# What are the technical obstructions that prevent scale relativity from being a viable theory of quantum-gravity?

+ 8 like - 0 dislike
1275 views

The astrophysicist Laurent Nottale develops since 1984 the scale relativity, which aims to unify quantum physics and relativity theory, using a fractal space-time.

I would like to understand why this theory, which seems have a good potential, is not taken seriously by the physics community, in the sense that it is not as developed as (of course) the string theory, but also the loop quantum gravity or the noncommutative geometry model of Alain Connes. Is it a political problem or a communication problem, or are they serious obstructions for such a theory to be valid?

Edit: Scale relativity is not at all in the category of "unpublished personal theories", see these references from the wikipedia page: the theory admits several papers published in peer-reviewed journals.

This post imported from StackExchange Physics at 2015-08-06 09:48 (UTC), posted by SE-user Sébastien Palcoux

recategorized Aug 7, 2015
The Wikipedia page seems to have been written by a strong proponent of the theory.

This post imported from StackExchange Physics at 2015-08-06 09:49 (UTC), posted by SE-user Danu
I have the feeling that hardly anybody knows of the theory (which in part is an answer to the question too). Like with Fractional anything, if no big solution to an old problem through it is being made popular and/or if the author isn't popular, getting ideas known is very hard. Nobody's who isn't payed for it is gonna invest the time to look into it in the first place - to take the time must presuppose a suspicion you can get something out of it. There are also tools like Gyrovector spaces nobody uses for SRT, and so on and so on.

This post imported from StackExchange Physics at 2015-08-06 09:49 (UTC), posted by SE-user NikolajK
@KyleKanos: I'm not interesting in opinions (subjective) of physicists, but obstructions (objective and physics content). If there is no obstruction, then this theory is not mainstream physics only because of subjective reasons, which is not fair in science.

This post imported from StackExchange Physics at 2015-08-06 09:49 (UTC), posted by SE-user Sébastien Palcoux

It seems kind of obvious to me that assuming a fractal space-time, with a fractal dimension related to h, would permit deriving at least some of the features of quantum theory (e.g. the uncertainty principle). I found Nottale's theory researching that, and I was also surprised that it's not discussed more widely. Did others write about scale relaitvity?

Scale relativity starts from the fundamental assumption of non-differentiabilty of paths. So comparing it with a smooth theory is not appropriate.

The maths can be made consistent so the overall theory has a great explanatory power.

+ 4 like - 0 dislike

The main result of Nottale is well known as just a consistency postulate of quantum gravity: that if the electromagnetic renormalisation of electron mass is cut off at Planck Scale, the correction is of the same order of magnitude that the electron mass itself. This is remarked eg in Polchiski string theory book.

Over this consistency postulate, Nottale adds a O(1) coefficient, I think that it was a 3/8 fraction, so that the mass is not just the same order but exactly electron mass. This coefficient looks ad-hoc, (and post-hoc: given that we know Plank mass and electron mass, it could be just a guess)

This post imported from StackExchange Physics at 2015-08-06 09:49 (UTC), posted by SE-user arivero
answered Aug 2, 2015 by (260 points)
+ 3 like - 0 dislike

Get the book by Laurent Nottale on scale relativity, which with its 750 pages should be a complete characterization of the theory with a clear explanation of all the ins and outs. You will find that it is a remix of well known facts and theories somehow smudged together by unnecessarily lengthy historical reviews, and unclear or outright incorrect metaphors and assertions.

There seems to be no complete "Scale relativity", there is only an endless effort to make people think that there exists a theory of that name. However, the mathematical objects of the alleged theory are ill-defined, their correspondence to experiment and the physical realm also, and there is no true rigid structure allowing the theory to be developed or used by anyone different than Nottale.

But do not take my word for it, read the book or his any other review on Scale relativity. Take for example the treatment of quantum mechanics, in "Scale relativity", this is simply a remix of Bohmian quantum mechanics smudged together with the path integral approach and Nelson's stochastic mechanics (meaning that either interpretation is used when more convenient).

Or take entanglement (p. 241 of the book), that is completely "magicked away". First a historical Schrödinger quote is given, then a spin entanglement experiment is commented upon, and suddenly magic, relativity of motion, "chaoticity of motion is dependent on the frame of reference" (which is not true!!!), which means that somehow only the relative spin between the two entangled particles makes sense. Everything is now fine because Nottale said so. (If this does not make sense to you, it is because it does not make sense at all. John Bell must be spinning in his grave.)

Particle physics in terms of true quantum-particle interactions is not treated at all. All that is done are relativistic quantum particles in "external fields" without a true resolution of the negative probability and energy problems which come with it.

I tend to be not as harsh in these matters, but the pseudo-science of the writings of Nottale is very painful. Furthermore, many would also say beyond the lines of scientific ethic because the "remixing" tendency can often be indiscernible from a "rip off", especially in the Applications section where the "Scale relativity" label is sticked on things commonly used or known for decades.

All and all, there are a few new ideas in "Scale relativity", but they are more like formal Ansatzes with unclear foundation. One of these is the logarithmic transformation law. But it is way too far-fetched to say there is a complete theory here.

The first step in developing it would be to truly understand the nature of the fundamental symmetry group, find it's linear counterpart, Lie algebra and so on, and then apply it to curved spacetime (or whatever the curved fractal counter-part may be). But the thing which is currently loosely proposed by Nottale is just a space-time with a stochastic fluctuation - this description may not even be compatible with the original fundamental symmetry group!

Simply speaking, "Scale relativity" does not describe gravity at all and the "quantum" is also undeveloped. So, since there is no dynamics of fields (quantum-particle interactions) and there is no gravity in "Scale relativity", Scale relativity cannot be considered a theory of quantum gravity at all!

answered Sep 1, 2015 by (1,635 points)

Thanks for this very clear and to the point review!

I just got the book and started glancing through. At a first glance, it does propose interesting ideas. Perhaps I will agree with your harsh assessment after reading more, but at this moment I find the (too easy) scare label "pseudocience" unnecessary and misleading. Probably Nottale didn't get everything right, probably his research is incomplete, some of the maths might be wrong, he might have been too careless with attributions... but isn't all that to be expected in research?

@giulio
The ideas seem great "from the table". A nonlinear transformation law due to fractal nature of space-time? The stochastic interpretation of quantum mechanics due to the bumping of particles over the fractal structure of space-time? The fundamental scale of the fractality is the Planck scale? Super-trooper awesome. But cutting the part where Nottale compiles existing theories and gives historical reviews (about 600 pages of the book), the theory is just a few possibly incompatible Ansatzes following these ideas.

I do not like to make scientific discussions personal but this really reminds me of many moments when having similarly attractive ideas, developing them for some time, but abandoning them because they quickly ran off into dead ends, contrivedness or implausibility. The fate of Nottale seems very similar with the exception that he does not let go. The label "pseudo-science" addresses not the shortcomings of the theory, calculations or citations. It addresses the way its case is pushed - not by presenting genuine scientific discussion but by constructing ad-hoc or simply wrong arguments to obtain results you "need", and by leveraging the theory by buzzword and hand-waivy connections to things where it does not bring anything new and has no real connection whatsoever.

Things I am positive on: The treatment of entanglement and quantum-mechanical non-locality is plain wrong. The theory is not a particle-physics theory in the sense of reproducing e.g. the predictions of the Standard model (resonances, detailed scattering outcomes...). The theory does not describe gravity, either in a classical limit nor in a quantum-gravity sense. The kinematics and dynamics of particles and fields such as Maxwell equations or charged particle motion in flat space-time with the log-law are not developed (these have to be partially postulated, of course, and could lead to a quick disproof of the theory).
I.e., if you just ignore my "science-ethical" remarks, the theory does not really seem appealing anyway.

Thanks for replying @void. I admit that my interest for Nottale's ideas is qualitative and developed at a first glance.

As you say, "A nonlinear transformation law due to fractal nature of space-time? The stochastic interpretation of quantum mechanics due to the bumping of particles over the fractal structure of space-time? The fundamental scale of the fractality is the Planck scale? Super-trooper awesome."

Actually I have had similar ideas at the back of my mind for years, and found Nottale's work by googling specific keywords like [spacetime "fractal geometry" quantum].

So I can't exclude that I would totally agree with you after studying the book and Nottale's paper carefully.

Yet... sometimes you have that powerful feeling that some conceptual approach is so basic and elegant that it can't be wrong. Nottale claims to derive the postulates of quantum mechanics from fractal geometry (plus an interpretative framework), which would extend Einstein's ideas all the way to the Planck scale. If he has really done that... WOW. If he hasn't, I do hope other researchers will.

Re "the label 'pseudo-science' addresses not the shortcomings of the theory, calculations or citations. It addresses the way its case is pushed." I understand that, but don't forget that Dante was criticized for writing in street language instead of respectable academic Latin. Some great scientists were also egomaniacs and jerks. I think an interesting scientific concept should be studied because it's interesting, regardless of the personality of its promoters.

By the way, do you know of any recent related works on the super-trooper awesome part?

+ 2 like - 0 dislike

I did some research and formed the impression that Nottale is guilty of violating many unwritten conventions in the research community, related to the choice of journals and publishers, other researchers to associate with, ways of promoting one's own work, etc.

From my time as a research physicist I remember that the scientific community can be very unforgiving about these things. So I have the impression that some "esprit de corps" prevents Nottale's ideas from being taken seriously by the physics community.

Of course that doesn't mean that Nottale is "right." But if I were a young researcher I would dedicate time and effort to exploring his approach, because it seems to me that it has some kind of basic elegance similar to general relativity, which I don't see in more fashionable approaches.

answered Sep 17, 2015 by (185 points)
+ 4 like - 3 dislike

I also don't think I can give a definitive answer. But maybe no one can because maybe no one knows enough about the theory and about why people don't know about the theory. But I will do my best.

As mentioned by Nikolajs maybe fee people think they can contribute to it or make use of it. This is partly because of the success of quantum mechanics and relativity in there domains of applicability which covers almost everything we have an opportunity to see. And partly because of having to learn new things.

But let's not confuse the issues. Peer review is one thing, and reviewers should be fair. But choosing to study an area is a personal choice, everyone chooses what to specialize it. Just because you choose an area because you think you skills and background and interests will allow you to make meaningful contributions down mean you think other specializations are wrong, they just aren't your cup of tea. At least right now (people do change their specializations).

So if you think another researcher is way ahead of you and isn't likely to be a coauthor, then that might discourage you. In a robust and healthy field you can have interplay between different subarea experts, for instance theorists and experimentalists can work together. And then their collaborations with other theorists and other theorists can lead to more people becoming aware of their work. You like to know what your collaborators are up to. Maybe not at first, but in a long term collaboration you find out the other things your collaborators are up to. In an area without active collaboration between for instance experiment and theory, there is a barrier to awareness.

But you specifically asked about comparison with loop gravity and string theory, surely those areas have just as much a disconnect with experiment. Fair enough. String theorists have a particular culture, of lots of people working on specific hard mathematical problems in a very competitive way. So if there is a large group of people working on the same problem you know others will appreciate your work, not just because they are a built in audience that understands it, but because of the competitive nature where if you publish first you can get their respect for doing hard work very quickly. This means lots of people can say good things about you, good things that speak well about you even outside of physics, which means there a clear payoff for succeeding. And since there are many strong leaders in the field that have a history of success their are expectations that success is possible, there is also a rich field of hypothesis that haven't been completed yet. Researchers like open problems, have them and make them clear and this is encouraging to research, that's why papers have sections about future work.

Now, not all of those things were always true of string theory so you could ask about the history and try to find out how it got that way. But any specific theory's history could be too accidental so let's talk a out what makes different theories appealing.

Obviously limiting towards known results in known regions that have been confirmed is good. It would be nice if there are testable predictions as well, particularly ones that could be tested soon. For instance Einstein had the bending of starlight which was doable. But there is also a desire for principled reasons.

For instance of you took the average global temperatures for the recent history and fit them with a large degree polynomial and then asserted that was your prediction for global temperatures few people would care how well it fits the data because the principles are so unappealing. You predict incredibly high and/ot incredibly low the temperatures for every time except times near now and base it on no physics. Almost no one will bother.

Physicists want to understand the universe. A theory with parameters that come out of no where and aren't stand ins for unknown experimentally measured parameters is unappealing. But partly that is because of high expectations for quantum gravity, some people want a theory of everything and they want it to predict everything, every mass, every coupling, everything. Those will be hard people to please. But even if you don't want all that, you still want a principle that makes sense that makes the universe seem less mysterious and makes it seem more understandable.

What's nice about GR, is that even if you haven't studied the detailed math of curvature, you have some intuition, so if someone says that they can explain why different massed objects more on the same paths as because they follow natural curves (like great circles on the earth). So it feels like it explains.

There are also things that are specifically unappealing about scale relativity. And some of that is cultural too. For instance the Planck length business. The plank length is just a length based on some constants. It is generally considered by physicists to be a length scale where quantum and gravitational effects can both be important. It is considered by lay people to be a minimum length in the universe. If scale relativity reproduces the lay person idea this makes the theory appealing to lay people and unappealing to physicists. Since we haven't observed a minimum length and don't expect to be able to soon (it is so small) and didn't actually think there was one, physicists aren't excited by that "prediction."

But that's just it. What are the principles? When I read the wikipedia article it is vague (which is understandable if I haven't studied fractal geometry and that is the math used) but then it ends up reading like a parody of physics with a bunch of buzzwords. And saying that the whole idea is that only relative scales matter sounds just like the fact that we have to use units. The fractal geometry had to be involved somehow and the way the theory is presented to new people sounds vacuous at best, or a rehash of the fact that we use units. Which doesn't mean that is a fair characterization. But if that's the best description to newcomers that 30 years has produced, maybe it will never catch on.

Think of it this way. If you have a better and principled way of understanding the universe, tell us why the (the principles) involved involved so that we can tell what is wrong with the alternatives. With GR, you can say that spacetime is curved and this explains why different masses follow the same paths, and that assuming spacetime is flat is an assumption not based on a principle.

What can scale relativity say? That we always pick the same scale and this is a problem somehow? We already use constants with different values, is scale relativity supposed to predict those constants in a non ad hoc way? Why would I want to be covariant to scale when my constants already change if I use different units. The principle involved is not articulated well.

And how about reproducing known results? If everything is non linear and hard to solve then how easy is it to see whether you get known results in known areas. People aren't interested in studying something whose predictions have already been disproven experimentally. With GR, there is a weak field limit that reproduces known results from Newtonian physics in the domain where Newtonian physics holds.

These are the kinds of things string theory had to deal with back when it was less popular. And there were promises (or at least strong advertising) that there would be a unique theory, that the constants would be predicted and that one idea would lead to a weak field theory that would agree with the standard model and with GR in the appropriate limits. These things did not pan out, but they did lure people in to help the field grow.

That doesn't mean you should try to lure people in, but it is a reason why people get interested in the early days.

Now, for further problems with scale relativity, that again might be just about how it is presented to people that haven't studied it. Which is a distrust of adjustable parameter explosions. Let's look at renomralizable QFT.

The idea is firstly that restricting to renormalizablr QFTs reduces the number of possible theories quite drastically thus it is a principle to reduce the number of theories, thus when one agrees with observations there is more reason to be excited (if string theory had developed the landscape issue right away fewer people would have joined). Secondly the idea isn't that you renormalize a theory to get finite predictions the point is that you do so with a finite number of experimentally determined parameters.

The introductory explanations of scale relativity make it seem either near pointless (pick a unit, then use it) or like it has an infinite number of parameters (coordinates become functions, so finite degrees of freedom become an infinite number of degrees of freedom) or like it has a landscape of possibilities were you can make whatever you want happen at any scale. It doesn't seem scientific. It doesn't seem like understanding the universe. It doesn't seem principled. It doesn't seem like you can do things other than post hoc retrodictions. And that doesn't mean those things are true, people claim to have predictions.

However, if the introductions don't make it sound like it is good and instead say things that make it sound appealing to lay people, that is not going to encourage people to join that don't personally know people in the field and know that it isn't a crank field.

So if your introductions don't sound appealing to people based on what made people find out theories appealing (uniqueness of theory, small number of parameters explaining lots of results, principles that seem explanatory, etcetera) then people might be more drawn to new/s areas that do those things or to more established/popular areas that have other things going for them like recognition of hard work from large group of other practitioners or from interaction/collaboration with other subspecialties ideally including experimentalists.

Sometimes it is about getting experimentalists happy. So again, leer review is for fair assessments of right or wrong. Choosing to invest your own time to learn something is a different issue. And making an experimentalist choose or a theorist choose might be different beasts.

I myself made fractal theories of physics on my own as a young person, not having heard about scale relativity, but even so reading the wikipedia page did nothing for making me think we get anything from it whatsoever.

Does it show an existing thing that we do wrong (don't agree with observation) and show how to do it right? It seems to be described as still in progress after 30 years.

And it is not just that the wikipedia article fails to convince me, it actively discourages me. For instance it says

Scientific theories usually do not improve by adding complexity, but rather by starting from a more and more simple basis. This fact can be observed throughout the history of science. The reason is that starting from a less constrained basis provides more freedom and therefore allows richer phenomena to be included in the scope of the theory. Therefore, new theories usually do not contradict the old ones, but widen their domain of validity and include previous knowledge as special cases. For example, releasing the constraint of rigidity of space led Einstein to derive his theory of general relativity and to understand gravitation. As expected, this theory naturally includes Newton's theory, which is recovered as a linear approximation under weak fields.

And if you have anomalies in the old theories (such as Mercury) that is great to have a wider space of theories. But some people are hoping for a smaller space of theories. So I don't get excited about a wider space of theories, this makes me less interested. It is physical principles that reduce the space of theories. So the covariance of scale relativity should be reducing the possibilities, but its not clear (in the introduction) that the covariance does something other than picking units at least without opening the doors to way too many possibilities.

And now for some of the really specific criticisms. Which is that I'm already familiar with theories that personally are easier for me to understand, have principles I understand, and seem to have the same (or at least similar) advantages. And if I do, then others do, so in general this could just mean that the space of theories is crowded do any one has to compete with the rest. So that means every unpopular theory has to compete not just with the popular theories you know but all of the many many many less popular theories.

For me for instance the Gauge Theory of Gravity e.g. by Lasenby, Doran, and Gull at Cambridge University has many of the same advantages. All comparisons are made between fields, the fields can locally change their orientation, boosts, and scale. It derives the equivalence principle instead of assuming it, and basically is based on the fact that we don't know where or when things are happening or a sense of scale but we only know how to compare. And the math it uses is math that is required to be used to study relativistic quantum mechanics, hence it contains things I already know or things I should learn anyway.

Again, I'm not trying to convince you that Gauge Theory of Gravity is better than scale relativity, but I list it as an example that other equally (or more) appealing alternatives exist so any theory has to compete with all the alternatives.

This might be landscape problem (too many possibilities) at a higher level. Making too many competitors for theories that handle scale. If that is the case then maybe an insight that encompasses them all and brings everyone together is the key, something that allows you to study them all easily and objectively sort through them.

This post imported from StackExchange Physics at 2015-08-06 09:49 (UTC), posted by SE-user Timaeus
answered Aug 2, 2015 by (70 points)

 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$ysicsOverf$\varnothing$owThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.