Fractal Space-Time and Microphysics: Towards a Theory of Scale Relativity

[110]

Hi all,

I was wondering if anyone of you has read the book of Laurent Nottale

Fractal Space-Time and Microphysics: Towards a Theory of Scale Relativity




why is not his approach adopted ?- as apparently, he extended the principle of relativity to scales and thus proposes a unifying frame between relativity and quantum mechanics.

See the review on amazon.com

"As Einstein indulged a long time in wondering how it would be like to be a photon, LN spent his time trying to slip into a fractal. For once it is in it, a particule which follows chaotic movements in a classical frame, goes straight ahead, and then one may understance the apparent disorders of microphysics. The most amazing is that, beyond the theoretical development, LN's scale relativity not only unifies both poles of the 20th century theoretical physics, namely General Relativity and Quantum Mechanics, but also gives us new philosophical insights about how to look at our world. Faithful to Einstein's ideas, he reintroduces the necessity of "the maximum elegance" in our description of the world, elegance which had been swept away by the quantum formalism. Roughly said, quantum mechanics is no longer an axiomatic theory but is now a consequence of a satisfying general principle for mind, namely the relativity principle. So what's the new point? We know since einstein that every momentum is relative (uniform momentum with special relativity, accelerated momentum with general relativity). Roughly said, I never absolutly move, I only move compared to another body. LN extends this beautiful idea of general relativity to the notion of scale. I am not tall, I am just taller than something. But this simple looking idea needs new mathematical tools to enter the hall of wonder that is called theoretical physics. There come the fractals. How these extraodinary and strange figures upset our sight of the whole universe, from microphysics to cosmology ? All this is brilliantly explained, in a simple and accessible way, in this book, where intuition and philosophical insights are as significant as theoretical ideas."

110

 

[yottzumm]

The idea of fractal space just popped into my mind just now, so I decided to come take a look who was discussing it online. It seems like if things on Earth show fractal nature, then space/time should have fractal nature too--not necessarily a continuous emptiness. Fractals might combat the second law of thermodynamics. I recall reading about fractal memories too. I seem to be having a fractal memory right now.

 

[DarkStar7]

Scale is almost universally believed not to be a dimension.If it were we could apply a scalar relativity.The universe is variant in scale.This implies that the Universe is non relative through scale.Is this an indication that Universe is non symetrical through 4d fractal spacetime? Funnel shape perhaps?

 

[yottzumm]

Seeing as I have only taken high school physics, I probably wouldn't understand the book very well. I did find part of it online, and the math overwhelmed me (I have a hard enough time reading w/o the math). If space is bent around massive objects, perhaps there is some quantum bending that is fractal in nature? Perhaps this "roughness" is what makes gravitons (packets of gravity)? Are we using too many differential equations and not enough difference equations? Are we flying through space, or bouncing through space? What is the shape of Earth's orbit around the sun? Believe me, I wish for fields (waves), and all I see is clods (particles,quanta). What is the happy medium? What is quantum/fractal bending of space?

If you use dimension on me again, I will ask you what a point is. Your best response will be something that is 1 dimensional. How many 1 dimensional points are there in the universe? How many 1 dimensional points are on [0,1]? If your answer is the same, why? It seems reasonable that dimensions are a sign of dementia. After all, wasn't Descartes sick in bed when he came up with the idea?

A point is 1 dimensional in time. That's the only way it can exist at all.

 

[MathematicalPhysicist]

a point doesn't have dimension/s.

 

[yottzumm]

a point doesn't have dimension/s.

I don't think points exist at all. Neither do lines, planes, or the cartesian coordinate system!

Actually, I think that points, etc. must exist in time, otherwise, we couldn't hold a conversation about them.

Many things have has fractional dimension, including our decimal and binary numbering systems (they're hierarchical, not linear).

The only numbering system that is linear is the unary, or base-1 numbering system.

John

 

[yottzumm]

Here's an interesting link: http://www.obspm.fr/actual/nouvelle/nottale/nouv.en.shtml

 

[matheinste]

Here's an interesting link: http://www.obspm.fr/actual/nouvelle/nottale/nouv.en.shtml

How is the theory of Relativity of Scale related to Einstein's Theory of Relativity.

It is interesting that at the bottom of the text in the link the only (two) references refer to the author and of all the references given in the To Know More link only one of them is not the author, Notalle. Call me an old cynic, but this is often not a good sign.

Matheinste.

 

[yottzumm]

There's a second link here, with more authors: http://www.obspm.fr/actual/nouvelle/nottale/pesp_en.html

 

[yottzumm]

There's also another review of the book on amazon.com. Seems like the book is rather expensive. Here it is on google: http://books.google.com/books?id=Fx...resnum=4&ved=0CCIQ6AEwAw#v=onepage&q=&f=false

 

[matheinste]

There's a second link here, with more authors: http://www.obspm.fr/actual/nouvelle/nottale/pesp_en.html

This is where you end up if you click on To Know More at the bottom of the original link. All but one of the references (which has multiple authors) refer to Nottale. Again it deals with Scale Relativity and, as far as I can see, is not about SR or GR, although gravitation is mentioned.

Matheinste.

 

[DarkStar7]

Could someone tell me why Laurants theory considered so insane.I may not be the brightest person in this forum.In simple terms why doesn't the hypothesis work?

 

[jtbell]

The idea of fractal space just popped into my mind just now, so I decided to come take a look who was discussing it online.

Please note the post that you responded to is nearly six years old, and you are the first person to respond to it! Nottale's work has in fact been discussed here occasionally, as a site-restricted Google search shows, so you might want to investigate some of those threads:

http://www.google.com/#hl=en&source=hp&q=nottale+site:physicsforums.com

I leave it to others who are more versed in such things to comment on why Nottale's ideas haven't been taken up more widely.

This thread started out in the Relativity forum, then got moved to the Science Books forum. I think if the focus stays on Nottale's ideas, the best place is probably here in "Beyond the Standard Model."

 

[yoda jedi]

from my bookmarks:



quantum mechanics derived from an invariance principle or space time geometry, fractal or a weyl geometry.

is quantum mechanics based on an invariance principle ?
http://arxiv.org/PS_cache/gr-qc/pdf/0610/0610142v2.pdf

 

[yoda jedi]

A Fractal Quantum World?

http://www.andyross.net/palmer.htm



Proc. R. Soc. A 8 October 2009 vol. 465
http://rspa.royalsocietypublishing.org/content/465/2110/3165

 

[Frame Dragger]

A Fractal Quantum World?

http://www.andyross.net/palmer.htm



Proc. R. Soc. A 8 October 2009 vol. 465
http://rspa.royalsocietypublishing.org/content/465/2110/3165

You're citing a blog, and a solo paper written by a meteorologist? Well, I'm bloody convinced!

 

[yoda jedi]

You're citing a blog, and a solo paper written by a meteorologist? Well, I'm bloody convinced!

oh sorry, a long time on the beach (a good sun, a lot of photons)

yes, palmer a meteorologist and einstein a patent clerk.
but bright minds...

without trying to convince anyone...

 

[sbrothy]

FYI:

"The Evolution and Development of the Universe"
-- http://arxiv.org/abs/0912.5508

It has some more on scale relativity and fractal space-time. Maybe more philosophical than physical though. And from the evo-devo people appearently.

 

[yoda jedi]

Fractal patterns spotted in the quantum realm.

http://physicsworld.com/cws/article/news/41659

 

[Frame Dragger]

Fractal patterns spotted in the quantum realm.

http://physicsworld.com/cws/article/news/41659

Can you link to the research, or is it unpublished as of yet?

 

[sbrothy]

"Visualizing Critical Correlations near the Metal-Insulator Transition in Ga1-xMnxAs"
---- http://arxiv.org/abs/1002.1037

"Seeing Quantum Fractals"
---- http://arxiv.org/abs/1002.1094

 

[Frame Dragger]

"Visualizing Critical Correlations near the Metal-Insulator Transition in Ga1-xMnxAs"
---- http://arxiv.org/abs/1002.1037

"Seeing Quantum Fractals"
---- http://arxiv.org/abs/1002.1094

Ahhh, papers.. the good stuff! Thanks, I'm going to take some time reading these.

EDIT: Wow, the first paper is impressive, and certainty-crushing. The second seems redundant, but the first and references make a real case. That's just on a first skim however, and all involved seem certain that this is more of a beginning than a conclusion.

 

[sbrothy]

No problem. This one also looks enticing. I only skimmed the abstract but it sure looks like it fits in here:

"Fractional Dynamics from Einstein Gravity, General Solutions, and Black Holes"
---- http://arxiv.org/abs/1004.0628

 

[Frame Dragger]

No problem. This one also looks enticing. I only skimmed the abstract but it sure looks like it fits in here:

"Fractional Dynamics from Einstein Gravity, General Solutions, and Black Holes"
---- http://arxiv.org/abs/1004.0628

Damn, not bad for a fifth post... I have some serious reading to do. Thank you sbrothy, and welcome to PF!

 

[Iam.HG]

I was thinking that in a scaled universe that is truly infinite - it would by necessity have to be subdivided into sets of graduated scale phases, each of which requiring a completely different set of physical laws, simply by virtue of scale. This could explain some of the unusual behaviors that appear to defy the laws of physics which have been witnessed at the extreme limits of our perception, on both the subatomic and the galactic scale.

For instance, I have read that the radiation after-glow left behind by the big bang seems to show that the universe originally expanded at many times the speed of light. At the other end of the scale, certain subatomic particles appear to be located in more than one place at the same moment in time. Could it be that we are observing things which are taking place at the extreme edge of "our scale phase" of the universe?

If a specific "scale phase" of the universe were indentified - let's say for argument sake that the substructure of a quark were discovered, and could be scaled up to the size relative to a galaxy. Now presume that this subatomic structure was discovered to contain the same relative complexity of our galaxy - all the way down, relative to our quark.

Such a small and complex structure would require a completely different set of physical laws in order to function or even to exist. It would be a comparable to an entire universe, being governed by one set of physical laws, contained within another universe that is governed by a completely different set of physical laws.

I pose this as a scenario to ask the following question. If the above set of facts were true, would not this represent a new [scale] dimension?

 

[arivero]

Hi all,

I was wondering if anyone of you has read the book of Laurent Nottale

I did. Has two problems. One, generic to fractal science, is vagueness. A second one is that some main predictions are known consequences of the renormalization group mathematics. I was impressed with the calculation of electron mass until I found the same calculation in Polchinski String Theory vol II, when he does a review of quantum field theory and the need of gravity scale cutoffs.

 

[yoda jedi]

On Nonlinear Quantum Mechanics, Noncommutative Phase Spaces,
Fractal-Scale Calculus and Vacuum Energy

Carlos Castro

http://www.springerlink.com/content/e655t784614422g0/fulltext.pdf

 

[yoda jedi]

Fractal Space-Time from Spin-Foams

http://arxiv.org/PS_cache/arxiv/pdf/0911/0911.0437v1.pdf