# Scale Relativity

Referring to Nottale's Theory of Scale Relativity (http://luth.obspm.fr/~luthier/nottale/arIJMP2.pdf), I've been reading an awful lot about this theory and it seems to present, in my opinion, the best candidate for a unifaction of quantum mechanics and general relativity.

The postulates of the theory are that the laws of physics apply equally regardless of coordinate system or scale. It also postulates that the speed of light is invariant in all coordinate systems and scales, and that there exists a minimum measure of distance/time, which is the Planck Length / Time, also invariant in all coordinate systems and scales.

The paper suggests that the schrodinger equation, the uncertainty principle, and many other aspects of QM flow from this, resolving the "quantum/classical" threshold problem. Other papers by the same author claim to resolve the renormalization problem of QFT, and to provide the framework for quantum gravity.

I'd like to get the experts' thoughts on this theory. Does it have any obvious failings? Why has it not gotten more attention?

Wow, the resounding response to this thread sort of makes my point. Why has Nottale's work not gotten more attention? Is this not a candidate for the "underlying fundamental explanation" of quantum behavior that so many here (myself included) are always asking about?

strangerep
Wow, the resounding response to this thread sort of makes my point. Why has Nottale's work not gotten more attention? Is this not a candidate for the "underlying fundamental explanation" of quantum behavior that so many here (myself included) are always asking about?
I looked at some of the papers, but was unimpressed because they never seemed to come to
grips with the essential Lie group theory that must underpin this sort of thing.

Perhaps I don't understand Lie Groups, but I thought one aspect of them was that they were continuous and differentiable. Nottale's theory is explicitly non-differentiable.

ANd who says that Lie Group theory must underpin a quantum theory of spacetime?

strangerep
Perhaps I don't understand Lie Groups, but I thought one aspect of them was that they were continuous and differentiable. Nottale's theory is explicitly non-differentiable.
Perhaps I should have said "Lie Algebras", allowing for the possibility of non-trivial
higher order cohomologies presenting obstructions against integration to a full Lie group.

ANd who says that Lie Group theory must underpin a quantum theory of spacetime?
If there's no algebra, there's no theory.
But I don't want to get into an argument about such speculations.
Sorry if my opinion annoyed you.

I have no emotional investment in the topic, therefore your opnion did not annoy me. I just don't understand it. I did understand the paper, however, and was extremely impressed by the derivations of, among other things, the schrodinger equation and the HUP, and the predictions Nottale made about, for example, extra-solar planetary orbits have since been confirmed.

I'd like to get the experts' thoughts on this theory. Does it have any obvious failings? Why has it not gotten more attention?
I think, that in keeping with the scientific method, for this theory to gain any steam it would have to make new predictions or drastically simplify the formulation of physics as we know it. I don't know about the former, but as for the latter, the paper seems pretty dense.

Well, scale relativity does make new predictions, particularly about the value of several fundamental constants, as well as the expected orbital formations of solar systems (since one result of the theory is that solar system formation is, at least partially, governed by the schrodinger equation).

Those aren't new predictions. A new prediction is like saying "Hey, if a star moves in front of a distant star, the image of the distant star will be lensed", so you go out and check, and sure enough, that happens.

It's easy to cook up things that reproduce known results. It may not be elegant, but it is easy.

nrqed
Homework Helper
Gold Member
Well, scale relativity does make new predictions, particularly about the value of several fundamental constants, ...
What sort of prediction? A true fundamental prediction (let's say between the mass of the electron, the values of G, $$\hbar$$, c and the fine structure constant) would be impressive as long as it's not numerology in disguise.

Nottale's work can not be qualified "theory", to the best it is "poetry". He does have ideas, but implements them only with vague analogies. It is unfortunate. In fact, many people have been working before him on this subject, starting with Weyl right after Einstein's original publications. The point is that scale invariance is a badly broken symmetry. You need to take that into account from the start. There are many tools to do so. But throwing a lagrangian and pretending to make calculations without justifying them is just not enough. Especially if you claim to predict so much, from the mass of the electron to planets' orbits. Unfortunately, he never published in any serious theoretical journal. Only astrophysics journal for which referees are not very much versed into fundemental theories.

I know it seems paradoxical to reproach a theory with making too many predictions. Let me make it clear that this reproach arises from the fact that none of them are well-justified. Building a nice lagragian and making calculation with it can be done by any student. That does not necessarilly shed light on the structure of space-time at a fundamental level !

Besides, Nottale it too busy selling his books and publishing in popular journal to answer the questions raised by the community. If you ask theoreticians, they will tell you that "If Nottale's approach worked, we would know it for a long time".
nrqed said:
as long as it's not numerology in disguise
I think the whole problem is right here...

anthony.gtez
Supposedly he predicts more accurate values than what is currently known (but within experimental error).

I hear a lot of poopooing of this theory/poem/whatever without any specific criticisms. In fact, just about everything I've heard here can be said of Einstein's 1905 paper on special relativity. Technically there were no new predicitions in that paper either. Here, in fact, there are.

I hear a lot of poopooing of this theory/poem/whatever without any specific criticisms. In fact, just about everything I've heard here can be said of Einstein's 1905 paper on special relativity. Technically there were no new predicitions in that paper either. Here, in fact, there are.
That is very unfair. You can not compare Einstein's rigour with Nottale's. Einstein did make an extensive use of the available maths at that time. Nottale simply refuses to even try to make a decent publication.

You know, I have been a lot interested in his researches. Being french, I even had the opportunity to talk to him. I have been in particular interested in trying to modify the conventional "canonical quantization", using a wavelet basis instead of an harmonic one. I later discovered that this line has been actively pursued by other people before. Nottale did not even care to contribute to this. However, we do know that we compute fractal (so-called anomalous) field dimensions (as opposed to canonical ones), in particular in QCD. I am still convinced that we do have fractal structures and that it is numerically relevant to use a more elaborate basis than a plane-wave one. This amounts to a re-definition of what you call "particle", equivalent to the older one in the free case.

So, to summarize, I beg your pardon but I do not think you have put much thoughts and efforts into that. Reading Nottale himself and no other source will of course confuse you. Just go to a theoretical conference where people try to quantize gravity, pick up any respectable physicist and go ask him his opinion on Nottale if you do not believe us. I have a personal friend who did exactly that with Penrose, and I took that information into account when reporting what I did here.

Whether a theory is worth time depends upon the individual. Does Nottale have anything to say about the Measurement Problem?

There is some justification for casting doubt on a spacetime quantum gravity theory of unification which does not relate to Lie symmetry groups in particular as considered by Garrett Lisi and Mohamed Elnaschie as well as in Heterotic superstring theory of M. Green and J. Schwarz. However, Laurent Nottale’s theory is related to E8 in a very subtle way which was never discussed not even by Nottale himself who is a highly gifted but also highly sensitive and a touchy scientist. The point is that a quantum particle in Nottale’s Fractal spacetime has a path with a Hausdorff dimension equal two. A fractal is an infinitely intricate structure and only deceptively simple.

If you lift such path to 9 + 1 dimensions, then you obtain 2 to the power of 9 which is 512. Now this is exactly 16 larger than the dimension of the largest exceptional Lie group E8E8. Taking only E8, you need at least 16/2 = 8 dimensions for spacetime embedding because its Gossett is made of 8-dimensional vectors called octonions, the well-known generalization of complex number. However, Nottale works in 4 spacetime dimensions only and he has never claimed that his scale relativity is exact. It is a nice theory closely related to that of G. Ord and M. El Naschie. Readers may like to visit the site of Garrett Lisi for more detailed discussion of this and related subjects.

Ramie

I appreciate what you're saying Humanino, but I still haven't heard anything indicating that something specific in Nottale's paper is incorrect or flawed, and no one is addressing his new predictions. It sounds like people don't like the work because he doesn't take the approach they would take.

But I'll tell you what, next time I pick up a theoretical physicist I'll ask him about Nottale. :)

+

Hi Peter,
I sympathize, and share your interest for Nottale's theory. I do believe that it is a worthwhile path of study, and am open to any specific critiques of the theory, as it is indeed a work in progress - though I find it more promising than the alternatives at the moment. I could say much on this, but choose to let it be at that.