Welcome to this blog dedicated to the Theory of Scale Relativity, one of the most promising theory aiming, amongst other things, to reconcile the two "tails" of current physics : cosmology and microphysics. Both are very well described by their own effective theory, respectively by General Relativity and Quantum Mechanics. But...
Aren't you bothered by the fact that, prior to any measure of a physical observable, you will have to know the (length and/or time) scale of the system on which the measurement will be performed in order to use the correct physical and mathematical tools ? Let me exemplify this point : if somebody asks you to describe the motion of a body, you could answer by writing Newton's second law
Now... wait ! You're being told that, actually, the body is an electron. Your answer will be : no problem, lets use the Quantum Mechanics apparatus, e.g. Schrödinger's equation
Thus, the scale of a system is a variable which decides what physical and mathematical tools we have to use. In the example above, classical Newtonian Mechanics (General Relativity if you were thinking about a body orbiting close to a black hole) or Quantum Mechanics.
Now, would it be possible to describe the events, objects, or any physical system of our Universe with a unique physical and mathematical theory whatever their scale ? The answer given by the Theory of Scale Relativity is : yes, it's possible if you include scales (or equivalently, space-time resolutions) in the definition of reference frames, system of coordinates and in the equations of physics. Constructing a scale dependent physics enables us to show that the two tails of modern physics are particular cases of a more general theory which supersedes them : this is what the Theory of Scale Relativity, developed by Laurent Nottale, is all about.
In the sections dedicated to the presentation of the theory, you will find posts about
- The foundations of the theory : dropping the (implicit) hypothesis of differentiability of current Physics and extending the Principle of Relativity to scale transformations;
- Its tools : non-differentiable geometry, fractal functions and the scale covariant complex derivative operator;
- Its results : retrodictions and predictions in the domains of microphysics, cosmology and complex / chaotical systems.
I invite the interested reader to download Laurent Nottale's papers for the full details of the development of the theory (still underway, see Structure of the Theory).
This blog was created recently (october 1st, 2007) and contains only a few posts in the Foundations, Tools and Results sections. All articles in these sections are excerpts (or adapted) from Laurent Nottale's publications.
One last thing : I'm not blessed with a native English tongue. I hope that the reader will not suffer too much from my insufficient mastery of the English language. I apologize for possible grammatical flaws.
Eric
11 comments:
Before you go any further, you ought to find out where you yourselves stand with respect to Einstein's advocacy of natural mathematics. You might be interested in some of the new history of set theory, which sheds a great deal of light on Poincare's understanding and his influence on Einstein. For some reason, we seem to be enjoying a renaissance in this field. It has importance for relativity, because Poincare's responses to the set theory discussions found their way into Science and Hypothesis, which so influenced Einstein. I think it is becoming more clear that Einstein's adoption of natural mathematics (what he called "practical geometry") through Poincare and others, was really the important step in his thinking, with consequences which were not so good.
Above all, you should read Garciadiego's book on Russell, in spite of its many typos. If you haven't read that yet, you should do so first thing.
I discuss some of the new work in the essay below.
Cordially yours,
John Ryskamp
Ryskamp, John Henry, "Paradox, Natural Mathematics, Relativity and Twentieth-Century Ideas" (May 19, 2007). Available at SSRN: http://ssrn.com/abstract=897085
Hello John
I've read some of your posts on the net. Sorry, but I can't buy the idea of relativity being flawed because of a lack of internal self-consistency arising from the use of 'natural mathematics'. As you know, many if not all physics theories make assumptions about their own foundations. So is the case for SR and GR, indeed. But in my opinion, the most important thing for a theory is to make retrodictions and predictions which can be put to the test in experiments (as SR and GR have done successfully so far), not to be proven logically consistent. Of course, it's always a good thing to have mathematical and logical consistency, and to build the theory from first principles (i.e. to have a minimal number of axioms), but it's not always feasible (see e.g. the case of QM).
About your main argument on the relativity of simultaneity : I think most readers of the train experiment given by Einstein have correctly understood / translated that he meant that the 'x' coordinate [...of the mid-point of the distance AB...] of the train coincide with the 'x' coordinate [...of the mid-point of the distance AB...] of the embankment at instant t0 when the flashes of lightning occur, not the 'y' and 'z' ones. So there are actually two Cartesian parallel coordinate systems, not one. And no contradiction either.
Hi! I'm so happy this site is up, I've been interesting in Scale Relativity for some time now. I'm not a fully-fledged physicist (not by a long shot), but a dedicated enthusiast. I've never taken a course in physics, but have been encouraged by the fact that even Einstein was rejected by the university :)
I've been struck again and again by how natural the framework seems to me; my main exposure to advanced mathematics is in fractal and/or chaotic systems. I'm however a bit surprised that ScR hasn't drawn more attention; specifically concerning dark matter and inflation!
Is that just due to academic conservatism (although new exotic scalars and particles seem pretty radical to me)?
Compared to the incomplete state of, say, M-Theory, ScR seems pretty mature to me?
I have just discovered the Scale Relativity Corner. I may be wrong, but its seems that there is no page dedicated to the mathematics used by this theory. Scale Relativity uses geometrical concepts such as Fractal Space, Geodesics on Fractal Space, Differential Calculus on Fractal Space. It is not at all evident or at least not demonstrated that these concepts have a coherent mathematical definition. It seems to me that Laurent Nottale uses these concepts as tools given by his intuition of physicist, and he is not wrong doing so as long as he is in a process of discovery of the unknow. A mathematician : Jacky Cresson has started a very interesting work aiming to clarify the status of the concepts listed above. The following two articles are worth to be studied, they precise the physical intuitions of Laurent Nottale :
Non Differentiable Deformations of R^n http://www.ihes.fr/PREPRINTS/2006/M/M-06-26.pdf
Scale Calculus and the Shrödinger Equation http://web.univ-pau.fr/~jcresson/cressonJMP.pdf
Other articles (some written with M Abba) are available on this subject at http://web.univ-pau.fr/~jcresson/publications.html
This message first to correct the wrong typing of the name of M Fayçal BEN ADDA in my first message (I wrote M Abba).
In addition, making a research on M BEN ADDA name, I found that he has published in October/November 2007 three articles on the theme of fractal manifold :
1. arXiv:0711.3582 Title: Mathematical model for fractal manifold Authors: Faycal Ben Adda Comments: 30 page, A new mathematical object that describe a variable geometry Journal-ref: International journal of pure and applied mathematics, V.38, N 2, p 159-190,2007 Subjects: General Physics (physics.gen-ph)
2. arXiv:0710.5387 Title: Expansion and hidden dimensions in a new cosmological model Authors: Faycal Ben Adda Comments: 31 pages, no major change exept some correction and clarification added Subjects: General Physics (physics.gen-ph)
3. arXiv:0710.4631 Title: The nature of light in an expanding universe Authors: Faycal Ben Adda, Helene Porchon-Ben Adda Comments: 25 pages Subjects: General Physics (physics.gen-ph)
The first of these articles makes reference to the work of L. Nottale o the Scale Relativity.
I have no more to say on this work of M Ben Adda work as it is a very recent discovery.
I am currently a student of physics - interested in working towards biophysics in graduate school, and have a long way to go, but I plan on studying Scale Relativity over the years, as it seems to be one of the most promising unifications that I have come across.
I think The Trouble with Physics by Lee Smolin sums up pretty much why a theory like Scale Relativity is not as well known. I don't see any reason to repeat his thoughts here, though I would recommend giving the book a read if you haven't already.
And thank you for making this site. As an undergraduate student, I could always use all the help I could get, though I don't necessarily expect to or even deserve to "get it" until I have had more years of study and consideration.
Eric, I did follow your recommendation and read Smolins' "Trouble". To me it is astonishing how near he turns around the core of SR and even jumps over it when shifting from continuous to discontinuous spaces. He looks quite honest in trying to give an as broad as possible overview, including even the most daring attempts on understanding physics’ foundations, but how can he then miss the whole group regularly publishing in Elseviers’ “Chaos, Solitons & Fractals”. Nottale’s painful case was even studied in the periphery of his own PI by Vincent Bontemps (http://ssi.sagepub.com/cgi/content/abstract/46/4/607).
I also do not agree with “The Five (main) Problems”. Why not even mentioning the huge dichotomy of the factual time irreversibility (he embraces the evolutionary paradigm) and the time reversibility of QM & GR. Not even a single quote to the life work of Prigogine, although he ends reconsidering his own roots confronting QM & thermodynamics.
It seems we’re not reaching the end of this very dark wormhole soon, but let’s not resign.
Further reading on this suffering and curing: http://cogprints.org/6096/1/AgainstTheTide.Archive.pdf
Bernard Goossens
A very free collaborator of ECCO Group VUB and Evo Devo Universe.
I spent 23 years developing what terns out to be scale relativity. Laurent Nottale greatly inspired my work. Chaos, Solitons, and Fractals has a summary article of five of my papers in press to be published soon. Three and soon all five of these papers will be available at leonardmalinowski.com
Please have a look.
Len Malinowski
Today I got even more astonisched than I already was, when reading that after years of promoting the idea of multiverse (including cosmological narural selection), Lee Smolin finally comes to the conclusion that there is a serious logical flaw there: http://physicsworld.com/cws/article/indepth/39306.
Welcome back to the Universe, after all this Time!
Dario Benedetti, a research fellow at the Perimeter Institute (Lee Smolin's think tank), wrote about:
"Fractal properties of quantum spacetime" in http://arxiv.org/PS_cache/arxiv/pdf/0811/0811.1396v2.pdf.
This could mean another step towards convergence.
Palmer's approach: http://www.newscientist.com/article/mg20127011.600-can-fractals-make-sense-of-the-quantum-world.html?full=true
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