.html?full=true
 

[bib]

Excellent!

I have always liked the idea of a fractal universe. To me it is obvious. At all scales, fractal or fractal-like structures can be observed. From the high distance universe structure simulations down to elementary particles, a wide a range of fractals can describe our universe.

So why not even infinitely deeper into elementary particles opening new universes, and so on ? The quantum theory would be like a view of what's down there, but with not enough "iterations" to see the details, only providing a statistical estimation.

 

[rloldershaw]

Hi All,

Tim Palmer's work is extremely encouraging to those who think fractal modeling of nature has been sadly neglected by the physics community.

I have spent 33 years developing a fractal model of the cosmos.

It appears that a discrete fractal model works best for the Universe, and the more classical continuous fractals abound within any particular cosmological Scale.

Have a look at www.amherst.edu/~rloldershaw if you are new to these ideas.

For more advanced readers, you might go straight to: http://independent.academia.edu/RobertLOldershaw , for several recent papers that discuss the physics in more detail.

Yours in science,
Knecht

[gamma]

Hi. I opened many times your web site and I seem to be unable to read it. It does not resonate with me. Objects that are fractals seem impossible to hold in hand. So far, in physics we had opportunity to hold matter and radiation as "substance" or as energy. We can understand it, comprehend it, work with it... Power of patterning physical reality sounds like a better approach, because it is self-explanatory why we find fractals at so many places. For example, DNA molecules can assemble Sierpinski gasket set by artificial manipulation. Scientists made it exciting because the gasket is assembling itself - which it does via calculating XOR operation during assembly. In other words, there is a catch why this fractal exists.

It appears that a discrete  fractal model works best for the Universe, and the more classical continuous fractals abound within any particular cosmological Scale.

Your statement sounds interesting and I wish I could understand just a little better. I wonder if you studied homeomorphisms? They are topological similarities, topological "matches". We can ask, does one structure represent some other structure in essence? DeVaney wrote all his papers about 2 homeomorphisms found in 2 equations for Julia set. If you know how to produce one Julia set that fits within definition of another set or perform such operations in general, then you can transform laws and known structures into what you want. :-))
http://math.bu.edu/people/bob/papers.html   

Of course, process of proving is pretty unpleasant. Devaney had trouble proving relation of two sets that are obvious. You would need to bring evidence from Space about fractal nature of nature itself. Its way too much. :-) I was going to make a remark on creative expression by designing objects sharing resemblance with some sets, sets of rules, principles...   

[Mihaly]

 It may be a way of enabling us to avoid some of the incalculable but it also has an appeal in the way it can describe things at several different scales.

Unfortuanately, I believe that a simplistic resort to mathematical fractal nature might be too appealing without also including some sense of understanding. In other words, I fear that an appeal to something like fractal mathematics despite its seemingly scale-invariant description isn't entirely suitable here, or at least, cannot fulfil the requirement of a complete mathematical decription - a T.O.E. (Theory of Everything) sort of idea, but if it is a scalar breaking model then definitely fractal mathematics is only a window onto it.

 In other words, I am breaking with the tradition that believes everything is only mathematics.

 I won't deny that it has an appeal, that everything might have a simplistic although recursive nature.

 But the very fact that it breaks symmetry is cause for concern.

 As Einstein says: If your theory breaks symmetry, then so much the worse for your theory"
(paraphrased)

 We have seen many successes in fractal/catastrophic maths, yet it i still tosome degree new as a mathod.

 I have no doubt it will play some role in the greater understanding we will achieve. But still I have strong doubts about some entire encapsulating theory of everything, I just can't see it. Maybe I am behind the times.

 I think we still have a long way to go. Anybody who suggests otherwise is merely playing for time.
Sincerely,
Michael Kortvelyesy.