# What ever happened to Scale Relativity?

1. Jul 8, 2008

### Saltlick

One of the intriging things to me about Causal Dymanical Triangulations is the implication of a fractal spacetime structure at small scales. Hunting around for related theories I came across Laurent Nottale's Scale Relativity theory. References to the theory after the late 90s are hard to find.

Was the theory abandoned, disproved, or considered a dead end?

2. Jul 8, 2008

### humanino

Nottale will carry it to the grave probably
He failed in getting enough credibility to attract collaborators. I talked to some people who contributed review commitees to some of his publication submissions, and they claimed he did not really attempt to address critics (which when done were done in a constructive manner). Basically, he published fundamental theories in other journals, usually dedicated to more phenomenological theories.

3. Jul 8, 2008

### Coin

I would be curious what some of those (presumably still unanswered) criticisms of scale relativity are, if it's not a bother.

In particular if you have some familiarity with this you might want to take a glance at the Scale relativity entry on wikipedia. Currently that entry contains some decent detail outlining the theory but contains absolutely zero text describing downsides, criticisms, or experimental flaws of the theory (which when I see an entry like that on Wikipedia it always makes me instantly suspicious...).

4. Jul 8, 2008

### humanino

Such as, for instance, how to use Einstein/Grommer theorem and Einstein/Infeld/Hoffman calculations, indicating that particles follow geodesics, but throw away differentiability ? To which he answers "ah, yeah... all right, let's take it as a postulate". This is weak.

A very important question is what happens if one tries to formulate rigorously in terms of conformal invariance (which is what scale invariance is about, what everybody uses, and what should be done). This is very unfortunate, but Nottale never bothered using this language, although people were interested to understand ! Castro in
Beyond Strings, Multiple Times and Gauge Theories of Area-Scalings Relativistic Transformations
mentions conformal invariance for instance, but I think it you see what I meant by "lack of rigor". This paper has practically no citation because it is just to ambitious. Chaos, Solitons, & Fractals does not usually publish about fundamental breakthrough in gravitation... Another instance is
url=[PLAIN]http://arxiv.org/abs/physics/0010072[/URL] [Broken]
(where was it published ?) which looks more like numerology.
Don't laugh :
Final steps towards a proof of the Riemann hypothesis.
Another :
Variable Fine Structure Constant from Maximal-Acceleration Phase Space Relativity :
were those posted on arXiv without submission ?

It might seem weird to reproach somebody with being too ambitious, but honestly when you collect Nottale claims, at some point it does not add up anymore. I just look at right now. Scale relativity is just so good, it does anything for you.
Gauge field theory in scale relativity
The Pioneer anomalous acceleration: a measurement of the cosmological constant at the scale of the solar system
A scale-relativistic derivation of the Dirac Equation
He sometimes does manage to publish :
Derivation of the postulates of quantum mechanics from the first principles of scale relativity
Non-Abelian gauge field theory in scale relativity

You know what would be worse : if Nottale is really on the right track, and his person and acts have distracted attention from his work. That would really be the worse shame possible for everybody.

Last edited by a moderator: May 3, 2017
5. Jul 9, 2008

### Fra

This caught my attention, I can't say I have any prior knowledge about scale relativity except I heard of it. But any paper with such a bold title at least deserves to be skimmed.

Since it claimes to reduce QM principles, to scale relativity principles, what's the best paper to learn these "first principles", which I assume is the foundations of his reasoning?

/Fredrik

6. Jul 9, 2008

### humanino

You'll have more papers to skim through here :
http://luth2.obspm.fr/~luthier/nottale/ukthema.htm
He refers http://luth2.obspm.fr/~luthier/nottale/ukdownlo.htm as "review" to this paper :
http://luth2.obspm.fr/~luthier/nottale/arAMS.pdf

Last edited by a moderator: Apr 23, 2017
7. Jul 9, 2008

### Fra

Generally, I have always felt that the action principle and variational ideas even in normal physics are not understood to a satisfactory level. In classical mechanics, the only "rigorous" justification of the geodesic thinking I've seen is that it's consistent with newtons equations.

But for sure the action formualation is seductively more beautiful, but beauty alone is not satisfactory for me.

But then that principle seems to somehow have been taken as a new fundamental principle, and the the path chose is the one with minimum action. But what is the real meaning of this action?

Somehow, we construct a measure of change (the action), and the change that we expect to observe is the one which minimized this measure.

Can such a fundamental measure only be constructed on differentiable manifolds? I personally don't think so.

But I agree that any strategy should motivate why minimizing this constructed measure is the way to go. Just because one can mathematically give a geometric formulation does not IMO motivate the physical assumption that geodesics correspond to physical changes.

It's not clear what the true physical nature of such measure really is, and wether this measure is an universal invariant, or if the construction of these measures are in related to local physical processes?

/Fredrik

8. Jul 9, 2008

### Fra

Last edited by a moderator: Apr 23, 2017
9. Jul 9, 2008

### humanino

Oh, I fully agree. Those are very interesting questions. One could address fractal structures in terms of wavelets for instance, and define rigorous measures. One could even push further to more powerful formalisms, and the degree of generality reached by non-commutative geometry (for instance) might very well be what is necessary to fully understand quantum space-time.

On one hand, Nottale's formalism is very rudimentary, and on the other hand the problems he claims to address very remarkable. That does attract attention. It might be deceptive, or it might just be an effective calculus that can be justified, but it would be quite stunning if the physics comes out fundamentally right.

10. Jul 9, 2008

### Chronos

I don't wish to argue, but, I do agree Nottale was brilliant.

11. Jul 9, 2008

### Fra

This is s 76 page papers but I just started skimming. The first skimming serves to extract to the exten possible his original logic of his reasoning....

On page 2 Nottale writes:

"We have suggested that the observation scale (i.e., in other words, the resolution at which a system is observed or experimented) should also be considered as characterizing the state of reference systems, in addition to position, orientation and motion."

This makes perfect sense to me. I need to write more, to as wether it's radical enough, but as I interpret this (having a different perspective here) is that he considers the general constraint that the "laws of nature" must look the same to all observers.

Then, the question is of course how to generate the set of all observers? IMHO the notion of "reference frames" common in mechanics, is a simplified view of the observer which really ignores completely the internal structure of the observer. Normally an observer has more degrees of freedom - and I would clearly expect these to matters. In my thinking I associate a "local logic" to this intenal structure, and this might determine how the local action measures look like. So there are constraints on the possible actions. I'm curious to see in what sense Nottale by his logic are able to produce constrains on the action measure. And considering that the action forms are usually associated to phenomenology, this should have a few things to say about that (predictions).

The "observational resolution" of an observer is such a key parameter and I like that thought. The idea that even "pointlike" observers can relate to infinite amounts of information about it's environment, hardly makes sense.

That's my projection of his introduction into my own thinking. And I like it. I will keep reading! :)

/Fredrik

Last edited by a moderator: Apr 23, 2017
12. Jul 9, 2008

### humanino

I don't wish to argue but for one thing we know that scale relativity does not apply to our world. Down to QCD we know there are scales.

When does his derivation of quantum mechanics explain how everybody has been wrong about Bell's inequalities and local theories ?

Do you really believe that we can explain the sizes of planets' orbits around the sun by the same principle that we can explain electrons orbits ?

I don't wish to tell you who said that, but the general feeling is "if it were true, that would already be known". If you are a researcher, you should also consider which time you decide to spend on which theories...

13. Jul 9, 2008

### Fra

I don't mean to argue either, I just wanted to orient myself, and discuss his ideas. I certainly didn't mean to say I think "he is right", as I don't know his theory after skimming a few pagers.

My first step is to sniff his logic of reasoning. If the logic on which he constructed the theory doesn't seem likely to be effective relative to my preferences, my choice is to not spend more time on it. If it does seem sound, I am willing to invest a little time, enough to learn more. At least the introductory parts seem reasonably sound (perfection is another story), and IMO perhaps even more so than some more popular programs. I haven't had time to read mroe today but I'll skim a little more another time.

I have treated all research programs in the same way. And even where one might disagree there could be hints. Not that I should judge anything, but for example, I like some of Rovelli's reasoning up to a certain point, where he looses me. I do not find his reasoning attractive anymore. He address some fundamental questions, but ignores others.

Similarly with String theory. There the story is differet for me. I think the foundations of string theory is really twisted. I just doesn't make sense to me personally. However, there are things in string theory that I do like. So I can't exclude that sometime in the far future string theory will be understood in a different light, but for the moment the logic of the string program is obscure to me.

So I guess I am looking for something that makes sense to me. I have my own questions I'm working on in parallell but I've realised how much work it is and clearly it would be far easier to find that something who coincides with my reasoning already say may "half the work".

It depends on what the nature of principles and explanations are. But a simple answer is that I think there are "principles of self-organisations" that transcend scales. And that there are questions asked in complex systems that are not distinguisahble in simple systems. So I do think seeing the similarities requires asking the right questions. I think these similarities aren't to be seen at conventional model or theory level, I think the similarities if at all, will be found at the construction and evolution of theories. So looking at the forms of Einsteins GR equations, and looking at the schrödinger or dirac euqation for electrons in an atom are IMO a too superficial level to look for such "principles".

I have personally gone back to the basics of the formalism and scientific methods, and question the meaning of probability, action, entropy and all the indexing of observations we do. What is the logic behind that? And does these measures evolve? I am starting by identifying as I see it the simplest possible starting points, and see how with the help of that, one can construct measures. The next step would be to try to model communicating measures, and I think this would provide the selection.

Unfortunately this is a massive reconstruction I am facing, that is why I hope to find something who has done parts of it already.

I find it unlikely that scale relativity does anything like that, but I still thought that it could contain ideas.

/Fredrik

14. Jul 9, 2008

### humanino

The begining of my post was rather a reference to Chronos
Honestly, when I was a teenager and I read Nottale in the public press, I thought I had to study what he did.
I would really be happy that somebody explains me where I miss the point.
That is a massive and bold enterprise. Impressive... Good luck !

15. Jul 9, 2008

### jal

This time
Similar Threads for: What ever happened to Scale Relativity?
were relevant and informative.
jal

16. Jul 9, 2008

### Chronos

I appreciate the jab, humanino! I too am skeptical of nottale, but, his ideas are still interesting. My objection is his squishy definition of 'scale' [or lack thereof]. On the other hand, the scale at which GR ceases to be relevant and QM rules is similarly vague. Perhaps QM is merely an approximation of GR at short distances, or GR is an approximation of QM at large scales. Perhaps neither theory is fundamentally correct. That is an attractive proposition IMO.

Last edited: Jul 9, 2008
17. Jul 9, 2008

### MTd2

This scale relativity does resamble Loll's aproach, if you take the following reasoning, as an example:

Take the haudorf dimension of the emergent space-time and equates the local hausdorf dimension, at a given time, to, let's say, the epsilon(D) of the scale relativity's dirac equation, or something that regulates dimensionaly this equation. From there, maybe you could generalize, and even demonstrate, by finding reasonable assumptions, that the local description of an emergent Loll's universe are given by Scale relativity.

Thus, you would get Loll's emegent space time (Global) -> scale relativity (Local).

Last edited: Jul 9, 2008
18. Jul 10, 2008

### humanino

And suddenly, Loll's work gets plagued by all of Nottale litterature. Maybe you could indicate what more you have to back up that claim, except from mentioning two definitions of dimension plus intuition ?

19. Jul 10, 2008

### Fra

I didn't get time to read anything more yet, but to comment on the scale notion from the point of view which was the induced impression while skimming his introduction...

I have done similar thinking on my own, and there to me, I associate the scale to the observational resolution between the observer and the environment.

To me, I find it plausible that this "scale", or observational resolution, somehow limits the evolution of the measures. And possible, at the bleeding edge of the evolving measures, these measures may take on a quantum nature.

To me one possible way of implementing the observational resolution, is to characterize the observer as having the capability to distiniguish only a bounded set of events. This could possibly be implemented both as discrete models and continuum models, but I prefer to think in terms of discrete models which are reduced to distinguishable states. So it doesn't matter if I can distinguish 10 complex numbers, or 10 integers. The number of distinguishable states is still just 10.

I suspect he didn't consider the construction of the measures, which could be a point of improvement.

Instead of focusing on an equation, and try to transform that, I consider the equation to be a state originating from an underlying process. And if we appyl the transformations to this process, I think more interesting things will happen. I envision that the observational resolution, constrains how measures evolves. I suspect QM could be a result of an constructive information processing subject to constrained observational resolution. I see a good logic to that. But I haven't worked it out yet.

That's what attracted me to the Nottales papers of emergent QM, but the first glimpse reveals that he doesn't do quite what I envision.

So to me the scale invariance, amounts to that no matter how complex systems, there is a a stable strategy of learning. However the "state" of knowledge or measures as it has evolves is totally different.

I'll see if I get around to reading more tonight.

/Fredrik

20. Jul 10, 2008

### MTd2

I wouldn't call Nottale's work a blight. His arguments and mathematics are too crude, but enough to give me intuition on how to use Loll's work to do anything useful, besides predicting a really tiny universe with a cosmological constant. I mean, she just took an ensamble of small universes and run them. The haudorf here is a kind of dimensional average, so, apply it to the exponentials of the derivatives of whatever equation you might get.

After all, her works are not that well defined either.

21. Jul 10, 2008

### humanino

I may be wrong, and you can start a poll about that if you feel like, but I believe that the community would consider Loll's work much more important than Nottale's.

vs
I think I provided very serious and specific arguments against Nottale's proper definitions. I think nobody read seriously Nottale's paper, because some of my arguments can be discussed by some of Nottale's material (or those who know those arguments already from before this discussion are aware that the debate can not be settled at the level of PF). In addition, please provide serious and specific arguments against Loll work. This, contrary to Nottale's, is built on decades of cooperative research, with misconceptions corrected one after the others, hundreds of textbooks, a very deeply studied field. Or answer serious and specific arguments against Nottale's. Otherwise we just have words, opinions, intuition, and no scientific content.

22. Jul 10, 2008

### MTd2

As you can see in other threads, I have a high opinion about her works, but the scope is extremely limited to a really small universe. It is an extremely computer power hunger, and we never know what would come after we modified parameters or waited for a bigger universe to develop. And, that's why I said not well defined, you can't be sure of what will happen later, it's just to complex. Maybe the use of some kind of statistics would be extremely welcome.

I noted that notale works is developed around fractional dimensions, so I thought of using it with Loll's works, as a basis for an statistical approach, because, as far as I know, fractional dimensions is something that I only saw emerging in her works, which is an awesome feature. If you know any other theory that uses fractional dimensions, that would be nice. Tell me please. Maybe it could be linked to Loll's theory.

23. Jul 10, 2008

### humanino

We have anomalous dimensions all over the place in QCD. Those really tell you that the fields are fractal in the SM.
It's no big news, and that's why you need renormalization procedures.

At the other extreme, I already mentionned non-commutative geometry where we get a rigorous meaning for
$$\int_{\Lambda}f = \int_{x\in\Lambda} \text{d}^{p}x\,f$$
as the coffecient of $$\log(\Lambda)$$ in $$Tr_{\Lambda}(f)$$, although traditionally we have no non-trivial topology on $$\Lambda$$ (hence no point $$x\in\Lambda$$ along which to integrate), and $$p$$ can be any real number. And that's how you get a rigorous definition of the renormalization procedure. And this is not a vague analogy stemming from the fact that similar calculations occur, this is published work.

24. Jul 10, 2008

### MTd2

No, they are not fractal, even though the feynman diagrams are, and that's because in the end of the renormalization, the limit is always be taken back to whatever is the target dimension. In Loll's case, you really get a fractional dimension, because the number of dimension is an emergent feature.

25. Jul 10, 2008

### humanino

What ?
What ?

Look, the anomalous dimension is something that has experimental consequences, it is not an "anomaly" (in the litteral meaning) in the calculation. Do you even know what anomaly refers to in this case ? People don't like to use buzzwords (like fractal) in serious papers, but when they calculate the conformal weight (which is not the buzzword, since it refers to something clearly defined, contrary to "fractal" which is a generic property the interpretation of which is debatable) of the energy-momentum tensor for quarks and/or gluons (take a look at Phys. Rev. D 77, 045029 (2008)), they really find that it does not scale classically. I actually think it must be the case for any field theory with non vanishing $$\beta-$$function, but I have no proof. It is interesting that some people dare using buzzwords :
KNO scaling 30 years later
z-Scaling at RHIC and Tevatron
and you will find a lot of this in pomeron phenomenology.

An anomalous dimension imposes at least one non-integer dimension. In the standard model, we assume space-time to be 4-dimensional, so the fields must be fractal. You can re-interpret this as an indication that space-time is not for dimensional :
Bounds for the fractal dimension of space (J. Phys. A: Math. Gen. 19 (1986) 3891-3902.)

Last edited: Jul 10, 2008